School Science Lessons
Physics - Force, dynamics, Newton, inertia
Updated: 2008-04-23 L
Please send comments to: J.Elfick@uq.edu.au
Table of contents
16.0.0 Force, dynamics, Newton's laws of motion,
inertia
16.1.0 Newton's first
law, inertia
16.2.0 Newton's second
law
16.3.0 Newton's third
law
16.4.0
Statics
of rigid bodies, moments
16.5.0 Applications of Newton's
laws, dynamic torque
16.6.0 Linear momentum
and collisions
7.107 Kepler's laws of planetary motion
(Johann Kepler 1571-1630)
7.108 Newton's universal law of
gravitation, gravitational
constant, G
7.109 Gravitational potential energy
13.0.0
Fluids, Dynamics of
fluids
19.0.0 Fluid mechanics, surface
properties,
surface tension
17.0.0 Friction
8.3.0 Gravity
21.0.0Mechanics, simple machines, work
and energy
12.1.0Pressure
15.8.0 Relative motion, Coriolis
effect,Coriolis force, Foucault pendulum
18.3.0
Rotational dynamics
16.1.0
Newton's first law,inertia
16.1.0.1 Application of inertia in
daily life, inertia tricks
16.1.1.0 Inertia of solids
16.1.2.0 Inertia of a fluid
16.1.2.4 Inertia of a gas
16.1.3.0 Inertia of motion
16.1.4.0 Rotationalinertia
4.2.5 Necessity of seat belts in a
motor car
5.25 Push and pull forces (Primary)
16.2.0 Newton's second law
16.2.0.1 Falling object
16.2.1 Force, mass and acceleration
16.2.2 Accelerometers
16.2.3 Complex systems, movement on a platform
balance
4.162 Equal forces on light and
heavy bodies
4.163 Equal forces from spring
clothes pegs
4.164 Action and reaction pushing
forces
4.165 Action and reaction when
stepping forward
4.166 Action and reaction with
balloons
4.167 Thrust from a hose, rifle
4.168 Action and reaction pulling
forces
4.169 Electric fan on a sailing boat
4.102 Action and reaction when
stepping forward
4.103 Action and reaction with
balloons
4.104 Thrust from a hose, rifle
4.106 Satellite launcher
4.86 Rotation period of the sun
16.3.0 Newton's third law
4.102 Action and reaction when
stepping forward
4.103 Action and reaction with
balloons
16.3.1 Action reaction engine, balloon-driven boat
16.3.2 Action reaction engine, balloon-powered
rocket
16.3.3 Pulling forces, link two spring balances
16.3.4 Pushing forces, push sponges together
16.3.5 Impulsive force, thrust from a garden hose
and lawn sprinkler
16.3.6 Measure
impulsive force,
thrust,
balloon on a balance
16.3.8 Push me pull me
carts
16.3.9 Model sailboat,
Newton's
sailboat,
fan on a sailing boat, fan on a roller skate, fan on train tracks
16.3.10 Helicopter
rotor
16.3.11 Cannon car, recoil
roller skate
16.3.12 Recoil, bow and arrow,
catapult, fire a
rifle
16.3.12.1 Throwing a ball
16.3.12.2 Liquid
nitrogen cannon
16.3.14 Acceleration
of light and
heavy
objects
16.3.15 Milk carton
sprinkler,
spinning
cylinder
16.3.16 Turning water
can, aeolipile
of Hero,
steam ball of Hero of Alexandria
16.3.17 Match rocket,
match missile
16.3.18 Drinking straw
rocket
Statics
of rigid bodies, moments
8.2.7. 0 Finding centre
of gravity
8.2.0 Exceeding centre
of gravity
8.2.3 Stable, unstable
and neutral
equilibrium
16.4.1.0 Resolution
of forces,
inclined
plane
16.4.1.1 Suspended
block
16.4.1.2 Hanging the
plank
16.4.1.3 Tension in a
string
16.4.1.4 Rope and
three weights
16.4.1.5 Rope and
three students
16.4.1.6 Weight on a
clothesline
16.4.1.7 Break wire
with hinge
16.4.1.8 Blackboard
force table
16.4.1.9 Rubber band
scale or spring
scale
16.4.1.10 Sail
against the wind
16.4.1.11 Stand on
an egg
16.5.0
Applications of Newton's
laws, dynamic torque
16.5.1.1 Tipping
block
16.5.1.2 Ladder against a
wall
16.5.1.3 Walking
the spool
16.5.1.4 Pull the
bike pedal
16.5.1.5 Traction
force roller
