Senior 2 practice book · Unit 5 of 10

Simple Machines

50 questions that complete the Senior 2 quiz for this unit: 26 core and 24 challenge. Easy and hard questions are mixed. Try each question, then tap “Show answer”.

Common misconceptions

A good machine reduces the work we have to do.No machine reduces the work needed. A machine lets a smaller force do the job by moving it through a larger distance; the work put in is always at least as large as the useful work out.
If a machine has a large velocity ratio, it must have a large efficiency.VR depends only on the design (distances). Efficiency = MA ÷ VR × 100 % depends on friction and the weight of moving parts; a screw jack has a huge VR but a low efficiency.
The heavier side of a see-saw or lever always goes down.What matters is the MOMENT, force × perpendicular distance from the pivot. A light child far from the pivot can balance a heavy child sitting close to it.
Oiling a machine increases its velocity ratio.Oil reduces friction, so less effort is needed: the MA and the efficiency increase. The VR is fixed by the machine's dimensions and does not change.
Every lever multiplies force.Third-class levers (tweezers, a broom, the forearm) have the effort closer to the pivot than the load, so MA and VR are less than 1; they multiply distance and speed, not force.

What this unit covers

Topics marked new are not tested much in the quiz, so this book gives them extra questions.

What simple machines do: load, effort, fulcrum; force multipliers, distance multipliers, change of direction
Mechanical advantage, velocity ratio and efficiency
Work input, useful work output and energy wasted in machines
Moment of a force and the principle of moments
Centre of gravity: moments of a beam's own weight (uniform rule, plank, bridge supports)
Classes of levers with everyday and body examples
VR and MA of levers from the effort arm and load arm
Pulleys: fixed, movable and block and tackle
Experiments on machines: effort–load and efficiency–load results and graphs
Inclined plane: VR = length ÷ height, work and efficiency
Screw, screw jack and wedge (pitch, VR = 2πR ÷ pitch)
Wheel and axle: windlass, spanner, steering wheel, tap
Gears and chain drives: gear ratio, speed and turning effect
Improving efficiency: lubrication, ball bearings, light parts, maintenance

Go to the questions

Questions (1–50)

Easier and harder questions are mixed, just like in a real exam. The 24 harder ones are marked ★ Challenge.

1True or false
Adding more pulleys to a block and tackle always increases its efficiency.
Show answer
Answer: False
More pulleys increase the VR, but they also add friction and a heavier lower block, so the efficiency usually falls.
Common mistakeAnswering true confuses VR with efficiency; extra pulleys reduce the effort but waste more energy.
2True or false · ★ Challenge
In every first-class lever the effort is smaller than the load.
Show answer
Answer: False
In a first-class lever the effort is smaller only if the effort arm is longer than the load arm; if the pivot is nearer the effort, the effort is larger.
Common mistakeAnswering true assumes the pivot is always near the load; the class says only that the pivot is BETWEEN effort and load.
3True or false
An axe head is a wedge, and a thinner wedge needs a smaller force to split a log.
Show answer
Answer: True
A wedge is a moving inclined plane; a thin wedge is like a long gentle slope, with a larger VR, so less force is needed.
Common mistakeThinking a thicker, heavier axe always splits more easily ignores the wedge's shape; a thin edge gives the larger VR.
4True or false · ★ Challenge
Two gear wheels whose teeth mesh directly with each other turn in the same direction.
Show answer
Answer: False
Meshed gears turn in opposite directions; a chain (as on a bicycle) or a third gear is needed to keep the same direction.
Common mistakeAnswering true mixes up meshed gears with sprockets joined by a chain, which do turn the same way.
5True or false
Greasing the axle of a well windlass makes its velocity ratio larger.
Show answer
Answer: False
VR = wheel radius ÷ axle radius depends only on the dimensions; grease reduces friction, so the MA and the efficiency increase, not the VR.
Common mistakeAnswering true confuses VR with MA; anything that reduces friction changes the effort, not the distances moved.
