Senior 1 practice book · Unit 3 of 9

Force and Equilibrium of Objects

50 questions that complete the Senior 1 quiz for this unit: 32 core and 18 challenge. Easy and hard questions are mixed. Try each question, then tap “Show answer”.

Common misconceptions

If an object is not moving, no forces act on it.A book resting on a table has its weight pulling it down and the normal reaction pushing it up. The forces are balanced, so the resultant is zero, but forces still act.
Friction is always a nuisance and should be removed.Without friction we could not walk, tyres could not grip the road and brakes would not work. Friction is reduced where it wastes energy and increased where we need grip.
The length of a loaded spring is proportional to the load.Hooke's law is about the EXTENSION (the increase in length), not the total length. Subtract the natural length first.
A heavy object is always stable.Stability depends on a low centre of gravity and a wide base. A tall, narrow cupboard can be heavy and still topple easily.
The centre of gravity must be inside the material of the object.For a ring, a horseshoe or a high-jumper arched over a bar, the centre of gravity can lie in the empty space.

What this unit covers

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

Force: meaning, SI unit and effects of a force
Types of forces: contact and non-contact (tension, normal reaction, upthrust, gravitational, magnetic, electrostatic)
Mass and weight: W = mg on the Earth and other bodies
Measuring force: spring balance, Hooke's law and spring constant
Resultant of forces along the same line
Resultant of perpendicular forces: calculation and scale drawing
Balanced forces and the condition for equilibrium
Centre of gravity of regular and irregular objects
States of equilibrium: stable, unstable and neutral
Stability: factors and everyday applications
Friction: advantages, disadvantages, increasing and reducing it
Free-body (force) diagrams
Elastic and plastic deformation; elastic limit in materials

Go to the questions

Questions (1–50)

Easier and harder questions are mixed, just like in a real exam. The 18 harder ones are marked ★ Challenge.

