9th Class Physics · Punjab Board · Complete learning guide
Chapter 3Dynamics
Every topic, every MCQ and every exercise question, explained step by step in simple language. Written for the Punjab Board new-syllabus Physics book, English medium.
The branch of mechanics that studies motion together with its cause, force.
Definition
Force
A push or a pull that changes, or tends to change, the state of rest or of motion of a body. It is a vector; SI unit newton (N).
What a force can do
Start a body moving, or stop a moving body.
Speed a body up or slow it down.
Change the direction of motion.
Change the shape or size of a body (squeezing a ball, stretching a spring).
Everyday forces: opening a door, kicking a football, lifting a school bag, and the seat pressing on you when a car turns a corner.
Remember
Since velocity is a vector, a force that only changes the direction (not the speed) still changes the motion.
Topic 2
Types of force
Definition
Contact force
A force that acts only when two bodies touch.
Definition
Non-contact force
A force that acts between bodies even when they do not touch (a force at a distance).
Contact forces
Non-contact forces
Friction
Gravitational force (weight)
Normal reaction
Magnetic force
Tension
Electrostatic force
Air resistance (drag)
Thrust, upthrust
Definition
Normal reaction
The push of a surface on a body resting on it, acting at right angles to the surface.
Definition
Tension
The pull in a stretched string, rope or cable.
Topic 3
Resultant force and force diagrams
Definition
Resultant (net) force
The single force that has the same effect as all the forces acting on a body together.
A force diagram (free-body diagram) shows a body as a box with an arrow for every force on it, drawn from the body in the direction of the force.
A block pushed along a table: the push and friction act along the table; weight and normal reaction act up and down.
Forces are…
Resultant force
Effect on the body
Balanced
Zero
Stays at rest, or keeps moving at constant velocity
Unbalanced
Not zero
Accelerates in the direction of the resultant
Worked exampleA 12 N push acts to the right on a box and friction is 4 N to the left. Find the resultant force.
Take right as positive: +12 N and −4 N.
Resultant = 12 − 4 = 8 N.
Answer8 N to the right
Topic 4
Newton's first law and inertia
Definition
Newton's first law
A body at rest stays at rest, and a body in motion keeps moving with uniform velocity in a straight line, unless a resultant external force acts on it.
Definition
Inertia
The tendency of a body to keep its state of rest or of uniform motion. The first law is also called the law of inertia.
Situation
What happens
Why
A bus starts suddenly
Passengers fall backward
Their bodies tend to stay at rest
A bus stops suddenly
Passengers lurch forward
Their bodies tend to keep moving
A carpet is beaten
Dust falls out
The dust stays at rest as the carpet moves
A coin on a card, card flicked away
The coin drops into the glass
The coin stays at rest
Remember
The first law cannot be seen fully on Earth, because friction and air resistance always slow moving bodies down. In free space, with no force, a moving body would keep going forever.
Exam tip
Seat belts are needed because of inertia: in a sudden stop your body keeps moving forward.
Topic 5
Mass and weight
Definition
Mass
The quantity of matter in a body, and the measure of its inertia. It is a scalar; SI unit kilogram (kg). It is the same everywhere.
Definition
Weight
The force with which the Earth (or another planet) pulls a body towards its centre. It is a vector; SI unit newton (N).
W = mg
g ≈ 10 m s⁻² on the Earth, 1.6 m s⁻² on the Moon
Mass
Weight
Meaning
Quantity of matter
Force of gravity on the body
Type
Scalar
Vector (towards the centre of the Earth)
Unit
kilogram (kg)
newton (N)
Changes with place?
No
Yes
Measured with
Beam (physical) balance
Spring balance
Worked exampleFind the weight of an 80 kg person on the Earth and on the Moon.
Earth: W = mg = 80 × 10 = 800 N.
Moon: W = 80 × 1.6 = 128 N.
The mass is 80 kg in both places.
Answer800 N on the Earth, 128 N on the Moon
Topic 6
Newton's second law
Definition
Newton's second law
When a resultant force acts on a body, it produces an acceleration in the direction of the force; the acceleration is directly proportional to the force and inversely proportional to the mass.
F = ma
Definition
Newton (N)
The force that gives a mass of 1 kg an acceleration of 1 m s⁻². So 1 N = 1 kg m s⁻².
The force in F = ma is the resultant force: if a push and friction both act, only their difference accelerates the body.
Worked exampleA 10 kg block on a frictionless surface accelerates at 2 m s⁻². Find the force. (Solved Example 3.1)
F = ma = 10 × 2.
Answer20 N
Worked exampleA force of 7500 N speeds up a 3000 kg truck from 36 km h⁻¹ to 72 km h⁻¹. Find (a) the acceleration (b) the time taken. (Solved Example 3.2)
Change the units: 36 km h⁻¹ = 10 m s⁻¹ and 72 km h⁻¹ = 20 m s⁻¹.
(a) a = F ÷ m = 7500 ÷ 3000 = 2.5 m s⁻².
(b) t = (vf − vᵢ) ÷ a = (20 − 10) ÷ 2.5 = 4 s.
Answer2.5 m s⁻² and 4 s
Topic 7
Newton's third law
Definition
Newton's third law
To every action there is an equal and opposite reaction. When body A exerts a force on body B, B exerts an equal force on A in the opposite direction.
Remember
Action and reaction act on different bodies, so they never cancel each other.
Action
Reaction
You push the ground backward with your feet
The ground pushes you forward, so you walk
A swimmer pushes water backward
The water pushes the swimmer forward
A rocket pushes hot gases backward
The gases push the rocket forward
A gun pushes the bullet forward
The bullet pushes the gun backward (recoil)
A book presses down on a table
The table pushes up on the book (normal reaction)
Gun and bullet push on each other with equal and opposite forces, so the gun recoils.
Topic 8
Momentum
Definition
Momentum
The product of the mass and the velocity of a body. It is a vector in the direction of the velocity; SI unit kg m s⁻¹ (= N s).
p = mv
A lorry is harder to stop than a bicycle at the same speed, and a bullet does damage despite its small mass, because both have large momentum.
Worked exampleA 15 g bullet moves at 150 m s⁻¹. Find its momentum. (Solved Example 3.3)
Mass in kg: 15 g = 0.015 kg.
p = mv = 0.015 × 150.
Answer2.25 kg m s⁻¹
Topic 9
Impulse and the second law in terms of momentum
Putting a = (vf − vᵢ) ÷ t into F = ma gives F = (mvf − mvᵢ) ÷ t: force equals the rate of change of momentum.
F = Δp ÷ t = (mvf − mvᵢ) ÷ t
Definition
Impulse
The product of a force and the time for which it acts. It equals the change in momentum; SI unit N s.
Impulse = F × t = Δp
The same change in momentum can come from a large force for a short time or a small force for a long time. To reduce a force, make the time longer.
