Newton's laws of motion

Which row of the table shows the correct units of weight and of mass?

State the name of a piece of equipment that can be used to measure mass.

Figure 13 shows the two forces acting on a beach ball as it falls through the air.

The resultant of these two forces is 0.92 N downwards.

The mass of the beach ball is 0.25 kg.

Calculate the acceleration of the beach ball as it falls.

Use the equation

acceleration =_........ m / s²

Calculate the size of the air resistance force on the beach ball.

Some students are investigating forces.

They use a newton meter to keep a trolley stationary on a sloping runway, as shown in Figure 14.

They measure the force needed to keep the trolley stationary on the sloping runway.

They do this at four different places on the runway.

When the height, h, of the runway is 0.60 m, their four readings for force are

2.1 N 2.7 N 2.5 N 2.2 N

Calculate the mean value of these forces.

The students then measure values of the force, F, for several different values of h, the height of the runway.

Figure 15 is a graph of F against h.

Use the graph in Figure 15 to determine the value of F when h = 0.80 m.

Determine the gradient of the graph in Figure 15.

gradient =_........ N / m

Figure 2 shows the two forces acting on a beach ball as it falls through the air.

The resultant of these two forces is 0.92 N downwards.

The mass of the beach ball is 0.25 kg.

Calculate the acceleration of the beach ball as it falls.

Use the equation

F = m × a

acceleration =_........ m / s²

Calculate the size of the air resistance force on the beach ball.

Some students are investigating forces.

They use a newton meter to keep a trolley stationary on a sloping runway, as shown in Figure 3.

They measure the force needed to keep the trolley stationary on the sloping runway.

They do this at four different places on the runway.

When the height, h, of the runway is 0.60 m, their four readings for force are

2.1 N 2.7 N 2.5 N 2.2 N

Calculate the mean value of these forces.

The students then measure values of the force, F, for several different values of h, the height of the runway.

Figure 4 is a graph of F against h.

Use the graph in Figure 4 to determine the value of F when h = 0.80 m.

Determine the gradient of the graph in Figure 4.

gradient =_........ N / m

Figure 14 shows a footballer and a ball.

The ball is stationary before it is kicked.

The mass of the ball is 0.43 kg.

The kick exerts a force of 2700 N on the ball.

The velocity of the ball just after it has been kicked is 36 m / s.

Calculate the momentum of the ball just after it has been kicked.

State the unit for momentum.

Calculate the amount of time that the footballer’s kicking foot is in contact with the ball.

Explain how Newton’s third law applies to the interaction between the kicking foot and the football.

Figure 15 shows a system consisting of two toy trolleys, S and T, on a straight, horizontal track.

T is not moving.

S is moving with a velocity of 0.36 m / s towards T.

S collides with T.

The trolleys stick together and move off together.

With reference to the momentum of the system, explain why the velocity of the trolleys after the collision is less than the velocity of S before the collision.

A car starts from rest and then travels for 70 s as shown on the graph in Figure 11.

Complete the sentence using data from Figure 11.

The car is travelling at constant velocity from_........ s

Use data from the graph in Figure 11 to show that the car travels a total distance of about 710 m in 70 s.

Calculate the average speed of the car for the total distance travelled.

The inertial mass of an object is a measure of how difficult it is to change the velocity of the object.

A force of 450 N acts on a car to give the car an acceleration of 0.35 m/s².

Calculate the inertial mass of the car.

inertial mass of car_........

Figure 12 shows a different velocity/time graph.

This straight line graph can be represented by the equation

Give the quantities that x and y represent in the equation.

Calculate the value of m from the graph in Figure 12.

State the value of c from the graph in Figure 12.

Figure 13 shows a ball being rotated in a horizontal circle.

Which arrow in Figure 13 shows the direction of the centripetal force on the ball?

The ball is moving at constant speed. Give one reason why the velocity of the ball is continuously changing.

Figure 14 shows a gymnast landing on a mat and coming to rest.

The gymnast has a mass of 53 kg.

The gymnast lands on the mat with a velocity of 4.0 m/s.

The average force exerted by the mat on the gymnast is 3500 N.

Calculate the time taken for the gymnast to come to rest.

Give your answer to an appropriate number of significant figures.

Use the equation

* (c) Figure 15 shows two trolleys, P and Q, moving at the same speed, v, directly towards each other.

The trolleys have the same mass.

When the trolleys collide, they stick together and stop.

Explain how momentum and energy are both conserved in this collision.

The graph in Figure 5 shows how the velocity of a car changes with time.

The car starts from rest and travels along a level, straight road for 50 s.

Which part of the graph shows when the car has constant velocity?

Which part of the graph shows when the car has the greatest acceleration?

Calculate the acceleration of the car in the first 10 s shown on the graph.