1True or false
If the forces on an object are balanced, the object must be at rest.
Show answer
Answer: False
Balanced forces mean zero resultant: the object is either at rest or moving at a constant velocity.
Common mistakeLearners forget the second possibility, steady motion in a straight line.
2True or false
When an object in stable equilibrium is tilted slightly, its centre of gravity rises.
Show answer
Answer: True
The centre of gravity rises, so the weight acts to bring the object back down to its original position.
Common mistakeSome learners think it falls; a fall in the centre of gravity happens for unstable equilibrium.
3True or false · ★ Challenge
A rubber band obeys Hooke's law for every stretch until it breaks.
Show answer
Answer: False
Rubber's extension is not proportional to the load; its force–extension graph is curved.
Common mistakeLearners assume every stretchy thing behaves like a steel spring; Hooke's law only fits some materials, and only up to a limit.
4True or false
Friction always acts in the opposite direction to the motion (or attempted motion) between two surfaces.
Show answer
Answer: True
Friction opposes the sliding of one surface over another.
Common mistakeSome learners think friction acts in the direction of motion because it lets us walk; it opposes the backward slip of the foot.
5True or false
The weight of an object is the same everywhere in the universe.
Show answer
Answer: False
Weight = mg, and g is different on different planets and moons, so weight changes; mass does not.
Common mistakeMixing up mass and weight leads to this; it is the mass that stays the same.
6True or false · ★ Challenge
A force is needed to keep an object moving at a constant speed across a perfectly smooth, level surface.
Show answer
Answer: False
With no friction there is nothing to slow the object, so no force is needed to keep it moving steadily.
Common mistakeEveryday experience with friction makes learners think motion always needs a push; it is friction that needs to be balanced.
7Fill in the blank
The pulling force in a stretched rope or string is called ______.
Show answer
Answer: tension
A taut rope pulls on whatever it is attached to with a force called tension.
Common mistakeLearners call it 'friction', but friction acts between surfaces sliding over each other.
8True or false · ★ Challenge
Two forces of 5 N and 12 N can never have a resultant of 20 N, whatever their directions.
Show answer
Answer: True
The biggest possible resultant is when they act in the same direction: 5 + 12 = 17 N.
Common mistakeLearners think any value is possible if you choose the angle, but the resultant is always between 7 N and 17 N.
9Fill in the blank
The upward push of the water on a boat floating on Lake Kivu is called ______.
Show answer
Answer: upthrust
Upthrust is the upward force of a liquid or gas on an object in it.
Common mistakeLearners write 'normal reaction', which is the push of a solid surface, not of a liquid.
10Fill in the blank
Friction between the moving parts of a machine wastes energy mainly as ______.
Show answer
Answer: heat
Rubbing surfaces get warm: kinetic energy is changed into heat (thermal) energy.
Common mistakeWriting 'sound' is a partial answer; some sound is made, but most energy becomes heat.
11Fill in the blank · ★ Challenge
Two forces of 7 N and 3 N act on the same point. The smallest possible resultant is ______ N.
Show answer
Answer: 4
The smallest resultant is when they act in opposite directions: 7 − 3 = 4 N.
Common mistakeAnswering 0 N assumes the forces could cancel, but they are not equal, so they cannot.
12Fill in the blank
A material that returns to its original shape when the force on it is removed is said to be ______.
Show answer
Answer: elastic
Elastic materials such as rubber and steel springs return to their original shape.
Common mistakeLearners write 'plastic', which describes the opposite behaviour.
13Multiple choice · ★ Challenge
A man carrying a heavy bucket of water in his right hand leans to his left. Why?
1. ATo make the bucket of water weigh a little less
2. BTo keep their combined centre of gravity over his feet
3. CTo make his own weight larger than the bucket's weight
4. DTo move the bucket's centre of gravity into his body
Show answer
Answer: B. To keep their combined centre of gravity over his feet
Leaning left moves the combined centre of gravity back over his feet, so he does not topple to the right.
Common mistake'To make the bucket weigh less' is wrong: leaning cannot change any weight, only where the combined weight acts.
14Fill in the blank
The spring constant is measured in N/m or in ______.
Show answer
Answer: N/cm
k = F/e, so its unit is a force unit divided by a length unit.
Common mistakeWriting just 'N' forgets that k is force per unit extension.
15Multiple choice
Which pair are BOTH contact forces?
1. AWeight and magnetic force
2. BTension and electrostatic force
3. CUpthrust and gravitational force
4. DFriction and rope tension
Show answer
Answer: D. Friction and rope tension
Friction and tension only act when objects touch (surfaces rub, a rope is attached).
Common mistakeUpthrust is a contact force, but gravitational force is not, so that pair is wrong.
16Multiple choice · ★ Challenge
A spring is 10.0 cm long with no load. It is loaded with 20 N, then the load is removed, and it now measures 11.2 cm. What can you conclude?
1. AIt obeyed Hooke's law, so it is still undamaged
2. BIts spring constant must be 20 ÷ 1.2 = 16.7 N/cm
3. CIt went past its elastic limit and stays stretched
