Newton's laws of motion

A tennis ball is dropped from a height above the ground.

Diagram 1 shows the tennis ball at the instant it is released.

Diagram 1

On diagram 1, draw a labelled arrow to show the force acting on the tennis ball at the instant it is released.

Diagram 2 shows the tennis ball at the instant it hits the ground.

Diagram 2

Just before hitting the ground, the tennis ball is moving downwards at a velocity of 2.5 m/s.

Just after hitting the ground, the tennis ball is moving upwards at a speed of 1.9 m/s.

The mass of the tennis ball is 0.057 kg.

Calculate the change in momentum of the tennis ball when it hits the ground.

Give the unit.

The ball is in contact with the ground for a time of 6.0 ms.

Calculate the force exerted on the ball by the ground.

Give the direction of this force.

The coefficient of restitution can be used to determine how high a ball will bounce. The higher the value of the coefficient of restitution, the higher the ball will bounce.

Diagram 3 shows a ball being dropped from a height (h₁) above the ground.

The ball hits the ground and bounces.

At the top of its bounce, the ball reaches a height (h₂) above the ground.

The coefficient of restitution can be determined using the formula

A student decides to do an investigation to compare the coefficient of restitution for different types of ball.

Design a method for the student’s investigation.

Your answer should include details of

• the variables in the investigation

• how to obtain accurate measurements

• how to obtain reliable results

You may add to diagram 3 or draw an additional diagram to help your answer.

State the principle of conservation of momentum.

The diagram shows object A and object B moving in opposite directions.

The arrows show the direction of the velocities of the two objects.

Before the collision object A has a momentum of 39 kg m/s.

After the collision object A and object B stick together and stop moving.

State the magnitude of the momentum of object B before the collision.

State the formula linking momentum, mass and velocity.

The mass of object A is 8.1 kg.

Calculate the velocity of object A before the collision.

The time taken for the collision is 0.56 s.

Calculate the average force on object A.

Give the direction and magnitude of the force on object B from object A.

A metal spring obeys Hooke’s law.

Sketch a graph to show that the spring obeys Hooke’s law as it is stretched.

You should label both axes with appropriate physical quantities.

Diagram 1 shows an object suspended from a support using a metal spring.

The object is initially at rest.

The object is pulled down and then released.

Diagram 2 shows the forces acting on the object at the instant it is released.

Determine the magnitude and direction of the resultant force acting on the object.

The object has a mass of 0.20 kg.

Calculate the acceleration of the object at the instant it is released.

acceleration =_........ ²

Explain how the magnitude of the acceleration of the object changes, from the instant the object is released until the first time the object returns to its initial resting position.

You should refer to the forces acting on the object in your answer.

A car accelerates with a constant driving force along a horizontal road and reaches its maximum speed.

This is the velocity-time graph for the car’s journey.

By drawing a tangent to the curve, determine the acceleration of the car at a time of 20 s.

acceleration =_........ ²

Determine the distance travelled by the car during the first 80 s of its journey.

Explain the motion of the car after 80 s.

The diagram shows the collision between two balls, A and B.

The masses and velocities of both balls are shown before and after the collision.

Ball B is stationary before the collision.

0.265 kg
0.265 kg

Before collision
After collision

When the balls collide, ball B applies a force on ball A, which causes the velocity of ball A to change.

Ball A also applies a force on ball B during the collision.

Describe how the force applied on ball A compares with the force applied on ball B during the collision.

Calculate the momentum of ball A before the collision.

momentum of ball A before collision =_........ kg m / s

Show that the velocity, v, of ball B after the collision is about 0.6 m / s.

A collision is considered elastic if the total kinetic energy before the collision is equal to the total kinetic energy after the collision.

Using data from the diagram, deduce whether this collision is elastic.

This question is about momentum and forces.

State the principle of conservation of momentum.

The diagram shows an air track that can be used to investigate motion without friction.

Air comes out through a series of small holes in the air track. The air lifts the glider slightly above the track.

A small spacecraft engine floats at rest on a cushion of air.

State the momentum of the spacecraft engine when it is at rest.

The spacecraft engine ejects large numbers of xenon ions to the left.

A mass of 2.6 × 10⁻⁸kg of xenon ions leaves the engine with a mean speed of 26 km / s.

Calculate the momentum of all the ejected xenon ions.

momentum =_........ kg m / s

State the magnitude and direction of the spacecraft engine’s momentum after these xenon ions leave the engine.

The ions exert a force of 2.6 mN on the spacecraft engine.

The spacecraft engine has a mass of 1.2 kg.

Calculate the acceleration of the engine.