Situation
How the time is made longer
Catching a cricket ball
The hands are drawn back with the ball
Car air bags and seat belts
The passenger is stopped gradually
Crumple zones in cars
The front folds up slowly in a crash
Landing after a jump
Bending the knees
Worked exampleA 160 g cricket ball hits a bat at 28 m s⁻¹ and leaves at 52 m s⁻¹ the other way. Contact lasts 4 × 10⁻³ s. Find the average force. (Solved Example 3.4)
Take the leaving direction as positive: vᵢ = −28 m s⁻¹, vf = +52 m s⁻¹, m = 0.16 kg.
Δp = m(vf − vᵢ) = 0.16 × (52 − (−28)) = 0.16 × 80 = 12.8 kg m s⁻¹.
F = Δp ÷ t = 12.8 ÷ 0.004.
Answer3200 N
Topic 10
Conservation of momentum
Definition
Isolated system
A group of bodies on which no external force acts; the bodies can only push on each other.
Definition
Law of conservation of momentum
The total momentum of an isolated system stays the same: total momentum before a collision or explosion equals total momentum after it.
m₁u₁ + m₂u₂ = m₁v₁ + m₂v₂
u = velocities before, v = velocities after. The total m₁u₁ + m₂u₂ equals m₁v₁ + m₂v₂.
It follows from the third law: during a collision the two bodies push on each other with equal and opposite forces for the same time, so their momentum changes are equal and opposite and cancel.
Worked exampleA gun of mass m₂ fires a bullet of mass m₁ with velocity v₁. Find the recoil velocity of the gun. (Solved Example 3.5)
Before firing, gun and bullet are at rest: total momentum = 0.
After firing: m₁v₁ + m₂v₂ = 0.
So v₂ = −(m₁ ÷ m₂) v₁. The minus sign shows the gun moves backward, and it moves slowly because m₂ is much larger than m₁.
Answerv₂ = −(m₁/m₂)v₁
Worked exampleA 3 kg ball moving at 5 m s⁻¹ hits a 2 kg ball at rest and they stick together. Find their common velocity. (Solved Example 3.6)
Momentum before = 3 × 5 + 2 × 0 = 15 kg m s⁻¹.
Momentum after = (3 + 2) × v = 5v.
5v = 15, so v = 3 m s⁻¹.
Answer3 m s⁻¹ in the original direction
Exam tip
Choose one direction as positive and give every velocity in the other direction a minus sign.
Topic 11
Friction
Definition
Friction
The force that opposes the motion, or the attempted motion, of one surface over another. It comes from the tiny bumps on the two surfaces catching on each other.
Definition
Static friction
The friction that keeps a body at rest when a force tries to move it. It grows as the applied force grows.
Definition
Limiting friction
The largest value of static friction, reached just before the body starts to slide.
Definition
Kinetic (sliding) friction
The friction acting on a body while it slides. It is a little less than limiting friction.
Definition
Rolling friction
The friction on a body that rolls, such as a wheel. It is much smaller than sliding friction.
Pull a block with a growing force: static friction matches the pull until limiting friction, then the block slides and friction drops to kinetic friction.
Friction is useful for
Friction is a nuisance because
Walking without slipping
It wears out tyres, shoes and machine parts
Brakes stopping a vehicle
It wastes energy as heat
Holding a pen and writing
It makes machines less efficient
Tyres gripping the road
Moving parts get hot
Ways to reduce friction
Lubricate with oil or grease, so the surfaces do not touch directly.
Use wheels or ball bearings, so sliding becomes rolling.
Make the surfaces smooth and polished.
Streamline shapes to reduce air or water resistance.
Exam tip
Tyres have treads so they keep gripping the road in the rain: the grooves push water away. Worn, smooth tyres skid easily.
Topic 12
Air resistance and terminal velocity
Definition
Air resistance (drag)
The friction force that air (or any fluid) exerts on a body moving through it. It grows as the body moves faster.
When a skydiver jumps, weight pulls down and air resistance pushes up. At first air resistance is small and the skydiver speeds up; as the speed rises, air resistance grows until it equals the weight.
Definition
Terminal velocity
The constant velocity a falling body reaches when the upward air resistance equals its weight, so the net force on it is zero.
Velocity rises and then levels off at terminal velocity, where air resistance balances weight.
Remember
Opening a parachute greatly increases air resistance, so the skydiver slows down to a new, much lower terminal velocity that is safe for landing.
The wording follows published solved exercises and every answer was re-checked by hand, so the wording or the order of options may differ slightly from your print.
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Set A: Textbook exercise 9 MCQs
The multiple-choice questions at the end of Chapter 3 in your book, in the book's option order.
Q3.1Newton's Laws of Motion
When we kick a stone, we get hurt. This is due to:
Answer(d) reaction
Step by step
The foot exerts a force (action) on the stone.
By Newton's third law, the stone exerts an equal and opposite force (reaction) on the foot.
That reaction force on the foot is what hurts.
Why the others are wrong
(a) inertia explains why the stone resists starting to move, not why the foot is pushed back.
(b) velocity is not a force and cannot push on the foot.
(c) momentum changes in the collision, but the pain comes from the force on the foot.
Remember
It hurts because the stone pushes back: reaction.
Q3.2Newton's Laws of Motion
An object will continue its motion with constant acceleration until:
Answer(b) the resultant force on it is zero
Step by step
By F = ma, a body accelerates only while a resultant force acts on it.
When the resultant force becomes zero, the acceleration becomes zero.
The body then keeps moving with constant velocity, as Newton's first law says.
Why the others are wrong
(a) a decreasing force would change the acceleration too, but the book's point is the first law: acceleration stops when the resultant force is zero. One answer key marks (a); (b) matches the explanation both keys give.
(c) an increasing force would increase the acceleration, not end it.
(d) a force at right angles to the velocity turns the body in a circle; it does not stop it accelerating.
Remember
No resultant force, no acceleration.
Q3.3Force and Types of Force
Which of the following is a non-contact force?
Answer(c) electrostatic force
Step by step
A contact force needs the bodies to touch; a non-contact force acts across a gap.
Friction, air resistance and tension all need contact.
Charged bodies attract or repel without touching, so electrostatic force is non-contact.
Why the others are wrong
(a) friction acts only between surfaces in contact.
(b) air resistance needs the air to touch the moving body.
(d) tension acts through a string attached to the body.
A ball with momentum p hits a solid wall and bounces back with the same speed. Its momentum p′ after the collision is:
Answer(b) p' = −p
Step by step
Momentum p = mv is a vector: it has a direction.
The ball comes back at the same speed, so the size of its momentum is unchanged.
Its direction is reversed, so p′ = −p. (The change in momentum is −2p.)
Why the others are wrong
(a) this ignores that the direction has reversed.
(c) the speed did not double.
(d) −2p is the change in momentum, not the final momentum.
Remember
Bounces back at the same speed: same size, opposite sign.
