Senior 2 practice book · Unit 3 of 10

Friction Force

50 questions that complete the Senior 2 quiz for this unit: 21 core and 29 challenge. Easy and hard questions are mixed. Try each question, then tap “Show answer”.

Common misconceptions

Friction only acts on things that are already moving.Static friction acts on a body at rest whenever something tries to move it; that is why a parked car stays still on a slope.
If I push a heavy cupboard and it does not move, the friction must be bigger than my push.Until the cupboard slips, the friction exactly equals the push. It grows with the push only up to its limiting value μR.
Friction always acts backwards, against the way we want to go.Friction opposes slipping between surfaces. When you walk, your foot pushes the ground backwards, so the ground's friction pushes you forwards.
A body moving at steady speed has no force on it in the direction of motion.A box pushed at steady speed still needs the push; the push is balanced by friction, so the RESULTANT force is zero.

What this unit covers

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

Nature and cause of friction: opposing relative motion, roughness of surfaces
Types of friction: static, limiting, kinetic (sliding) and rolling
Laws of solid friction (normal reaction, nature of surfaces, not area of contact)
Normal reaction and the coefficient of friction μ = F/R
Resultant force and acceleration when friction acts, including braking and skidding
Advantages and disadvantages of friction
Ways of reducing and increasing friction (lubricants, bearings, rollers, treads, sand)
Fluid friction: air resistance, drag, streamlining and terminal velocity
Static friction adjusts to the applied force up to the limiting value
Experiment to measure μ with a spring balance; F–R graphs and reliable results
Friction on a tilted board: slipping angle and μ = height ÷ horizontal distance
Work done against friction: heating, energy wasted and efficiency
Direction of friction in walking, driving wheels and conveyor belts

Go to the questions

Questions (1–50)

Easier and harder questions are mixed, just like in a real exam. The 29 harder ones are marked ★ Challenge.

1True or false
A friction force can act on a body that is not moving.
Show answer
Answer: True
Static friction acts on a body at rest when a force tries to move it, for example a parked car on a hill.
Common mistakeLearners think friction needs motion; static friction is what keeps resting bodies still.
2True or false · ★ Challenge
On a tilted plank, a heavy block and a light block of the same material start to slide at the same angle.
Show answer
Answer: True
A heavier block is pulled down the slope more, but its limiting friction is larger in the same proportion, so the slipping angle depends only on μ.
Common mistakeLearners expect the heavier block to slide first; its larger weight also presses harder on the plank, raising the friction equally.
3True or false
Friction is always a nuisance, so engineers try to remove it from every part of a vehicle.
Show answer
Answer: False
Vehicles need friction in tyres, brakes and clutches; engineers reduce it only in places like bearings and engines.
Common mistakeThinking of friction only as waste forgets that grip on the road and braking both depend on it.
4True or false · ★ Challenge
When a cyclist pedals along a level road, the friction from the road on the rear (driving) wheel acts forwards.
Show answer
Answer: True
The driven wheel pushes the road backwards, so the road's friction on the wheel acts forwards and propels the bicycle.
Common mistakeLearners think all friction on a vehicle acts backwards; on a driving wheel it is the force that moves it forwards.
5True or false · ★ Challenge
If the spring balance is tilted slightly upwards while pulling a block, the reading at which the block starts to slide is smaller than with a horizontal pull.
Show answer
Answer: True
The upward part of the pull lifts the block a little, so the normal reaction and the limiting friction become smaller.
Common mistakeLearners think the angle makes no difference; any upward pull reduces R and so changes the friction being measured.
6True or false
Friction between moving parts of a machine turns some useful energy into heat, which lowers the machine's efficiency.
Show answer
Answer: True
Energy used to overcome friction becomes heat instead of useful work, so the useful output is less than the input.
Common mistakeLearners sometimes think lost energy is destroyed; it is still there, but as heat that is not useful.
