School Science Lessons
16. Dynamics, (force, mass and acceleration), Newton's laws, inertia, moments, momentum, recoil, Hooke's law
2012-05-04 SPwP
Please send comments to: J.Elfick@uq.edu.au
Table of contents
16.0.0 Dynamics, force and motion
16.5.0 Applications of Newton's laws, dynamic torque
16.6.5 Collisions in one dimension
16.6.6 Collisions in two dimensions, equal and unequal mass collisions
16.6.2 Conservation of linear momentum
16.2.1 Force, mass and acceleration
16.6.0 Linear momentum, seat belts
16.6.3 Mass and momentum transfer
16.1.0 Newton's first law, inertia
16.2.0 Newton's second law
16.3.0 Newton's third law, action and reaction, normal reaction
16.7.0 Power
16.3.12 Recoil
16.6.4 Rockets
16.4.2 Static torque, moments
16.4.0 Statics of rigid bodies, moments
16.5.0 Applications of Newton's laws, dynamic torque
16.6.6.7 Change of force direction
16.5.1.8 Couples
16.5.1.6 Extended traction force
16.5.1.2 Ladder against a wall
16.5.1.3 Pull on a spool
16.5.1.4 Pull the bike pedal
16.5.1.1 Tipping block
16.5.1.5 Traction force roller
16.6.5 Collisions in one dimension
16.6.5.3 Air track collision gliders
16.6.5.5 Bouncing dart
16.6.5.2 Collision balls
16.6.5.8 Double air glider bounce
16.6.5.7 Double ball drop
16.6.5.1 High bounce paradox
16.6.5.6 Pendulum collisions
16.6.5.4 Velocity of a softball
16.6.6 Collisions in two dimensions, equal and unequal mass collisions
16.6.6.4 Air table collisions, equal mass, unequal mass
16.6.6.6 Focussing collisions
16.6.6.5 Lost momentum
16.6.6.3 Photograph golf ball collisions
16.6.6.2 Shooting pool (billiards, snooker)
16.6.6.1 Super ball bouncing
16.6.2 Conservation of linear momentum
16.6.2.4 Exploding basketballs
16.6.2.3 Exploding pendulums
16.6.2.2 Motion on a rolling board
16.6.2.6 Recoiling magnets
16.6.2.1 See-saw centre of mass
16.6.2.5 Spring apart air track gliders
16.2.1 Force, mass and acceleration
4.160 Force and motion
16.01 Force, Fundamental forces
6.3.04 Force, (weight) (Primary)
11.0 Force (Primary)
29.2.6 Forces on current in wires
29.2.3 Forces on magnets
29.2.5 Forces on moving charges
16.2.2 Accelerometers
16.2.1.8 Air track cart
16.2.1.9 Atwood's machine
4.146 Balance with a metre stick, centre of mass, centre of gravity
16.2.1.12 Ball in a thrown tube
16.2.1.10 Candle in a bottle, candle in dropped jar
6.11 Coins on a slope (Primary)
16.2.3 Complex systems, movement on a platform balance
16.2.1.13 Drop a leaking bucket
16.2.1.15 Drop a mass on a spring
16.2.1.17 Drop a pendulum
16.2.1.16 Drop a slinky spring
16.2.1.11 Elevator paradox
16.2.1.18 Elevators
16.2.1.7 Equal forces on light and heavy objects
16.2.1.2 Hold a big balloon
16.2.1.1 Ice-skating
16.2.1.3 Press fingers together
16.2.1.14 Vanishing weight
16.6.0 Linear momentum, seat belts
Order online: Magnetic Accelerator, Gaussian rail gun, conservation of energy and momentum