Q3.5Conservation of Momentum
A particle of mass m moving with velocity v collides head-on with an identical particle at rest. In an elastic collision, the velocity of the first particle after the collision is:
Answer(c) 0
Step by step
Momentum before = mv + 0 = mv.
In an elastic head-on collision of equal masses the two simply swap velocities.
So the first particle stops (velocity 0) and the second moves off with v; momentum after = 0 + mv.
Why the others are wrong
(a) the first particle cannot keep its full velocity after hitting the other one.
(b) bouncing straight back at v would need the second particle to be much heavier, like a wall.
(d) −v/2 does not conserve momentum here. (If the particles stuck together they would move at +v/2.) The book prints this option as "−1/2", a misprint.
Remember
Equal masses, elastic, one at rest: they swap velocities (think of Newton's cradle).
Q3.6Conservation of Momentum
Conservation of linear momentum is equivalent to:
Answer(c) Newton's third law
Step by step
During a collision, body 1 pushes body 2 and body 2 pushes back equally (third law).
Both forces act for the same time, so the impulses, and hence the momentum changes, are equal and opposite.
They cancel, so the total momentum is conserved: the conservation law comes from the third law.
Why the others are wrong
(a) the first law is about a single body with no resultant force.
(b) the second law links force and the rate of change of momentum of one body; conservation needs the action-reaction pair.
(d) it is linked to the third law.
Remember
Equal and opposite forces → equal and opposite momentum changes → total conserved.
Q3.7Momentum and Impulse
A 5 kg object moving at 10 m s⁻¹ is acted on by a constant force for 5 s, after which it moves at 2 m s⁻¹ in the opposite direction. The force is:
Answer(c) −12 N
Step by step
Take the first direction as positive: vᵢ = +10 m s⁻¹ and vf = −2 m s⁻¹.
Change in momentum = m(vf − vᵢ) = 5 × (−2 − 10) = −60 kg m s⁻¹.
F = change in momentum ÷ time = −60 ÷ 5 = −12 N.
Why the others are wrong
(a) 5 N does not come from these numbers.
(b) −10 N uses only the stopping part (10 → 0) and forgets the reversal to −2.
(d) −15 N does not come from these numbers.
Remember
Reversing direction means the final velocity gets a minus sign.
Q3.8Momentum and Impulse
When a large force acts on an object for a very short time, which is easiest to determine?
Answer(c) the product of force and time
Step by step
In a hit or a kick the force is huge and the contact time very short, so both are hard to measure.
Impulse = force × time = change in momentum.
The change in momentum is found from mass and the velocities before and after, so the product F × t is easy to determine.
Why the others are wrong
(a) the force changes during the very short contact and is hard to measure.
(b) the contact time is too short to measure easily.
(d) the impulse can be found.
Remember
Impulse = F × t = Δp.
Q3.9Friction
A lubricant is put between two surfaces because it:
Answer(c) prevents direct contact between the surfaces
Step by step
Friction comes from the tiny bumps of two surfaces catching on each other.
A lubricant forms a thin layer between the surfaces.
The surfaces no longer touch directly, so friction is much smaller.
Why the others are wrong
(a) less friction does mean less heating, but that is a result, not the reason.
(b) ball bearings are a separate way of reducing friction (rolling).
(d) a lubricant does not turn sliding into rolling.
Remember
Lubricants keep surfaces apart.
Set B: More MCQs from this chapter 15 MCQs
Extra questions on the same ideas, of the kind set in board papers and class tests.
QB1Force and Types of Force
The SI unit of force, the newton, is equal to:
Answer(b) kg m s⁻²
Step by step
F = m × a.
Units: kg × m s⁻² = kg m s⁻², which is named the newton.
Why the others are wrong
(a) kg m s⁻¹ is the unit of momentum.
(c) kg m² s⁻² is the joule, the unit of energy.
(d) kg s⁻² has no metre in it.
Remember
1 N gives 1 kg an acceleration of 1 m s⁻².
QB2Mass, Weight and Inertia
The inertia of a body depends on its:
Answer(a) mass
Step by step
Inertia: the tendency of a body to keep its state of rest or of uniform motion.
A heavier (more massive) body is harder to start or stop, so inertia depends on mass.
Why the others are wrong
(b) a body at rest has inertia too.
(c) shape does not change how hard a body is to accelerate.
(d) colour has nothing to do with inertia.
Remember
More mass, more inertia.
QB3Mass, Weight and Inertia
The weight of a 5 kg bag on the Earth (g = 10 m s⁻²) is:
Answer(d) 50 N
Step by step
Weight is the force of gravity on a body: W = mg.
W = 5 kg × 10 m s⁻² = 50 N.
Why the others are wrong
(a) 0.5 N divides by g instead of multiplying.
(b) 5 is the mass in kg, not the weight in newtons.
(c) 15 N adds instead of multiplying.
Remember
Weight in newtons ≈ mass in kg × 10.
QB4Mass, Weight and Inertia
When a body is taken from the Earth to the Moon, its mass:
Answer(b) stays the same
Step by step
Mass is the quantity of matter in a body.
Moving the body does not add or remove matter, so its mass is the same.
Its weight W = mg falls, because g on the Moon is about 1.6 m s⁻².
Why the others are wrong
(a) it is the weight that becomes about one-sixth.
(c) neither mass nor weight increases on the Moon.
(d) matter does not disappear.
Remember
Mass stays; weight changes.
QB5Newton's Laws of Motion
A force of 20 N acts on a 4 kg body. Its acceleration is:
Answer(c) 5 m s⁻²
Step by step
From F = ma, a = F ÷ m.
a = 20 ÷ 4 = 5 m s⁻².
Why the others are wrong
(a) 80 multiplies instead of dividing.
(b) 0.2 is m ÷ F, upside down.
(d) 24 adds the numbers.
Remember
Acceleration = force ÷ mass.
QB6Momentum and Impulse
The momentum of a 2 kg ball moving at 3 m s⁻¹ is:
Answer(a) 6 kg m s⁻¹
Step by step
Momentum p = mass × velocity.
p = 2 × 3 = 6 kg m s⁻¹.
Why the others are wrong
(b) 1.5 divides instead of multiplying.
(c) 5 adds instead of multiplying.
(d) 9 does not come from p = mv here.
Remember
Momentum = mass × velocity.
QB7Momentum and Impulse
The unit of momentum, kg m s⁻¹, is the same as:
Answer(d) N s
Step by step
1 N = 1 kg m s⁻².
N × s = kg m s⁻² × s = kg m s⁻¹, the unit of momentum.
Why the others are wrong
(a) N m is the unit of work (the joule) or torque.
(b) the joule is the unit of energy.
(c) N s⁻¹ is force per second.
Remember
Impulse (N s) = change in momentum (kg m s⁻¹).
QB8Newton's Laws of Motion
Action and reaction forces:
Answer(b) act on different bodies
Step by step
When A pushes B, B pushes A back equally and oppositely.