6True or false · ★ Challenge
A machine with a mechanical advantage of exactly 1 is of no use.
Show answer
Answer: False
A single fixed pulley has MA ≈ 1 but is very useful: it lets you pull DOWN, using your weight, to lift a load UP.
Common mistakeAnswering true assumes machines are only for multiplying force; changing the direction of a force is also a useful job.
7True or false
The weight of a uniform metre rule can be taken to act at its 50 cm mark.
Show answer
Answer: True
For a uniform body the centre of gravity is at its middle, so the whole weight acts there.
Common mistakeSome learners think the weight acts at the pivot or spreads out with no single point; for moments it acts at the centre of gravity.
8True or false · ★ Challenge
If all friction were removed from a pulley system with a heavy lower block, its efficiency would be 100 % for every load.
Show answer
Answer: False
Even without friction, part of the effort lifts the lower block, which is not useful work, so the efficiency stays below 100 % (and rises as the load gets heavier).
Common mistakeAnswering true blames friction alone; the weight of moving parts also wastes energy.
9True or false
Two machines have the same velocity ratio. The one with less friction has the larger mechanical advantage.
Show answer
Answer: True
Less friction means less effort for the same load, so MA = load ÷ effort is larger, while VR is unchanged.
Common mistakeAnswering false assumes MA is fixed by the design like VR; MA depends on the effort actually needed, which friction increases.
10Fill in the blank
The point through which the whole weight of a body appears to act is called the centre of ______.
Show answer
Answer: gravity
For a uniform rule or plank it is at the middle.
Common mistakeWriting 'centre of the pivot' confuses the point where the weight acts with the point about which the body turns.
11Fill in the blank · ★ Challenge
A pair of scissors cuts cardboard 3 cm from the pivot while the fingers push 9 cm from the pivot. The velocity ratio of the scissors is ______.
Show answer
Answer: 3
VR = effort arm ÷ load arm = 9 ÷ 3 = 3.
Common mistakeWriting 1/3 swaps the arms; that is why cutting near the pivot (short load arm) makes cutting easier.
12Multiple choice · ★ Challenge
A car screw jack has a handle that turns in a circle of radius 35 cm, and its screw has a pitch of 0.5 cm. What is its velocity ratio?
1. A70
2. BAbout 440
3. CAbout 220
4. DAbout 4400
Show answer
Answer: B. About 440
In one turn the effort moves 2πR = 2 × 3.14 × 35 ≈ 220 cm while the load rises 0.5 cm: VR = 220 ÷ 0.5 ≈ 440.
Common mistakeChoosing about 220 stops at the circumference; it must still be divided by the pitch, 0.5 cm.
13Multiple choice
The pitch of a screw is:
1. AThe total length of the screw from head to tip
2. BThe radius of the screw head or the handle
3. CThe number of turns needed to drive it in
4. DThe distance between two neighbouring threads
Show answer
Answer: D. The distance between two neighbouring threads
The pitch is the distance between neighbouring threads, which is how far the screw moves forward in one full turn.
Common mistakeChoosing 'the number of turns' mixes up the pitch with its effect; the pitch is a distance, measured in mm or cm.
14Multiple choice
Which tool is a second-class lever?
1. AA bottle opener
2. BA pair of scissors
3. CA pair of tongs
4. DA claw hammer pulling a nail
Show answer
Answer: A. A bottle opener
In a bottle opener the pivot is at the tip on top of the cap, the load (the cap's edge) is in the middle and the effort is at the handle.
Common mistakeChoosing the claw hammer is tempting, but its head rests on the wood as the pivot BETWEEN the nail and the hand, so it is first class.
15Multiple choice · ★ Challenge
A machine is 75 % efficient and has a mechanical advantage of 3. What is its velocity ratio?
1. A4
2. B2.25
3. C0.25
4. D225
Show answer
Answer: A. 4
Efficiency = MA ÷ VR, so VR = MA ÷ efficiency = 3 ÷ 0.75 = 4.