4. DIt was not stretched at all by the 20 N load
Show answer
Answer: C. It went past its elastic limit and stays stretched
A spring that is not back to its original length has been stretched beyond its elastic limit.
Common mistakeWorking out k = 20 ÷ 1.2 uses the permanent stretch after unloading, not an extension under load, so it means nothing.
17Multiple choice
Which of these is an ADVANTAGE of friction?
1. AIt wears out the soles of our shoes
2. BIt heats up the moving parts of engines
3. CIt lets tyres grip the road when braking
4. DIt slows machines down and wastes energy
Show answer
Answer: C. It lets tyres grip the road when braking
Without friction between tyres and road, a moto could not stop or turn.
Common mistakeLearners often see friction only as a problem; wearing and heating are disadvantages, not advantages.
18Multiple choice
Racing cars are built low and wide mainly so that they:
1. AWeigh much less than ordinary road cars
2. BFeel less friction from the surface of the road
3. CCan carry more passengers on long journeys
4. DDo not overturn easily when they go round bends
Show answer
Answer: D. Do not overturn easily when they go round bends
A low centre of gravity and a wide wheelbase make the car stable on bends.
Common mistakeLearners link 'low' with 'light', but stability depends on where the weight is, not on how much there is.
19Multiple choice · ★ Challenge
A box on smooth ice is pulled with 24 N north and 7 N east. What is the size of the resultant force?
1. A25 N
2. B31 N
3. C17 N
4. D168 N
Show answer
Answer: A. 25 N
R = √(24² + 7²) = √(576 + 49) = √625 = 25 N.
Common mistake31 N adds the forces as if they were in the same direction; at right angles we use Pythagoras.
20Multiple choice
Which material shows plastic deformation when squeezed?
1. AModelling clay
2. BA rubber band
3. CA steel spring
4. DA tennis ball
Show answer
Answer: A. Modelling clay
Clay keeps its new shape after the force is removed, which is plastic deformation.
Common mistakeA rubber band changes shape easily, but it returns to its shape, so it is elastic.
21Multiple choice
Which method reduces friction in the moving parts of a bicycle?
1. AFitting new tyres with a much deeper tread
2. BPressing gently on the brakes while riding
3. CPutting a little dry sand on the chain
4. DOiling the chain and using ball bearings
Show answer
Answer: D. Oiling the chain and using ball bearings
Oil and ball bearings let surfaces slide or roll over each other easily.
Common mistakeDeeper tread increases grip on the road; it does not reduce friction in the moving parts.
22Multiple choice · ★ Challenge
A box is pushed to the right across a rough floor at a steady speed. How many forces should its free-body diagram show?
1. A2
2. B3
3. C4
4. D5
Show answer
Answer: C. 4
Push (right), friction (left), weight (down) and normal reaction (up): 4 forces.
Common mistakeAnswering 2 shows only the horizontal forces; the vertical forces still act even though they balance.
23Multiple choice
Which example shows a force changing ONLY the shape of an object?
1. ABraking a moving bicycle until it stops
2. BSqueezing a lump of clay in your hands
3. CKicking a football that was lying still
4. DA moto turning a corner at steady speed
Show answer
Answer: B. Squeezing a lump of clay in your hands
Squeezing clay changes its shape but does not set it moving; the other examples change speed or direction.
Common mistakeA moto turning is tempting because nothing seems to speed up, but its direction of motion changes.
24Short answer · ★ Challenge
Explain why steep roads in hilly areas are sometimes made with rough cobbles or grooves, and why riding on a wet murram road is dangerous.
Show answer
Model answer: Rough surfaces increase friction between tyres and road, giving grip for climbing and braking on steep slopes. On wet murram, water and mud act like a lubricant, reducing friction, so tyres can skid and braking distances become longer.
Common mistakeLearners say wet roads are dangerous because of water alone; the real reason is the drop in friction.
25Multiple choice
A balloon rubbed on your hair sticks to a wall. Which force holds it there?
1. AMagnetic force
2. BElectrostatic force
3. CGravitational force
4. DTension force
Show answer
Answer: B. Electrostatic force
Rubbing gives the balloon an electric charge, which attracts the wall by an electrostatic force.
Common mistakeMagnetic force is tempting because it also acts without contact, but balloons and walls are not magnetic.
26Multiple choice
A lamp hangs at rest from the ceiling by a cord. Which forces belong on its free-body diagram?
1. AOnly its own weight, acting straight down
2. BIts weight down and the cord's tension up
3. CIts weight down and a normal reaction up
4. DThe tension down and its weight acting up
Show answer
Answer: B. Its weight down and the cord's tension up
Only two forces act on the lamp: gravity (weight) down and the cord's tension up.
Common mistakeA normal reaction comes from a surface pushing on the object; here the cord pulls, so it is tension.
27Multiple choice
A ruler hangs freely from a nail through a hole near one end. What type of equilibrium is it in?
1. AUnstable
2. BStable
3. CNeutral
4. DNo equilibrium
Show answer
Answer: B. Stable
If pushed aside, its centre of gravity rises and it swings back to hang below the nail: stable equilibrium.
Common mistakeNeutral is tempting because it can swing, but it always comes back to the same position.
28Short answer · ★ Challenge
Describe the free-body diagram of a moto moving at a steady speed on a level road. Name each force and say which forces are equal in size.