16.6.1.6 Egg in sheet
16.6.1.3 Fire extinguisher thrust
16.6.1.2 Model rocket impulse
16.6.1.7 Pile driver with foam rubber
16.6.1.5 Seat belts, Car crashes
4.2.5 Seat belts, Necessity of seat belts in a motor car
38.5.9.1 Seat belts warning (electronics)
16.6.1.4 Throw ball on a blackboard, deform clay
16.6.1.9 Time of contact
16.6.1.1 Water stream impulse
16.6.3 Mass and momentum transfer
16.6.3.7 Air track ball catcher
16.6.3.2 Catapult a ball from cart to cart
16.6.3.5 Drop a sandbag on a cart
16.6.3.1 Floor carts and medicine ball
16.6.3.4 Shoot a ballistic air glider
16.6.3.3 Thrust cars
16.6.3.6 Vertical catapult from a moving cart
16.1.0 Newton's first law, inertia
16.1.0 Newton's first law, inertia
16.1.0.1 Inertia in daily life
16.1.2.0 Inertia of a fluid
16.1.2.4 Inertia of a gas
16.1.1.0 Inertia of a solid
4.155 Inertia of a stone
16.1.3.0 Inertia of motion
4.156 Inertia of two drink-can pendulums
4.157 Inertia tricks
4.13 Inertia tricks (Primary)
4.2.5 Necessity of seat belts in a motor car
5.25 Push and pull forces (Primary)
16.1.4.1 Rotational inertia
16.2.0 Newton's second law
16.2.0 Newton's second law
4.168 Action and reaction, pulling forces
4.164 Action and reaction pushing forces
4.165 Action and reaction when stepping forward
4.166 Action and reaction with balloons
6.11 Coins on a slope (Primary)
4.169 Electric fan on a sailing boat
4.163 Equal forces from spring clothes pegs
4.162 Equal forces on light and heavy bodies
16.2.0.1 Falling object
4.106 Satellite launcher
4.167 Thrust from a hose, rifle
16.3.0 Newton's third law, action and reaction
16.3.0 Newton's third law, action and reaction
16.3.14 Acceleration of light and heavy objects
16.3.1 Action reaction engine, balloon-driven boat
16.3.2 Action reaction engine, balloon-powered rocket
16.3.11 Cannon car, recoil roller skate
16.3.18 Drinking straw rocket
16.3.10 Helicopter rotor
16.3.6 Impulsive force, thrust, balloon on a balance
16.3.5 Impulsive force, thrust, garden hose, lawn sprinkler
16.3.12.2 Liquid nitrogen cannon
16.3.17 Match rocket, match missile
16.3.15 Milk carton sprinkler, spinning cylinder
16.3.9 Model sailboat, Newton's sailboat, fan on a sailing boat, fan on a roller skate, fan on train tracks
16.3.19 Pop pop boat
16.3.8 Push me pull me carts
16.3.3 Pulling forces, link two spring balances
16.3.4 Pushing forces, push sponges together
16.6.4 Rockets
16.6.4.3 Air track rocket
16.6.4.5 Ball bearing rocket cart
16.6.4.4 Carbon dioxide cartridge rocket, rocket to the moon, Dangerous experiment!
16.6.4.1 Fire extinguisher rocket
16.6.4.6 Nozzle reacts against a water jet, reaction to a stream of water
16.6.4.2 Water rocket
16.3.12 Recoil, bow and arrow, catapult, fire a rifle
16.3.12.1 Throwing a ball
16.3.16 Turning water can, aeolipile of Hero, steam ball of Hero of Alexandria, Hero's steam turbine
16.4.0 Statics of rigid bodies, moments
4.146 Balance with a metre stick, stationary meeting point, centre of mass, centre of gravity
16.4.1.8 Blackboard force table
16.4.1.7 Break wire with hinge
8.2.0 Centre of gravity, balancing
8.2.3 Centre of gravity, stability of an object
8.2.7 Find centre of gravity
16.4.1.2 Hanging the plank
16.4.1.0 Resolution of forces, inclined plane
16.4.1.5 Rope and three students
16.4.1.4 Rope and three weights
16.4.1.9 Rubber band scale, spring scale
16.4.1.10 Sail against the wind
16.4.1.11 Stand on an egg
16.4.1.1 Suspended block
16.4.1.3 Tension in a string
16.4.1.6 Weight on a clothesline
16.1.1.0 Inertia of a solid
16.1.1.5 Coin keeps moving
16.1.1.3 Inertia of a coin
16.1.1.1 Inertia of a stone
4.156 Inertia of two drink-can pendulums
4.157 Inertia tricks
16.1.1.4 Moment of inertia, inertia and mass
16.1.1.2 Tablecloth pull
16.1.2.0 Inertia of a fluid
16.1.2.1 Inertia of a drop of liquid
16.1.2.2 Inertia of a liquid in an alcohol thermometer
16.1.2.3 Inertia of two bucket pendulums
16.1.2.4 Inertia of a gas
16.1.2.4.1 Cooled hand
16.1.2.4.2 Exhaust fan flag
16.1.2.4.3 Helium balloon in a motor car
16.1.3.0 Inertia of motion
16.1.3.2 Cart on a cart
16.1.3.1 Water hammer
16.1.4.0 Rotational inertia
16.1.5.0 Inertia balance to measure inertia
16.1.4.2 Inertia of rotational solid
16.1.4.3 Spin dryer for clothes
18.3.1.2.1 Spinning eggs, forces with a fresh egg and hard-boiled egg
16.1.4.4 Spinning ice skater
16.2.2 Accelerometers
16.2.2.6 Accelerometer on tilted air track
16.2.2.3 Balloon accelerometer
16.2.2.4 Float accelerometer
16.2.2.2 Glycerine accelerometer
16.2.2.1 Iron ball and cork accelerometer
16.2.2.5 Spirit level (level tube) accelerometer
16.2.3 Complex systems, movement on a platform balance
16.2.3.1 Acceleration on a balance
16.2.3.4 Funnel of water on a balance
16.2.3.3 Hourglass on a balance
16.2.3.5 Reaction balance
16.2.3.2 Yo-yo on a balance
16.4.2 Static torque, moments
16.4.2.14 Arm model
4.146 Balance with a metre stick, stationary meeting point, centre of mass, centre of gravity
16.4.2.3 Balance with a see-saw (teeter-totter)
16.4.2.2 Balanced fork and spoon
16.4.2.15 Grip bar
16.4.2.13 Hanging gate
16.4.2.9 Loaded beam
16.4.2.6 Metre stick balance
16.4.2.0 Moments
16.4.2.1 Moments, parallel forces in equilibrium +
16.4.2.11 Roberval balance
2.23 See-saw balance (teeter-totter) (Primary)
16.4.2.4 Rocking candle, balancing candle, burn a candle at both ends
16.4.2.12 Suspended ladder
16.4.2.01 Torque beam
16.4.2.02 Torque wrench
29.2.7 Torques on coils
16.4.2.8 Walking the plank
16.01 Force, fundamental forces
The four fundamental forces are gravity, electromagnetism, strong and weak nuclear forces. However, most interactions and phenomena can be explained by considering gravity and electromagnetism. The forces that act on objects influence their motion, shape, internal energy and state of equilibrium. When forces act they may be balanced or unbalanced. Unbalanced forces change the motion of objects. Gravity is an attractive force that reaches further than the other forces to keep planets in orbit, but it is the weakest in magnitude. In the general theory of relativity gravity is defined as the curvature of space time around an object with mass. Electromagnetism is the force interaction of particles with an electrical charge. Charged particles at rest interact by electrostatic forces but in motion interact by electrical and magnetic forces. The weak nuclear force acts on the atomic nucleus to control the radioactive decay of atomic nuclei. The strong nuclear force keeps protons and neutrons together, even binding two positively charged protons in the helium nucleus. This strongest force allows gluons to bind quarks together to form the nucleons.
16.1.0 Newton's first law, inertia
See diagram 16.4.0: Forces
Order online: Bottle Jet Drag racer, Newton's laws
Newton's first law (Isaac Newton 1642 -1727) measuring inertia, inertia of rest, inertia of motion, ticker timer, force and acceleration (mass constant), mass and acceleration (force constant), mass and inertia, the mass of a body measures its inertia, quantitative treatment of mechanical contact forces and weight F = ma W = mg, forces acting in one dimension including friction, forces acting in two dimensions involving the vector addition of forces and resolving forces into their components at right angles (using diagrams and a mathematical treatment), inclined plane problems, equilibrium problems 1. Inertia is a property of a body keeping the state of motion. The mass of the object reflects the size of inertia. The greater the mass, the greater the inertia of the body. The property of a body to maintain its velocity unless external action on it is also called inertia. An object in a state of motion remains in that state of motion unless acted on by an external force. This is Newton's First Law, i.e. commonly called the law of inertia. The state of motion referred to could be rest (v = 0), so that an object remains at rest if no force act on it. The state of motion could also be an existing steady velocity. Unless a force acts, the velocity remains constant. The quantitative characteristic of inertia is a physical quantity called the mass of the body.
Newton's first law of motion
When a body remains at rest or is moving in a straight line with constant velocity the total force on it is zero. Conversely, if the total force on a body is zero it is either remaining at rest or is moving in a straight line with constant velocity. An object continues in its state of rest or uniform velocity, unless acted upon by an external resultant force. Inertia opposes any change in an object's state of motion, i.e. opposes acceleration. Inertial mass measures opposition to acceleration in kilograms.
Inertia is the resistance of a body to change in its state of motion either at rest or with uniform motion in a straight line, as stated in Newton's first law of motion. The larger the mass of a body the greater its inertia, so a measurement of mass is a measurement of inertia. Mach's principle states that the inertia of a body is caused by the gravitational interaction between that body and all the bodies in the rest of the universe. So if a body could be isolated from the gravitational forces from all other bodies it would have zero inertia.
16.1.0.1 Inertia in daily life
1. Make a pile of books. Grasp the book at the bottom of the pile and pull very quickly. You can remove the bottom book without upsetting the pile because of the inertia of the books above it.
2. Forcibly shake the dust or water off clothing.
3. A worker digging a drain must stop the shovel suddenly in the air when he throws the shovel from the bottom of the drain to the ground.
4. When a bus breakers suddenly the passengers may fall due to their inertia.
5. Do not leave objects on a shelf below the back window of a car. If the car stops suddenly the objects will keep moving due to inertia and perhaps hit the passengers.
6. When a car is towing a trailer or caravan, applying the brakes suddenly is very dangerous while turning. The car slows or stops but the trailer or caravan keeps moving by inertia in the direction when you applied the brakes. The car and trailer will "jack-knife"!
7. An empty bottle on the floor of a bus or train will roll forwards or backwards as the bus or train slows or accelerates.
8. Build a tower using children's building blocks. Hold the back of a ball point pen with a spring clip next to a middle block. Discharge the spring clip. The middle block flies out but the tower does not fall over.
9. Place an egg in a matchbox case and put his on a bread board over a basin of water. Pick up the breadboard then move it very quickly to the side. The egg has great inertia so it falls into the water. The matchbox case has little inertia so it moves to the side.
10. Cut a round potato half way through with a knife. Hold the knife horizontally with the potato stuck to it. Hit the back of the knife with the back of another knife. You cut the potato in halves because it stayed at rest when you hit the knife. Put a round potato on a cutting board and stab it down the middle with a sharp knife. The potato stays in place with the end of the knife in it. Hold the knife and potato with the knife handle down and hit the cutting board with the end of the knife handle. The potato moves down the blade of the knife. The potato stayed in motion when hitting the cutting board stopped the movement of the knife.
11. Make a pile of coins. Flick another coin at the coin at the bottom of the pile. The bottom coin leaves the pile.
12. Half fill a bucket with water. Swing the bucket forwards and backwards. The water "climbs up" the side of the bucket due to its inertia. Similarly if you swing a lighted lantern forwards and backwards the flame pointed to the direction of movement because the heavier air around the lighter flame is left behind due to its inertia.
13. Suspend two large cylinders, 3 kg wood, and 50 kg iron, then compare displacements when struck by a hammer.
14. A blindfolded volunteer compares a mass on a string with a mass on a roller cart.
15. Suspend two heavy iron balls hung separately between lengths of string, pull slowly on one and jerk quickly on the other.
16. Attach a rope between a heavy iron ball and a hammer head so that a fast swing of the hammer takes up the slack and breaks the rope without moving the ball.
17. Place a lead block or a brick on your hand and hit it with a hammer!
18. Hit nails into a 50 kg wood block placed on a student's head!
19. Pull a low friction tablecloth from under a place setting.
20. Jerk a sheet of paper out from under a thin steel cylinder.
21. Snap a card out from under a tall object. Snap a playing card from under a steel ball.
22. Place a pizza pan on three beakers and place cardboard tubes on the pan directly above the beakers and eggs on the tubes, then knockout the pizza pan.
23. Put a coin on a playing card placed over the mouth of an empty glass. Ask someone to remove the card but not the coin. Flick the card away quickly with your finger. The coin falls into the glass. The coin does not move sideways because of its inertia.
24. Scoop up a spade full of dry earth. Pitch the earth away from you. When the spade stops, the earth keeps moving because of its inertia.
25. Place a bottle on a strip of paper. Pull the paper quickly from under the bottle with no motion of the bottle. Cut a strip of paper the size of a ruler. Place the strip at right angles half over the side of a table. Put an object, e.g. a pencil, on the part of the strip over the table. Hold the end of the strip out so that the part of the strip not over the table is almost horizontal. Use your pointing finger of the other hand to hit the middle of the strip not over the table. The pencil does not move and the strip falls down.
16.1.1.1 Inertia of a stone
See diagram 16.240: Inertia of a stone
1.0 Use a stone weighing about 1 kg. Suspend the stone with a light string that is just strong enough to support the stone. Attach two pieces of the same string to the stone and let them hang down.
1.1 Grasp firmly the lower end of one hanging string, B, and give it a quick jerk with a sudden impulsive pull. The lower string breaks and leaves the stone suspended by string A because of the inertia of the stone. If you leave some slack in string B then pull it you have a greater force. Also you can attach a short iron
bar to the end of string B.
