Momentum (Cambridge O Level Physics)

Fig. 2.1 shows a train.

The total mass of the train and its passengers is 750 000 kg. The train is travelling at a speed of 84 m/s. The driver applies the brakes and the train takes 80 s to slow down to a speed of 42 m/s.

Calculate the impulse applied to the train as it slows down.

impulse = .........................................................

Calculate the average resultant force applied to the train as it slows down.

force = .........................................................

Suggest how the shape of the train helps it to travel at high speeds.

The train took 80 s to reduce its speed from 84 m/s to 42 m/s. Explain why, with the same braking force, the train takes more than 80 s to reduce its speed from 42 m/s to zero.

On a wet day, the train travels a greater distance before it stops along the same track. The train has the same speed of 84 m / s before the brakes are applied.

 
Suggest a reason for this.

Fig. 1 shows two railway trucks A and B travelling towards each other on the same railway line which is straight and horizontal.

Fig. 1 

The trucks are involved in a collision. They join when they collide and then move together.

Truck A has a total mass of 27 000 kg and truck B has a total mass of 22 000 kg.

Just before the collision, truck A was moving at a speed of 3.6 m s^–1 and truck B was moving at a speed of 2.4 m s^–1.

Calculate the speed of the joined trucks immediately after the collision.

During the collision each truck experiences an impulse acting on it.

The trucks come to a stop after 3.0 minutes.

Calculate the deceleration of the joined trucks.

Explain why the trucks stop moving.

A shell, of mass 30 g, is fired from the barrel of a rifle, of mass 1.9 kg, with a momentum 36 kg m/s.

State the total momentum of the rifle and the bullet before the rifle is fired and give a reason for your answer.

Calculate the velocity of the shell just after the rifle is fired.

Continue to calculate for the moment just after the rifle has been fired.

The shell has a momentum of 9.8 kg m/s just before it hits a target.

It takes 4.5 ms for the bullet to the stopped by the target.

Calculate the average force needed to stop the bullet.

Until the second half of the 20th century, cars were designed as strong rigid boxes, which designers thought would protect passengers in accidents. In fact, although average speeds were much slower than today, passengers were often very badly injured.

Modern cars are designed with safety features including 'crumple zones'. The crumple zones are at the front and rear of the car but do not include the passenger section. In a crash, the crumple zone is designed so that it deforms and bends. This is shown in Fig. 1.1.

The use of crumple zones explains why the front and rear of cars are badly damaged during accidents.

Another safety feature of modern cars is air bags. During a collision, air bags quickly inflate, filling the space between the driver and the steering wheel and windscreen. This is shown in Fig. 1.2.

Two cars are crash-tested to assess how much protection air bags provide in a road-traffic accident.

Car A does not have an air bag, whilst car B does.

Car A has a mass of 1200 kg and car B has a mass of 1500 kg.

Both cars have a driver of mass 70 kg and they both crash to a stop from an initial speed of 30 m/s.

At the moment of impact, the drivers are thrown forwards, taking different amounts of time to come to a stop. The driver of car A takes 0.3 seconds to stop, while the driver of car B takes 0.7 seconds to stop.

Using this information, calculate the forces which would be experienced by the drivers due to the impact.

The velocity of an object of mass m increases from u to v.

State, in terms of m, u and v, the change of momentum of the object.

In a game of tennis, a player hits a stationary ball with his racquet.

Complete Fig. 2.1 by writing in the right-hand column the name of the quantity given by the product in the left-hand column.

Fig. 2.2 shows a man hitting a ball with a golf club.

The ball has a mass of 0.046 kg. The golf club is in contact with the ball for 5.0 × 10^–4 s and the ball leaves the golf club at a speed of 65 m/s.

Define impulse.

The pellet has a mass of 1.1 × 10^–4 kg.

Determine: 

The pellet melts when it strikes the target.

Describe how the molecular structure of the liquid metal differs from that of the solid metal.

State the equation for impulse in terms of the velocity of an object. Define the variables used.

In a game of croquet, a player hits a ball which was initially at rest with a mallet.

The mallet has mass of 1.36 kg.

Calculate the velocity of the mallet at the moment it hit the ball.