16.5.1.6 Extended
traction force
16.5.1.7 Rolling
uphill
16.5.1.8 Couples
16.5.2 Friction
16.5.3 Pressure
8.3.0 Gravity
30.0.10 Universal
gravitational
constant
16.6.0
Linear
momentum and collisions, impulse and thrust
16.6.1.1 Water stream
impulse
16.6.1.2 Model rocket
impulse
16.6.1.3 Fire
extinguisher thrust
16.6.1.4 Throw ball
on a blackboard,
deform
clay
16.6.1.5 Car crashes,
seat belt
16.6.1.6 Egg in sheet
16.6.1.7 Pile driver
with foam
rubber
16.6.1.8 Karate blows
16.6.1.9 Time of
contact
16.1.1.0
Inertia of
solids
4.155 Inertia with a
stone
4.156 Inertia with
two drink-can
pendulums
4.157 Inertia tricks
16.1.1.1 Inertia
with a stone
16.1.1.2 Tablecloth
pull
16.1.1.3 Inertia of a
coin
16.1.1.4 Moment of
inertia, inertia and mass
16.1.1.5 Coin keeps
moving
16.1.2.0
Inertia of a
fluid
16.1.2.1 Inertia of a
drop of liquid
16.1.2.2 Inertia of
liquid in an alcohol
thermometer
16.1.2.3 Inertia with
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
16.1.3.1 Water hammer
16.1.3.2 Cart on a
cart
16.1.4.0
Rotational
inertia
16.1.4.1 Spinning
fresh egg and hard-boiled egg
16.1.4.2 Inertia of
rotational solid
16.1.4.3 Spin dryer
for clothes
16.1.4.4 Spinning ice
skater
16.1.5.0 Measuring
inertia, inertia balance
16.2.1
Force, mass and
acceleration
16.2.1.1 Ice-skating
16.2.1.2 Hold a big
balloon
16.2.1.3 Press
fingers together
16.2.1.7
Effect of
equal forces on light and
heavy
objects
16.2.1.8 Air track cart
16.2.1.9 Atwood's
machine
16.2.1.10 Candle in
a bottle, candle in
dropped jar
16.2.1.11 Elevator
paradox
4.145
Balance
with a
see-saw (teeter-totter)
4.146 Balance with a
metre stick,
stationary
meeting point, centre of mass, centre of gravity
16.2.1.12 Ball in a
thrown tube
16.2.1.13 Drop a
leaking bucket:
16.2.1.14 Vanishing
weight
16.2.1.15 Drop a
mass on a spring
16.2.1.16 Drop a
slinky spring
16.2.1.17 Drop a
pendulum
16.2.1.18 Elevators
6.11 Forces on coins on a slope (primary)
16.2.2
Accelerometers
16.2.2.1 Iron ball
and cork accelerometer
16.2.2.2 Glycerine
accelerometer
16.2.2.3 Balloon
accelerometer
16.2.2.4 Float
accelerometer
16.2.2.5 Spirit level
accelerometer
16.2.2.6
Accelerometer on tilted air track
16.2.3
Complex systems,
movement on a platform
balance
16.2.3.1 Acceleration
on a balance
16.2.3.2 Yo-yo on a
balance
16.2.3.3 Hourglass on
a balance
16.2.3.4 Funnel of
water on a balance
16.2.3.5 Reaction
balance
16.4.2.0 Static torque, moments
4.145 Balance with a
see-saw
(teeter-totter)
4.146 Balance with a
metre stick,
stationary
meeting point, centre of mass, centre of gravity
16.4.2.1 Moments,
parallel forces in
equilibrium +
16.4.2.2 Balancing
fork and spoon
16.4.2.3 Balance with
a seesaw (teeter-totter)
16.4.2.4 Grip bar
16.4.2.5 Torque
wrench
16.4.2.6 Metre stick
balance
16.4.2.7 Torque beam
16.4.2.8 Walking the
plank
16.4.2.9 Loaded beam
16.4.2.11 Roberval
balance
16.4.2.12 Suspended
ladder
16.4.2.13 Hanging
gate
16.4.2.14 Arm model
16.6.2.0
Conservation
of linear
momentum
16.6.2.1 See-saw
centre of mass
16.6.2.2 Motion on a
rolling board
16.6.2.3 Exploding
pendulums
16.6.2.4 Exploding
basketballs
16.6.2.5 Spring apart
air track gliders
16.6.2.6 Recoiling
magnets
16.6.3.0
Mass and
momentum transfer
16.6.3.1 Floor carts
and medicine ball
16.6.3.2 Catapult a
ball from cart to cart
16.6.3.3 Thrust cars
16.6.3.4 Shoot a
ballistic air glider
16.6.3.5 Drop a sandbag
on a cart
16.6.3.6 Vertical
catapult from a moving cart
16.6.3.7 Air track
ball catcher
16.6.4.0
Rockets
16.6.4.1 Fire
extinguisher rocket
16.6.4.2 Water rocket
16.6.4.3 Air track
rocket
16.6.4.4 Carbon
dioxide cartridge rocket,
rocket to the
moon Dangerous experiment!