1.2 Pull steadily on the other hanging string, B. The upper string A breaks and the stone falls. The steady application of force has set the stone in motion. The stone was "reluctant" to accelerate because of its inertia.
2.0 Suspend a stone with a piece of thin cotton thread just able to withstand the weight of the stone. Tie another piece of the same thread around the middle of the stone and let the end of the thread hang down. Suspend the stone from a firm support. Quickly pull the lower thread hanging down. The thread hanging down breaks but the thread suspending the stone does not break. The stone remains suspended. The inertia of the stone slows the transfer of downward force to the upper suspending thread, so the lower
thread breaks.
2.1 Suspend the stone again. Slowly pull the lower thread hanging down. The thread suspending the stone breaks and the stone falls down. You evenly distribute the downward force in the two threads. So this force and the weight of the stone break the upper suspending thread.
16.1.1.2 Tablecloth pull
Cover a table with a tablecloth. Place some plastic dishes on the tablecloth. Now, gather the tablecloth up at one edge and pull horizontally and as fast as possible. The tablecloth will leave the table, but the plastic dishes will remain on the table. The dishes on the table are in a state of rest and will remain at rest unless a force acts on them. The horizontal force on the dishes is due to kinetic friction between the dishes and the tablecloth as you pull the tablecloth horizontally. If you pull the tablecloth very quickly, friction between the dishes and the table surface rapidly removes any horizontal velocity of the dishes. This experiment shows Newton's first law and impulse momentum. Both the force and the time during which it acts are small resulting in a small change in momentum of the dishes.
16.1.1.3 Inertia of a coin
See diagram 16.4.8: Flick a card under a coin
1. Use two coins with a big mass difference. Support the playing card on two fingers of your left hand. Shoot the card off quickly with the index of your right hand and let the coin fall on the fingers of your left hand. Some people can balance the coin on the card on one fingertip, flick the card and let the coin remained balanced on the finger tip.
2. Put a stiff cardboard playing card on a beaker. Put a coin on the card. Flick the card quickly with your forefinger. The card moves horizontally but the coin drops vertically into the beaker.
3. Bend a strip of semi-rigid paper into an arc so that the ends are within the rim of the beaker. Put a coin on the strip of paper. Flick the strip of paper quickly with your forefinger so that it moves away. The coin falls down into the beaker.
4. Cut a 1 cm wide hoop from a plastic drink bottle. Stand it over the mouth of a wide mouth jar. Put a coin on top of the hoop. Flick the inside the hoop with your index finger. The hoop moves away and the coin drops into the jar.
16.1.1.4 Moment of inertia, inertia and mass
1. Put carbon copy paper on a slippery table top with the long edge of the paper parallel and to near the edge of the table. Separately put three weights of 50 g and 100 g and 500 g on the carbon paper on a line parallel to the long edge of the paper. Quickly pull the carbon paper off the table. The weights fall on the table. Pull the carbon paper with different speeds to find which weight is the easiest and most difficult to move along with the paper.
2. Repeat the experiments with three identical drink cups containing different amounts of water.
3. Some people can pull a table cloth off a table laid with glasses of water and never spill the water or break the glasses. However, this trick needs a lot of practice.
16.1.1.5 Coin keeps moving
Use a wood block with a slippery surface. Put the wood block on a slippery tabletop. Put a coin on the wood block. Keeping your other hand at the front, hit the wood block with your hand so that it moves quickly in a straight path on the table. When your hand stops the wood block suddenly, the coin continues to move horizontally. If you place a heavy bag next to the back window of a motorcar and the car stops suddenly, the bag keeps going and hits you on the back of the head!
16.1.2.1 Inertia of a drop of liquid
1. Use a glass tube with an open-mouthed end and inner diameter more than 10 cm. Put it on a horizontal plane. Put coloured water into the horizontal glass tube with a glass tube or a drinking straw with a small rubber ball. After the water is at rest, forcibly hit the end of the glass tube with a small stick. Observe the movement of the coloured water when the glass springs out in a straight path.
2. Cut off 1 / 4 of a side wall of a large plastic drink bottle. Put a big drop of water on the upper edge of the inner wall. The drop of water runs down to the lowest level then moves some distance up the other side. The drop continues to move forwards and backwards with decreasing height up the side wall until it settles at the lowest level.
16.1.2.2 Inertia of a liquid in an alcohol thermometer
Use an alcohol thermometer of 100oC range. Put it into the boiling water at a cup. When the alcohol column increases fast to 50oC to 60oC, slowly get it out the water and quickly dry it with a paper towel. You notice that the alcohol column keeps going up some distance, then stops, then falls back.
16.1.2.3 Inertia of two bucket pendulums
See diagram 16.241: Two bucket pendulums
1. To experience the relationship of the inertia of an object to its mass use two buckets and pieces of  string. Tie each bucket to the ceiling. Fill one bucket full of sand but let the other bucket remain empty. Push the two buckets and compare which bucket is easier to push. Try to stop the buckets moving and compare which bucket is more difficult to stop.
2. Use long strings to suspend from the ceiling two large identical buckets. Fill one bucket with sand. Use the hook of a spring balance to push each bucket. Note what force is necessary to start the buckets moving. Use your hand to stop the buckets when they are moving. You can feel the difference in inertia of the two buckets.
16.1.2.4.1 Cooled hand
Wet the back of your left hand. Extent horizontally your arms and keep your left palm horizontal. Move your right hand fast then stop moving it suddenly 10 cm from the back of the left hand. The back of the left hand feels cool because the air pushed by the right hand keeps moving after the right hand stops moving.
16.1.2.4.2 Exhaust fan flag
Cut out a piece of light and soft paper of 4 cm × 10 cm. Paste the 4 cm edge of the paper to a stick. Blow the paper to make it wave nearly horizontally. The paper falls back when the air current stops. Hold the stick with your hand and put the part pasted with the paper under an exhaust fan entry in a kitchen. The paper waves when you turn on the exhaust fan but does not stop waving at once when you turn the exhaust fan off.
16.1.2.4.3 Helium balloon in a motor car
Hold the string of a helium balloon in a motor car travelling at constant speed. The balloon maintains it position relative to your hand. However, if the motor car accelerates, the balloon moves forward. If the motor car reduces speed due to breaking, the balloon moves backwards. If the motor car turns a corner, the balloon moves inwards. The air in the motor car has inertia as you have and all the contents of the motor car have. The balloon floats towards the air of lowest density.
16.1.3.1 Water hammer
Evacuate a tube except for some water. When you stop the tube suddenly, the water strikes the end of the tube with a click. Check for water hammers when you turn off a tap at home. When you shake a tube partially filled with water and evacuated, the water hits the bottom of the tube with enough force to make an audible sound.
16.1.3.2 Cart on a cart
Put a smaller roller cart or skateboard on a larger cart so that when you stop the larger cart the smaller cart continues to move.
16.1.4.1 Rotational inertia
Projectiles, bullets, rockets and footballs (Rugby football or American football) are "spin stabilized". They make them to spin about the axis of their direction of motion then do not tumble end over end and be retarded by extra air resistance. A children's top falls over when place on its tip but a rotating top remains upright until it loses all its angular momentum to friction between the tip and the ground and some air resistance.
16.1.4.2 Inertia of rotational solid
Observe the inertia of an object at the state of rotational motion. Rotate a coin with your middle finger and thumb on a slippery tabletop. When leave the fingers off the coin, it does not stop rotating at once. It keeps moving for a long time then falls down. Use a 25 cm piece of string. Fasten one end of the string to a clip. Hold the other end of the string to quickly rotate the clip differently at upright, horizontal and inclined planes. When your hand holding the string stops suddenly, the string and clasp always keep rotating several circles before they stop.
16.1.4.3 Spin dryer for clothes
Half fill a spin dryer with wet clothing. Turn on then turn off the spin dryer and count the number of  rotations and record the time until it stops. Observe the arrangement of the clothing in the stopped spin dryer. Repeat the experiment with the spin dryer 3 / 4 full of wet clothing and make the same observations. The more wet clothing in the spin dryer, the more rotations when you turn it off because of the greater rotational inertia. The clothing dried off is always distributed equably with more on the outside. However, if the spin dryer contains only pieces of wet clothing, the spin dryer barrel does not rotate normally because of unequal distribution of mass.
16.1.4.4 Spinning ice skater
Go to an ice stadium or watch on television the actions of an athlete rotating at high speed. Observe the positions of the body, arms and legs of the athlete starting to rotate, rotating, stopping rotating, the changes in position, the relationship of the changes to the velocity and time of the rotation. The positions of the body, arms and legs of athletes affect their rotational inertia through affecting the distribution of their mass. An ice skater can start a spin on one toe with one leg extended and both arms extended, (I is large and ω is small), but when the ice skater brings both legs and both arms together (now I is small and ω is large), the moment of inertia decreases and speed of spin increases, the skater spins much faster due to conservation of angular momentum.