Use the equation

acceleration =_........ m / s

Calculate the distance the car travels in part QR shown on the velocity / time graph in Figure 5.

A different car has a mass of 1200 kg.

Calculate the force needed to give this car an acceleration of 2.4 m / s².

Use the equation

F = m × a

Which of these is a scalar quantity?

A student has some cupcake cases.

One cupcake case is shown in Figure 14.

The student drops a stack of cupcake cases with the base facing downwards, as shown in Figure 15.

(Source: © Elena Schweitzer/Shutterstock)

Figure 15

The speed of the falling stack of cupcake cases depends on the number of cupcake cases in the stack.

The student also has a stop clock and a metre rule.

Describe an investigation to show how the speed of the falling stack of cupcake cases depends on the number of cupcake cases in the stack.

A stack of cupcake cases has a mass of 0.005 kg.

Calculate the weight, in newtons, of the stack of cupcake cases.

Gravitational field strength = 10 N / kg

Use the equation

W = mg

Figure 16 shows a cupcake case that is falling at a constant velocity.

Draw an arrow on Figure 16 to show the force due to air resistance on the cupcake case.

State the value of the acceleration of the cupcake case when it is falling at a constant velocity

A car travels along a straight road.

The car accelerates at 3 m / s² for a time of 7 s.

Calculate the change in velocity of the car.

Use the equation

change in velocity = acceleration × time taken

Which of these is a scalar quantity?

A student has some cupcake cases.

One cupcake case is shown in Figure 2.

The student drops a stack of cupcake cases with the base facing downwards, as shown in Figure 3.

(Source: © Elena Schweitzer/Shutterstock)

Figure 3

The speed of the falling stack of cupcake cases depends on the number of cupcake cases in the stack.

The student also has a stop clock and a metre rule.

Describe an investigation to show how the speed of the falling stack of cupcake cases depends on the number of cupcake cases in the stack.

A stack of cupcake cases has a mass of 0.005 kg.

Calculate the weight, in newtons, of the stack of cupcake cases.

Gravitational field strength = 10 N / kg

Use the equation

W = mg

Figure 4 shows a cupcake case that is falling at a constant velocity.

Draw an arrow on Figure 4 to show the force due to air resistance on the cupcake case.

State the value of the acceleration of the cupcake case when it is falling at a constant velocity.

An atom of mass 6.6 × 10^–26kg is moving with a velocity of 480 m / s.

Calculate the momentum of the atom.

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

Figure 18 shows a ball before and after it collides with a wall.

The arrows show the direction of movement of the ball.

Before the collision, the momentum of the ball is 0.80 kg m / s.

After the collision, the momentum of the ball is 0.60 kg m / s in the opposite direction.

The ball is in contact with the wall for a time of 70 ms during the collision.

Calculate the force exerted on the ball by the wall.

Use an equation selected from the list of equations at the end of the paper.

*(c) Newton’s second law can be stated as

force = mass × acceleration

A student is provided with a trolley and a runway on a bench, as shown in Figure 19, and access to other equipment.

Describe a procedure the student could use to investigate how the acceleration of the trolley depends on the force applied to the trolley.

You may add to the diagram in Figure 19 to help your answer.

Which of these is a unit of momentum?

Students investigate conservation of momentum using two identical trolleys.

A card is then added to trolley A.

Some of the apparatus is set up as shown in Figure 8.

Describe an investigation the students could carry out to show that momentum is conserved when these two trolleys collide.

You may add to the diagram to help with your answer.

Give a reason for the runway being at a slope.

Figure 9 shows a racket and a tennis ball.

The tennis ball is travelling towards the racket at a velocity of 8.2 m/s.

The ball is hit back in the opposite direction at a velocity of 15 m/s.

The ball has a mass of 0.075 kg.

The ball is in contact with the racket for 12 ms.

Calculate the average force exerted by the ball on the racket.

Use the equation

Describe how Newton’s Third Law of Motion applies to the collision between the racket and the ball.

Figure 8 is a velocity/time graph showing a 34 s part of a train’s journey.

Calculate the acceleration of the train in the 34 s.

Give your answer to an appropriate number of significant figures.

acceleration =_........ ²

Calculate the distance the train travels in the 34 s.

Figure 9 shows a rocket soon after it takes off from the ground.

The force that the rocket engines produce remains constant during the first few seconds after take-off.

Explain what happens to the acceleration during the first few seconds.

Figure 10 shows a small steel ball held at a height, h, above the ground.

The ball is released and allowed to fall to the ground.

The height h is 1.4 m.

Calculate the time, t, for the ball to reach the ground.

Use the equation

Two students use the arrangement shown in Figure 10.

They use a stopwatch to time the ball falling through the height of 1.4 m.

The students repeat the measurement many times, but their average value for t is different from the calculated value.