One force acts on B, the other on A: different bodies.
Forces on different bodies cannot cancel, so each body can still accelerate.
Why the others are wrong
(a) if they acted on the same body they would cancel, and nothing could ever accelerate.
(c) they act on different bodies, so they do not cancel.
(d) they are always opposite in direction.
Remember
Action and reaction: equal, opposite, on different bodies.
QB9Momentum and Impulse
Air bags and seat belts reduce injuries in a crash because they:
Answer(c) increase the time over which the momentum changes
Step by step
In a crash the passenger's momentum changes from mv to 0, whatever happens.
F = Δp ÷ t, so a longer stopping time means a smaller force.
Air bags and belts stretch out the stopping time, so the force on the body is smaller.
Why the others are wrong
(a) they reduce the force; that is the point.
(b) the mass does not change.
(d) the passenger still stops, so the change in momentum is the same.
Remember
Same Δp, more time, less force.
QB10Friction
The force of friction always acts:
Answer(a) opposite to the motion (or attempted motion)
Step by step
Friction acts along the surfaces in contact.
It always opposes sliding, or the attempt to slide.
Why the others are wrong
(b) friction never helps the sliding motion.
(c) the force at right angles to the surfaces is the normal reaction.
(d) friction acts along the surface, not upward.
Remember
Friction always fights the motion.
QB11Friction
Compared with sliding friction, rolling friction is:
Answer(c) much smaller
Step by step
In sliding, the whole contact surface rubs along.
A wheel rolls: each part touches the ground briefly and lifts off without rubbing.
So rolling friction is much smaller, which is why wheels and ball bearings are used.
Why the others are wrong
(a) it is the other way round.
(b) rolling friction is much smaller.
(d) it is small, but not zero.
Remember
Wheels and ball bearings: rolling beats sliding.
QB12Force and Types of Force
Which of the following is a contact force?
Answer(d) normal reaction
Step by step
A contact force needs the bodies to touch.
A table pushes up on a book only where they touch: the normal reaction.
Why the others are wrong
(a) gravity acts across empty space.
(b) magnets attract without touching.
(c) charges attract or repel without touching.
Remember
Gravitational, magnetic and electrostatic forces act at a distance.
QB13Air Resistance and Terminal Velocity
A skydiver is falling at terminal velocity. The net force on the skydiver is:
Answer(c) zero
Step by step
As the skydiver speeds up, air resistance grows.
At terminal velocity air resistance has grown to equal the weight.
The forces balance: net force 0, so acceleration 0 and constant velocity.
Why the others are wrong
(a) that would be the net force only at the very start, before air resistance builds up.
(b) the net force can never exceed the weight while falling.
(d) the forces balance, so the net force is zero.
Remember
Terminal velocity: forces balanced, no acceleration.
QB14Newton's Laws of Motion
A rocket moves forward because:
Answer(a) it pushes hot gases backward and the gases push the rocket forward
Step by step
The engine forces hot gases out backward at high speed (action).
The gases push the rocket forward with an equal force (reaction).
No air is needed, which is why rockets work in space.
Why the others are wrong
(b) rockets work in space, where there is no air to push against.
(c) gravity pulls the rocket back down, not forward.
(d) air friction opposes the rocket's motion.
Remember
Rockets push on their own exhaust, not on the air.
QB15Conservation of Momentum
A 4 kg gun fires a 20 g bullet at 200 m s⁻¹. The recoil speed of the gun is:
Answer(b) 1 m s⁻¹
Step by step
Before firing, the total momentum is 0.
After: m₁v₁ + m₂v₂ = 0, with m₁ = 0.02 kg, v₁ = 200 m s⁻¹, m₂ = 4 kg.
0.02 × 200 + 4 × v₂ = 0, so v₂ = −4 ÷ 4 = −1 m s⁻¹ (backward).
Why the others are wrong
(a) 0.5 m s⁻¹ is half the correct value.
(c) 2 m s⁻¹ is double the correct value.
(d) 4 is the bullet's momentum in kg m s⁻¹, not the gun's speed.
What changes can a force bring about in the motion of a body?
Answer
A force can start a body moving or stop it, speed it up or slow it down, and change its direction of motion. Because velocity is a vector, changing either its size or its direction is a change in motion.
Short Q 3.2
Give five examples of contact forces.
Answer
Friction
Normal reaction
Tension
Air resistance (drag)
Thrust
Short Q 3.3
An object moves with constant velocity in free space. How long will it continue to move with this velocity?
Answer
Forever, as long as no force acts on it. By Newton's first law a body keeps moving with uniform velocity unless a resultant force acts on it, and in free space there is no friction or air resistance to slow it.
Short Q 3.4
Define impulse of force.
Answer
Definition
Impulse
The product of a force and the (short) time for which it acts: impulse = F × t. It equals the change in momentum of the body; SI unit N s.
Short Q 3.5
Why is Newton's first law of motion not seen in action on the Earth?
Answer
On the Earth, friction and air resistance always act on moving bodies and slow them down. So a body never keeps moving forever on its own, as the first law describes; we only see it approximately, for example on smooth ice.
Short Q 3.6
When a car starts suddenly, the passengers are pushed back into their seats. Why?
Answer
Because of inertia. The passengers' bodies were at rest and tend to stay at rest. The car and seat move forward suddenly, so the seat presses into their backs and they seem to be pushed back.
Short Q 3.7
Why is the force in Newton's second law a net force?
Answer
A body's acceleration depends on all the forces acting on it together. Forces in opposite directions cancel partly, so only the resultant (net) force produces the acceleration: F = ma uses the net force.
Short Q 3.8
How can you show that rolling friction is less than sliding friction?
Answer
Pull a heavy box across the floor with a spring balance and note the reading. Then put the box on rollers (round pencils or a trolley) and pull again. The reading is much smaller, so rolling friction is much less than sliding friction.
Short Q 3.9
Define terminal velocity.
Answer
Definition
Terminal velocity
The constant velocity a falling body reaches when the upward air resistance becomes equal to its weight, so the net force and the acceleration become zero.
Velocity levels off at terminal velocity.
Short Q 3.10
An astronaut floating in space wants to get back to the spaceship using a hand rocket. In which direction should he fire it?
Answer
He should fire the rocket away from the spaceship. The exhaust gases are pushed away from the ship (action), and by Newton's third law they push the astronaut towards the ship (reaction).
These test whether you really understand. Give a reason every time.
CRQ 3.1
Two ice skaters of masses 60 kg and 80 kg stand together on frictionless ice and push each other apart. The 60 kg skater moves off at 4 m s⁻¹. Use Newton's third law to explain what happens, and find the velocity of the other skater.
Answer
Each skater pushes the other with an equal and opposite force (third law) for the same time, so they get equal and opposite momentum and move apart.
Worked exampleVelocity of the 80 kg skater
Before the push, both are at rest: total momentum = 0.