16.1.5.0 Inertia balance to measure inertia
Load the cups on a torsion pendulum with various masses. A horizontal leaf spring acts as an inertial balance if you place masses on a platform supported by horizontal leaf springs. You can use an inertia balance to measure mass independent of the earth's gravitational force. It has two platforms connected by two horizontal spring-steel blades. A cylinder can rest in the hole in one platform or be suspended by a hook. Calibrate the apparatus by determining the vibration frequency for known platform loads using the platform with the hole. Calculate the period in seconds for each load and plot period against the weight of  the corresponding load. Find the mass of the unknown from the calibration curve, and compare the value with the weight using a balance.
16.2.0 Newton's second law
Force, weight, falling object, force, mass, and acceleration, accelerated reference frames, complex systems, the newton, F = ma, ticker timer, mass constant, mass and acceleration (force constant), accelerated reference frames, earth's gravitational field strength, g = 9.8 N / kg = 9.8 m / s2
Force is proportional to the time rate of change of momentum it produces,  i.e. force ∝ time rate of velocity × mass. Force ∝ mass × acceleration. Force = constant × m ×a. However, if the unit of force is defined as equal to that force which will produce unit acceleration in unit  mass, the constant = 1, so F = m × a, F = ma.
A change in the motion of an object, i.e. a change in its velocity (the acceleration of the object), is caused by the action of other objects on it. If an object acts on another object and causes its acceleration, the measure of this action is a vector quantity, which is called force.
The SI unit of force is a newton (N) (1 newton = 1 kg m s-2). You may measure force directly using a spring balance. If a force applied to an object can be replaced by another force without altering the motion of the object, these forces are called equivalent forces. In particular, when a single force replaces a system of forces, this force is called the resultant.
Forces are caused by the interactions of pairs of bodies. The effect of an unbalanced applied force on an object is to cause it to accelerate in the direction of this resultant force. Acceleration is directly proportional to this force and inversely proportional to inertial mass of the object.
F = ma, where F = force in newton, N, m = mass in kilograms, kg, a = acceleration in metre / second2, m s-2.
Weight of an object is the gravitational force exerted on it by the Earth, F = mg, F = weight in newton, N, m = mass in kilograms, kg, g = Earth's gravitational field strength at the place = 9.8 N / kg, 9.8 N kg-1.
16.2.0.1 Falling object
Speed and acceleration of falling objects, average acceleration, uniform acceleration, deceleration (retardation)
If an object falls without friction with the air where the gravitational field = 9.8 N / kg, the force acting on  it will be mg newton, its weight. F= ma = mg, so free fall acceleration = 9.8 m / sec2.
16.2.1.1 Ice-skating
Wear a pair of ice skates with idler wheels and stand on a cement floor. Hold a basketball with hands and forcibly throw the ball ahead overhead. Experience the force acting on your hands from the ball and feel that you move backwards. Repeat the experiment but throw the ball backward.
16.2.1.2 Hold a big balloon
Inflate a big balloon and fasten its mouth. Lift it over your head with your hands. Make sure the balloon's  mouth upright against your head. When you untie the string on the balloon's mouth, you may feel the air current spurting out of the balloon. Besides your hands feel that the balloon tries to move upward. You may redo the experiment but hold the balloon horizontally and wearing a pair of ice skates. Observe that the direction of your body's movement is opposite to air current's spurting and the time when your body feels
some force.
16.2.1.3 Press fingers together
Let your middle fingers just touch. When you press the left middle finger with the right, you may find not only the left middle finder reacted but also the finger to its right reacts. Observe the changes in shape of the two fingers and whether they are the same. Repeat the experiment using your left middle finger to press your right middle finger. Use your right hand to clap your left hand then observe whether simultaneously the two hands feel pain.
16.2.1.7 Equal forces on light and heavy objects
See diagram 16.4.11: Equal forces on light and heavy objects
1. Draw a one metre line on a slippery tabletop with chalk and mark the line every five centimetres. Attach a wooden spring clothes peg to each end of a one metre piece of elastic. Pull the elastic out 25 cm along the line then release the ends simultaneously. Observe how the two clothes pegs meet at the middle of the elastic. Pull the elastic out 35 cm along the line then release the ends simultaneously.
Repeat the experiment with two attached clothes pegs. The single clothes pegs move faster than the two attached clothes pegs.
The distance the single clothes pegs move is longer than the distance the two clothes pegs move.
Repeat the experiment with different numbers of clothes pegs attached to the ends of the elastic.
2. Use a wooden clothes peg and several nuts with different masses. Use string to fasten the back part of  the clothes peg to make its front open. Place the tied clothes peg on the middle of a slippery tabletop.
Place a heave and light nut close to either side of the clothes peg. Use a lit match to burn off the string fastening the clothes peg. Observe which nut moves faster.
16.2.1.8 Air track cart
Accelerate an air track cart up an inclined track by the string pulley and mass system. Include a Newton scale on the cart to measure the tension in the string directly.
16.2.1.9 Atwood's machine (George Atwood 1784)
See diagram 16.4.14: Atwood's machine
Used to verify laws of motion if constant acceleration. Two objects mass m1 and m2 connected by an inextensible string over an ideal pulley. If m1 = m2, the system is in neutral equilibrium regardless of the position of m1 and m2. If m1 is not equal to m2 both masses have uniform acceleration
weight = m1g or m2g. If m1 > m2, m2 has two forces acting it, an upward force T exerted by the string and down force m2g, its weight.
If T > m2g, upward acceleration a occurs
(i) T - m2g = m2a
m1 has an upward pull T on it and downward force m1g on it
(ii) m1g -T = m1a
so by combining (i) with (ii), m1g - m2g = m1a + m2a
a = g (m1 -m2) / (m1 + m2)
d = ½ gt2, so find the time taken by m1 or m2 to travel a distance to calculate a.
T = 2gm1m2 / (m1 + m2)
Hang two equal masses from a light pulley and move one mass to the other side. Place 1 kg on each side of a light pulley on good bearings then add 2 g to one side. Measure the distance the mass falls and the time taken to fall through this distance.
16.2.1.10 Candle in a bottle, candle in dropped jar
Drop, throw up and throw a bottle containing a lighted candle. Drop a closed jar containing a lighted candle. Throw a jug with a lighted candle into the air. A candle in a dropped chimney goes out due to absence of convection currents.
16.2.1.11 Elevator paradox
A large hydrometer flask in a beaker of water remains at its equilibrium position as you move the beaker up and down.
16.2.1.12 Ball in a thrown tube
Invert and throw a Plexiglas tube full of water that contains a cork. The rising cork will remain stationary during the throw. Throw or drop a long water-filled tube containing a cork or rubber stopper or air bubble.  A rising bubble in a jar remains stationary while you throw the jar. Join a lead weight and cork with a spring, then put the assembly in a tube of water so the cork just floats and when you drop the tube, the cork sinks. Drop a ball in a tube from the ceiling so that the ball strikes the bottom of the tube after the tube hits the floor.
16.2.1.13 Drop a leaking bucket
Punch a hole in the bottom of a bucket and fill it with water so that when you drop the bucket no water will run out. Drop a can with several vertical holes to show no flow in free fall use a pulley system to accelerate the bucket greater than g then the top hole will issue the longest stream of water.
16.2.1.14 Vanishing weight
Pull a strip of paper from between two weights. It will tear unless dropped. Drop a mass on a spring scale. Drop an object with a second object hanging by a rubber band. Stretch a rubber band over the edge of a container and drop.
16.2.1.15 Drop a mass on a spring
Drop a frame with an oscillating mass on a spring and the mass will be pulled up but stop oscillating.
16.2.1.16 Drop a slinky spring
Hold a slinky spring so some of it extends downward then drop it to show the contraction.
16.2.1.17 Drop a pendulum
Suspend a pendulum from a stick. Drop the stick when the pendulum is at an extreme and the stick and pendulum will maintain the same relative position.
16.2.1.18 Elevators
Quickly raise and lower a spring balance and hanging mass. Construct in an elevator, a rope over a ceiling-mounted pulley with a weight on one side and a spring scale and lighter weight on the other side. Observe a passenger standing on a spring scale in an elevator.
16.2.2.1 Iron ball and cork accelerometer
Suspend an iron ball from the top and a cork ball from the bottom of a clear box filled with water mounted on wheels.
16.2.2.2 Glycerine accelerometer
Mount a clear plastic box containing coloured glycerine on a cart and roll it down an incline or give it a push up an incline.
16.2.2.3 Balloon accelerometer
Suspend a balloon filled with air from the top of a clear box mounted on wheels and suspend a helium balloon from the bottom of a clear box mounted on wheels.
16.2.2.4 Float accelerometer
Observe a float in a glass of water on an accelerating cart. Cork on a string in a clear water-filled box.
