School Science Lessons
21. Mechanics, machines, gears, inclined plane, levers, pile-driver, pulleys, wheel and axle
2012-01-27
Please send comments to: J.Elfick@uq.edu.au
Table of contents
21.0.0 Mechanics, machines
4.170 Machines experiments, UNESCO
21.0.0 Units of work and energy, joule and calorie, kilowatt-hour
21.0.2 Three functions of machines, mechanical advantage, velocity ratio, efficiency
21.1.01 Balances
21.4.0 Gears
21.3.0 Inclined planes
21.1.0 Levers
21.0.1 Pile-driver
21.5.0 Pulleys
21.2.0 Wheel and axle (screwdriver, windlass, crank handle, steering wheel)
21.1.01 Balances
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)
8.1.0 Balances, Mass and weight, weighing devices
7.0 Balances,Weighing devices (Primary)
21.4.0 Gears
21.4.0 Gears
4.179 Belt drives
21.2.2 Belt drives, transmission belts
21.4.1 Bicycle gears
21.4.2 Bottle top gears
4.180 Gear wheel
21.4.3 Rolling coins
21.3.0 Inclined planes
21.3.0 Inclined plane, ramp, screw, thread, wedge
21.3.1 Forces on inclined plane
17.184 Friction blocks on an inclined plane (GIF)
17.185 Friction blocks up an incline, force to pull body up an incline (GIF)
4.178 Inclined planes
21.3.4 Mechanical car jack
21.5.3 Paper inclined plane, paper screw thread
4.187 Propeller
21.3.01 Screw, screw jack
21.3.02 Surfing, motion of a surfer on a surfboard
21.3.03 Swell, ocean swell, "State of sea" and "State of swell"
21.3.2 Wedge
21.1.0 Levers
21.1.4 Application of levers in everyday life
3.16 Move your arms (Primary)
17.5.19 Push a wheelbarrow
21.1.3.1 Use chopsticks
4.170 Three orders of lever, machines, mechanical advantage, velocity ratio
Types of levers
21.1.1 Type 1 levers
21.1.2 Type 2 levers
21.1.3 Type 3 levers
4.171 First order lever, type 1 lever
4.172 Second order lever, type 2 lever
4.173 Third order lever, type 3 lever
21.5.0 Pulleys
21.5.0 Pulleys, block and tackle, broomstick pulley
21.5.1 Pulleys, Systems of pulleys
21.5.2 Block and tackle
6.10 Pull with pulleys (Primary)
4.175 Simple pulley
4.176 Single fixed pulley
4.177 Single movable pulley
21.2.0 Wheel and axle, screwdriver, windlass, crank handle, steering wheel
4.174 Wheel and axle
21.2.1 Windlass, raising weight with rotary pencil sharpener
21.0.0 Units of work and energy, joule and calorie, kilowatt-hour
See diagram 21.0.0: Work and wheels
1. Work done = force X distance in direction of the force, W = Fs.
The work done by a force F in moving its point of application through a distance s in the direction of the force is given by the equation: W = FS
When a wheel is moved by a force, the work done = displacement X component of the force in the direction of the displacement
2. Energy is the capacity for doing work. The joule, J, is the SI unit of work and energy. A joule is equal to the amount of work done when the point of application of a force of one newton moves one metre in the direction of the force. So 1 joule = 1 newton.metre.
3. The calorie is the CGS unit of heat. The 15oC calorie is the quantity of heat required to raise the temperature of 1 g of pure water by 1oC at 15oC = 4.1855 J. However the International Table calorie = 4.186 J. Nowadays the SI unit the joule, J, is used. 1 calorie (cal) = 4.184 J, commonly, 4.2 joules. The nutrition industry still uses the calorie but that unit is too small for nutrition calculations so the kilocalorie is used, i.e. 1000 cal. Popular information on diet and cooking in the daily press, cooking literature and women's magazines refers to "calories" which are really kilocalories.
4. The kilowatt-hour, KWh, is the energy used when when an appliance with the power of one kilowatt runs for one hour. A power of one watt = one joule per second, so a kilowatt-hour = 3,600,000 J, about the energy used by one bar of an household electric heater. A 40-watt bulb runs at 0.4 of a kilowatt but a tumble clothes dryer runs at 3 to 4 kilowatts.
5. Work done on an object changes its energy that may be stored as potential energy or cause change in speed, kinetic energy.
6. Kinetic energy is the energy a body possesses because of its motion and so can be measured by the work done in coming to rest. If a body mass m moving with constant velocity v, and brought to rest by application of a constant force F, producing a constant negative acceleration (retardation) a, work done = F × s, where s is the distance travelled in the direction opposed to F.
From the equations of uniformly accelerated motion,
0 = v2 = 2as (initial velocity v, and final velocity 0)
as = ½ v2
mas = ½ m v2
F = ma
Fs = ½ m v2
Kinetic energy of any mass, m, moving at speed, v = ½ mv2. Change in kinetic energy, joule = work done, joule.
7. Potential energy is the energy a body possesses because of its position and can be measured by the work it could do by passing from its position to some defined position. The gravitational potential energy of a body at height h, above some defined level equals the work that must be done to raise it from that defined level to the given height. The force required to lift a body mass m is equal to the weight of the body, mg. So when the body is lifted vertically through height h, the work done = mg × h = mgh, so the increase in potential energy = mgh.