7Multiple choice · ★ Challenge
When you walk forwards, the friction force from the ground on your foot points:
1. ABackwards, opposite to the direction of your motion
2. BDownwards, into the ground
3. CUpwards, along your leg
4. DForwards, in the direction you walk
Show answer
Answer: D. Forwards, in the direction you walk
Your foot pushes the ground backwards; friction opposes that slip, so the ground pushes your foot forwards.
Common mistakeChoosing 'backwards' follows the rule 'friction opposes motion' too literally; it opposes the SLIPPING of the foot, which would be backwards.
8Multiple choice · ★ Challenge
The same crate is moved on the same floor in three ways. Which order is correct, from the LARGEST friction force to the smallest?
1. AKinetic friction, then limiting friction, then rolling friction on rollers
2. BRolling friction on rollers, then limiting friction, then kinetic friction
3. CLimiting friction, then kinetic friction, then rolling friction on rollers
4. DLimiting friction, then rolling friction on rollers, then kinetic friction
Show answer
Answer: C. Limiting friction, then kinetic friction, then rolling friction on rollers
Limiting (starting) friction is the largest, kinetic (sliding) friction is a little less, and rolling friction is much smaller than both.
Common mistakePutting kinetic friction first reverses the usual result: a body is harder to start than to keep sliding.
9True or false
For low and moderate sliding speeds, the kinetic friction between two solid surfaces is roughly the same whatever the speed.
Show answer
Answer: True
This is one of the laws of solid friction: kinetic friction is nearly independent of the speed of sliding.
Common mistakeLearners mix up solid friction with air resistance, which DOES increase strongly with speed.
10Multiple choice · ★ Challenge
A box slides to the right across a floor while a strong wind blows on it from the right. In which direction does the friction from the floor act on the box?
1. ATo the right, to balance the wind
2. BTo the left, opposite to its sliding
3. CUpwards, together with the normal reaction
4. DIn no direction, as the wind already slows it
Show answer
Answer: B. To the left, opposite to its sliding
Friction opposes the relative motion of the surfaces; the box slides right over the floor, so friction acts to the left.
Common mistakeChoosing 'to the right' assumes friction balances other forces; it always opposes the sliding, whatever else acts.
11Fill in the blank
When walking, your foot pushes backwards on the ground, so the ground's friction pushes your foot ______.
Show answer
Answer: forwards
Friction on the foot opposes its backward slip, so it acts forwards.
Common mistakeWriting 'backwards' gives the direction of the foot's push on the ground, not the ground's force on the foot.
12Multiple choice · ★ Challenge
A box of tea leaves stands on a conveyor belt in a factory. The belt starts to move forwards and the box moves with it without slipping. The friction force on the box acts:
1. ABackwards, against the belt's motion
2. BNowhere, as the box does not slip on the belt
3. CForwards, in the direction the belt moves
4. DDownwards, pressing the box onto the belt
Show answer
Answer: C. Forwards, in the direction the belt moves
The box tends to stay behind as the belt speeds up, so static friction acts forwards on it and accelerates it with the belt.
Common mistakeChoosing 'nowhere' is tempting because there is no slipping, but static friction acts precisely to prevent slipping.
13Fill in the blank
Hardened steel balls placed between a turning wheel and its axle so that the parts roll instead of slide are called ball ______.
Show answer
Answer: bearings
Ball bearings change sliding friction into much smaller rolling friction.
Common mistakeWriting 'grease' names a lubricant, not the rolling steel balls.
14Multiple choice · ★ Challenge
A sledge of firewood is dragged over the same ground. Its load is doubled, and at the same time it is given runners twice as wide. By what factor does the limiting friction change?
1. A2
2. B4
3. C1
4. D0.5
Show answer
Answer: A. 2
Limiting friction is proportional to the normal reaction (doubled) and does not depend on the area of contact, so it doubles.
