Newton's laws of motion

An electric car of mass 1700 kg is tested to measure its maximum speed.

Fig. 16.1 shows a graph of velocity v against time t for the first 18 seconds of the test.

During this time the force produced by the motor is constant.

Fig. 16.1

Describe using Fig. 16.1, the method you would use to estimate the distance travelled in 18 s.

Use the graph in Fig. 16.1 to show that the acceleration of the car at time t = 12 s is about 1.5 m s^–2.

Use Fig. 16.1 to calculate the change of momentum of the car in 18 s.

=........ kg m s^–1

Fig. 16.2 shows a graph of resultant force against time during the test.

Fig. 16.2

Explain, in terms of the forces acting on the car, the shape of the graph in Fig. 16.2.

Explain why the value you have calculated in (a)(iii) is the area under the graph in Fig. 16.2.

The diagram below shows one of the wheels of the car that is driven by the electric motor.

Use Newton’s third law to explain how frictional forces cause the car to accelerate.

Calculate the resultant force acting on the car at t = 12 s, using your answer to (a)(ii).

A scientist uses a rocket to study the Earth’s atmosphere.

The scientist launches the rocket from rest at the point A at t = 0 seconds. The force produced by the rocket’s engine causes it to accelerate.

At t = 50 seconds, the rocket’s engine no longer produce an accelerating force as all of the fuel has been used. The rocket has reached point B. Its velocity is now 3.1 km s^–1 at an angle of 75° to the horizontal.

The rocket engine works by expelling hot gas backwards.

Explain, using Newton’s laws of motion, how the engine causes the rocket to accelerate between t = 0 and t = 50 s.

The length of an unloaded spring is approximately 4 cm.

The force constant k of the spring is 0.62 N cm^–1.

Describe how you could determine k using an appropriate experiment.

Calculate the magnitude of the block’s initial acceleration at the instant that the force F is removed.

Assume that the spring is not extended beyond its limit of proportionality.

acceleration =........ m s^–2

The block now moves with simple harmonic motion.

Calculate the frequency of this motion.

The block is replaced by a strong magnet L of slightly greater mass.

The oscillation frequency of this new arrangement is 2.5 Hz.

The magnet L is placed inside a coil X of insulated copper wire.

The coil X is connected with long wires to a second, identical coil Y.

A second strong magnet M is placed inside Y and attached to a vibration generator.

The vibration generator is then forced to oscillate with a frequency of approximately 2.5 Hz by

As magnet M oscillates, it moves in and out of coil Y.

........

The frequency of the vibration generator is now varied between 0.5 Hz and 5.0 Hz.

Suggest how the amplitude and frequency of the oscillations of L will change as the frequency of the generator is varied.

You may draw a diagram to support your answer.

The diagram shows a road where vehicles travel at high speeds.

Markings painted on the road surface are spaced 40 m apart.

Drivers are advised to keep at least two markings visible on the road between them and the vehicle in front.

The maximum speed vehicles travel at on the road is 110 km/hr. The table shows data from a driving manual for a vehicle travelling on a straight, horizontal road.

Calculate the maximum speed v of vehicles on the road in S.I. units.

A vehicle passes over one of the markings.

Calculate time taken to travel the 40 m distance between the two markings.

Using the table, explain why having markings 40 m apart helps prevent collisions.

A vehicle with mass 1600 kg is travelling at 110 km / hr. The driver sees an obstruction and applies the brakes to bring the vehicle to rest in 5.6 s.

Estimate the magnitude of the average resultant force F required to bring the vehicle to rest.

Explain the effect on the distance required to bring the vehicle to rest if the road has an upwards slope.

A sealed container contains n moles of an ideal gas. The gas has pressure p, absolute temperature T and occupies volume V.

The mass of one mole of the gas is M.

Use an ideal gas equation to show that the density of the gas is given by the expression

An airship has a cabin suspended underneath a gasbag inflated with helium.

The airship is floating above the ground and is stationary.

The volume of the gasbag is 12 000 m³. The temperature of the helium and the surrounding air is 20 °C. Atmospheric pressure is 1.0 × 10⁵ Pa. The molar mass of air is 0.029 kg mol^–1. The volume of the cabin is negligible compared to the volume of the gasbag.

Show that the density of air under the conditions described is about 1.2 kg m^–3. (i)

Calculate the weight of air displaced by the airship.

weight of air........ N

Explain why the weight of air displaced by the airship has the same magnitude as the weight of the airship and its contents.

The pressure of the helium in the gasbag is maintained at a value only slightly greater than atmospheric pressure. Suggest why a larger pressure is not used.

The airship engine drives a fan which moves 7.8 kg of air per second at a relative speed of 45 m s^–1, so the airship starts to move.

All other conditions given in (b) remain the same.

Calculate the thrust that the engine produces.

The airship has a higher maximum speed at high altitudes, but also produces less thrust from the engine.

Explain these observations.

The table shows some data on the planet Venus.

Calculate the magnitude of the gravitational field strength g at the surface of Venus.