Show answer
Model answer: Four forces: the driving force forwards and friction/air resistance backwards (equal, because the speed is steady); the weight downwards and the normal reaction of the road upwards (equal, because there is no vertical motion).
Common mistakeLearners draw the driving force bigger than friction; at steady speed they are balanced.
29Multiple choice
Which statement gives the condition for an object to be in equilibrium under forces acting along one line?
1. AIt must not be moving at all
2. BAll the forces on it are the same size
3. CNo forces at all are acting on it
4. DThe resultant force on it is zero
Show answer
Answer: D. The resultant force on it is zero
Equilibrium means the forces balance, so their resultant is zero.
Common mistake'No forces at all' is tempting, but objects in equilibrium usually have several forces acting that cancel out.
30Short answer · ★ Challenge
A moto carries tall stacked crates of drinks tied on the back. Explain why this is dangerous on a sharp bend, and give two ways to make the load safer.
Show answer
Model answer: The tall load raises the centre of gravity, so a small tilt on the bend moves the vertical line through it outside the base (the tyres), and the moto topples. Safer: carry fewer crates so the stack is lower, put the heavier ones at the bottom, or spread the load lower on both sides.
Common mistakeLearners only say 'the load is heavy'; the danger comes from the HIGH centre of gravity.
31Multiple choice
A potter makes a flat, uniform round clay plate. Where should a single support be put under it so that it balances?
1. AUnder any point on its rim
2. BUnder the thickest part of the rim
3. CAnywhere, as it always balances
4. DExactly under its centre
Show answer
Answer: D. Exactly under its centre
For a uniform regular shape the centre of gravity is at its geometric centre.
Common mistakeChoosing the thickest part of the rim ignores that a uniform plate has its weight evenly spread, so its centre of gravity is at its centre.
32Short answer · ★ Challenge
A high-jumper using the 'Fosbury flop' arches her body over the bar. Explain how her centre of gravity can pass below the bar while her body goes over it.
Show answer
Model answer: When her body is arched like a bent bow, much of her mass is below the bar on each side, so her centre of gravity lies outside her body, below the bar. She needs less energy to raise her centre of gravity, so she can clear a higher bar.
Common mistakeLearners think the centre of gravity must always be inside the body, but for a curved shape it can be in the empty space.
33Multiple choice
Two forces act at right angles to each other. Which statement about their resultant R is always true?
1. AR is exactly equal to the sum of the two forces
2. BR is exactly equal to the difference of the forces
3. CR is bigger than each force but less than their sum
4. DR is zero, because the forces act at right angles
Show answer
Answer: C. R is bigger than each force but less than their sum
At right angles R = √(F₁² + F₂²), which is always between the larger force and the sum.
Common mistakeAdding the forces is the usual slip; that only works when they act in the same direction.
34Multiple choice
A framed picture hangs at rest from a nail by one vertical string. The picture weighs 15 N. What is the tension in the string?
1. A15 N
2. B30 N
3. C7.5 N
4. D0 N
Show answer
Answer: A. 15 N
The picture is in equilibrium, so the upward tension equals its weight, 15 N.
Common mistake7.5 N halves the weight as if there were two strings; here one string holds all the weight.
35Short answer · ★ Challenge
Explain, in terms of what happens to its centre of gravity when it is tilted, why a cone standing on its base is stable but one balanced on its tip is unstable.
Show answer
Model answer: On its base, tilting the cone raises its centre of gravity, so its weight turns it back down to its original position: stable. On its tip, any tilt lowers the centre of gravity and the weight turns it further over: unstable.
Common mistakeLearners say 'because the base is wide' without linking it to the centre of gravity rising or falling.
36Multiple choice
Why does a standing electric fan have a heavy, round base?
1. ATo keep its centre of gravity low
2. BTo make the fan blades spin much faster
3. CTo stop electricity leaking into the floor
4. DTo increase the air pushed by the blades
Show answer
Answer: A. To keep its centre of gravity low
A heavy, wide base lowers the centre of gravity and widens the base, so the tall fan is hard to knock over.
Common mistakeThinking the base helps the motor confuses stability with how the fan works.
37True or false
On a free-body diagram you also draw the forces that the object exerts on other objects.
Show answer
Answer: False
A free-body diagram shows only the forces acting ON the chosen object.
Common mistakeIncluding forces the object exerts (such as the book pushing on the table) mixes up two different objects.
38Short answer
Give two everyday uses of elastic materials and two uses of plastic deformation in Rwanda.
Show answer
Model answer: Elastic: springs in a mattress or in a spring balance; rubber in a catapult or bicycle tyre tubes. Plastic deformation: shaping clay into pots and bricks; a blacksmith hammering hot iron into hoes.
Common mistakeLearners give 'plastic bags' as plastic deformation; the word here means keeping a new shape, not the material plastic.
39Multiple choice · ★ Challenge
A rock weighs 48 N on the Moon, where g = 1.6 N/kg. What does it weigh on Earth (g = 10 N/kg)?