Common mistakeChoosing 4 multiplies by 2 for the load AND by 2 for the area; the area of contact has no effect.
15Fill in the blank
A heavy wardrobe needs a bigger push to start it moving than to keep it moving, because ______ friction is greater than kinetic friction.
Show answer
Answer: limiting (static)
The maximum static (limiting) friction is larger than the friction once the surfaces slide.
Common mistakeWriting 'rolling' is wrong: the wardrobe slides; rolling friction is the smallest of all.
16Multiple choice · ★ Challenge
A skydiver of mass 60 kg falls at her terminal velocity (g = 10 N/kg). What is the air resistance on her?
1. A0 N
2. B60 N
3. C600 N
4. DMore than 600 N
Show answer
Answer: C. 600 N
At terminal velocity there is no acceleration, so air resistance balances the weight: 60 × 10 = 600 N.
Common mistakeChoosing 0 N assumes no force acts when the speed is steady; it is the RESULTANT that is zero.
17Fill in the blank · ★ Challenge
A machine part is pushed 4.0 m against a steady friction force of 25 N. The work done against friction, which becomes heat, is ______ J.
Show answer
Answer: 100
W = F × d = 25 × 4.0 = 100 J.
Common mistakeWriting 6.25 J divides force by distance; work is force MULTIPLIED by distance.
18Multiple choice
Which of these is mainly an example of rolling friction?
1. AA wheelbarrow's wheel turning along a path
2. BA sledge sliding down a steep, sandy slope near the lake
3. CA book resting on a sloping shelf
4. DA parachute falling through the air
Show answer
Answer: A. A wheelbarrow's wheel turning along a path
A wheel turns over the ground without sliding, so the friction is rolling friction.
Common mistakeChoosing the sledge is wrong: it slides over the sand, so it has sliding (kinetic) friction.
19Short answer · ★ Challenge
Explain how a layer of oil between two metal parts reduces friction, and why an engine run without oil can be damaged in a few minutes.
Show answer
Model answer: The oil keeps the metal surfaces slightly apart, so their bumps do not catch on each other; the parts slide over the oil instead. Without oil the metal surfaces rub directly, friction is large, a lot of heat is produced and the parts wear quickly, expand and can even weld or seize together.
Common mistakeSaying oil works because it is 'slippery' does not explain anything; the key idea is that it separates the two surfaces.
20Multiple choice
Which everyday job would be IMPOSSIBLE without friction?
1. AFloating a boat on Lake Kivu
2. BSeeing sunlight reflected by the Moon
3. CLetting a stone fall to the ground
4. DTying a knot in a rope that stays tied
Show answer
Answer: D. Tying a knot in a rope that stays tied
A knot holds only because friction between the strands stops them from sliding apart.
Common mistakeChoosing the falling stone confuses friction with gravity; without friction (and air) a stone would still fall.
21Short answer · ★ Challenge
Raindrops fall from clouds more than 1 km high, yet they do not hit us at dangerous speeds. Describe and explain the motion of a raindrop as it falls.
Show answer
Model answer: At first the drop is slow, air resistance is small and it accelerates downwards. As its speed increases, the air resistance increases, so the resultant force and the acceleration get smaller. When air resistance equals the weight, the resultant force is zero and the drop falls at a steady terminal velocity of only a few metres per second.
Common mistakeSaying the drop keeps accelerating at g for the whole 1 km ignores air resistance, which grows with speed.
22Multiple choice · ★ Challenge
A plank is tilted until blocks just slip. The horizontal distance between its ends is 80 cm. The raised end is 32 cm high for wood, 64 cm for rubber and 16 cm for plastic. Which material has the largest μ, and what is it?
1. APlastic, μ = 0.2
2. BRubber, μ = 1.25
3. CWood, μ = 0.4
4. DRubber, μ = 0.8
Show answer
Answer: D. Rubber, μ = 0.8
μ = height ÷ horizontal distance: rubber 64 ÷ 80 = 0.8, wood 0.4, plastic 0.2. Rubber needs the steepest slope, so it grips best.