After: 60 × 4 + 80 × v₂ = 0.
240 + 80v₂ = 0, so v₂ = −3 m s⁻¹.
Answer3 m s⁻¹, in the opposite direction
Remember
The lighter skater moves faster, because the same momentum is shared by a smaller mass.
CRQ 3.2
In terms of momentum, what advantage do inflatable air bags give over seat belts?
Answer
In a crash the passenger's momentum has to change from mv to zero either way. From F = Δp ÷ t, the force on the body is smaller if the change happens over a longer time.
A seat belt holds the body, but the head can still jerk forward and hit something hard quickly. An air bag cushions the head and chest and lets them stop more gradually over a larger area, so the force and the injury are smaller.
CRQ 3.3
A horse refuses to pull a cart, saying: "By Newton's third law, the cart pulls me back as hard as I pull it, so the forces cancel and I can never move it." What is wrong with this argument?
Answer
Action and reaction act on different bodies: the horse's pull acts on the cart, and the cart's pull acts on the horse. Forces on different bodies cannot cancel each other.
Whether the cart moves depends only on the forces on the cart: if the horse's pull is greater than the friction on the cart, the cart accelerates. The horse itself moves forward because the ground pushes it forward (reaction to its hooves pushing back on the ground).
CRQ 3.4
Why does a fielder draw his hands back while catching a fast cricket ball?
Answer
The ball's momentum must be brought to zero. Drawing the hands back makes the stopping time longer, so by F = Δp ÷ t the force of the ball on the hands is smaller and they do not get hurt.
CRQ 3.5
Why does a person often fall into the water when jumping from a small boat onto the bank?
Answer
To jump forward, the person pushes the boat backward with their feet. By the third law the boat pushes the person forward, but the light boat also moves backward away from the bank.
So the person gets less push than expected and the boat slides away, and they fall short into the water. Momentum is shared: the boat's backward momentum equals the person's forward momentum.
CRQ 3.6
What might life be like if friction suddenly disappeared?
Answer
Some effects
We could not walk: our feet would slip on the ground.
Vehicles could neither start nor stop: tyres would spin and brakes would not work.
Nothing would stay in place: objects on a table would slide off at the slightest touch.
We could not hold a pen to write, tie a knot, or fix a nail in wood.
Once moving, things would keep sliding until they hit something.
Set A: Textbook comprehensive questions 6 questions
The long questions at the end of the chapter in your book.
Long Q 3.1
Explain the concept of force with the help of practical examples.
Answer
Definition
Definition
Force
A push or a pull that changes, or tends to change, the state of rest or of motion of a body. It is a vector; SI unit newton (N).
Effects of a force, with examples
A force can…
Example
Start a body moving
Pushing a box makes it slide; kicking a ball at rest
Stop a moving body
A goalkeeper catches the ball; brakes stop a car
Change its speed
Pressing the accelerator or the brake
Change its direction
A batsman hits the ball back; a car turns a corner
Change its shape or size
Squeezing a sponge; stretching a spring
Forces in daily life
Opening a door: a push or pull at the handle turns the door.
Turning a corner in a car: the seat pushes sideways on you, which is why you feel pressed against it.
Pushing a wheelbarrow: you push forward to move it; to turn it, you push harder on one handle than the other.
Kinds of force
Contact forces
Non-contact forces
Friction, normal reaction, tension, air resistance, thrust
Gravitational, magnetic, electrostatic
Conclusion
A force can change speed or direction (or both); since velocity is a vector, either is a change in motion.
Long Q 3.2
State and explain Newton's laws of motion.
Answer
Newton's first law (law of inertia)
Definition
Statement
A body at rest stays at rest, and a body in motion keeps moving with uniform velocity in a straight line, unless a resultant external force acts on it.
Explanation: every body resists a change in its state of motion; this is inertia. A force is needed to start, stop, speed up, slow down or turn a body.
Examples
Passengers lurch forward when a bus stops suddenly.
Dust falls out of a carpet when it is beaten.
Newton's second law
Definition
Statement
When a resultant force acts on a body, it produces an acceleration in its own direction that is directly proportional to the force and inversely proportional to the mass.
F = ma
a ∝ F (twice the force, twice the acceleration) and a ∝ 1/m (twice the mass, half the acceleration). Combining them gives F = ma.
Definition
Newton
The force that gives a 1 kg mass an acceleration of 1 m s⁻². 1 N = 1 kg m s⁻².
Newton's third law
Definition
Statement
To every action there is an equal and opposite reaction. The two forces act on different bodies.
Examples
A book presses down on a table; the table pushes up on the book (normal reaction).
A gun pushes a bullet forward; the bullet pushes the gun back (recoil).
Your feet push the ground backward; the ground pushes you forward, so you walk.
Forces on a block on a table, including the normal reaction.
Remember
Action and reaction act on different bodies, so they never cancel each other.
Long Q 3.3
Define momentum and express Newton's second law in terms of change in momentum.
Answer
Momentum
Definition
Momentum
The product of the mass and velocity of a body: p = mv. It is a vector in the direction of the velocity; SI unit kg m s⁻¹ (= N s).
A loaded truck is harder to stop than a bicycle at the same speed because it has more momentum; a bullet is dangerous despite its tiny mass because of its huge velocity.
Second law in terms of momentum
Worked exampleDerivation
Start from F = ma.
Acceleration a = (vf − vᵢ) ÷ t, so F = m(vf − vᵢ) ÷ t.
Multiply out: F = (mvf − mvᵢ) ÷ t.
mvf is the final momentum and mvᵢ the initial momentum, so F = (change in momentum) ÷ time.
AnswerF = Δp ÷ t
Statement
The resultant force on a body equals its rate of change of momentum, and the change in momentum is in the direction of the force.
Impulse
Rearranging: F × t = Δp. The product F × t is called impulse.
Worked exampleA 0.16 kg ball hits a bat at 28 m s⁻¹ and leaves at 52 m s⁻¹ the other way in 0.004 s
Δp = 0.16 × (52 − (−28)) = 12.8 kg m s⁻¹.
F = 12.8 ÷ 0.004.
Answer3200 N
Long Q 3.4
State and explain the law of conservation of momentum.
Answer
Statement
Definition
Law of conservation of momentum
The total momentum of an isolated system (one with no external force) remains constant.
m₁u₁ + m₂u₂ = m₁v₁ + m₂v₂
total momentum before = total momentum after
Explanation
Two balls before and after a collision.
During a collision ball 1 pushes ball 2, and ball 2 pushes ball 1 back with an equal and opposite force (third law).
Both forces act for the same time, so the impulses are equal and opposite.
Ball 2 gains exactly the momentum that ball 1 loses, so the total does not change.
Example
Worked exampleA 3 kg ball at 5 m s⁻¹ hits a 2 kg ball at rest, and they stick together
Momentum before = 3 × 5 + 2 × 0 = 15 kg m s⁻¹.