16.2.2.5 Spirit level accelerometer
A glass tube with a special shape is nearly filled with methylated spirit, or similar liquid, to leave a visible bubble of air and spirit vapour. The bubble always rises to the highest level in the glass tube. The spirit level is used to test whether the surface to which it is applied is horizontal. It is found in many kinds of surveying instruments, e.g. theodolite and dumpy level, and instruments to assist carpenters, brick layers and builders. The bubble of a spirit level, carpenter's level, moves in the direction of acceleration, so you
can use it as an accelerometer.
16.2.2.6 Accelerometer on tilted air track
The water surface of a liquid accelerometer on a tilted air track remains parallel to the angle of the air track during acceleration.
16.2.3.1 Acceleration on a balance
Burn the string extending a mass on a spring on a taped platform balance.
16.2.3.2 Yo-yo on a balance
Hang a yo-yo from one side of a balanced critically damped platform scale.
16.2.3.3 Hourglass on a balance
Observe an hour glass running down on a taped critically damped balance. Put a very large hour glass on a critically damped balance and note the deflection as the sand starts, continues, and stops falling. The centre of mass is accelerating upwards during most of the process.
16.2.3.4 Funnel of water on a balance
Put a funnel full of water on a taped platform balance, release the water and collect in a beaker.
16.2.3.5 Reaction balance
Support one mass on an equal arm balance by pulleys at the end. The balance is in equilibrium if the string holding the mass is not touched or pulled in uniform motion.
16.3.0 Newton's third law, action and reaction, normal reaction
Action and reaction, getting out of a boat, fluid friction, terminal velocity, Bernoulli principle, recoil, stable, unstable and neutral equilibrium
See diagram 16.4.2: Normal reaction
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The mutual actions of two bodies on one another are equal in magnitude and opposite in direction, whether the bodies are moving or at rest. A body pulled along a surface by a string exerts a force on the string equal and opposite to the force exerted on it by the string. If an object A exerts a force on object B, B exerts an equal and opposite force on A. This is Newton's third law of motion. It shows the fact that forces always interact between objects and thus always occur in pairs. When one object exerts a force on another, the second object exerts an equal and opposite force on the first object. To every action, there is an equal and opposite reaction. When an object is resting on a horizontal surface, the normal reaction perpendicular to the surface balances its weight.
16.3.1 Action reaction engine, balloon-driven boat
Insert a short glass tube into the mouth of the balloon and bind around the balloon mouth and tube with adhesive tape. Punch a hole the size of the glass tube in the side of a waterproof paper box. Put the balloon into the box and push the end of the glass tube through the hole. Tie string around the box so that the balloon cannot jump out. Inflate the balloon through the glass tube and cover the end of the glass tube tightly with your finger. Put the balloon in the box on the water. Remove your finger from the end of the
glass tube and observe the movement of the paper box boat.
16.3.2 Action reaction engine, balloon-powered rocket
Inflate a long balloon and seal the mouth by tying tightly with string. Attach a drinking straw to the balloon along its long axis with adhesive tape. Attach a long fishing line to a post and pull the other end tight. Attach something thin and heavy, e.g. a needle, to the end of the fishing line then thread it through the drinking straw. Pull tight again to the end of the fishing line now with the balloon attached to it. Cut the string around the mouth of the balloon and watch the balloon move along the string.
16.3.3 Pulling forces, link two spring balances
Screw a ring screw into the top and bottom of a cork. Hook a spring balance in each ring of the ring screw. Put a finger of your left hand through a ring of a spring balance and put a finger of your right hand through the ring of the other spring balance. Your left hand does not exert force but must keep the system steady, just like a wall. Pull out with your right hand and observe the readings on two spring balances. Change the direction of the pull and observe the readings on two spring balances. Repeat the experiment with both hands pulling apart at the same time.
16.3.4 Pushing forces, push sponges together
Put together two blocks of bathroom sponge or artificial sponge, with long sides opposite. Push them face to face using right hand only, left hand only, both hands pushing. Observe the change in shape of the two blocks of sponge.
16.3.5 Impulsive force, thrust, garden hose, lawn sprinkler
Hold a garden hose in one hand and turn on the water with the other hand. Feel the movement just when the flow of water increases suddenly. Observe the direction of rotation of lawn sprinklers and the direction of the water spurting out. Observe the change in velocity of a lawn sprinkler when you suddenly increase the flow of water.
16.3.6 Impulsive force, thrust, balloon on a balance
Measure the size of impulsive force. Use a pan balance, some weights, an inflated balloon. Put a balloon on the right pan of a pan balance. Put small weights on the left pan so that the weight on the left pan is more than the weight of the balloon. Untie the mouth of the balloon a bit and let the air rush out of the balloon hitting the right pan of the balance. So an impulsive force is exerted on the right pan of the balance. Adjust the weight on the left pan to balance the force from the balloon on the right pan.
16.3.8 Push me pull me carts
See diagram 16.168: Push me pull you carts
Two people stand on identical roller carts or boats or skateboards. Both pull on a rope or push with a long stick. With both carts at rest one person pulls on the rope but both move.
16.3.9 Model sailboat, Newton's sailboat, fan on a sailing boat, fan on a roller skate, fan on train tracks
1. Fix a sail in front of a battery-powered fan on an air track cart or toy boat, or use a balloon to provide a wind source.
2. Put a battery-operated fan on a model sailing boat. When it blows against the sail the boat does not move forward because an equal and opposite force acts on the fan. Repeat the experiment with the fan on the shore. The wind from the fan blows the boat forward.
3. Fix a potable electric fan and six 1.5 v batteries connected in series on a roller skate or on a toy train carriage on rails. Turn on the fan and the skate moves in the opposite direction. Attach a strong cardboard sail at right angles to the axis of the skate and direction of the fan. Turn on the fan and the skate or carriage does not move because of the equal and opposite forces on it.
4. Cut a drink-can with a ring on the top into two half parts along the diameter. Use one half as the hull. Cut two 40 cm wide strips off the other half of the jar. Use adhesive tape to connect them into a longer strip. Fold the strip into an L shape and put it into the hull then put a wood block of 30 mm × 30 mm × 10 mm on the bottom of the strip. This is the sail of the boat. Place the boat on the water at a large basin. Blow the sail and observe the direction of the boat moving. Use a candle according to the height of the
sail. Light the candle then paste it with waxen oil on the block. Remove the position of the block to adjust the balance of the boat. Take care to keep a certain distance from candle flame to the top of the sail. Observe the movement of the boat now.
16.3.10 Helicopter rotor
A symmetric propeller deflects air down causing upward lift.
16.3.11 Cannon car, recoil roller skate
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1. A small brass cannon mounted on one cart fires a bullet into a wood block on another cart of equal mass. If string ties the carts together, no motion will result.
2. Attach a heavy rubber band to the front of a roller skate such that it can be used as a catapult. Pull back the rubber band with a string tied in the middle of it and attach the other end of the string to the back of the roller skate. Put a marble in the central loop of the rubber band. Cut the tight string. The marble shoots forward due to the catapult action and simultaneously the roller-skate moves backwards slightly because the mass of the marble is much less than the mass of the roller skate.
16.3.12.1 Throwing a ball
Sit on a stand on a roller cart and throw a heavy medicine ball. Throw a ball while sitting on a stool mounted on a conveyor.
16.3.12.2 Liquid nitrogen cannon
Fire a cork out of a liquid nitrogen cannon mounted freely on a railway track or fixed to the track.
16.3.14 Acceleration of light and heavy objects
See diagram: 4.4.3: Blocks on the table
Place a ruler horizontally on a table. Screw a ring screw into the centre of the smallest side of a wood block, 5 × 7.5 × 13 cm. Tie the one end of a piece of elastic to the ring of the screw and put the other end of the elastic on the table and close to the 0 cm mark on the ruler. Press down this end of the elastic then pull out the elastic 15 cm by pulling the block, i.e. align the front of the block to the 15 cm scale. Release the block. Observe the movement of the block. Repeat the experiment with different elongation of the elastic. Compare how fast the state of motion of the block changes with different elongation of the elastic. To repeat the experiment, put another block on this block and secure them together. Compare how fast the state of motion of the block changes when the mass increases.
16.3.15 Milk carton sprinkler, spinning cylinder
See diagram: 4.4.4: Milk carton sprinkler, spinning cylinder
1. Make four identical small holes in the bottom end of the sides of a milk carton. Fill the milk carton with water. Tie a string through a hole in the upper lid. Let the milk carton twist as water rushes out through the holes. Note the relationship of the position of the holes and the direction of the turn. If each hole is in the bottom right hand corner of the carton, when the water spurts out an equal and opposite inwards force at each hole occurs so the milk carton turns anticlockwise.