16.6.4.5 Ball bearing
rocket cart
16.6.4.6 Nozzle
reacts against a water jet,
reaction to
a stream of water
16.6.5.0
Collisions in
one
dimension
16.6.5.1 High bounce
paradox
16.6.5.2 Collision
balls
16.6.5.3 Air track
collision gliders
16.6.5.4 Velocity of
a softball
16.6.5.5 Bouncing
dart
16.6.5.6 Pendulum
collisions
16.6.5.7 Double ball
drop
16.6.5.8 Double air
glider bounce
16.6.6.0
Collisions in
two
dimensions, equal and unequal mass collisions
16.6.6.1 Super ball
bouncing
16.6.6.2 Shooting
pool (billiards, snooker)
16.6.6.3 Photograph
golf ball collisions
16.6.6.4 Air table
collisions, equal mass,
unequal mass
16.6.6.5 Lost
momentum
16.6.6.6 Focussing
collisions
16.1.0
Newton's first law,
inertia
See diagram 16.1.0: Forces
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
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.
16.1.0.1
Application of
inertia in
daily life, inertia tricks
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 "jackknife"!
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 with a stone
See diagram 4.155
1. 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. 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: 16.1.1.3
1. 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.
2. 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.
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
See diagram: 16.1.5
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.
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
See diagram: 16.1.6.1
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 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 with two
bucket
pendulums
See diagram: 16.1.2.3
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
See diagram: 16.1.6.2
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 x 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.
16.1.4.0
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.
6.1.4.1
Spinning fresh egg
and
hard-boiled egg
See diagram: 16.1.7
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 or
ballet dancer
uses the conservation of angular momentum. If the ice skater starts a
spin
with arms and one leg extended (I large, omega small) then moves the
arms and
leg back parallel to the body (I small, omega large) the moment of
inertia
decreases and speed of spin increases.
16.1.5.0
Measuring inertia,
inertia
balance
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
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
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
Effect of equal
forces on
light and heavy objects
See diagram: 4.2.1.7
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.
3. Accelerate a car on a track with a mass on a string over a pulley.
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
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.
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
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.
Complex Systems - movement on a
platform balance
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, getting out of a boat, fluid friction, terminal velocity,
Bernoulli principle, recoil, stable, unstable and neutral equilibrium
See diagram 16.06: Normal
reaction
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, lefthand only,
both
hands pushing. Observe the change in shape of the two blocks of sponge.
16.3.5
Impulsive force,
thrust from a
garden hose and 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
Measure 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
Two people stand on identical roller carts or boats and both pull on
a rope or
push with a long stick.
16.3.9 Model
sailboat, Newton's
sailboat, fan on a sailing boat, fan
on a roller skate, fan on train tracks
See diagram: 16.4.2
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 x
30 mm x 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.
Lit
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
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: 16.4.3
Place a ruler horizontally on a table. Screw a ring screw into
the centre of the
smallest side of a wood block, 5 x 7.5 x 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: 16.4.4
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
See diagram: 16.4.5
Be careful! Do not scald yourself!
Drill two holes to fit two 1-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 1-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: 16.4.6
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 1-hole stopper to a plastic drink bottle. Attach a thin
glass tube, open
at both ends, through the 1-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 buildup 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.
16.4.1.0
Resolution of forces, resolution
into rectangular
components, forces in cables, parallelogram law, resolving a force,
inclined
plane
See diagram: 16.06: 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
Forces parallel and perpendicular to the plane will support the car
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.
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.
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
or 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.
16.4.2.1
Moments, parallel
forces in
equilibrium
See diagram: 1.11
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: 16.3.1
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 4.21d: Sea-saws
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 from 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.
16.4.2.4
Grip bar
Use wrist strength to try to lift 1 kg at the end of a rod
attached perpendicularly to a handle.
16.4.2.5
Torque wrench
Use a torque wrench to break aluminium and steel bolts.
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.
16.4.2.7
Torque beam
Put 5 g on the end of a metre stick and extend it over the edge of
the bench
until it is just about to tip over.
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.
16.5.1.1
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
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
Walking the spool
Pull on the cord wrapped around the hub of a spool at various angles
to make the
spool change directions.
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
16.5.1.7
Rolling uphill
See also 8.2.4: Uphill
roller
A disc with a non-uniform mass distribution is placed on an incline
so it rolls
uphill. A loaded disc is put on an inclined plane so it rolls uphill. A
large
wood disc weighted on one side will roll uphill or to the edge of a
table and
back.
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
See diagram 16.1.0: Forces
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
Impulse and momentum
Impulse = force X 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
Car crashes, seat
belt
See also 4.2.5:
Necessity of seat
belts in a car, whiplash effect
See also 38.5.9.1:
Seat belt warning
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.
16.6.1.8
Karate blows
Not many physics teachers will be able to do these demonstrations!
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 weighting 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
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 1.10: 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.
16.6.5.0
Collisions in one
dimension
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 also 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.