Momentum after = (3 + 2) v = 5v.
Answerv = 3 m s⁻¹
Applications
Recoil of a gun: the gun moves back as the bullet goes forward.
Rockets: hot gases thrown backward push the rocket forward.
Newton's cradle: equal balls in an elastic collision swap their motion; the moving ball stops and the other moves off with the same speed.
Long Q 3.5
Describe the motion of a block on a table, taking friction into account. Explain static and kinetic friction.
Answer
The experiment
A wooden block rests on a table. A string tied to it passes over a pulley at the edge and holds a light pan. Weights are added to the pan one by one, so the pull on the block grows slowly.
What happens
With small weights the block does not move. Friction from the table pulls back on the block exactly as hard as the string pulls it forward: this is static friction.
As weights are added, static friction grows to match the pull.
Static friction can only grow up to a maximum value, called limiting friction.
When the pull becomes just greater than limiting friction, the block starts to slide.
While it slides, a slightly smaller kinetic friction acts, so a slightly smaller pull keeps it moving at steady speed.
Friction against the applied force.
Definitions
Definition
Static friction
The friction on a body at rest that stops it sliding; it can have any value up to limiting friction.
Definition
Limiting friction
The maximum value of static friction, just before sliding begins.
Definition
Kinetic (sliding) friction
The friction on a body while it is sliding; slightly less than limiting friction.
Remember
It is harder to start pushing a heavy box than to keep it moving, because limiting friction is greater than kinetic friction.
Long Q 3.6
Explain the effect of friction on the motion of a vehicle, with reference to the tyre surface and the braking force.
Answer
Grip: friction that makes a car move
When the engine turns the wheels, each tyre pushes backward on the road. By the third law, friction from the road pushes the tyre, and so the car, forward. Without friction the wheels would just spin, as on ice.
Braking
The brakes slow the turning of the wheels. Friction between the tyres and the road then provides the backward force that slows and stops the car. The greater this friction, the shorter the stopping distance.
Tyre surface (treads)
Treads (grooves) on a tyre push water out from under it on a wet road, so the rubber keeps touching the road and gripping it.
Worn, smooth tyres cannot clear water, so they lose grip and can skid.
On wet or oily roads friction is smaller, so braking takes longer; drivers must slow down and keep a bigger gap.
Unwanted effects
Friction wears tyres down over time.
It heats the tyres and brakes.
Friction in the engine and air resistance waste fuel energy.
Conclusion
In a vehicle, friction is both useful (grip and braking) and a nuisance (wear, heat, wasted fuel).
Set B: More important long questions 6 questions
Long questions often set in board papers from this chapter, answered in the same full style.
Imp. LQ 1
What is inertia? Explain it with examples. How is it related to mass?
Answer
Definition
Definition
Inertia
The tendency of a body to keep its state of rest or of uniform motion in a straight line, and to resist any change in it.
Newton's first law is called the law of inertia because it describes this property.
Inertia of rest
When a bus starts suddenly, passengers fall backward: their bodies tend to stay at rest.
A coin on a card over a glass drops into the glass when the card is flicked away quickly.
Dust falls out when a carpet is beaten: the carpet moves, the dust stays.
Inertia of motion
When a bus stops suddenly, passengers lurch forward: their bodies tend to keep moving.
An athlete runs on past the finishing line before stopping.
Seat belts are needed because the body keeps moving forward in a sudden stop.
Inertia and mass
The more mass a body has, the harder it is to start, stop or turn: mass is the measure of inertia. An empty trolley is easy to push and stop; a loaded one is not.
Remember
Inertia depends only on mass, not on speed, shape or colour.
Imp. LQ 2
Differentiate between mass and weight.
Answer
Mass
Definition
Mass
The quantity of matter in a body, and the measure of its inertia. Scalar; SI unit kilogram (kg).
Weight
Definition
Weight
The force with which the Earth (or another body) pulls an object towards its centre. Vector; SI unit newton (N).
W = mg
Differences
Mass
Weight
Quantity of matter
Force of gravity on the body
Scalar
Vector, towards the centre of the Earth
Unit kg
Unit N
Same everywhere
Changes with g: less on the Moon, zero far out in space
Measured with a beam (physical) balance
Measured with a spring balance
Worked exampleAn 80 kg person
Weight on the Earth = 80 × 10 = 800 N.
Weight on the Moon = 80 × 1.6 = 128 N.
Answermass 80 kg in both places
Imp. LQ 3
What is friction? Explain its advantages and disadvantages and the methods of reducing it.
Answer
Definition
Definition
Friction
The force that opposes the motion, or attempted motion, of one surface over another.
Cause
Even smooth-looking surfaces have tiny bumps. When two surfaces touch, the bumps catch on each other and resist sliding.
Advantages (friction is useful)
We can walk without slipping.
Vehicles can start, turn and brake.
We can hold a pen and write, and grip things.
Nails and screws stay in wood; knots hold.
Disadvantages (friction is a nuisance)
It wears out tyres, shoe soles and machine parts.
It produces unwanted heat in engines and machines.
It wastes energy and fuel, making machines less efficient.
Methods of reducing friction
Method
How it helps
Lubricants (oil, grease)
A thin layer keeps the surfaces apart
Ball bearings and wheels
Change sliding into rolling, which has far less friction
Smooth, polished surfaces
Fewer bumps to catch on each other
Streamlining
Reduces air and water resistance on cars, aircraft, boats
Remember
We reduce friction where it wastes energy and increase it where we need grip, for example with treaded tyres and studded shoes.
Imp. LQ 4
What is rolling friction? Why is it less than sliding friction? Explain the use of ball bearings.
Answer
Rolling friction
Definition
Rolling friction
The friction that acts on a body that rolls over a surface, such as a wheel or a ball.
Why it is less than sliding friction
In sliding, the whole contact area rubs along the surface and the bumps keep catching. A rolling wheel touches the ground at only a small area, and each part of it is lifted off the ground rather than dragged along. So rolling friction is very much smaller, in many cases about a hundred times smaller, than sliding friction.
Worked exampleA simple test
Pull a heavy box across the floor with a spring balance and note the reading.
Put the box on round pencils or a trolley and pull again.
Answerthe reading is much smaller: rolling friction < sliding friction
Ball bearings
Ball bearings are small hard steel balls placed between the moving parts of a machine, for example between a wheel and its axle. The parts then roll on the balls instead of sliding against each other, so friction, heat and wear are greatly reduced. They are used in bicycles, cars, fans and motors.
Remember
Wheels and ball bearings work by changing sliding friction into much smaller rolling friction.
Imp. LQ 5
Define impulse. Explain, with daily-life examples, how a longer time of impact reduces the force.
Answer
Definition
Definition
Impulse
The product of a force and the time for which it acts. It equals the change in momentum; SI unit N s.