Potential energy is the stored energy that an object has due to the state it is in, e.g. steam compared with water, compressed spring compared with relaxed spring, or its position, e.g. height compared to ground level above the earth. Work can be done when potential energy is released from storage. If an object falls, the gravitational potential energy lost, Ep = mgh = the kinetic energy gained, Ek, = ½ mv2 .
21.0.1 Pile-driver
See diagram 21.184: Laboratory pile driver
A pile driver is a machine for driving piles into the ground usually by repeatedly dropping a dense heavy mass on the pile.
A laboratory device has a 4 kg mass that can slide up and down on two vertical rails attached to a metal base. It is used to find the average force needed to: 1. drive a nail through a block of wood, 2. crush a metal drink-can. Each time the mass falls the nail moves a distance down or the drink-can is squashed a distance down so work is performed, W = FS.
21.0.1.1 Stabbed rice experiment
A pile-driver used in civil engineering construction pushes a pile down. It can do this because the pile pushes earth particles to the side. Nearly fill a metal drink-can with uncooked white rice and stab down into it with a knife. Some rice has moved aside to let the knife blade descend. Add more rice to the drink-can, pull the knife up and stab down again. After repeating this action a few times, when you pull up the knife the drink-can and packed rice rises as well because of the pressure between the knife, rice grains and wall of the drink-can. The pressure from the sharp knife is enough to force the rice grains apart, but then they settle back into place and lock into each other and hold the knife in place. The experiment may work better if you stab at an angle, not vertically.
21.0.2 Three functions of machines, mechanical advantage, velocity ratio, efficiency
1. Amplify force
A man with a strong hand shake can exert 20 kg force but using pliers he can exert a force of more than 60 kg force. In the ear there 3 tiny connecting bones pass on x 30 or more the force from sound waves.
2. Amplify movement and speed
Increasing displacement and speed: Sometimes a machine passes on only a fraction of the force which is applied to it, but it will then increase or amplify movement and speed. A lever of this type is common in jib cranes.
3. Change direction of force
The single fixed pulley just changes the direction of an applied force from up to down. Sometimes it is more convenient to pull down than to pull up
See diagram 21.254: Simple pulley | See diagram 21.255: Single fixed pulley | See diagram 21.256 Single moveable pulley
Machines allow a force called the effort to overcome another force called the load. If an effort of 10 N applied to a machine can move a load of 25 N, the mechanical advantage, MA, of that machine = 25 / 10 = 2.5. If MA > 1, i.e. heavier loads are moved by smaller efforts, then the effort must move further than the load. Velocity ratio, VR, = distance travelled by the effort / distance travelled by the load. Machines lets us overcome a resistance at one place with an effort by applying a force at another place to move a load. Most people cannot crush an empty match box between their thumb and fingers however crushing the matchbox with pliers needs little effort. The effort force is multiplied because the distance to where you grip the handles of the pliers is much greater than the distance to the end of the jaws of the pliers. A big stone may be too heavy to carry but you can move it on a wheelbarrow. your fingers may be too big to pick up very small objects or pick up objects inside small spaces but you can use tweezers to help us. Lever, pulley and axle are simple machines developed according to the lever principle. Inclined plane, wedge and screw are simple machines developed according to the principle of inclined plane. The machines may save labour but do not save work because force (effort) X distance (effort) = force (load) X distance (load), neglecting the force of friction. Mechanical advantage (MA) is the number of times the load moved by a machine is greater than the effort applied to that machine, i.e. MA = load / effort. MA has no unit, as it is a ratio. If MA > 1, load > effort, i.e. you an use a smaller effort to move a bigger load. However the effort must move further than the load. Distance moved by the effort / distance moved by the load = velocity ratio, VR. Efficiency of a machine = energy output / energy input, as percentage. No machine is 100% efficient because always some energy is lost due to friction. Work = force X distance. Efficiency = work done on the load / work done by the effort = load X distance moved by the load / effort X distance moved by the effort = MA X 1 / VR = MA / VR X 100%.
21.1.0 Levers, moments, levers. parallel forces, couples, beams, structures
The 3 types of lever
The distance of the effort from the fulcrum is called the effort: arm and the distance of the load from the fulcrum, the load arm. To arrange the lever so that a small effort would lift a big load the effort arm must be as long as possible and the load arm as short as possible. A fishing rod gives a loss in force, but gives a gain in distance and speed instead. Examples of levers include scissors, wheelbarrow, forearm, claw hammer to draw a nail, sugar tongs, boat oars, nut-crackers, pliers, can opener, bottle opener, crow bar.
A lever is a simple machine consisting of a rigid rod pivoted at a fixed point called the fulcrum, used for shifting or raising a heavy load or applying force. The lever principle states that motive force × the arm of the motive force = resistance × the arm of resistance.
Classify levers into 3 orders or types according to where the effort is applied, and the load moving force developed, in relation to the position of the fulcrum:
1. A first order or type 1 lever has the load and effort on opposite sides of the fulcrum, e.g. seesaw, beam balance, pair of scissors (two first order levers!), tin snips, bolt cutters.