Common mistakeChoosing μ = 1.25 divides 80 by 64; the height goes on top.
23Multiple choice
Racing cyclists in the Tour du Rwanda wear tight clothes and crouch low over the handlebars mainly to:
1. AIncrease the friction between tyres and road
2. BMake their bodies heavier and so more stable
3. CKeep warm on cold mornings in the hills
4. DReduce air resistance so they lose less energy
Show answer
Answer: D. Reduce air resistance so they lose less energy
A smaller, smoother shape facing the air reduces drag, which is the main resistance at racing speeds.
Common mistakeChoosing more tyre friction confuses grip on the road with the air resistance acting on the rider's body.
24Multiple choice · ★ Challenge
A 1200 kg car's engine gives a forward force of 3000 N. The total friction and air resistance is 1200 N. What is the car's acceleration?
1. A2.5 m/s²
2. B1.5 m/s²
3. C3.5 m/s²
4. D1.0 m/s²
Show answer
Answer: B. 1.5 m/s²
Resultant = 3000 − 1200 = 1800 N; a = F ÷ m = 1800 ÷ 1200 = 1.5 m/s².
Common mistakeChoosing 2.5 m/s² ignores the resistance (3000 ÷ 1200); always subtract the friction first.
25Multiple choice · ★ Challenge
A girl pulls a 15 kg sledge of firewood across level grass at constant velocity with a horizontal force of 45 N (g = 10 N/kg). What is the coefficient of kinetic friction?
1. A3
2. B0.3
3. C0.03
4. D0.75
Show answer
Answer: B. 0.3
At constant velocity friction = pull = 45 N. μ = F ÷ R = 45 ÷ 150 = 0.3.
Common mistakeChoosing 3 divides 45 by the mass (15 kg) instead of by the normal reaction (150 N).
26Multiple choice
A sack of beans rests without sliding on the sloping tailboard of a lorry. Which force stops it from sliding down?
1. AFriction from the board, acting down the slope
2. BStatic friction from the board, acting up the slope
3. CThe normal reaction from the board, acting straight up the slope
4. DIts weight, acting up along the slope
Show answer
Answer: B. Static friction from the board, acting up the slope
The sack tends to slide down, so static friction acts up the slope to stop it.
Common mistakeChoosing 'down the slope' gives friction the direction of the tendency to move; friction always opposes it.
27Multiple choice · ★ Challenge
A 10 kg cupboard stands on a floor where μ = 0.5 (g = 10 N/kg). A pupil pushes it horizontally with 30 N and it does not move. What is the friction force on the cupboard?
1. A50 N
2. B20 N
3. C30 N
4. D0 N
Show answer
Answer: C. 30 N
Limiting friction = μR = 0.5 × 100 = 50 N. The 30 N push is smaller, so static friction just balances it: friction = 30 N.
Common mistakeChoosing 50 N uses F = μR, but that is only the MAXIMUM friction; below the limit, friction equals the push.
28Multiple choice
The horizontal pull on a resting block is increased slowly from zero. How does the friction force on the block change?
1. AIt equals the pull until it reaches its limit, then falls a little once sliding starts
2. BIt stays at its limiting value all the time, even while the pull on the block is still very small
3. CIt is zero until the block moves, then it jumps to its limiting value
4. DIt decreases as the pull increases, so that the block can start to move
Show answer
Answer: A. It equals the pull until it reaches its limit, then falls a little once sliding starts
Static friction matches the pull up to the limiting value; once the block slides, kinetic friction (a little smaller) acts.
Common mistakeChoosing 'zero until the block moves' ignores static friction, which is what holds the block still against small pulls.
29Multiple choice · ★ Challenge
A moto climbs a steep murram road made slippery by rain. Which action best increases the grip of its tyres?