Impulse = F × t = Δp
Why a longer time means a smaller force
When a moving body is stopped, its momentum must change from mv to zero; the change Δp is fixed. Since F = Δp ÷ t, making the stopping time t longer makes the force F smaller.
Examples
Situation
What is done
Result
Catching a fast cricket ball
The hands are drawn back with the ball
Smaller force, hands not hurt
Car crash
Air bags, seat belts and crumple zones stop the passenger gradually
Smaller force on the body
Jumping down
Bending the knees on landing
Smaller force on the legs
Packing glassware
Wrapping it in foam or paper
Smaller force if the box is dropped
High jump and pole vault
Landing on a thick soft mattress
Smaller force on the athlete
Worked exampleA 0.4 kg ball hits the hands at 20 m s⁻¹ and is stopped
Δp = 0.4 × 20 = 8 N s.
Stopped in 0.01 s: F = 8 ÷ 0.01 = 800 N.
Stopped in 0.1 s (hands drawn back): F = 8 ÷ 0.1 = 80 N.
Answerten times the time, one-tenth of the force
Imp. LQ 6
Explain terminal velocity with the example of a skydiver.
Answer
Forces on a falling body
Two forces act on a skydiver: weight, pulling down, and air resistance, pushing up. Air resistance is small at low speed and grows as the speed grows.
Stages of the fall
Just after jumping: speed is low, air resistance is small, so the net force is downward and the skydiver accelerates.
Speeding up: as the speed rises, air resistance grows, so the net force and the acceleration get smaller.
Terminal velocity: air resistance grows until it equals the weight. The net force is zero, so the acceleration is zero and the skydiver falls at a steady speed.
Parachute opens: air resistance suddenly becomes much larger than the weight, so the skydiver slows down until a new, much lower terminal velocity is reached for a safe landing.
Velocity rises and then levels off at terminal velocity.
Definition
Terminal velocity
The constant velocity reached by a falling body when the air resistance on it equals its weight.
Remember
At terminal velocity the body is still moving fast; only its acceleration has become zero.
A force of 5 N acts on a 10 kg block resting on a smooth (frictionless) surface. Find (a) its acceleration (b) its velocity after 5 s.
Given Data
F = 5 N
m = 10 kg
vᵢ = 0
t = 5 s
To Find
(a) Acceleration a
(b) Velocity vf after 5 s
Formulas
a = F ÷ m
vf = vᵢ + at
Calculation
(a) a = F ÷ m = 5 ÷ 10 = 0.5 m s⁻².
(b) vf = vᵢ + at = 0 + 0.5 × 5 = 2.5 m s⁻¹.
Result
(a) 0.5 m s⁻² (b) 2.5 m s⁻¹
Numerical 3.2
A person has a mass of 80 kg. Find his weight on the Earth (g = 10 m s⁻²) and on the Moon (g = 1.6 m s⁻²).
Given Data
m = 80 kg
g (Earth) = 10 m s⁻²
g (Moon) = 1.6 m s⁻²
To Find
Weight on the Earth
Weight on the Moon
Formula
W = mg
Calculation
On the Earth: W = mg = 80 × 10 = 800 N.
On the Moon: W = mg = 80 × 1.6 = 128 N.
Result
800 N on the Earth, 128 N on the Moon
Note: His mass is 80 kg in both places; only his weight changes.
Numerical 3.3
What force is needed to increase the speed of an 800 kg car from 10 m s⁻¹ to 30 m s⁻¹ in 10 s?
Given Data
m = 800 kg
vᵢ = 10 m s⁻¹
vf = 30 m s⁻¹
t = 10 s
To Find
Force F
Formulas
a = (vf − vᵢ) ÷ t
F = ma
Calculation
a = (vf − vᵢ) ÷ t = (30 − 10) ÷ 10 = 2 m s⁻².
F = ma = 800 × 2.
Result
F = 1600 N
Numerical 3.4
A 5 g bullet is fired from a 10 kg gun with a speed of 300 m s⁻¹. Find the recoil speed of the gun.
Given Data
m₁ = 5 g = 0.005 kg
v₁ = 300 m s⁻¹
m₂ = 10 kg
total momentum before firing = 0
To Find
Recoil velocity of the gun v₂
Formula
m₁v₁ + m₂v₂ = 0
Calculation
By conservation of momentum: m₁v₁ + m₂v₂ = 0.
0.005 × 300 + 10 × v₂ = 0, so 1.5 + 10v₂ = 0.
v₂ = −1.5 ÷ 10 = −0.15 m s⁻¹.
Result
The gun recoils at 0.15 m s⁻¹, opposite to the bullet
Numerical 3.5
A 70 kg astronaut floating in space throws a 300 g wrench away at 3.5 m s⁻¹. Find (a) the astronaut's recoil speed (b) how far the astronaut moves in 30 minutes.
Given Data
m₁ (wrench) = 300 g = 0.3 kg
v₁ = 3.5 m s⁻¹
m₂ (astronaut) = 70 kg
t = 30 min = 1800 s
To Find
(a) Recoil speed of the astronaut
(b) Distance moved in 30 min
Formulas
m₁v₁ + m₂v₂ = 0
S = v × t
Calculation
(a) Momentum is conserved and was zero: 0.3 × 3.5 + 70 × v₂ = 0, so v₂ = −1.05 ÷ 70 = −0.015 m s⁻¹.
(b) In space nothing slows the astronaut, so the speed stays 0.015 m s⁻¹.
Distance = speed × time = 0.015 × 1800 = 27 m.
Result
(a) 0.015 m s⁻¹, opposite to the wrench (b) 27 m
Numerical 3.6
A railway bogie of mass 6.5 × 10³ kg moves at 0.8 m s⁻¹. A second bogie of mass 9.2 × 10³ kg moving at 1.2 m s⁻¹ in the same direction catches up and couples with it. Find their common velocity.
Given Data
m₁ = 6.5 × 10³ kg, u₁ = 0.8 m s⁻¹
m₂ = 9.2 × 10³ kg, u₂ = 1.2 m s⁻¹
coupled: one common velocity v
To Find
Common velocity v after coupling
Formula
m₁u₁ + m₂u₂ = (m₁ + m₂)v
Calculation
Momentum before = 6500 × 0.8 + 9200 × 1.2 = 5200 + 11 040 = 16 240 kg m s⁻¹.
Momentum after = (6500 + 9200) × v = 15 700 v.
v = 16 240 ÷ 15 700 ≈ 1.03 m s⁻¹.
Result
v ≈ 1.03 m s⁻¹ in the same direction
Numerical 3.7
A 55 kg cyclist rides a 5 kg bicycle. Starting from rest, the cyclist applies a force of 90 N for 8 s and then rides at constant speed for another 8 s. Find the total distance travelled.