2. A second order or type 2 lever has the load and effort on the same sides with the load nearer the fulcrum, e.g. nutcrackers, wheelbarrow, fishing rod, broomstick, biceps muscle on upper arm.
3. A third order or type 3 lever has the effort nearer the fulcrum than the load with both on the same side of it, e.g. tweezers, tongs, chopsticks.
Machines are used to change the direction of a forces. Usually they allows a smaller applied force, the effort, to overcome a larger resistance force, the load. Levers have a rigid beam supported a one point, the fulcrum (F) with a load force (L) applied at one point and an effort force (F) applied at another point. The Lever Principle can be stated as: Load x Length of load arm = Force x Length of force arm. Each side of this equation is a moment, i.e. Force x Perpendicular distance to pivot. Hence moments clockwise = moments anti-clockwise.
The three types of lever depend upon the relative positions of F, L, and E:
Type 1 Fulcrum between load and effort (E F L),
Type 2 Load between effort and fulcrum (F L E),
Type 3 Effort between fulcrum and load (L E F).
The mechanical advantage of a machine, M. A., is the ratio of the load to the effort, L / E. The velocity ratio of a machine, V. R., is the ratio of the distance moved by the effort to the distance moved by the load. The efficiency of the machine is the ratio M. A.  / V. R. Efficiency is always less than 100% because when a machine is used there is always some energy loss.
21.1.1 Type 1 lever
See diagram 21.252.1: Lever 1
1. Use a metre stick with a hole drilled in the centre. Hammer a nail horizontally into the side of a table. Suspend the metre stick at the centre by the nail through the hole. Use a loop of string and a small mass to balance the metre stick. Tie a loop of string around the metre stick each side of the nail. Attach a spring balance to one loop, hanging down. Attach a weight to the other loop. Tie a loop of string to a weight. Move the loops to any position along the bar. Pull down on the ring end of the spring balance to raise the weight. Note the weight, the reading on the spring balance, the distance from weight loop to nail, the distance from spring balance loop to nail. Also, note how far the spring balance loop moves down and how far the weight loop moves up.
2. Use a board the same height as a desk. Place a stick across the board and use it as a lever to raise the table. Note that the longer end of the stick moves further than the shorter end. The force exerted by the shorter end, load, is greater than the force used to move the longer end, effort.
3. Close a wooden match box and try to crush it between the thumb and fingers. You cannot do it. Hold the match box in the jaws of a pair of pliers. You can easily crush it by squeezing the handles together. Pliers, tin snips, and bolt cutters have two Type 1 levers with each fulcrum as a pivot. When cutting paper or cloth with scissors the effort < load because you want a long length of scissors blade and cloth does nor require much force to cut it. Try using a pair of scissors as tin snips to feel the difference.
4. Hammer a nail into a big piece of wood. Try to pull the nail out with your fingers. You cannot do it. Use a claw hammer to pull out the nail. The load is the force of the nail on the claw. The fulcrum is the round part of the hammer head. The effort is your pull on the handle. The hammer is being used as a bent lever to pull out the nail.
21.1.2 Type 2 levers
See diagram 21.252.2: Lever 2
Use a metre stick with a hole drilled in the centre near one end. Hammer a nail horizontally into the side of a table. Suspend the metre stick at one end by the nail through the hole and attach a spring balance to the other end. Tie a loop of string to a weight. Pass the bar through the loop so that the bar can support the weight. Move the loop to any position along the bar. Examples include wheelbarrow, nutcracker.
21.1.3 Type 3 levers
See diagram 2.252.3: Lever 3 | See diagram 9.232: Arm joint
1. Use the same apparatus as for Type 2 lever but put the weight, load, at the end of the bar and suspend the bar by a loop of string attached to a spring balance, effort. Since a Type 3 lever has the effort between the fulcrum and the load, the effort is always greater than the load, M. A. < 1. Pick up something heavy with tweezers, forceps, or chopsticks. They consist of two Type 3 levers joined at the fulcrum. For chopsticks the fulcrum is the angle between your thumb and forefinger. The force you apply with your fingers, effort, is greater than the force exerted by the ends of the tweezers or chopsticks, load. Type 3 levers are convenient for picking up small things.
1.1 Catch a fish with a rod and line. The load is the pull of the fish. The effort is your pull on the rod. The fulcrum is where you hold it lower down or where the rod touched the ground.
1.2 Keep your upper arm vertical and your forearm horizontal in front of the body. Pat a heavy stone in the palm of your hand and move it up towards your mouth without moving the upper arm. The load is the weight of the stone. The effort comes from the shortening of the biceps muscle in your upper arm. The fulcrum is the elbow joint.
2. Use a wooden ruler, a spring balance, a weight of mass 50g, a large wood board, a piece of string. Saw the wood board into several small boards according to the sizes. Drill a hole of F5 differently at two vertical boards and the place with 50 cm mark on the ruler. To be more accurate, drill a small pit with a nail then drill a hole. Place the two vertical boards hole to hole on a level board. Make sure the distance between the two vertical boards just fit to insert the ruler. Fixed the two vertical boards on the level board with nails. Insert the ruler into the crack between the two vertical boards and make the hole on the ruler just opposite to the holes on the boards. Fix them with a set of screws through the holes. Do not screw too tightly. Use string to make two sheaths. Tie a sheath on the weight and tie the other sheath on the hook of the spring balance. Fix the weight at some point of the ruler and record the scale. Slowly remove the spring balance. When the system balances, record the reading of the ruler scale, the spring location and the reading on the spring balance.