2. Observe water sprayed from a spinning box. A paper box spins caused by water spouting from it. Make four small holes in the sides of a milk carton, each in the right hand lower corner. Tie a string through a hole in the top of the carton, to hang it or lift it by your hand. Fill the carton full with water, observe the state of  water flowing from the holes. Then turn string around, remove your hand, observe if the spinning direction of the carton is the same to that of flowing water. The water sprays due to the centrifugal force.
3. Observe water from a spinning cylinder.
Use a transparent plastic cylinder. Punch three holes on top of it and four holes at the bottom of it distributed evenly. Tie thread through the three holes on the top and hang it. Fill it half full with water. Cover the four small holes at the bottom with your right hand fingers except the middle finger. Hold the bottom of  the cylinder upward to loosen the thread. Then rock it along a circular line in horizontal plane in one direction, i.e. in the direction of clockwise, until the surface of water in the cylinder forms a deeper whirlpool. Place it down rapidly until the thread is pulled tightly, then remove your hand, observe the spinning of the cylinder and if the spinning direction of it is opposite to that of the flowing water. This is because the cylinder is acted on reaction exerted by both spinning water and sprayed water.
16.3.16 Turning water can, aeolipile of Hero, steam ball of Hero of Alexandria, Hero's steam turbine
See diagram: 4.4.5: Aeolipile
Be careful! Do not scald yourself!
Drill two holes to fit two one-hole stoppers in the opposite sides of around metal can, a short distance from the top. Insert short glass tubes bent at right angles through the holes in the one-hole stoppers. Turn the ends of the glass tubes to point in opposite directions. Fill the can of water. Heat the water in the can with a Bunsen burner. When the water in the can is boiling and steam is coming out of the glass tubes in opposite directions, observe the movement of the can. The can turns in the opposite direction to the steam coming out of the glass tubes. If you apply more heat the temperature of the boiling water is not raised but the spin velocity increases.
16.3.17 Match rocket, match missile
See diagram: 4.4.6: Match rocket
Be careful! Do not stand in the direction of shooting! Open a "slide-on" paper clip so that the angle between the two arms is 45oC. Fix a matchstick with the match head in one of the loops of the paper clip. Wrap around the match stick and paper clip loop tightly with kitchen aluminium foil or the silver paper used to wrap chocolates. Enclose the match head but leave an open tube around the end of the match stick. Hold the paper clip by one arm so that the other arm with the matchstick is pointing upwards at 45oC.
Heat the match head through the silver paper. The match head ignites and the matchstick missile shoots out.
16.3.18 Drinking straw rocket
Fit a one-hole stopper to a plastic drink bottle. Attach a thin glass tube, open at both ends, through the one-hole stopper. Seal one end of a drink straw with Plasticine or modelling clay and place it over the thin glass tube, sealed end out. Squeeze the plastic drink bottle suddenly and the drinking straw shoots out like a rocket. Air from the plastic drink bottle is forced out through the thin glass tube to increase air pressure in the drinking straw. Air rushes out through the back open end of the drinking straw so the opposite reaction occurs causing the straw rocket to move forwards.
16.3.19 Pop pop boat
See diagram 16.3.19: Pop pop boat
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This toy boat has a simple metal boiler made from a drink-can, or very thin metal or even a coiled copper tube connected to a copper tube or two drinking straws, at a small angle, leading out of the rear of the toy boat. The boiler and tubes are almost filled with water. A small lighted candle is placed under the "flash boiler" to convert water in the boiler to steam that pushes out the column of water in the rear tubes or tubes. This backward force causes the forward movement of the boat in accordance with Newton's third law of motion. Any remaining steam in the boiler condenses to reduce the pressure and so water enters the boiler and rear tubes again. However, whereas the water cylinder expelled from the tubes moves in one direction backwards the water re-entering the rear tubes enters from all directions so there is a net forward force to keep the boat moving forward. The "pop pop" noise is caused by water column moving backwards and forwards in the tubes and so expanding and compressing the contents of the boiler. This toy boat is also called a pop pop boat, putt putt boat, flash-steamer, hot air boat, jet boat, pulsating water engine.
16.4.1.0 Resolution of forces, inclined plane
Resolution of forces, resolution into rectangular components, forces in cables, parallelogram law, resolving a force, inclined plane
See diagram: 4.4.1: Normal reaction on inclined plane
If the angle of an inclined plane = a, then the component of the weight perpendicular to the inclined plane = W cos a, is balanced by the normal reaction of the plane. The component of the weight that would cause the object to accelerate down the inclined plane,
if no friction = W sin a, or (W sin a - force of friction).
16.4.1.1 Suspended block
See diagram 16.4.15: Suspended block
Forces parallel and perpendicular to the plane will support the block in midair when the plane is removed. The components of force of a block on an inclined plane are countered by weights. Then remove the inclined plane. A 1.5 kg block rests on the slope of a 3:4:5 triangle. When the three blocks are stable the triangle can be moved to the left and removed leaving the block suspended by the 0.9 kg and 1.2 kg blocks.
16.4.1.2 Hanging the plank
Suspend a heavy plank from three spring scales in several configurations.
16.4.1.3 Tension in a string
Compare the weight of a mass hung from a single spring scale to the weight shown on a spring scale between two masses over pulleys. Suspend a spring scale between strings running over pulleys to equal weights.
16.4.1.4 Rope and three weights
Suspend a rope over two pulleys with masses on the ends and hang another mass from the centre to deflect the rope. Measure the deflection rope and three weights.
16.4.1.5 Rope and three students
Two large strong students pull on the ends of a rope and a small student pushes down in the middle. The small student can easily deflect the rope if it is held very tightly by the large students.
16.4.1.6 Weight on a clothesline
Hang a 1 newton weight from a clothes line and pull on one end of the line with a spring scale.
16.4.1.7 Break wire with hinge
Suspend a 1 kg mass from a length of wire. Break a length of similar wire by placing the same mass on the back of a large hinge. Pushing down on a slightly bent hinge will break the wire fastened to the ends.
16.4.1.8 Blackboard force table
1. Hang a weight on a string suspended between two spring scales in front of the blackboard. Start with the strings vertical then increase the angle.
2. Sit on a chair that hangs from a chain attached to loads on each end of the chain in front of the blackboard.
16.4.1.9 Rubber band scale, spring scale
Calibrate rubber bands or springs for force vs length then predict the mass of an object hung in a non-collinear configuration.
16.4.1.10 Sail against the wind
Fix a sail on an air track cart or toy train carriage or a cork boat with a keel. Supply the wind from different angles with a table fan until it can accelerate against the wind.
16.4.1.11 Stand on an egg
Stand on three eggs in a triangle pattern in foam depressions between two plates. However, you can squeeze a raw egg between two hard foam rubber pads with a force of more than 70 kg.
16.4.2.0 Moments
See diagram 16.4.1.01: Moments
1. The moment of a force about a point = force × perpendicular distance from the point to the line of action of the force.
2. The moment of a force about an axis = component of the force in a plane at right angles to the axis × perpendicular distance to the axis from the line of action of the component.
3. The size and direction of the resultant, R, for two like parallel forces, P and Q = P + Q, passing through point O between P and Q where P × AO = Q × OB.
4. The size and direction of the resultant, R, for two unlike parallel forces, P and Q = P - Q, passing in the direction of the greater of the forces through point O beyond the greater force where P × AO = Q × OB
5. A couple consist of two equal and opposite parallel forces that have a turning effect, moment, called a torque = one of the forces × perpendicular distance between their lines of action. The turning effect is about an axis which is normal to the plane of the forces. The SI unit for the torque of the couple is newton metre.
(A torque converter in an automatic transmission system of a motor vehicle varies or multiplies torque.)
16.4.2.01 Torque beam
See diagram 16.165: Torque beam
1. To show different torque in equilibrium, use different combinations of masses at different distances from a pivot.
2. A uniform rod mass 500g and length 120 cm is supported horizontally by two vertical strings, T1 at one end A, and T2 at 30 cm from the other end B. What is the tensions in the strings when a mass of 200 g hangs from end B? (see diagram)
16.4.2.02 Torque wrench
A torque wrench is a tool for setting and adjusting the tension of nut and bolts. Use a torque wrench to break aluminium and steel bolts.
16.4.2.1 Moments, parallel forces in equilibrium
See diagram: 16.13: Beam balance, moments
The moment of a force is a measure of the turning effect, or torque, produced by the force acting on an object. It is equal to the product of the force and the perpendicular distance from its line of action to the point, or pivot, about which the object will turn. Its SI unit is the newton metre (Nm) If the magnitude of the force is F newton and the perpendicular distance is d metres then the moment is given by: moment = Fd.