Suggest a reason why the students’ value for t is different from the calculated value.

Suggest one improvement the students could make to their procedure so that their value for t is closer to the calculated value.

Figure 11a shows a box falling towards a hard floor.

The box hits the floor and crumples a little before it comes to rest as shown in Figure 11b.

The momentum of the box just before it hits the floor is 8.7 kg m/s.

The box comes to rest 0.35 s after it first hits the floor.

Calculate the magnitude of the force exerted by the floor on the box.

Use an equation selected from the list of equations at the end of this paper.

State the magnitude and direction of the force exerted by the box on the floor.

Figure 12 shows a ball held in a clamp at R, above the ground.

The ball is released from the clamp and falls.

S is 3.8 m below R.

At S the momentum of the ball is 0.40 kg m/s.

Calculate the mass of the ball.

Acceleration due to gravity, g, = 10 m / s²

mass of the ball_........

Which of these is the correct equation that relates force, mass and acceleration?

A cyclist has a mass of 70 kg.

Calculate the force needed to accelerate the cyclist at 2.0 m / s².

State the unit.

force =_........ unit =_........

Another cyclist travels 1200 m in a time of 80 s.

Calculate the average speed of the cyclist.

Use the equation

average speed =_........

A student wants to measure the average speed of a cyclist.

The student estimates that one of his own steps is 1 m.

He counts 100 steps between two posts on a track.

He uses a stopwatch to measure the time the cyclist takes to travel between the two posts.

Figure 2 shows the set‑up used to measure the average speed.

State two improvements the student could make to this method.

Figure 12 is a diagram showing a rocket that is sent into space to try and change the path of a small asteroid.

The rocket has a mass of 5.510⁵kg and is travelling to the right at 14 km / s.

Which of these is a correct calculation of the momentum of the rocket in kg m / s?

Use the equation

The asteroid has a momentum of 7.510¹⁰kg m / s and a mass of 8.0 × 10⁶kg.

Calculate the speed of the asteroid.

speed of the asteroid =_........

*(b) A student investigates the effect of a crumple zone on the force exerted during a collision.

The student has one trolley with a spring at the front and another trolley without a spring.

trolley spring trolley

The student uses the arrangement in Figure 13.

After a trolley is released, it accelerates down a slope and bounces off a rigid wall.

The speed of a trolley can be measured just before a collision with the wall and just after a collision with the wall.

The silver foils are connected to a millisecond timer.

The silver foils make contact with each other during the collision, so the time they are in contact can be read from the millisecond timer.

Explain how the student could investigate the effect of a crumple zone on the average force exerted during the collision.

Your explanation should include:

• how to determine the force (you may wish to refer to an equation from the list of equations at the end of this paper)

• how the effect of crumple zones may be shown in the investigation

• precautions that may be necessary to achieve accurate results.

Newton’s third law, when applied to the collision of the rocket and the asteroid as shown in Figure 12, can be stated as follows:

The force exerted by the rocket on the asteroid is equal and opposite to the force exerted by the asteroid on the rocket.

Explain how this statement links to the conservation of momentum in the collision.

The force that keeps an object moving in a circular path is known as the

Figure 11 shows an object moving in a circular path.

Draw an arrow on Figure 11 to show the direction of the force that keeps the object moving in a circular path.

The object in Figure 11 is moving at constant speed.

Explain why it is not moving with constant velocity.

Figure 12 shows a skier on a slope.

The skier travels down the slope with a constant acceleration.

The speed of the skier is measured at points P and Q.

The table in Figure 13 gives some data about the skier making one downhill run.

Calculate the distance from P to Q.

Use an equation selected from the list of equations at the end of this paper.

Calculate the time taken for the skier to travel from P to Q.

Which of these speeds would be normal for a person walking?

Figure 1 shows a block hanging from a spring balance.

Use a word from the box to complete the sentence below.

The quantity measured by the spring balance in Figure 1 is

A toy car has a mass of 0.10 kg. The toy car accelerates at 2.0 m/s².

Calculate the force producing this acceleration. State the unit.

Use the equation

F = m × a

Use words from the box to complete the sentences below.

Vectors have size and_........ .

Scalars have only_........ .

(a) A student investigates the relationship between force and acceleration for a trolley on a runway.

Figure 12 shows some of the apparatus the student uses.

Describe how the student could increase the accelerating force applied to the trolley.

Describe how the mass of the moving system can be kept constant.

Explain how the student could improve the procedure to compensate for the effects of frictional forces acting on the trolley.

*(b) Figure 13 shows two objects, Q and R, before and after they collide.

The arrows show the direction of movement of the objects. The arrows are not to scale.

Explain how momentum is conserved in the collision.

Use Newton’s third law and Newton’s second law in your answer.

Newton’s second law can be written as