Common mistakeChoosing 2.25 comes from multiplying 3 × 0.75; rearranging η = MA/VR gives VR = MA/η, which is larger than the MA.
16Fill in the blank
In an experiment with a machine, the effort should be read while the load is moving at a steady ______, not at the moment it starts to move.
Show answer
Answer: speed
At a steady speed the effort just balances the load and friction; a jerk at the start gives a reading that is too large.
Common mistakeReading the effort as the load is jerked into motion gives too large an effort and too small an MA.
17Multiple choice · ★ Challenge
A uniform plank 4 m long and of weight 200 N rests on a support 1 m from one end. What downward force at that end keeps the plank horizontal?
1. A100 N
2. B400 N
3. C600 N
4. D200 N
Show answer
Answer: D. 200 N
The weight acts at the centre, 2 m from the end, i.e. 1 m beyond the support. F × 1 = 200 × 1, so F = 200 N.
Common mistakeChoosing 400 N measures the weight's distance from the END (2 m) instead of from the support (1 m); moments are always taken from the pivot.
18Multiple choice
Which of these machines multiplies DISTANCE (and speed) rather than force?
1. AA bottle opener lifting a bottle cap
2. BA wheelbarrow carrying a heavy load of bricks and sand
3. CA broom used for sweeping, held near the top
4. DA screw jack raising a heavy car
Show answer
Answer: C. A broom used for sweeping, held near the top
In a broom the effort (lower hand) is closer to the pivot (upper hand) than the load (the bristles), so the bristles move further and faster than the hand.
Common mistakeChoosing the wheelbarrow comes from thinking every machine is a distance multiplier; a wheelbarrow has its load nearer the pivot, so it multiplies force.
19Multiple choice · ★ Challenge
A worker can pull with at most 350 N. What is the smallest number of rope sections supporting the lower block of a pulley system that would let him lift a 1200 N load, assuming an ideal machine?
1. A3
2. B4
3. C2
4. D5
Show answer
Answer: B. 4
Ideal effort = load ÷ n: with 3 sections 1200 ÷ 3 = 400 N (too much); with 4 sections 1200 ÷ 4 = 300 N, which is within 350 N.
Common mistakeChoosing 3 comes from rounding 1200 ÷ 350 = 3.4 down; the number of sections must be rounded UP so the effort is not too large.
20Multiple choice
Which change would most increase the efficiency of a pulley system used on a building site?
1. AUsing a lighter lower block that turns on ball bearings
2. BAdding two more rope sections to the lower block
3. CUsing a heavier, thicker rope that is much stronger and safer
4. DPulling the rope much faster than before
Show answer
Answer: A. Using a lighter lower block that turns on ball bearings
A lighter lower block and ball bearings mean less energy is wasted lifting moving parts and overcoming friction.
Common mistakeChoosing 'more rope sections' confuses VR and efficiency: more sections lower the effort but add friction and weight.
21Multiple choice · ★ Challenge
A pulley system raises a 500 N load by 3 m, and the effort does 2000 J of work. What is the efficiency?
1. A133 %
2. B25 %
3. C33 %
4. D75 %
Show answer
Answer: D. 75 %
Useful work = 500 × 3 = 1500 J. Efficiency = 1500 ÷ 2000 × 100 = 75 %.
Common mistakeChoosing 133 % divides input by output; efficiency is work OUT ÷ work IN and can never be above 100 %.
22Short answer · ★ Challenge
A cyclist climbing the steep road from the Nyabarongo valley up to Kigali changes to the largest sprocket on the back wheel. Explain why this makes the climb easier, and what she gives up.
Show answer
Model answer: With a large rear sprocket, the back wheel turns fewer times for each turn of the pedals, so the gear ratio gives a larger turning effect on the wheel for the same force on the pedals; the climb needs less force. She gives up speed: each turn of the pedals moves the bicycle a shorter distance, so she must pedal more turns to climb the hill.
Common mistakeSaying the large sprocket makes the bicycle 'faster' is wrong; it gives more turning effect at the cost of speed.