1. ASpreading gravel or sand on the slippery part
2. BPumping the tyres harder so they are firmer
3. CPouring a little oil on the road surface
4. DFitting new tyres with smooth, flat surfaces
Show answer
Answer: A. Spreading gravel or sand on the slippery part
Gravel or sand makes the surface rougher and breaks through the wet layer, increasing μ.
Common mistakeChoosing smooth new tyres is tempting because they are new, but without treads they slide on wet surfaces.
30Fill in the blank
A man of weight 600 N stands still on a level floor. The normal reaction of the floor on him is ______ N.
Show answer
Answer: 600
On a level surface with no other vertical forces, R balances the weight: R = 600 N.
Common mistakeWriting 60 confuses the weight with the mass; R is a force equal to the weight here.
31Short answer · ★ Challenge
A 40 kg desk rests on a floor with μ = 0.4 for starting it (g = 10 N/kg). A pupil pushes it horizontally with 50 N, then 100 N, then 150 N, then 200 N. For each push, state the friction force and whether the desk moves.
Show answer
Model answer: Limiting friction = 0.4 × 400 = 160 N. For 50 N, 100 N and 150 N the desk stays still and the friction equals the push (50 N, 100 N, 150 N). At 200 N the push is more than 160 N, so the desk starts to slide and accelerates.
Common mistakeSaying the friction is 160 N for every push is wrong: 160 N is only the largest value static friction can reach.
32Multiple choice · ★ Challenge
A pupil drags a 20 kg sack of maize 15 m across a level floor at steady speed against a friction force of 90 N. How much energy is turned into heat by friction? (g = 10 N/kg)
1. A1350 J
2. B3000 J
3. C300 J
4. D6 J
Show answer
Answer: A. 1350 J
Work against friction = friction × distance = 90 × 15 = 1350 J, which becomes heat.
Common mistakeChoosing 3000 J multiplies the weight (200 N) by the distance; the work against friction uses the friction force.
33Fill in the blank
A loaded crate needs a push of 80 N to start moving. When it is pushed with only 45 N it stays still, so the friction on it is ______ N.
Show answer
Answer: 45
The crate is in equilibrium, so friction balances the push exactly: 45 N.
Common mistakeWriting 80 N gives the limiting friction; the friction is only as big as it needs to be to stop motion.
34Fill in the blank
A coin just begins to slide on a tilted book when the raised edge is a quarter of the horizontal distance. The coefficient of static friction is ______.
Show answer
Answer: 0.25
μ = height ÷ horizontal distance = 1 ÷ 4 = 0.25.
Common mistakeWriting 4 turns the ratio upside down; a gentle slope means a small μ.
35Short answer · ★ Challenge
A block lies on a plank. One end of the plank is raised slowly; the block just starts to slide when that end is 30 cm higher than the other, and the horizontal distance between the ends is 60 cm. Using μ = height ÷ horizontal distance, find μ, and explain why the plank must be raised slowly.
Show answer
Model answer: μ = 30 ÷ 60 = 0.5. The plank must be raised slowly and smoothly so that the block starts to slip only because the slope is steep enough, not because it was jerked, and so that the height can be read at the exact moment it slips.
Common mistakeUsing the length of the plank instead of the horizontal distance gives the wrong ratio; the formula needs the horizontal distance.
36Short answer · ★ Challenge
In the rainy season a moto's back wheel spins in the mud but the moto does not move forwards. Explain why, and suggest one way to get it moving.
Show answer
Model answer: The turning wheel pushes backwards on the ground; the forward friction from the ground is what drives the moto. Wet mud has a very small μ, so the limiting friction is too small and the wheel slips instead of gripping. Putting gravel, sand, branches or sacks under the wheel (or using less throttle) increases the grip.
Common mistakeSaying the engine is too weak misses the point: more engine force only makes the wheel spin faster when the friction is too small.