Give your answer to 2 significant figures.

acceleration =_........ m / s²

The engine is designed to accelerate a spacecraft while the spacecraft is travelling through space.

The spacecraft carries a mass of 0.75 kg of xenon ions for the engine.

When the engine is used, 9.9 × 10⁻⁸kg of xenon ions leave the engine each second.

A student suggests that this small spacecraft engine would not be useful because the acceleration it produces is very small.

Evaluate the student’s suggestion.

The driver of a racing car makes a pit stop during a race to change the tyres on the racing car.

The area where the tyres are changed is called the pit lane.

Before entering the pit lane, the speed of the car must decrease for safety reasons.

The mass of the racing car is 830 kg.

The maximum braking force is 41 000 N.

Show that the maximum deceleration of the racing car is approximately 50 m / s².

The racing car is travelling at an initial speed of 72 m / s.

Calculate the minimum distance needed to decrease the speed of the racing car from 72 m / s to 26 m / s.

The racing car slows down using its brakes.

The brakes work using friction.

The brakes become very hot when the racing car slows down.

Using ideas about energy, explain why the brakes become hot.

The tyres of the racing car also get very hot during a race.

A mechanic has to handle the hot tyres during the pit stop.

They wear protective gloves which have several layers of insulating materials.

Explain how the layers of insulating materials in the gloves reduce the risk of the mechanic burning their hands on the hot tyres.

The photograph shows a dummy during a test of the safety features of a car in a collision.

(Source: © fStop Images GmbH/Alamy Stock Photo)

Before the collision, the dummy in the car is travelling at a velocity of 14 m / s.

The dummy has a momentum of 1100 kg m / s.

State the formula linking momentum, mass and velocity.

Show that the mass of the dummy is approximately 80 kg.

The dummy is brought to rest during the collision by a mean force of 15 kN.

Calculate the time taken for the dummy to be brought to rest in the collision.

The car being tested is fitted with airbags.

Using ideas about momentum, explain how an airbag reduces the force experienced by the dummy in the collision.

The diagram shows the forces acting on a firework at take-off.

Calculate the magnitude of the resultant force on the firework.

State the formula linking resultant force, mass and acceleration.

The mass of the firework is 160 g.

Calculate the acceleration of the firework.

Explain how the acceleration of the firework changes between take‑off and running out of fuel.

You can assume that the thrust force stays the same as the firework burns the fuel.

The firework makes a sound with constant frequency.

As the firework moves upwards, people on the ground notice that the frequency of the sound they hear changes.

This is called the Doppler effect.

Explain how the Doppler effect causes the observed frequency of sound to change for the people on the ground.

Diagram 1 shows a wooden plank balanced horizontally on two supports, A and B.

A block is suspended from the plank between the supports by a cable of negligible weight.

The weight of the block is 260 N.

State the formula linking moment, force and perpendicular distance from the pivot.

By taking moments about support A, calculate force F.

Assume the weight of the plank is negligible.

Explain what will happen to the magnitude of force F if the block is moved towards support B.

The centre of gravity of the block is located at point X.

Draw an arrow on diagram 2 to show the weight of the block.

The block also experiences a force due to the tension in the cable.

Explain why the block remains stationary when it is supported by this tension force.

Explain why the forces acting on the block are not an example of Newton’s third law of motion.

A crumple zone is a safety feature in a car.

It is a part of the car that is designed to collapse during a collision.

A student investigates the effectiveness of crumple zones.

The student rolls two model cars down a ramp.

Each car comes to rest when it hits a large metal block.

A data logger measures the mean force applied to the car during the collision with the block.

The diagram shows the equipment used in the investigation.

Car 1 has a paper crumple zone at the front.

Car 2 has no paper crumple zone.

The table shows the student’s results.

The mass of each car is 0.074 kg.

Calculate the time taken for the velocity of car 1 to decrease from 3.0 m/s to 0.0 m/s.

State the magnitude and direction of the force on the metal block, when car 2 collides with the block.

Explain why the mean force from the block on car 1 is smaller than the mean force on car 2.

Diagram 1 shows an ice cube floating at rest in a beaker of water.

State the value of the resultant force on the ice cube.

Diagram 2 shows the ice cube pushed down into the water by force X.

The ice cube is at rest in this new position.

State the formula linking pressure difference, height, density and gravitational field strength.

The bottom of the ice cube is 0.041 m below the surface of the water.

The density of water is 1000 kg/m³.

Show that the pressure difference between the bottom of the ice cube and the surface of the water is about 400 Pa.

State the formula linking pressure, force and area.

The area of the base of the ice cube is 0.0017 m².

Calculate the upward force on the bottom of the cube from the water due to the pressure difference.