1. A76.8 N
2. B4.8 N
3. C300 N
4. D30 N
Show answer
Answer: C. 300 N
m = W/g = 48 ÷ 1.6 = 30 kg; on Earth W = 30 × 10 = 300 N.
Common mistake30 N stops at the mass and gives it the wrong unit; 30 kg must still be multiplied by 10 N/kg.
40Short answer
Give one example from a Rwandan farm of a force that (a) starts something moving, (b) stops something moving, (c) changes the shape of something.
Show answer
Model answer: (a) An ox pulling a plough starts it moving. (b) A farmer catching a falling sack of maize stops it. (c) A hoe pressing into soil changes the shape of the ground (or squeezing a ripe avocado).
Common mistakeLearners often give the same type of example three times; each part needs a different effect of a force.
41Multiple choice · ★ Challenge
Spring A has k = 50 N/m and spring B has k = 200 N/m. Each holds a 10 N load. Which spring stretches more, and by how much?
1. AA, by 20 cm
2. BB, by 20 cm
3. CA, by 5 cm
4. DB, by 5 cm
Show answer
Answer: A. A, by 20 cm
e = F/k: A stretches 10 ÷ 50 = 0.2 m = 20 cm; B stretches 10 ÷ 200 = 0.05 m = 5 cm. A stretches more.
Common mistakeChoosing B confuses a large spring constant with a large stretch; a bigger k means a stiffer spring.
42Short answer
Copy and complete for mass and weight: what each one is, its SI unit, the instrument used to measure it, and whether it changes when you go from the Earth to the Moon.
Show answer
Model answer: Mass: the amount of matter in a body; kilogram (kg); beam (or electronic) balance; does not change. Weight: the force of gravity on a body; newton (N); spring balance; it changes (about six times smaller on the Moon).
Common mistakeLearners write kg for weight because shops say 'weighs 2 kg'; in physics weight is a force in newtons.
43Multiple choice
On Jupiter, g is about 25 N/kg. What would a 4 kg bag weigh there?
1. A100 N
2. B6.25 N
3. C0.16 N
4. D40 N
Show answer
Answer: A. 100 N
W = mg = 4 × 25 = 100 N.
Common mistake40 N uses Earth's g = 10 N/kg; the weight depends on the g of the planet you are on.
44Short answer · ★ Challenge
Describe an experiment to test Hooke's law using a spring, a metre rule, a pointer and slotted masses. Say what you measure and what graph you plot.
Show answer
Model answer: Hang the spring from a clamp with a pointer at the bottom beside a vertical metre rule; record the starting reading. Add masses one at a time, recording the new reading each time; extension = reading − starting reading, load = mg. Plot load against extension: a straight line through the origin shows Hooke's law is obeyed.
Common mistakeLearners plot the total length instead of the extension; that line does not pass through the origin.
45Multiple choice
A spring has a spring constant of 40 N/m. What force stretches it by 5 cm?
1. A200 N
2. B8 N
3. C0.125 N
4. D2 N
Show answer
Answer: D. 2 N
e = 5 cm = 0.05 m, so F = ke = 40 × 0.05 = 2 N.
Common mistake200 N comes from using 5 instead of 0.05 m; k is in N/m, so the extension must be in metres.
46Short answer
A crate on the floor is pushed with a horizontal force of 80 N but does not move. What is the size and direction of the friction force on it? Explain.
Show answer
Model answer: The friction force is 80 N, acting opposite to the push. The crate stays at rest, so the forces on it are balanced and the resultant is zero.
Common mistakeLearners say friction is bigger than the push; if it were, the crate would move backwards.
47Short answer · ★ Challenge
Forces of 40 N east and 30 N north act on a post. Using a scale of 1 cm : 10 N, describe how to find the resultant by scale drawing, and state its size and direction.
Show answer
Model answer: Draw a 4 cm arrow east, then from its tip a 3 cm arrow north. Join the start of the first arrow to the tip of the second: this line is the resultant. It measures 5 cm, so R = 50 N, at about 37° north of east (measured with a protractor).
Common mistakeLearners join the two tips together; the resultant must start where the first arrow starts.
48Multiple choice
A lorry is stuck in mud. A tractor pulls it forwards with 3000 N, five people each push it forwards with 300 N, and the mud resists with 4000 N. What is the resultant force?
1. A4500 N forwards
2. B8500 N forwards
3. C500 N forwards
4. D1300 N backwards
Show answer
Answer: C. 500 N forwards
Forward forces = 3000 + 5 × 300 = 4500 N; resultant = 4500 − 4000 = 500 N forwards.
Common mistake4500 N forgets to subtract the resistance of the mud, which acts in the opposite direction.
49Multiple choice
A graph of force against extension for a spring is a straight line through the origin up to point P, then it curves. Point P is the:
1. ABreaking point of the spring
2. BLimit of proportionality
3. CZero error of the spring
4. DCentre of gravity of the spring
Show answer
Answer: B. Limit of proportionality
Up to P the extension is proportional to the force (Hooke's law); beyond P it is not.
Common mistakeChoosing the breaking point is wrong: the spring can still stretch a lot past P before it breaks.
50Short answer · ★ Challenge
A student's free-body diagram for a book at rest on a table shows its weight as 5 N down and the normal reaction as 8 N up. What is wrong, and how should it be corrected?
Show answer
Model answer: The book is at rest, so the forces must be balanced: the normal reaction must be 5 N, the same size as the weight. With 8 N up there would be a 3 N resultant upwards and the book would rise.
Common mistakeLearners think the table must push harder than the weight to hold the book up; equal forces are enough.