37Multiple choice
Why do the brake discs of a minibus get hot after it has stopped many times in town?
1. ASunlight falls on the spinning discs and warms them up
2. BAir rushing past the spinning discs squeezes them and so makes them very hot
3. CFriction between the pads and the discs turns kinetic energy into heat
4. DThe engine sends some of its heat along the axles to the wheels
Show answer
Answer: C. Friction between the pads and the discs turns kinetic energy into heat
Each time the pads grip the discs, sliding friction changes the minibus's kinetic energy into heat.
Common mistakeChoosing the air explanation is tempting, but moving air actually COOLS the discs; the heat comes from friction.
38Multiple choice · ★ Challenge
A graph of limiting friction F (y-axis) against normal reaction R (x-axis) is a straight line through the origin that passes through the point R = 40 N, F = 14 N. What is μ?
1. A2.9
2. B0.35
3. C14
4. D0.035
Show answer
Answer: B. 0.35
μ = gradient = F ÷ R = 14 ÷ 40 = 0.35.
Common mistakeChoosing 2.9 divides R by F (40 ÷ 14); μ = F ÷ R, friction on top.
39Multiple choice
When measuring friction with a spring balance, why should the balance be held horizontal?
1. ASo that the spring balance reads zero before the pull starts
2. BSo that the block presses harder on the bench and does not tip over while pulled
3. CSo that the block moves off quickly at a high, steady speed
4. DSo that the whole pull acts along the bench and can balance the friction
Show answer
Answer: D. So that the whole pull acts along the bench and can balance the friction
Friction acts along the surface; only a pull along the surface balances it fully, so the reading then equals the friction.
Common mistakeChoosing 'reads zero' confuses checking the zero error (done before the experiment) with how the balance is held during the pull.
40Short answer · ★ Challenge
A moto taxi brakes to rest over 5.0 m. The average friction force of the brakes is 2000 N. Calculate the work done against friction, say what it becomes, and explain why brakes can overheat on the long descent from Musanze to Kigali.
Show answer
Model answer: Work = F × d = 2000 × 5.0 = 10 000 J (10 kJ). It becomes heat in the brake pads and discs (plus a little sound). On a long descent the brakes are used for many minutes, so heat builds up faster than it escapes, and the pads can become so hot that they work poorly.
Common mistakeSaying the energy 'disappears' is wrong: friction changes kinetic energy into heat, it does not destroy it.
41Short answer · ★ Challenge
A student pulls a block by hand with a spring balance and gets 3.0 N, 4.2 N and 2.6 N in three trials. Suggest three improvements to make the results more reliable.
Show answer
Model answer: Any three: increase the pull slowly and steadily and read the balance at the moment the block starts to slide; keep the balance horizontal; use the same clean, dry part of the bench each time; check the zero of the balance; repeat more times and take the mean; or pull with a string over a pulley and add sand slowly to a pan.
Common mistakeJust 'repeating and averaging' widely scattered readings does not remove the cause; the pulling method itself must be steadier.
42Short answer
A tailor's sewing machine squeaks and its moving parts feel warm after a long day of use. Name two disadvantages of friction shown here and suggest one remedy.
Show answer
Model answer: Friction produces unwanted noise (squeaking) and wastes energy as heat; it also wears the moving parts. Oiling the moving parts regularly reduces the friction.
Common mistakeCalling the warmth 'harmless' misses that it is wasted energy and a sign of wear.
43Short answer · ★ Challenge
A learner places the same brick on a table on its large face, then on its side, then on its end, and measures the pull needed to just make it slide: 6.1 N, 5.9 N and 6.0 N. What law of friction do the results support? Why are the readings not exactly equal?
Show answer
Model answer: They support the law that limiting friction does not depend on the area of contact (the weight and the surfaces were the same). The small differences come from experimental error, such as reading the balance at slightly different moments or small differences in roughness on the faces.