Explain why the ice cube will accelerate upwards when force X is removed.

A driver of a car sees an obstruction in the road ahead and must stop the car.

State the formula linking average speed, distance travelled and time taken.

A car travels at 21 m / s.

The driver’s reaction time is 0.14 seconds.

Calculate the distance travelled by the car during the driver’s reaction time.

The car experiences a braking force of 7600 N.

The car has a mass of 1200 kg.

State the formula linking force, mass and acceleration.

Calculate the acceleration of the car.

acceleration =_........ m / s²

Calculate the braking distance travelled as the speed of the car is reduced from 21 m / s to 0 m / s.

Which of these is a device used to measure force?

Airbags are safety devices used in cars to protect the driver if there is a crash.

State the formula linking momentum, mass and velocity.

A person inside a car has a mass of 72 kg and a velocity of 13 m/s.

Show that the momentum of the person is about 900 kg m/s.

The person experiences a crash and comes to rest in 0.29 s.

Calculate the force on the person.

Which statement explains how airbags protect the driver?

Cricket is a sport played with bats and balls.

A cricket player hits a ball with a bat. Before the ball is hit, it is moving to the left with a momentum of 4.2 kg m/s.

The bat is in contact with the ball for 0.012 s.

After the ball is hit, it moves to the right with a momentum of 6.7 kg m/s.

Calculate the mean force the bat exerts on the ball and state the direction of the force.

State the magnitude and direction of the mean force the ball exerts on the bat.

The cricket player wears padded protective equipment.

This protective equipment reduces the risk of injury to the player if they are struck by the cricket ball.

Explain how this protective equipment reduces the risk of injury to the player.

Use ideas about momentum in your answer.

A student does an investigation to show how the velocity of a toy car changes when the car rolls down a ramp onto a table and hits a wooden block.

The graph shows how the velocity of the toy car changes with time.

Calculate the distance travelled by the car during the first 0.4 seconds.

Calculate the acceleration of the car between 0.40 s and 0.45 s.

acceleration =_........ ²

State the formula linking resultant force, mass and acceleration.

The car has a mass of 0.13 kg.

Calculate the resultant force on the car as it slows down.

A piece of soft material is fixed to the front of the toy car.

Explain how this will affect the gradient of the velocity-time graph after the car hits the block.

The diagram shows an air track that can be used to investigate motion without friction.

Air comes out through a series of small holes in the air track, which lifts the gliders slightly above the track.

There are two gliders on the track.

Each glider has a magnet.

The poles of the magnets nearest each other are alike.

Explain the direction of the force acting on magnet A from magnet B.

The gliders collide and the magnets cause them to rebound.

Before the collision, the momentum of glider A is 0.045 kg m/s to the right and glider B is at rest.

State the total momentum of glider A and glider B after the collision.

After the collision, the momentum of glider A is 0.021 kg m/s to the left.

Calculate the momentum of glider B after the collision.

momentum of glider B =_........ kg m/s

The time taken for glider B to change its momentum is 0.19 seconds.

Calculate the average force on glider B that causes this change in momentum.

Give the direction of the force on glider B from glider A.

The diagram shows a child’s toy for accelerating steel balls.

This is how the toy works.

• the toy uses three identical steel balls, each with a mass of 4.1 g

• ball A moves towards the magnet

• ball B is in contact with the magnet

• balls B and C are initially at rest and are in contact with each other

• when ball A collides with the magnet, ball C moves away from the magnet

Ball A moves towards the magnet with an initial velocity of 0.15 m/s.

Calculate the initial momentum of ball A.

initial momentum =_........ kg m/s

Ball A is attracted to the magnet.

Explain how this attraction affects the momentum of ball A as it approaches the magnet.

When ball A collides with the magnet, a force of 1.3 N is exerted on ball C for a time of 0.0025 s.

This causes ball C to move away from the magnet.

Calculate the change in velocity of ball C due to this force.

The ink drop experiences a horizontal electrostatic force as it falls.

Explain the direction of the electrostatic force exerted on the ink drop by the charged plates.

On the diagram, draw the path of the ink drop as it falls between the charged plates until it hits the paper.

The ink drop experiences a horizontal force of 8.510^–7N when it is between the charged plates.

The mass of the ink drop is 1.110^–10kg.

Calculate the horizontal acceleration of the ink drop when it is between the charged plates.

acceleration =_........ ²

The ink drop has no initial horizontal velocity before it passes between the charged plates.

After passing between the charged plates, the horizontal velocity of the ink drop is 3.9 m/s.

Calculate the horizontal distance travelled by the ink drop as it passes between the charged plates.

Give your answer in mm.