16.4.2.2 Balanced fork and spoon
See diagram 16.4.7: Balanced fork and spoon
Observe a fork and spoon in moment equilibrium on the glass rim Observe the burning stops at the point which is the boundary of the two objects. Attach the spoon to the fork by pushing it in between the teeth so that one tooth is held out by the convex surface of the spoon and other teeth are in the concave surface of the spoon. Place a toothpick between two of the forks. The toothpick should be in the same plane with normal axis of the handle of the spoon and fork. Adjust the angle between fork and toothpick, as the fork is above the glass. Once the spoon and fork are in balance on the glass rim, burn the end of the toothpick or match inside the glass. As the heat of the flame is absorbed by the glass, the temperature drops below the wood's ignition temperature and the burning of the toothpick stops exactly at the forger the glass rim. Burn the other end of the toothpick. The burning wilts at the top of the fork and the heat of the flame is absorbed by the metal. Observe the equilibrium of the fork and spoon about the toothpick on the glass rim.
16.4.2.3 Balance with a see-saw (teeter-totter)
See diagram 16.4.13: See-saws | See diagram 8.145: Balance with a see-saw
1. Use a strong board 3 m long and a saw horse to make a see-saw, or use a playground see-saw. Select two students of similar weight. Tell them to sit at either end of the board so that they balance and the see-saw is horizontal. Measure the distance from the balance point, the fulcrum, to each student. They are similar distances from the fulcrum. For each student, calculate the moment by multiplying the distance rom the fulcrum by the student's weight. The moments clockwise should equal the moments anticlockwise.
Select a heavier student and a lighter student and repeat the experiment. Tell them to sit on the board so that they balance. Measure the distance from the balance point to each student. Multiply the distance by the student's weight to calculate the moments clockwise and moments anticlockwise. For objects in equilibrium the moment in one direction is equal to the moment in the opposite direction.
2.1 Make a see-saw with 3 m board and a sawhorse for a fulcrum. Use two students of equal weight. Sit at either end of the board so that they balance. Measure the distance from the fulcrum, balance point, to each student. Multiply the distance by the weight of the student.
2.2 Select a heavier student and a lighter student. Tell them to sit on the board so that they balance. Measure the distance from the fulcrum to each student. Multiply the distance by the student's weight.
2.3 Select a heavier student, weight m1, and a lighter student, weight m2. Sit on the board so that they balance. Measure the distance from the fulcrum to each student, d1 and d2. Multiply the distance by the student's weight. You will discover that m1d1 = m2d2.
2.4 Select a heavier student, weight m1, and two lighter students, weight m2 and m2. Sit on the board so that they balance. Measure the distance from the fulcrum to each student. Multiply the distance by the student's weight. Add the products for the two lighter students. m1d1 = m2d2. m1d1 = m2d2 + m3d3.
16.4.2.4 Rocking candle, balancing candle, burn a candle at both ends
1. Use a cylindrical table candle, not a tapered candle. Use a knife to trim each end of the candle to expose 1 cm of wick. Put the candle on a fulcrum to find the mid-point. Put two glasses over waxed paper on the table. Use a hot needle to make a hole through the centre of the candle at right angles to the length. Push a knitting needle through the hole then balance the candle with the rims of the two glasses supporting the knitting needle. Light both wicks. One end of the candle dips down slightly then dips down more because the flame is closer to the candle wax that at the other end of the candle. More wax melts and drips off the end of melts and vaporizes so that end becomes lighter and the other end of the candle dips down to become lower. The candle develops a faster see-saw motion, a simple harmonic motion, as the differences between the weight each end of the candle become less.
2. Cut wax away from around the wick at the bottom of the candle so that you have the same length of  wick sticking out of each end of the candle. Push a nail or knitting needle through the middle of the candle so that the candle will balance when you place the nail across the sides of two beakers. Put the apparatus in the sink or, to catch candle drips, put a piece of aluminium foil under it if on the table. Simultaneously light both ends of the candle. The burning candle rocks up and down. When you light both ends, one end is sure to burn faster than the other end so it loses more candle wax and becomes lighter than the other end that then tilts downwards. The other end then burns faster, becomes lighter then tilts upwards. The tilted down ends burn faster because the flame becomes closer to the wax. The candle rocks because its centre of gravity, originally through the axis of the nail or needle, moves away from the end burning faster. The centre of gravity continually moves from one side of the axis to the other.
16.4.2.6 Metre stick balance
Hang weights from a beam that pivots in the centre on a knife edge. Use a metre stick suspended at the centre as a torque balance.
16.4.2.8 Walking the plank
Place a 25 kg block on one end of a long plank, hang the other end of the lecture bench and walk out as far as you can.
16.4.2.9 Loaded beam
Put large masses on a board resting on two platform balances. Move a heavy toy truck across a board bridge supported on two platform scales then two spring scales.
16.4.2.11 Roberval balance
Neutral equilibrium is maintained at any position on the platform.
16.4.2.12 Suspended ladder
Model of a ladder suspended from two pairs of cords inside an aluminium frame.
16.4.2.13 Hanging gate
A gate initially hangs on hinges then add cords and remove the hinges leaving the gate suspended in mid air.
16.4.2.14 Arm model
Place a spring scale on a skeleton in the place of the biceps muscle and hang a weight from the hand arm model. Simulate both biceps and triceps muscles to throw a ball.
16.4.2.15 Grip bar
See diagram 16.164: Grip bar
Suspend a 1 kg mass from hooks on a bar at 5 different distances from the handle grip. The further from the handle grip the more difficult to keep the bar level or rotate it upwards using wrist strength.
16.5.1.1 Tipping block
Pull with a spring scale at various angles on the edge of a block. A large wooden block is tipped over with a spring scale. A spring scale is used to show the least force required to overturn a cube. The force needed is not related to the position of the centre of mass.
16.5.1.2 Ladder against a wall
See diagram 16.166: Ladder against a wall
Set a model ladder against a box and move a weight up a rung at a time. Forces on a ladder: Mount a set of wheels at the top of a ladder anyplace some shoes at the bottom to decrease friction and climb the ladder until you fall down.
16.5.1.3 Pull on a spool
See diagram 16.167: Pull on a spool
Pull on the cord wrapped around the hub of a spool, e.g. a cotton reels, at various angles to make the spool change directions. Note the angle of pull on the cord when the spool does not roll but slides in the direction of the pull.
16.5.1.4 Pull the bike pedal
Pull backward on a pedal at its lowest point and the bike will move backward.
16.5.1.5 Traction force roller
You can pull a large pulley by either pulling on the axle or on a string wrapped around the perimeter. Try each method while the pulley is resting on a roller cart.
16.5.1.6 Extended traction force
Pull on a string wrapped around the circumference of a cylinder placed on an air track. A string wound around a cylinder hoop and spool is pulled while the objects are on a roller cart and the reaction force direction is surprising.
16.5.1.8 Couples
Two index fingers rotating a metre stick about the centre of mass.
16.6.0 Linear momentum and collisions, impulse and thrust, conservation of momentum
See diagram 16.4.0: Forces
Order online: Newton's Cradle, conservation of momentum, periodical motion
Order online: AstroBlaster, high bounce balls, conservation of momentum
Inelastic collision, elastic collision, Mass velocity = MV, Conservation of Linear Momentum, colliding steel balls + explosions, jet principle, explosions and recoil. Problems involving friction (non-closed systems), rockets, jets, force and momentum F = (mv - mu) / t, Kick a ball, Colliding balls, p = mv (vectorial), F t = p (vectorial), problems limited to linear situations
From Newton's second law, force, F ∝ time rate of change of momentum. When the change of momentum is uniform, F ∝ time rate of change of momentum / t, so Ft ∝ change of momentum, Ft = constant × change in momentum.
If the constant = 1, Ft = change on momentum = mv - mu. Ft is called the impulse of the force. The conservation of linear momentum states that if there is no external force acting on a body or system in a given direction, the total momentum of the body or system will be constant. If there is a force acting on a body or system in a given direction, the change of momentum in that direction will be equal to the impulse of the force. It follows that if two bodies moving in the same direction collide, the momentum gained by one body will equal the momentum lost by the other body.
Impulse and momentum
Impulse = force × time, newton second, Impulse (newton.sec) = change in momentum (kg.m / sec).
Momentum = mv, kg m / second, Conservation of momentum m1v1 + m2v2 = m3v3
Collisions, elastic collisions involving kinetic energy and momentum conservation, inelastic collisions In an elastic collision the paths of the colliding objects are the same for coming together or moving apart, momentum is conserved and the total kinetic energy before the collision is equal to the total kinetic energy after the collision. In an inelastic collision, some kinetic energy is lost during the collision. In a head on, elastic collision, with a stationary object all the momentum and kinetic energy are transferred to the stationary mass.
16.6.1.1 Water stream impulse
Let the impulse supplied by a counterweight equal the loss of horizontal momentum of a jet of water then calculate the exit velocity of the water jet and check by measuring the range. Measure the vertical height of a water jet, collect the water to find the flow and match the deflection of the nozzle by hanging weights with the flow turned off.
16.6.1.2 Model rocket impulse
Modify a toy rocket to maintain continuous discharge then attach to a platform scale.