21.1.3.1 Use chopsticks
To use chopsticks in a Chinese restaurant, hold one the thicker end of one chopstick in the crook of the hand, i.e. where the first finger and the thumb join on the hand. Let it rest on the end of the middle finger. This lower chopstick never moves during the eating motion. Hold the upper chopstick between the end of the thumb and the end of the forefinger (index finger, second finger) with the thumb touching a thicker part than the forefinger. The thinner ends of the the two chopsticks should meet so that you can pick up piece of food with a pincer motion. Tap the ends of the chopsticks on the table to even them. Grasp a piece of food by closing the end of the upper chopstick down onto the end of the lower chopstick. The action of the upper chopsticks is that of a type three lever. The end of the thumb is the fulcrum. The end of the index finger supplies the effort. The resultant force of the food on the ends of the chopsticks is the load. The action is similar to the action of tweezers or forceps. Note the mechanical disadvantage but the advantage of being able to select and pick up the small pieces of food and dip them into sauces, a practice characteristic of Chinese cuisine.
21.1.3.2 Drinking straw lever
See diagram 21.1.3.2: Drinking straw lever
Lift a bottle with a drinking straw by turning it into a lever. Push the drinking straw down into a bottle so that it makes a sharp bend at the bottom of the bottle and the bottom end pushes against the side of the bottle. The shorter piece of drinking straw is between the bend and the side of the bottle. The longer piece of drinking straw must extend outside the bottle. The fulcrum of the lever is where the drinking straw is sharply bent. The section of the drinking straw between the fulcrum and where it pushes against the side of the bottle is the load arm. The effort arm is the section of the drinking straw up from the fulcrum. Grab the top end of the drinking straw and pull up to lift the bottle as the drinking straw acts as a lever.
21.1.4 Application of levers in everyday life
See diagram 21.1.2: Different levers | See diagram 21.1.2.1 Compare the convenience of using the hand only with using a tool.
Look for levers used at everyday life and classify them according to the type of lever, e.g. Chopsticks belongs to the third order lever. Using it needs greater effort but can prevent food from slipping away.
Balances
2.232 Balance with a see-saw
See diagram 21.252.1: Type 1 levers | See diagram 21.13: Beam balance
1. Use a strong board about three metres long and a sawhorse to make a see-saw. Use two students of equal weight. Sit at either end of the board so that they balance. Measure the distance from the balance point to each student. Multiply the distance by the student's weight.
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 balance point to each student. Multiply the distance by the student's weight.
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 balance point to each student, d1 and d2. Multiply the distance by the student's weight. You will discover that m1d1 = m2d2.
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 balance point to each student. Multiply the distance by the student's weight. Add the products for the two lighter students.
In each experiment the ratio of the masses is the reciprocal of the ratio of the distances from the balance point or centre of mass for the system,
m1d1 = m2d2
m1d1 = m2d2 + m3d3
8.2.7 Balance with a metre stick
See diagram 8.2.7: Balance with a metre stick
Rest a metre stick lightly on your two forefingers. Place your fingers under the ends of the metre stick. Move your fingers towards the centre of the metre stick. Where do your fingers meet?
Place the finger of your right hand under one end of the metre stick and the finger of your left hand half way between the centre of the stick and the other end. Where do your fingers meet?
Place the finger of your left hand under one end of the metre stick and the finger of your right hand is placed about halfway between the centre and the other end. Note where your fingers meet now. Your fingers should meet at the balance point, or centre of mass, for the system.
21.2.0 Wheel and axle, screwdriver, windlass, crank handle, steering wheel
See diagram 21.253: Wheel and axle
A set of wheel and axle consists of two wheels having different radii. The large wheel has radius R and the small wheel an axle, has radius r, such that R > r. Wind one rope around the wheel and another rope in the opposite direction around the axle. Pulling on the wheel rope supplies the effort. The wheel around the axle bears the load. When you pull on the wheel so that it make one complete turn, a point on the circumference of the wheel has moves through 2 π R and a point on the circumference of the axle has moved through 2 π r. So velocity ratio = 2 π R /  2 π r = R / r. Taking moments about the centre of the axle effort X R = load X r so R / r = load / effort = mechanical advantage.
21.2.1 Windlass, raising weight with rotary pencil sharpener
See diagram 21.2.1: Windlass
Remove the cover from a pencil sharpener and tie a string tightly around the end of the shaft. When you turn the handle you find the force needed to turn the handle is much less than the force of gravity on the books. Feel the magnitude of the force lifting the heavy weight. Lift the heavy weight directly. Compare the magnitudes of the forces at two conditions.
21.2.2 Belt drives, transmission belts
See diagram 21.2.2: Simple transmission belt
1. Drive two long nails into a block of wood. Place spools, one larger than the other, over the nails so that these can be used as axles. Slip a rubber band over both spools. Rotate the larger spool through one turn and note whether the smaller spool makes more or less than one full turn. In which direction does the small spool turn? Try crossing the rubber band and observe the result.