Give your answer to 3 significant figures.

=........ N kg^–1 g

Two identical space probes, A and B, land on a flat surface on Venus.

Probe A lands at the north pole. Probe B lands on the equator.

Each probe has mass 760 kg and volume 1.7 m³.

Calculate the centripetal acceleration a of probe B at the equator due to the rotation of Venus about its axis.

=........ m s^–2 a

The atmosphere exerts the same upthrust on each probe.

Using your answer to (a), calculate the upthrust acting on each probe.

Explain which probe will experience the greater normal contact force from the surface of Venus.

A tennis ball is hit with a racket. The force applied by the racket on the ball is F. The ball has a vertical path through the air.

Which statement is correct when the ball is at its maximum height?

A The ball has a downward acceleration.

B The force acting on the ball is F.

C The ball experiences greatest drag.

D The weight of the ball is equal to the drag.

Your answer

A kiln used to harden ceramics is shown below.

The internal chamber is a cube. Each side of this cube has length 0.46 m. The chamber is sealed and full of argon. Argon behaves as an ideal gas.

The kiln is initially at 20 C. The argon in the kiln has an initial pressure of 100 kPa.

Calculate the amount of argon n in the chamber in moles.

The temperature of the kiln is increased from 20 C to 1300 C.

Calculate the pressure in kPa at 1300 C.

The temperature of the kiln is 1300 C. A single atom of argon is travelling horizontally towards the vertical side X of the chamber. The initial speed of this atom is 990 m s^–1. After collision, it rebounds at the same speed.

Calculate the change in momentum p of this atom.

• mass of argon atom = 6.6 × 10^–26 kg

=........ kg m s^–1 p

Assume that this atom does not collide with any other argon atoms inside the chamber. Instead, it travels horizontally, making repeated collisions with the opposite vertical walls of the chamber.

1 Show that the atom makes about 1000 collisions with side X in a time interval of 1.0 s.

2 Calculate the average force F on side X made by the atom.

Without calculation, explain how your answer to (ii)2 could be used to estimate the total pressure exerted by the atoms of the argon gas in the kiln.

A student uses a motion-sensor connected to a laptop to investigate the motion of a hollow ball of mass 1.2 × 10^–2 kg falling through air.

The ball is dropped from rest. It reaches terminal velocity before it reaches the ground.

The upthrust on the ball is negligible.

Fig. 17 shows the variation with time t of the velocity v of the ball as it falls towards the ground.

Draw a tangent to the curve at t = 0.25 s and determine the acceleration of the ball.

acceleration =........ m s^–2

Calculate the resultant force F acting on the ball at t = 0.25 s.

Use your answer in (b) to calculate the drag on the ball at time t = 0.25 s.

The student now adds a small amount of sand inside the hollow ball. As before, the ball is dropped from rest and it also reaches terminal velocity before it reaches the ground.

Describe how the forces acting on the sand-filled ball at v = 0.50 m s^–1 compare with the forces acting on the hollow ball at this speed.

Explain why the terminal velocity of the sand-filled ball will be greater than the terminal velocity of the hollow ball.

A bicycle manufacturer carries out tests on the braking system of their new model. A cyclist on this new bicycle travels at a constant initial speed U. The cyclist applies the brakes at time t = 0 and the bicycle comes to a stop at time t = 2.0 s.

Fig. 20.1 shows the variation of the braking force F on the bicycle with time t.

Use Newton’s second law of motion to explain the physical quantity represented by the area under the graph shown in Fig. 20.1.

The total mass of cyclist and bicycle is 71 kg.

Use Fig. 20.1 to calculate the initial speed U.

=........ m s^–1 U

Complete Fig. 20.2 to show the variation of the speed of the bicycle from t = 0 to t = 2.0 s.

A toy rocket is made from a 1.5 litre plastic bottle with fins attached for stability.

The bottle initially contains 0.30 litres of water, leaving 1.2 litres of trapped air at a temperature of 17 °C. A pump is used to increase the pressure of the air within the plastic bottle to 2.4 × 10⁵ Pa at the start of lift-off.

Fig. 1.1 shows the rocket at the start of lift-off.

1 litre = 10^–3 m³

Calculate, in moles, the amount of trapped air in the bottle at the start of lift-off.

The trapped air pushes the water downwards out of the hole, causing the rocket to rise. The temperature of this air remains constant.

Calculate the final pressure of the trapped air just before all the water has been released.

Use the data above to show that the upwards force on the rocket at the start of lift-off is about 15 N.

Hence calculate the initial vertical acceleration of the rocket.

initial acceleration =........ m s^–2

Discuss whether adding more water initially would enable the rocket to reach a greater height.

The diagram shows two opposite vertical forces of magnitude 1.2 N and 2.1 N acting on an object.

Which of the following statements could be correct?

1 The object is accelerating and moving up. 2 The object is decelerating and moving down. 3 The magnitude of the resultant force is 0.9 N.

A Only 3

B Only 1 and 3

C Only 2 and 3

D 1, 2 and 3

Your answer