17. Exercises

Calculate the kinetic energy of a car, of mass 1200 kg, travelling at 30 \displaystyle \text{m}{{\text{s}}^{-1}}.

Calculate the kinetic energy of a ball, which has mass 250 grams, and which is travelling at 9 \displaystyle \text{m}{{\text{s}}^{-1}}.

A ball, of mass 0.125 kg, is thrown so that its initial speed is 12 \displaystyle \text{m}{{\text{s}}^{-1}}. As the ball moves upwards its speed decreases to 4 \displaystyle \text{m}{{\text{s}}^{-1}} when it is at its maximum height.

a) Calculate the initial kinetic energy of the ball.

b) Calculate the minimum kinetic energy of the ball.

c) Calculate the potential energy of the ball at its maximum height.

A brick, of mass 2 kg, is allowed to fall from rest at a height of 3.2 m. Find the kinetic energy and speed of the brick when it hits the ground;

a) assuming that no resistance forces act on the brick as it falls,

b) assuming that a constant resistance force of magnitude 10 N acts on the brick.

A rock, which has mass 3 kg, is thrown from a bridge over a river at speed of 3 \displaystyle \text{m}{{\text{s}}^{-1}}. When it hits the water, it is moving at a speed of 15 \displaystyle \text{m}{{\text{s}}^{-1}}.

a) Find the kinetic energy gained as the rock falls.

b) Find the potential energy lost as the rock falls.

c) Find the height of the bridge above the river.

A particle of mass 5 kg is attached to the end of a rope of length 8 metres. The other end of the rope is fixed. The particle is released from rest with the rope at an angle of 30\displaystyle {}^\circ to the vertical as shown in the diagram.

a) Calculate the initial potential energy of the particle.

b) Find the speed of the particle when the string is vertical.

c) As the particle swings it looses some energy due to air resistance. Because of this the string makes an angle of 28\displaystyle {}^\circ with the vertical when the string is on the opposite side to the starting position. Calculate how much energy was lost during the first swing.

A simple pendulum consists of a particle of mass 0.05 kg and a light string of length 0.8 m. When the string is vertical, the particle is moving at a speed of 1.2 \displaystyle \text{m}{{\text{s}}^{-1}}.

a) Calculate the initial kinetic energy of the particle.

b) Find maximum angle between the string and the vertical.

A ball football is kicked so that it leaves the ground travelling at 18 \displaystyle \text{m}{{\text{s}}^{-1}}. As it moves its speed drops to a minimum of 12 \displaystyle \text{m}{{\text{s}}^{-1}}.

a) Find the maximum height of the ball.

b) Explain why you did not need to know the mass of the ball.

A child of mass 40 kg, slides from rest down a water slide. The difference in height between the start and end of the water slide is 12 m.

a) Assume that there is no resistance to the motion on the slide and calculate the speed of the child at the bottom of the slide.

b) If the speed of the child at the bottom of the slide is 8 \displaystyle \text{m}{{\text{s}}^{-1}}, calculate how much energy has been lost as the child moved down the slide.