Common mistakeConcluding that the largest face gives most friction reads too much into 0.1–0.2 N differences that are within experimental error.
44Short answer
Explain why a match bursts into flame when it is struck along the rough side of the matchbox.
Show answer
Model answer: Rubbing the match head over the rough strip produces a lot of friction. The work done against friction turns kinetic energy into heat, which raises the temperature of the match head until its chemicals catch fire.
Common mistakeSaying the box 'contains fire' misses the physics: the heating comes from work done against friction.
45Short answer · ★ Challenge
A 50 kg crate starts from rest and is pushed with 220 N across a floor where the kinetic friction is 120 N. Find its acceleration and its speed after 4 s.
Show answer
Model answer: Resultant = 220 − 120 = 100 N; a = 100 ÷ 50 = 2 m/s². v = u + at = 0 + 2 × 4 = 8 m/s.
Common mistakeUsing the full 220 N in F = ma gives 4.4 m/s²; only the resultant force accelerates the crate.
46Multiple choice · ★ Challenge
A pupil drags a 4 kg box across a table while also pressing straight down on it with a force of 10 N (μ = 0.3, g = 10 N/kg). What is the limiting friction?
1. A12 N
2. B3 N
3. C50 N
4. D15 N
Show answer
Answer: D. 15 N
R = weight + push = 40 + 10 = 50 N; limiting friction = μR = 0.3 × 50 = 15 N.
Common mistakeChoosing 12 N uses only the weight (0.3 × 40); the downward push also presses the surfaces together and increases R.
47True or false
A book lying on a level table with nothing pushing or pulling it sideways has no friction force acting on it.
Show answer
Answer: True
Nothing tries to slide the book, so there is no relative motion to oppose and the friction is zero.
Common mistakeLearners think friction is always present between surfaces in contact; it only appears when something tries to slide them.
48Short answer · ★ Challenge
A student loads a block and records the spring balance reading just as it starts to slide. Total mass (kg): 0.5, 1.0, 1.5, 2.0. Reading (N): 1.8, 3.5, 5.4, 7.1. Taking g = 10 N/kg, find the normal reaction for each load and use the results to estimate μ.
Show answer
Model answer: R = mg = 5, 10, 15, 20 N. F ÷ R = 1.8 ÷ 5 = 0.36, 3.5 ÷ 10 = 0.35, 5.4 ÷ 15 = 0.36, 7.1 ÷ 20 = 0.355. The mean is about 0.36, so μ ≈ 0.36.
Common mistakeDividing the reading by the mass in kg (1.8 ÷ 0.5 = 3.6) forgets that R is a force; convert the mass to a weight first.
49Short answer
Explain, in terms of the surfaces, why sandpaper rubbed on a wooden desk gives much more friction than a sheet of writing paper.
Show answer
Model answer: All surfaces have tiny bumps and hollows. The hard grains on sandpaper are large and sharp, so they dig into the wood and catch on its bumps; much more force is needed to drag them past each other. Writing paper is much smoother, so its bumps interlock less.
Common mistakeSaying sandpaper is 'sticky' is wrong; the extra friction comes from rough grains interlocking with the wood.
50Short answer · ★ Challenge
The coefficient of friction between rubber tyres and a road is about 0.8 on dry tarmac, 0.5 on wet tarmac and 0.1 on a muddy, flooded road. For a car of mass 1000 kg (g = 10 N/kg), calculate the largest friction force the road can give in each case, and say what this means for drivers.
Show answer
Model answer: R = mg = 1000 × 10 = 10 000 N. Dry: 0.8 × 10 000 = 8000 N; wet: 0.5 × 10 000 = 5000 N; flooded mud: 0.1 × 10 000 = 1000 N. With less friction the car cannot brake or turn as hard, so drivers must slow down and keep further apart on wet or muddy roads.
Common mistakeUsing the mass (1000) instead of the weight (10 000 N) for R gives forces ten times too small.