16.6.1.3 Fire extinguisher thrust
Use a fire extinguisher cart to get exhaust velocity and average thrust for a variable mass system.
16.6.1.4 Throw ball on a blackboard, deform clay
Throw a silicone ball at a dirty blackboard then measure the diameter of the mark and place weights on the silicone ball until it is squashed to the same diameter. Compare the imprint of a sponge ball thrown against a dirty blackboard with the force required to get an equal size deformation and calculate the interaction time. Drop a 50 g mass on a blob of softened clay then add masses slowly to another identical blob of clay until the depression is equal.
16.6.1.5 Seat belts, car crashes
Roll a car down an incline to smash drink-cans. Vary the bumpers to change the impulse. Roll a cart rolls down an incline and smash a drink-can against a brick wall. To study car safety on the air track use models of a person with a head seat belt and a head rest placed on an air track cart.
16.6.1.6 Egg in sheet
Throw an egg into a sheet held by two students.
16.6.1.7 Pile driver with foam rubber
Break a bar of Plexiglas supported on two blocks with a pile driver then add foam to a second bar and it doesn't break. A pile driver breaks a plastic sheet supported at the sides but add a piece of formatter and the plastic does not break.
16.6.1.9 Time of contact
Let a ball swing against a plate to complete an electrical circuit allowing an oscillator to feed a counter to measure the collision time.
16.6.2.1 See-saw centre of mass
Let two carts magnetically repel each other on a see-saw (teeter-totter). Let identical weight magnet carts on a balanced board repel when a constraining string is burned then repeat with carts loaded unequally. Burn a string holding two carts with opposing horseshoe magnets and observe if they remain balanced on a board as they repel.
16.6.2.2 Motion on a rolling board
Start and stop a radio-controlled car on a board on rollers. Use a straight train track mounted on a movable board and change the weight of the train to change the relative velocities of the train and track. Use a circular toy train track for conservation of angular momentum.
16.6.2.3 Exploding pendulums
Let two large pendulums of unequal mass hold between them a compressed spring tied with cord and note the maxima of the pendulums when the spring is released.
16.6.2.4 Exploding basketballs
Explode a firecracker between a light and heavy basketball are suspended near the ceiling. Explode a firecracker in a cart on model railroad track.
16.6.2.5 Spring apart air track gliders
Burn a string holding a compressed spring between two unequal mass air gliders.
16.6.2.6 Recoiling magnets
Hold two small horseshoe magnets together on an overhead projector and observe the recoil. Pull apart two elastic band reaction carts of unequal mass attached with an elastic band. A stretched rubber band pulls two carts together with accelerations inversely proportional to their masses.
16.6.3.1 Floor carts and medicine ball
Two people on roller carts throw a medicine ball to each other.
16.6.3.2 Catapult a ball from cart to cart
Catapult a ball of equal mass as the cart into a catcher in the second cart. Conservation of momentum of a thrust producing a stream of water is shown by two carts on a track, one with a nozzle and the other a bucket to catch the water.
16.6.3.3 Thrust cars
Pull the plug on a container of water on a cart to show conservation of momentum by reaction to discharging water stream.
16.6.3.4 Shoot a ballistic air glider
Shoot a 0.22 bullet into a wood block mounted on an air glider and use a timer to find the velocity.
16.6.3.5 Drop a sandbag on a cart
A cart passes by a device that drops a sandbag of equal mass on a cart then use timers to measure the velocity before and after the transfer. Two people on roller carts push against each other.
16.6.3.6 Vertical catapult from a moving cart
Shoot a ball of equal mass from a moving cart into a catcher and time to find the velocity before and after the transfer. Run at constant velocity and jump on a roller cart.
16.6.3.7 Air track ball catcher
Shoot a stream of balls at a moving air cart until the cart stops.
16.6.4.1 Fire extinguisher rocket
Mount a fire extinguisher on a cart and take a ride!
16.6.4.2 Water rocket
See diagram 34.7.1: Water rocket
Order online: Water Rocket Launcher, pump and plastic drink bottle
Pump a toy water rocket the same number of times first with only air and then with water.
16.6.4.3 Air track rocket
Use air from a rubber balloon to propel an air cart.
16.6.4.4 Carbon dioxide cartridge rocket, rocket to the moon
See 3.3.5: Carbon dioxide syphon bulbs
Be careful! Dangerous experiment! Carbon dioxide cylinders should not be used as a source of  propellant gases! Carbon dioxide powered car accelerates across the bench small carbon dioxide powered rocket rides a wire across the classroom. A carbon dioxide cartridge in the back of a model plane propels it around in circles. A small carbon dioxide cartridge rotates a counter balanced bar.
16.6.4.5 Ball bearing rocket cart
A cart is propelled down a track by ball bearings rolling down a chute attached to the cart. Use 15 large steel ball bearings to fall through a chute to propel a cart so that the last ball moves in the same direction as the cart.
16.6.4.6 Nozzle reacts against a water jet, reaction to a stream of water
Tie one end of a rubber hose to a spring and turn on the air then cut the string.
16.6.5.1 High bounce paradox
Flip a half handball inside out and drop on the floor then it bounces back higher than the height from which it was dropped.
16.6.5.2 Collision balls
Six billiard balls are mounted on bifilar suspensions. Use a large frame to hold seven bowling balls on quadfilar supports. Use billiard balls in a V track. Roll a ball down an incline into a trough with five other balls. Use identical steel balls on bifilar suspensions and insert wax for inelasticity. Many collisions occur in a 3:1:1 system, elastic and inelastic collisions.
16.6.5.3 Air track collision gliders
Two sets of air track carts one with springs and the other with "Velcro" give elastic and inelastic collision. Air gliders have springs on one end and the post / clay on the other. Place a metre stick on two carts and lift it up before one hits an end bumper. Use a metre stick resting on top of two air track carts to give equal velocities then after one hits the end bumper you have equal and opposite velocities. A small cart with bumper springs hits a big cart elastically placed so that after the collision both carts hit the ends simultaneously then the carts will again collide at the original place. Mount a plunger on one air track and a cylinder packed with modelling clay on the other.
16.6.5.4 Velocity of a softball
Throw a softball into a box, inelastic collision, and find the velocity of the box from the recoil distance.
16.6.5.5 Bouncing dart
A dart hits a block of wood with a thud, inelastic collision, but when thrown with the pointer removed, elastic collision, the dart knocks the block over showing greater impulse associated with elastic collisions.
16.6.5.6 Pendulum collisions
Release simultaneously two pendulums of equal mass, one of steel and the other of clay, from equal height to strike low friction carts and note greater momentum transfer during the elastic collision is observed.
16.6.5.7 Double ball drop
Drop a softball on a basketball with a 1:3 mass ratio and observe the high bounce. Drop two stacked super balls. Modify the two ball drop with a double mass spring collision on a guide rod to allow more control than the double ball method.
16.6.5.8 Double air glider bounce
Let two air gliders accelerate down 30 cm of track and measure the rebound as the mass of the leading glider is increased.
16.6.6.1 Super ball bouncing
See 3.4.04: Super ball
Analyse the trajectory of a super ball from the floor to the underside of a table and back to the hand.
16.6.6.2 Shooting pool (billiards, snooker)
Use a framework to allow a billiard ball pendulum to strike another on an adjustable tee. Let ink coated balls roll down chutes onto a stage placed on the overhead projector. Use a pool shooting box with a soapy glass surface and plans for a ball shooter.
16.6.6.3 Photograph golf ball collisions
Suspend two golf balls from a ring then take a time lapse photograph of the collision after you pull one golf ball to the side and release it.
16.6.6.4 Air table collisions, equal mass, unequal mass
Vary the angle of impact between a moving and stationary air puck. The path left by liquid air pucks on a  table sprinkled with Lycopodium powder show the 90o scattering law for particles of equal masses. Use  unequal dry ice pucks to do two-dimensional collisions.
16.6.6.5 Lost momentum
Modify the air pucks so the line of force during the collision passes through the centre of mass.
16.6.6.6 Focussing collisions
Suspend balls from one string and spaced at a distance of 3r. Depending on the angle the collision is initiated, the collisions will either focus or defocus.
16.6.6.7 Change of force direction
Use a cylindrical cardboard map container with a removable end. Lightly push a broomstick handle inside the container to push off the removable end. Pour coarse salt into the container. Again, lightly push the broomstick handle inside the container to push off the removable end. Much more force is needed to push off the removable end because the salt crystals have deflected the force from the broomstick handle against the walls of the cardboard container.
16.7.0 Power (power Latin: posse, to be able)
Power is the time rate of doing work, Average power = work done / time taken. If the rate is constant, power = work / time = work done per second. If a body is moving with uniform velocity and work is being done to overcome a constant resistance the rate of work done is constant and the power = work done per second = force × distance travelled per second = force × velocity.
If a body is moving with uniform acceleration the power is not constant but at any instant power = force × velocity.