2. Use several spools with different diameters, a wooden block, two long nails, a piece of elastic. Nail the two nails on the block. Cover the two spoons on the two nails to make the nails as axles. Cover the elastic on the two spools. Tighten the elastic at fit degree, not too loose and not too tight. Rotate the spool with a larger axle a circle and meanwhile observe the small spool's rotating amount and direction. Again cover the elastic across on the two spools. Repeat the experiment and observe the small spool's rotating amount and direction again. Compare the above two conditions and find the difference. Redo the experiment but differently using two spools with the same diameters and using two spools with very different diameters. Compare and analyse the experiment data to find the relationship of the spool's diameter and the way of covering the spool with elastic to the rotating amount and direction.
21.3.0 Inclined plane, ramp, screw, thread, wedge
See diagram 21.3.1: Inclined plane
Use a smooth board at an angle of 30o to the table. Weigh the trolley by suspending it from a spring balance. This is the effort needed to lift the trolley from the table to the top of the board. Put the trolley on the smooth board. Pull it slowly up the board noting the reading on the spring balance. The effort will be about its weight. The smooth plank is twice as long as it is high at the top. By taking a longer path, the slope will be less and the effort less. Inclined plane is a slope that allows a load to be raised gradually using a smaller effort than would be needed if it lifted vertically upwards. So it is a force multiplier. The ratio of the height of the top point of the inclined plane to the length of the plane is called the gradient. The smaller the gradient the more force is saved.
21.3.01 Screw
See diagram 21.3.01: Screw jack
A screw is a simple type of machine, acting like an inclined plane rolled up in a helix. The pitch of the screw is the distance between the threads. So for one revolution of the screw, it moves laterally through a screwed nut a distance equal to the pitch. The screw is usually turned by a force applied tangentially at one end of an arm. The other end of the arm is fixed to the screw.
Work done by the effort = effort × distance travelled by the effort = effort × 2 π × r, where r = radius of the screw
Work done on the load = load × pitch
So load × pitch = effort × 2 π × r
Mechanical advantage = load / effort = 2 π × r / pitch
A screw may transfer between translation and rotation. The screw thread is a ridge in the form of a helix on a cylindrical core. The ridge may be triangular (v-shape) or square or round. If the screw thread is triangular, greater friction may be used. If the screw thread is square, larger loads may be lifted. The distance between the adjacent threads of a screw or bolt is called pitch. When you turn a screw through one full turn, it moves up or down a distance equal to the pitch of its thread. Different standard screw threads include pre metric British Standard Whitworth (BSW) with an angle of 55o, Sellers or USS screw thread (pre metric USA standard) with an angle of 60o, and various metric screw threads.
An Archimedes screw is a hollow inclined screw so that rotation of the screw raises water. It was invented by Archimedes but apparently was not invented in China. A micrometer screw gauge allows very accurate measurement. A wood screw is like a wedge wrapped around a cylinder so that turning the screw forces two pieces of wood together. A screw jack, "jack" is used to raise motor vehicles to change a tyre. A screw thread in a clamp movers the jaws of a the clamp together. A worm gear uses screw threads to to transmit the rotary movement of one shaft to another shaft at right angles to it. Screws turning in bolts are used to fasten things together. Screw mechanisms are used to adjust the focus of camera lenses.
21.3.02 Surfing, motion of a surfer on a surfboard
Water waves are a combination of transverse and longitudinal waves resulting in the water molecules describing a roughly circular path about a fixed point. At the crest of the wave the molecules are moving forwards in the direction of the wave but at the base of the wave they are moving backwards (undertow). All forms of circular motion require a centripetal force. This comes from the forces of adhesion between the water molecules. A surfer sitting on a surfboard will just bob up and down as the crest of the waves pass. However there may be some movement in the direction of the wave due to frictional forces between the water molecules near the surface and the surfboard. If the surfer puts the legs down into the water, this movement will increase due to more friction with the legs. The friction component might come from the linear velocity that is tangential to the circular motion of the water molecules. A centripetal force is in the direction towards the centre of the circular motion. However this force is negligible when describing surfing the wave. The surfer "catches the wave" by matching the wave's velocity by paddling then moving the weight of the body forward of the centre of gravity of the surfboard that then tends to slide down the wave. This is like an object moving down an inclined plane. However to "stay on the wave" the surfboard must move at the same speed as or faster than the wave in transverse direction. The surfer must have some component of his motion in the direction of the wave's propagation and at the same speed of the wave's propagation. If the surfer's motion in the direction of wave propagation is greater than the wave's the surfer will be in front of the wave and no longer sliding (surfing) down the incline. This is why surfers surf across waves and not straight down the face. If they surf straight down the face two things can and often do happen. If the nose of the surfboard does not plough straight into the water at the base of the wave tossing the surfer forward over the front of the board, the surfer's velocity, in the direction of propagation, exceeds that of the wave and the surfer simply surfs off the front of the wave. This is done by applying force through paddling or moving the weight of the body more forward of the centre of gravity. The steeper the transverse progressive wave the less extra force is needed. The surfer can "get off " the wave by transferring weight to a point behind the centre of gravity. A surfer standing on a surfboard does this by applying a torque. One foot is kept above the centre of gravity and the other foot is place behind the centre of gravity. The torque is applied by shifting more weight in to the back foot. The effect of this is to reduce the velocity of the surfer to less than that of the wave allowing the wave to simply pass on by. A surfer riding a breaking wave is helped by the mass of broken water also sliding down the inclined plane of the forward wave surface. So the wave is like a moving inclined plane made of water with water flowing up the plane. The surfer can use this upward flow to stop falling down the plane by pushing rails and fins on the bottom of the surfboard into the water at the exact angle needed. On a perfect wave the surfer can stand still and maintain speed.