23Fill in the blank
A machine has a velocity ratio of 6. When the effort moves 3 m, the load moves ______ m.
Show answer
Answer: 0.5
VR = effort distance ÷ load distance, so load distance = 3 ÷ 6 = 0.5 m.
Common mistakeMultiplying 3 × 6 = 18 m gets the direction backwards; with VR greater than 1 the load moves LESS than the effort.
24Multiple choice · ★ Challenge
A nut is placed 2 cm from the hinge of a nutcracker, and the hand presses 14 cm from the hinge. The nut cracks under a force of 280 N. What effort is needed (ignore friction)?
1. A1960 N
2. B47 N
3. C280 N
4. D40 N
Show answer
Answer: D. 40 N
Moments about the hinge: E × 14 = 280 × 2 = 560, so E = 560 ÷ 14 = 40 N.
Common mistakeChoosing 47 N uses 12 cm (14 − 2) as the effort arm; both arms are measured from the HINGE, not from each other.
25Multiple choice
Lorries and buses have larger steering wheels than small cars. Why?
1. AA larger steering wheel makes the lorry turn round the corner more quickly
2. BA larger wheel radius gives a larger VR, so less effort is needed to turn the wheels
3. CA larger steering wheel removes the friction in the steering system
4. DA larger wheel gives a smaller moment, so the steering is safer to use
Show answer
Answer: B. A larger wheel radius gives a larger VR, so less effort is needed to turn the wheels
VR = wheel radius ÷ axle radius; a larger wheel lets the driver's effort act at a bigger radius, giving a bigger moment.
Common mistakeChoosing 'turns more quickly' gets it backwards; a big steering wheel must be turned through a LONGER distance for the same turn.
26Fill in the blank
A water tap handle of radius 4 cm turns a spindle of radius 0.5 cm. The velocity ratio of the tap is ______.
Show answer
Answer: 8
VR = wheel radius ÷ axle radius = 4 ÷ 0.5 = 8.
Common mistakeWriting 0.125 divides the axle radius by the wheel radius; the effort acts on the larger radius, so VR > 1.
27Multiple choice · ★ Challenge
A market trader's beam balance is pivoted at its centre. A 2 kg mass hangs 15 cm to the left of the pivot, and a bunch of bananas hung 12 cm to the right balances it. What is the mass of the bananas?
1. A1.6 kg
2. B2.5 kg
3. C3.0 kg
4. D25 kg
Show answer
Answer: B. 2.5 kg
Principle of moments: m × 12 = 2 × 15 = 30, so m = 30 ÷ 12 = 2.5 kg.
Common mistakeChoosing 1.6 kg comes from 2 × 12 ÷ 15; the object on the SHORTER arm must be heavier to balance.
28Multiple choice
A block and tackle has 3 pulleys in the upper (fixed) block and 3 in the lower (movable) block, with one rope passing round all of them. What is its velocity ratio?
1. A3
2. B9
3. C6
4. D2
Show answer
Answer: C. 6
Each pulley in the system adds one rope section supporting the lower block: 6 sections, so VR = 6.
Common mistakeChoosing 3 counts only the pulleys in one block; the VR equals the number of rope sections holding up the lower block.
29Short answer · ★ Challenge
Explain why a third-class lever, such as a broom or the human forearm, always has a velocity ratio less than 1, and what is gained by using it.
Show answer
Model answer: In a third-class lever the effort is between the fulcrum and the load, so the effort arm is always shorter than the load arm, and VR = effort arm ÷ load arm < 1. The effort must be larger than the load, but the load moves a greater distance and faster than the effort, which gives speed and a wide range of movement (e.g. sweeping, throwing).
Common mistakeThinking a lever with VR < 1 is badly designed misses that it trades force for distance and speed.
30Fill in the blank
A machine wastes 250 J of energy while doing 750 J of useful work. Its efficiency is ______ %.
Show answer
Answer: 75
Work in = 750 + 250 = 1000 J. Efficiency = 750 ÷ 1000 × 100 = 75 %.