Given Data
total mass m = 55 + 5 = 60 kg
F = 90 N for t₁ = 8 s from rest
then constant speed for t₂ = 8 s
To Find
Total distance travelled
Formulas
a = F ÷ m
vf = vᵢ + at
S = vᵢt + ½at²
S = v × t
Calculation
Acceleration: a = F ÷ m = 90 ÷ 60 = 1.5 m s⁻².
Speed after 8 s: v = 0 + 1.5 × 8 = 12 m s⁻¹.
Distance while accelerating: S₁ = ½at² = ½ × 1.5 × 8² = 48 m.
Distance at constant speed: S₂ = 12 × 8 = 96 m.
Total = 48 + 96 = 144 m.
Result
Total distance = 144 m
Numerical 3.8
A 0.4 kg ball is dropped from a height of 1.8 m onto the floor and bounces back up to 0.8 m. Find the magnitude and direction of the impulse the floor gives it (g = 10 m s⁻²).
Given Data
m = 0.4 kg
dropped from 1.8 m
rebounds to 0.8 m
g = 10 m s⁻²
To Find
Impulse from the floor (size and direction)
Formulas
v² = 2gh
Impulse = Δp = m(vf − vᵢ)
Calculation
Speed on hitting the floor: v² = 2gh = 2 × 10 × 1.8 = 36, so v = 6 m s⁻¹ downward.
Speed leaving the floor: v² = 2 × 10 × 0.8 = 16, so v = 4 m s⁻¹ upward.
Take upward as positive: vᵢ = −6 m s⁻¹, vf = +4 m s⁻¹.
The branch of mechanics that studies motion together with its cause, force.
Force
A push or a pull that changes, or tends to change, the state of rest or of motion of a body. It is a vector; SI unit newton (N).
Contact force
A force that acts only when two bodies touch.
Non-contact force
A force that acts between bodies even when they do not touch (a force at a distance).
Normal reaction
The push of a surface on a body resting on it, acting at right angles to the surface.
Tension
The pull in a stretched string, rope or cable.
Resultant (net) force
The single force that has the same effect as all the forces acting on a body together.
Newton's first law
A body at rest stays at rest, and a body in motion keeps moving with uniform velocity in a straight line, unless a resultant external force acts on it.
Inertia
The tendency of a body to keep its state of rest or of uniform motion. The first law is also called the law of inertia.
Mass
The quantity of matter in a body, and the measure of its inertia. It is a scalar; SI unit kilogram (kg). It is the same everywhere.
Weight
The force with which the Earth (or another planet) pulls a body towards its centre. It is a vector; SI unit newton (N).
Newton's second law
When a resultant force acts on a body, it produces an acceleration in the direction of the force; the acceleration is directly proportional to the force and inversely proportional to the mass.
Newton (N)
The force that gives a mass of 1 kg an acceleration of 1 m s⁻². So 1 N = 1 kg m s⁻².
Newton's third law
To every action there is an equal and opposite reaction. When body A exerts a force on body B, B exerts an equal force on A in the opposite direction.
Momentum
The product of the mass and the velocity of a body. It is a vector in the direction of the velocity; SI unit kg m s⁻¹ (= N s).
Impulse
The product of a force and the time for which it acts. It equals the change in momentum; SI unit N s.
Isolated system
A group of bodies on which no external force acts; the bodies can only push on each other.
Law of conservation of momentum
The total momentum of an isolated system stays the same: total momentum before a collision or explosion equals total momentum after it.
Friction
The force that opposes the motion, or the attempted motion, of one surface over another. It comes from the tiny bumps on the two surfaces catching on each other.
Static friction
The friction that keeps a body at rest when a force tries to move it. It grows as the applied force grows.
Limiting friction
The largest value of static friction, reached just before the body starts to slide.
Kinetic (sliding) friction
The friction acting on a body while it slides. It is a little less than limiting friction.
Rolling friction
The friction on a body that rolls, such as a wheel. It is much smaller than sliding friction.
Air resistance (drag)
The friction force that air (or any fluid) exerts on a body moving through it. It grows as the body moves faster.
Terminal velocity
The constant velocity a falling body reaches when the upward air resistance equals its weight, so the net force on it is zero.
Common mistakes to avoid
Thinking action and reaction cancel: they act on different bodies.
Using the applied force in F = ma instead of the resultant force.
Giving weight in kilograms: weight is a force, in newtons.
Forgetting to change grams to kilograms (5 g = 0.005 kg).
Forgetting the minus sign when a body reverses direction, so the change in momentum comes out too small.
Saying mass changes on the Moon: only weight changes.
Thinking a moving body needs a force to keep moving: it needs a force only to change its motion.
Mixing up limiting friction (largest static friction) and kinetic friction (while sliding).
Extra practice tap a question to see its answer
Find the force that gives a 2 kg body an acceleration of 3 m s⁻².Show answer
F = 2 × 3 = 6 N
A 12 N force acts on a body and gives it 4 m s⁻². Find its mass.Show answer
m = 12 ÷ 4 = 3 kg
Find the weight of a 50 kg student on the Earth.Show answer
50 × 10 = 500 N
A 600 N man stands on the Moon. What is his weight there?Show answer
Mass = 60 kg; weight = 60 × 1.6 = 96 N
A 12 N push and 5 N of friction act on a 7 kg box. Find its acceleration.Show answer
Net force 7 N; a = 7 ÷ 7 = 1 m s⁻²
Find the momentum of a 1000 kg car moving at 20 m s⁻¹.Show answer
1000 × 20 = 2 × 10⁴ kg m s⁻¹
A 0.5 kg ball's velocity changes from 4 m s⁻¹ to 10 m s⁻¹. Find the impulse.Show answer
0.5 × (10 − 4) = 3 N s
That change happened in 0.1 s. Find the average force.Show answer
3 ÷ 0.1 = 30 N
A 2 kg gun fires a 10 g bullet at 400 m s⁻¹. Find the recoil speed.Show answer
0.01 × 400 ÷ 2 = 2 m s⁻¹ backward
A 4 kg trolley at 3 m s⁻¹ hits a 2 kg trolley at rest and they join. Find the common velocity.Show answer
12 ÷ 6 = 2 m s⁻¹
A 0.2 kg ball hits a wall at 5 m s⁻¹ and bounces back at 5 m s⁻¹. Find the change in momentum.Show answer
0.2 × (−5 − 5) = −2 kg m s⁻¹ (2 N s, away from the wall)
A 1500 kg car brakes from 20 m s⁻¹ to rest in 5 s. Find the braking force.Show answer
a = −4 m s⁻²; F = 1500 × (−4) = −6000 N
Name the friction that acts on a box that is being pushed but has not started moving.Show answer
Static friction
A falling stone reaches terminal velocity. What is its acceleration?Show answer
Zero: air resistance balances its weight
Final self-test
Final self-test: all 24 MCQs, no answers
Give yourself 25 minutes. Pick one option for each question, then submit to see your score and which questions to revise. Any question you get wrong tells you which topic to read again.