21.3.03 Swell, ocean swell, "State of sea" and "State of swell"
An ocean swell consists of stable surface waves with long wavelengths that travel long distances after being generated by storm winds. The swell may consist of groups or waves all with the same speed and wavelength to eventually arrive on a beach one after another. Surfers are interested in the swell size and period because these waves are usually better for surfing than locally-generated choppy sea waves. Height of swell waves (significant wave height), is measured from crest to trough from the average height of about one third of a set of waves. Similarly, period is the average time between each wave in a set but the "significant period" may be measured from the third largest waves in a wave set. Swell-generated waves mix with locally-generated sea waves so are difficult to detect if not much bigger than locally-generated sea waves. Seamen distinguish between swell waves that are smooth and wind waves that are pointed or crested with white caps.
Make observations of "State of sea" and "State of swell" at scheduled observations time, except at night or during periods of low visibility.. Observe the waves where they are not deformed by shallow water, nor deflected or reflected by rocks, breakwaters or other objects. The observations point must be fully exposed to seaward and not sheltered by headlands or shoals. Sea waves are generated locally and move in the same direction as the surface wind but swell waves have been generated elsewhere and have travelled out of their generating area. Waves travel in groups, with each group consisting of a few waves of varying height, with the higher waves occurring near the centre of the group. A relatively flat area separates the groups, consisting of two or more waves of slight development. Sea waves have a more irregular appearance than swell waves. Swell waves travel in regular succession and in a well-defined direction, with generally long and rounded crests. Observe the best examples of swell waves on days of almost no wind for several hours.
Wave identification. If observing only one system, classify it as sea waves if the surface wind is blowing in the same direction as the waves are moving, otherwise classify it as swell waves. When the waves move in more than one direction, the sea waves will be those aligned with the surface wind direction, or those waves with the more irregular wave forms. Swell waves will usually have a regular pattern. If observing two wave forms and their movement is in the direction of the surface wind, the system that has the longer distance between crests and the more regular form is considered the swell. When estimating the height of a wave system, calculate the average of only the well-developed waves in the centre of the groups. Exclude the flat and badly-formed waves between the groups. Observe and calculate the average of fifteen to twenty waves. Of course the average height of the waves will be less than the height of the largest waves observed. Include in the average calculation all the well-developed waves and not just the largest waves. To measure the period of the swell, time the passage of two successive wave crests past a fixed point. Do this for four or five well-developed waves and calculate the average. Estimate the direction from which the swell is coming to the nearest eight points of the compass.
"State of sea" table
Classification of sea
 Height of sea waves (metres)
 Effect
Calm sea
 0 m
 No waves breaking on the beach
Calm sea (rippled) 0-0.1 m
 "
Smooth sea (wavelets) 0.1 - 0.5 m
 Slight waves breaking on the beach
Slight sea
 0.5 - 1.25 m
 Waves rock buoys and small craft
Moderate sea
 1.25 - 2.5 m
 Sea becoming furrowed
Rough sea
 2.4 - 4.0 m
 Sea deeply furrowed
Very rough sea
 4.0 - 6.0 m
 Sea much disturbed, rollers with steep fronts
High sea
 6.0 - 9.0 m
 ", damage to foreshore
Very high sea
 9.0 - 14.0 m
 Towering seas
Phenomenal sea > 14.0 m
 Precipitous seas, occur only in hurricanes
"State of swell" table
Classification Height of swell waves (metres) Period (seconds) Swell wavelength (metres)
Low swell of short
or average length		 0 - 2 m
 < 11 sec.
 0-200 m
Long low swell
 0 - 2 m > 11 sec. > 200 m
Short swell of
moderate height		 2 - 4 m < 8 sec. 0 - 100 m
Average swell of moderate height
 2 - 4 m > 8 sec.
 100 - 200 m
Long swell of moderate height 2 - 4 m < 11 sec. > 200 m
Short heavy swell > 4 m > 8 sec.
 0 - 100 m
Average length
heavy swell
 > 4 m < 11 sec. 100 - 200 m
Long heavy swell > 4 m > 11 sec.
 > 200 m
21.3.1 Forces on inclined plane
See diagram 21.3.1: Forces on inclined plane | See diagram 17.184 Friction blocks on an inclined plane | See diagram 17.185: Force to pull body up an incline
1. Attach a heavy toy car or a roller skate to a spring balance and pull it up an inclined plane. Note the force required to move the car and compare it with the force needed to lift it vertically. Note also that in moving up the inclined plane, the force is exerted over a greater distance than when the car is lifted vertically to the same height above the table. Neglecting friction, the work required is the same in both cases. Point out that this is also true for other simple machines.