Common mistakeDividing 250 ÷ 750 or 750 ÷ 250 uses the wrong pair; the input is useful work PLUS wasted energy.
31Short answer · ★ Challenge
A farmer uses a windlass that is 70 % efficient to raise water from a well. Where does the other 30 % of the work go, and why does this not break the law of conservation of energy?
Show answer
Model answer: The 30 % is used to overcome friction at the axle and the rope (becoming heat and sound) and to lift the rope and bucket. The energy is not destroyed; it is changed into forms that are not useful for the job, so the total energy output (useful + wasted) still equals the input.
Common mistakeSaying the energy is 'lost' or 'destroyed' is wrong; energy is conserved, only the useful part is less than the input.
32Short answer
A learner says: 'Machines are useless because they never give out more work than we put in.' Give three different ways a simple machine makes a job easier, with an example of each.
Show answer
Model answer: (1) It lets a small effort overcome a large load (force multiplier), e.g. a crowbar or a car jack. (2) It changes the direction of the force to a more convenient one, e.g. a fixed pulley on a flagpole lets you pull down to raise the flag. (3) It makes the load move further or faster than the effort (distance multiplier), e.g. a bicycle's gears and wheel, or a broom.
Common mistakeThe usual error is to judge machines only by work; they are useful because they change the size, direction or speed of a force, not because they save work.
33Multiple choice · ★ Challenge
Before oiling, a rusty pulley system with VR = 3 needs an effort of 250 N to lift a 600 N load. After oiling it needs only 220 N. How does its efficiency change?
1. AFrom 80 % to about 70 %
2. BFrom 125 % to 110 %
3. CFrom 80 % to about 91 %
4. DFrom 40 % to about 45 %
Show answer
Answer: C. From 80 % to about 91 %
Before: MA = 600 ÷ 250 = 2.4, η = 2.4 ÷ 3 × 100 = 80 %. After: MA = 600 ÷ 220 ≈ 2.73, η ≈ 91 %.
Common mistakeChoosing 125 % to 110 % uses VR ÷ MA; efficiency is MA ÷ VR and must be below 100 %.
34Short answer
Classify each of these levers as first, second or third class, and give the order of load (L), fulcrum (F) and effort (E): (a) a nutcracker, (b) a fishing rod, (c) a pair of pliers.
Show answer
Model answer: (a) Nutcracker: second class, F–L–E (the nut is between the hinge and the hand). (b) Fishing rod: third class, F–E–L (the front hand is between the end held against the body and the fish). (c) Pliers: first class, L–F–E (the pivot is between the jaws and the handles).
Common mistakeLearners often classify by what the tool 'looks like'; the class depends only on which of L, F or E is in the middle.
35Multiple choice · ★ Challenge
In an experiment on a pulley system, a graph of effort (y-axis) against load (x-axis) is a straight line that cuts the effort axis at 20 N. What does this intercept show?
1. AAbout 20 N of effort is needed just to overcome friction and lift the lower block
2. BThe machine is 20 % efficient for all of the loads that were tested
3. CThe velocity ratio of the pulley system used in the test is equal to 20
4. DThe load will rise by itself if an effort of more than 20 N is removed
Show answer
Answer: A. About 20 N of effort is needed just to overcome friction and lift the lower block
At zero load the effort is still 20 N; this effort is wasted on friction and on lifting the moving parts.
Common mistakeChoosing '20 % efficient' confuses an effort in newtons with a percentage; efficiency must be calculated from MA ÷ VR at each load.
36Multiple choice
A crowbar has an effort arm of 90 cm and a load arm of 15 cm. What is its velocity ratio?
1. A0.17
2. B75
3. C6
4. D105
Show answer
Answer: C. 6
VR of a lever = effort arm ÷ load arm = 90 ÷ 15 = 6.
Common mistakeChoosing 0.17 divides the load arm by the effort arm; the effort moves further, so VR = effort arm ÷ load arm.