Explain how another ink drop could be deflected in the opposite direction by a greater distance using the charged plates in the inkjet printer.

The diagram shows some of the forces acting on a large rubbish bin on wheels.

The weight of the bin acts through point G.

Give the name of point G.

The mass of the bin is 23 kg.

What is the weight of the bin?

State the principle of moments.

A person applies force F to the bin to keep it stationary.

Calculate the magnitude of force F.

State the magnitude and direction of the force applied to the person by the bin.

This question is about a folding table.

The diagram shows some of the forces acting on the table.

The weight of the table acts through point G.

State the name of point G.

State the formula linking moment, force and perpendicular distance from the pivot.

The moment of the weight force of the table about the hinge is 92 N m.

By using the principle of moments, calculate the force S that a person applies to keep the table in equilibrium.

State Newton’s third law.

State the magnitude and the direction of the force that the table applies to the person holding the table.

Curling is a sport played on ice.

A player slides stone A across the ice towards a scoring zone.

The ice reduces friction so that there is negligible friction when the stone is sliding.

Stone A leaves the player’s hand with a velocity of 2.90 m/s.

The mass of stone A is 17 kg.

State the formula linking momentum, mass and velocity.

Show that the momentum of stone A is approximately 50 kg m/s.

Stone A slides towards the scoring zone.

In the scoring zone, stone A collides with a stationary stone, B.

After the collision, both stones move in the same direction as the initial direction of stone A.

The velocity of stone A after the collision is 0.40 m/s.

Calculate the velocity of stone B after the collision.

[mass of stone B = 19 kg]

When the stones collided, they were in contact for a time of 25 ms.

Calculate the magnitude of the force stone A exerted on stone B in this collision.

A metalworker uses a hammer of mass 1.8 kg to deform a piece of metal on an anvil.

Calculate the increase in the hammer’s gravitational potential energy (GPE) store when the hammer is raised through a height of 0.95 m above the metal.

[GPE gained = mass × gravitational field strength × height]

The metalworker moves the hammer down to strike the metal.

The hammer must have at least 21 J of energy in its kinetic energy (KE) store as it hits the metal to deform it.

Explain why the metalworker must do at least 4 J of mechanical work on the hammer to deform the metal.

Calculate the velocity of the hammer just before it strikes the metal.

[KE of hammer = 21 J]

When the hammer hits the metal, the hammer comes to rest without rebounding.

Calculate the mean (average) force needed to bring the hammer to rest in a time of 0.12 s.

Diagram 1 shows a van accelerating along a horizontal road.

The horizontal forces acting on the van are shown.

Force X opposes the motion of the van.

State the name of force X.

The resultant force acting on the van is 1500 N.

Calculate the magnitude of force X.

[assume X is the only horizontal force opposing the motion of the van]

Diagram 2 shows the resultant force acting on the van when it brakes.

State the formula linking resultant force, mass and acceleration.

The mass of the van is 1900 kg.

Calculate the acceleration of the van when it brakes.

Give the unit.

The van was travelling at an initial speed of 18 m/s before braking and coming to rest.

Calculate the distance travelled by the van while it is braking.

[assume that the acceleration remains constant]

Describe two factors that would increase the braking distance.

When the van is fully loaded its mass increases to 2500 kg.

Calculate the time taken to bring the fully loaded van to rest when it is travelling at an initial speed of 18 m/s.

[assume that the resultant force during braking remains at 14 kN]

This is a question about alpha particles.

Describe the nature of an alpha particle.

The diagram shows the path of an alpha particle as it passes close to a nucleus.

Draw an arrow from point X to show the force on the alpha particle due to the nucleus.

Label this force Y.

Draw an arrow to show the force on the nucleus due to the alpha particle.

Label this force Z.

Explain how the path of the alpha particle shows whether the nucleus is positive, negative or neutral.

The alpha particle experiences a resultant force of 3.6 N and has a mass of 6.610^–27kg.

Calculate the acceleration of the alpha particle.

A game is played on a table with balls of different colours.

The diagram shows the white ball moving across a flat surface.

State the formula linking momentum, mass and velocity.

The white ball has a mass of 170 g.

Calculate the momentum of the white ball.

momentum =_........ kgm/s

The white ball collides with a stationary black ball.

white ball
black ball
white ball
black ball

before collision
after collision

The black ball has a mass of 160 g.

After the collision, the black ball moves away from the white ball with a velocity of 5.0 m/s.

Calculate the velocity of the white ball after the collision.

During the collision, the white ball exerts a force of 80 N on the black ball.

The direction of this force is to the right.

State the magnitude and direction of the force the black ball exerts on the white ball during the collision.