2. Using an inclined plane to lift weights can save force, and the relations between saving force and inclined angle, saving force and the distance. Use a piece of elastic band, a piece of black thread and a small plastic bottle. Tie an elastic band to the neck of the bottle containing water. Use a smooth long wooden board supported at one end several books. Adjust the height of the inclined plane by pushing the books towards the lower end of the plane, not by changing the number of books. Tie a black thread marker to the elastic about 20 cm from the neck of the bottle. Place the bottle at the bottom of the inclined plane at minimum inclined angle. Pull the bottle to the top of the inclined plane and note the distance from the black thread marker to the neck of the bottle. Repeat the experiment by increasing the slope of the inclined plane five times. In each experiment try to maintain the same speed of pulling. Observe which situation the deformation of the elastic band is the smallest and longest.
21.3.2 Wedge
See diagram 21.3.2: Different kinds of wedge
A wedge is two inclined planes, base to base. Their wedges give a large gain in force. Wedges are to split logs and to split off blocks of stone in quarries. A wedge has two inclined planes and a third surface that may be hit to apply force to lift an object (under one leg of an unsteady table) or lock (door jamb) or split (woodcutter's wedge) or cut (axe). Many tools are in the shape of a wedge, e.g. knife, chisel, the spade, drill, awl. The mechanical advantage of an inclined plane increases as the angle decreases. Also the sharper edge of a wedge allows a small force to produce a large pressure. Use a pile of heavy books. Try to put your small finger inside that lowest book. Fold cardboard then open it to make an angle. Hold the folded cardboard in your hand and push the thin edge between the pages of the bottom book. Put your small finger in this angle and take the book out of the pile.
21.3.4 Mechanical car jack
See diagram 21.257.3: Lifting jack
1. Make a simple lifting jack. Bore a hole through a block of wood to fit a carriage bolt. Select a bolt that is threaded nearly its entire length. Sink the head of the bolt in the wood, so that it is flush with the surface and nail a piece of board over it. Over the projecting threads put a nut, then a washer and short piece of metal pipe. The inside diameter of the pipe must be slightly larger than the diameter of the bolt. By turning the nut with a wrench the device acts as a lifting jack.
2. To make a model jack use two wooden blocks of about 10 cm length. Drill a hole at the centre of the smaller block. Use a screw of more than twice of the block thickness. Make a groove with a knife at the centre of the other block so that the screw can be placed in the groove. Use a screw with a six angle head or flat-head head. Forcibly twist the screw through the hole on the smaller block. Put the groove on the larger block on the screw cap. Put the two blocks together then tightly nail them together with small nails. Make sure that the screw does not rotate and it is not loose. The contact surface between the two blocks is flat and level. If the screw is loose because the hole is too large, twist a nut to fix it. If it is very difficult to make the groove that can contains the screw cap, place cardboard or iron gaskets between the two blocks instead of the groove. The iron gaskets should be able to be just passed by the nails nailing the two blocks. Place the device upside down. Twist a nut on the screw and put an iron gasket on the nut and cover a piece of sawed iron tube on the gasket. The inner diameter of the iron tube should be slightly larger than the screw and its outer diameter should be smaller than the gasket so that it can stay on the gasket, not to slip away. The iron tube may is slightly shorter than the pole of the screw appearing. Rotate the nut and the tube will go up or down. When use the device to lift a heavy object, use a spanner to screw the nut and underlay the tube with a rigid board to reduce the pressure of the tube. A real screw jack is upright like the model and when the screw is turned through one full turn the heavy is lifted up or down a distance equal to the pitch of its thread.
21.4.0 Gears
Gear wheel, gear train, motor vehicle gears, servo-mechanism, transmission systems, clutch, differential gear, automatic gear change
See diagram 21.4.0: Motor vehicle gears
Gears mesh directly into each other without any chain. A car has a box of gears which can be changed. Imagine a large gear wheel and a small one. When the larger gear wheel is attached to the engine, and the small gear wheel is attached to the back axle you say the car is in top gear because you get maximum revolutions of the car wheels per revolution of the engine. If a smaller gear wheels is attached to the engine and a larger gear wheel is attached to the back axle you say the car is in low gear. If a toothed gear wheel with 10 teeth is meshed with a toothed gear wheel with 20 teeth. For each complete revolution of the 20 teeth wheel the 10 teeth wheel makes 2 revolutions. If the effort is supplied to the 10 teeth wheel to drive the 20 teeth wheel, the velocity ration is 2 = number of teeth on the driven gear (load) / number of teeth on the driving gear (effort)
21.4.1 Bicycle gears
Examine the gearing of a bicycle by counting the teeth on the sprocket wheel attached to the back wheel and the teeth on the large sprocket wheel to which the pedals are attached., e.g. 16 and 48. Each time you push the pedals round once, you pull around enough chain to cover 48 teeth. However there are only 16 teeth in the back sprocket, so it is turned more than once, 48 / 16 = 3 times. So each time you turn the pedals once, the back wheels rotates three times. When you reach a hill your bicycle will be easier to push if you used a back sprocket with more teeth or you used a pedal sprocket with fewer teeth so that one revolution of the pedals would give you fewer revolutions of the wheel.
1. Turn a bicycle upside down. Turn the pedal wheel exactly one turn and note the number of turns made by the rear wheel.