37Multiple choice
A force of 30 N is applied at right angles to a spanner, 0.4 m from the centre of a nut. What is the moment of the force?
1. A75 N m
2. B12 N m
3. C30.4 N m
4. D0.013 N m
Show answer
Answer: B. 12 N m
Moment = force × perpendicular distance = 30 × 0.4 = 12 N m.
Common mistakeChoosing 75 N m divides 30 by 0.4; a moment is force TIMES distance.
38Short answer · ★ Challenge
A mechanic needs a turning moment of 30 N m to loosen a wheel nut. (a) What force must he apply at the end of a 20 cm spanner? (b) He slides a pipe over the handle so that he pushes 50 cm from the nut. What force is needed now?
Show answer
Model answer: (a) F = moment ÷ distance = 30 ÷ 0.20 = 150 N. (b) F = 30 ÷ 0.50 = 60 N. The longer handle acts like a larger wheel, so the same moment needs a smaller force.
Common mistakeUsing 20 instead of 0.20 m gives 1.5 N; the distance must be in metres when the moment is in N m.
39Short answer · ★ Challenge
Roads that climb steep hills, such as the road from Musanze to Rubavu, zigzag up the slope instead of going straight up. Explain why, using the idea of the inclined plane.
Show answer
Model answer: A zigzag road is a longer inclined plane up the same height. VR = length ÷ height is larger, so a smaller force (from the engine or from a cyclist's legs) is enough to climb, although the distance travelled is longer. Vehicles can climb without stalling, and braking on the way down is safer.
Common mistakeSaying the zigzag 'reduces the work' is wrong; the same height is climbed, so at least the same work is done, but with a smaller force.
40Short answer
A maize mill in a village keeps slowing down and its motor gets hot. Suggest three ways to make the mill more efficient, and explain how each helps.
Show answer
Model answer: (1) Oil or grease the bearings and moving parts, which reduces friction so less energy becomes heat. (2) Replace worn bearings with ball bearings, which roll instead of rubbing. (3) Keep the belts at the right tension and the parts clean and aligned, so less energy is wasted on slipping and rubbing. (Also: use lighter moving parts.)
Common mistakeSaying 'use a bigger motor' does not improve efficiency; it only supplies more energy while the same fraction is wasted.
41Multiple choice · ★ Challenge
A 400 N sack is pulled up a ramp 5 m long onto a platform 1.25 m high with an effort of 125 N along the ramp. How much work is done against friction?
1. A125 J
2. B500 J
3. C625 J
4. D1125 J
Show answer
Answer: A. 125 J
Work in = 125 × 5 = 625 J. Useful work = 400 × 1.25 = 500 J. Work against friction = 625 − 500 = 125 J.
Common mistakeChoosing 1125 J adds the two works; the energy wasted is the DIFFERENCE between the work in and the useful work.
42Short answer
Explain why it is easier to open a heavy door by pushing at the handle than near the hinges, and why pushing on the edge of the door straight towards the hinges does not open it at all.
Show answer
Model answer: The moment = force × perpendicular distance from the hinge (pivot). At the handle the distance is large, so a small force gives the moment needed; near the hinges a much bigger force is needed. Pushing along the door towards the hinge, the line of the force passes through the pivot, so the perpendicular distance is zero and the moment is zero.
Common mistakeLearners forget the word 'perpendicular': a large force whose line passes through the pivot has no turning effect.
43Fill in the blank
An inclined plane with a gentler slope (a longer ramp for the same height) has a ______ velocity ratio.
Show answer
Answer: larger (greater)
VR = length ÷ height, so a longer ramp for the same height gives a larger VR.
Common mistakeWriting 'smaller' confuses a gentle slope with a weak machine; a gentle slope needs less effort, so it has a larger VR.
44Short answer · ★ Challenge
A model crane in the school laboratory has a velocity ratio of 3. The results are: load 50 N, effort 30 N; load 100 N, effort 45 N; load 150 N, effort 60 N; load 200 N, effort 75 N. Calculate the efficiency for each load and describe the trend.