2. Study the speed of rotation and transmission of roller chain. Use a bicycle without chain box. Turn the bicycle upside down and let it stand on its saddle and handle. Count the amount of the teeth of the large gear at the middle shaft and that of the small gear at the back shaft. Forcibly rotate a pedal of the bicycle a circle then differently count the amount of the circles the large gear and the small gear rotating. For convenience, mark with colour on some tooth of each gear beforehand. Calculate the ratio of the amounts of their circles and teeth and find the relationship of the two ratios. Observe how to transmit the large gear' rotation to the small one. Observe the direction of the large gear and that of the small one. Find the relationship of the direction of transmission to the directions of rotations of the large gear and small one.
21.4.2 Bottle top gears
See diagram 21.260: Gear wheels
Punch holes exactly in the centres of bottle tops. Put two of the bottle tops on a block of wood so that the tooth like projections mesh. Fasten them to the wood with small nails, but make sure that they still turn easily. Turn one of the bottle tops and note the direction that the other turns. Add a third bottle top and note the direction that each turns.
Gear is a toothed wheel that transmits the turning movement of one shaft to another shaft. Gear wheels may be used in pairs, or in threes if both shafts are to turn in the same direction. Gear with different shaped teeth or shaft may rotate at different angle. The gear ratio, the ratio of the number of teeth on the two wheels, determines the torque ratio, the turning force on the output shaft compared with the turning shaft on the input shaft. The ratio of the angular velocities of the shafts is the inverse of the gear ratio.
21.4.3 Rolling coins
Put two identical coins edge to edge and flat on the table. Hold the first coin in a fixed position while you roll the second coin around it. The second coin turns twice around its own axis when rolling once around the first coin. If the radius of the coins = r, and the circumference = 2 X π X r, the centre of the second coin travels a distance of 2 X π X 2r.
21.5.0 Pulleys, block and tackle, broomstick pulley
See diagram 21.5.0: Types of pulleys | See diagram 21.254: Simple pulley | See diagram 21.255: Single fixed pulley | See diagram 21.256: Single movable pulley
Observe the tension in a string or rope. Tie the upper end of a string to a support, and tie a brick to the lower end. The string will be tight, i.e. have tension all along it.
21.5.1 Systems of pulleys
See diagram 21.5.2.1: First and second system of pulleys | See diagram 21.5.2.2: Third system of pulleys
1. First system of pulleys, M.A. = 2n, (where n == number of pulleys). The effort is lessened by the calculated effective mass of the pulleys.
In the diagram T3 = 1 / 2 T2 = 1 / 4 T1 = 1 / 8 mg
The mechanical advantage of a single fixed pulley = 1, if no friction.
The mechanical advantage of a single free pulley = 2, if no friction, pulley is weightless and strings are parallel to the load.
2. Second system of pulleys, the block and tackle has equal tension through the flexible string. so T = E.
4T = L, so 4 E = L,
so M.A. = L / E = 4
The mechanical advantage = number of supporting strings if no friction and lower block is weightless. The block and tackle is the most useful system of pulleys.
3. Third system of pulleys requires the determination of the line of action of parallel forces, T3, T2, T1 which should go through L if the system is to be in equilibrium.
21.5.2 Block and tackle
See diagram 21.5.2: Single fixed pulley, single free pulley, block and tackle
This pulley system is used in cranes and lifts. In a car garage, the mechanics can lift a car engine out of a car by hand using a block and tackle. You will notice that they pull down a long way while the engine block moves up a short way. In the diagram the pulleys have been separated here to show the path of the rope more clearly. Find the gain in force from the number of strings supporting the load. The tension in the string remains constant and is one fourth of the upward pull on the load.
21.5.3 Paper inclined plane, paper screw thread
See diagram 21.257.2: Paper inclined plane
A screw thread is an inclined plane wound around a cylinder. Make an imitation of a screw thread by wrapping a right angled triangle around a pencil, starting with the shorter of the two sides about the right angle parallel to the axis of the pencil. The hypotenuse represents the path of the screw thread. The pitch of a screw is small compared to its circumference, so the slope is very gentle and the gain in force is high. A further gain in force is added when a lever, the spanner, is used to turn the nut. For one complete turn of the nut, it advances by the distance of one pitch.
1. Make a simple screw thread. Cut a piece of white paper to make a right angle triangle 50 cm hypotenuse and 30 cm along its shortest side. Use a round rod about 40 cm long and roll the triangular piece of paper on the rod beginning at the short side and rolling towards the point of the triangle. Keep the base line of the triangle even as it rolls. Observe that the inclined plane, the hypotenuse, spirals up the rod as a screw thread. A screw thread is an inclined plane.
2. Make a simple screw thread. Cut out several vertical triangles from a sheet of paper, each triangle has a different size. Draw an obvious line in texts along the edge of the hypotenuse in each triangle. Roll each triangle cardboard around a pencil to make it like a screw nail. Compare the distance of the screw of each nail, analyse the difference between them. The principle of the screw nail is similar to the inclined plane in which a weight is pushed upward. Although a screw is a spiral inclined plane, it acts like a second class lever. The screw's point is the fulcrum, where the thread meets a substance such as wood is the load, and the effort is applied to the head of the screw.