Show answer
Model answer: MA = 1.67, 2.22, 2.5, 2.67. Efficiency = MA ÷ 3 × 100 ≈ 56 %, 74 %, 83 %, 89 %. The efficiency increases as the load increases, because the effort wasted on friction and moving parts becomes a smaller fraction of the total effort.
Common mistakeAssuming efficiency is the same for every load (because VR is fixed) is wrong; the MA, and so the efficiency, changes with the load.
45Multiple choice
A wheelchair ramp at a hospital entrance rises 0.6 m. How long must it be to have a velocity ratio of 10?
1. A0.06 m
2. B16.7 m
3. C6 m
4. D10.6 m
Show answer
Answer: C. 6 m
VR = length ÷ height, so length = 10 × 0.6 = 6 m.
Common mistakeChoosing 0.06 m divides 0.6 by 10; a larger VR needs a LONGER, gentler ramp.
46Short answer · ★ Challenge
A uniform plank bridge 6 m long of weight 1200 N rests on supports at its ends A and B. A farmer of weight 600 N stands 2 m from A. Find the upward force from each support.
Show answer
Model answer: Moments about A: R(B) × 6 = 1200 × 3 + 600 × 2 = 3600 + 1200 = 4800, so R(B) = 800 N. Upward forces = downward forces: R(A) = 1200 + 600 − 800 = 1000 N. The support nearer the farmer (A) pushes harder.
Common mistakeA common error is to forget the plank's own weight, which acts at its middle (3 m from A); every weight must be included.
47Multiple choice
A driving gear with 15 teeth turns a driven gear with 45 teeth. Compared with the driving gear, the driven gear turns:
1. A3 times faster, with 3 times the turning effect
2. B3 times faster, with a third of the turning effect
3. CAt the same speed and with the same turning effect
4. D3 times slower, with 3 times the turning effect
Show answer
Answer: D. 3 times slower, with 3 times the turning effect
Gear ratio = 45 ÷ 15 = 3: one turn of the large gear needs 3 turns of the small one, so it turns 3 times slower but with about 3 times the moment.
Common mistakeChoosing 'faster with more turning effect' gets something for nothing; a machine that gains force always loses speed.
48Short answer · ★ Challenge
A screw jack has a velocity ratio of 400 and an efficiency of 25 %. Find the effort needed to lift one corner of a car that pushes down with 12 000 N, and explain why a low efficiency is actually useful in a screw jack.
Show answer
Model answer: MA = efficiency × VR = 0.25 × 400 = 100. Effort = 12 000 ÷ 100 = 120 N. The large friction in the thread stops the screw from turning back by itself, so the car stays up when the worker lets go of the handle.
Common mistakeUsing the VR instead of the MA gives an effort of only 30 N; real effort must use MA = η × VR.
49Short answer
A builder uses a single movable pulley, pulling the free end of the rope upwards, to raise a 360 N bucket of mortar by 5 m. How far must his hand move, and what is the effort if friction and the pulley's weight are ignored?
Show answer
Model answer: Two rope sections support the pulley, so VR = 2. The hand moves 2 × 5 = 10 m. Ideal effort = 360 ÷ 2 = 180 N.
Common mistakeSaying the hand moves 5 m forgets that BOTH rope sections must shorten by 5 m to lift the pulley 5 m.
50Short answer · ★ Challenge
In a test of a machine, an effort of 96 N lifts a 240 N load. The effort moves 1.8 m while the load rises 0.6 m. Find the MA, the VR and the efficiency, and say whether the machine is a force multiplier or a distance multiplier.
Show answer
Model answer: MA = 240 ÷ 96 = 2.5. VR = 1.8 ÷ 0.6 = 3. Efficiency = 2.5 ÷ 3 × 100 ≈ 83 %. Since MA > 1 (the load is bigger than the effort), it is a force multiplier.
Common mistakeA frequent slip is to use the forces for VR or the distances for MA; MA uses forces (load ÷ effort) and VR uses distances (effort distance ÷ load distance).