5.2 Energy: GPE & KE

A BASE jumper of mass 70 kg jumps from the top of a bridge and reaches a speed of 45 m s⁻¹ after falling a distance of 150 m.

Calculate the change in the jumper's gravitational potential energy.

Calculate the kinetic energy gained by the jumper.

Explain why the values in (a) and (b) are not equal.

Calculate the average resistive force acting on the BASE jumper as they fall.

A cyclist of mass 80 kg riding a bicycle of mass 12 kg freewheels from rest 650 m down a hill.

The foot of the hill is 20 m lower than the cyclist's starting point and the cyclist reaches a top speed of 12 m s⁻¹ before they start to brake at the foot of the hill.

For this situation, calculate

For the cyclist and bicycle

Calculate the average resistive force acting on the cyclist during the descent.

The cyclist buys a set of tyres which claim to 'increase efficiency by 30% compared to your old tyres'.

The cyclist tests out the new tyres by riding down the same hill. With the new tyres, the cyclist achieves a top speed of 14 m s⁻¹ at the bottom of the hill.

Deduce whether the claim is correct or incorrect.

A pulley system is arranged so that a toy tractor of mass 400 g can be lifted by allowing an 800 g mass to fall from its initial position, as shown in Fig. 1.1.

Resistive forces in the pulleys are negligible.

Fig. 1.1

For the mass-tractor system

(i)

Calculate the initial potential energy  of the 800 g mass.

[2]

(ii)

Calculate the final potential energy  of the tractor.

[1]

(iii)

Write an expression for the final kinetic energy of the whole system.

[2]

The ramp exerts a frictional force of 2.0 N on the tyres of the toy tractor.  

Calculate the work done as the tractor is pulled up the slope.

Using the principle of conservation of energy, write an expression to describe the energy transfers in the system in terms of , , ,  and 

Use the expression from (c) to calculate the speed of the 800 g mass immediately before it hits the floor.

A car on a roller coaster has a mass of 4200 kg and is designed to carry up to 10 passengers each with an average mass of 65 kg.

The car is moving at a speed of 2.0 m s⁻¹ when it starts to descend through a drop of 50 m. It reaches a top speed of 24 m s⁻¹ after travelling 75 m along the track.

For the car with its maximum capacity of passengers, calculate

Calculate the kinetic energy of the car and passengers after the descent.

For the roller coaster car and passengers

Calculate the average resistive force that acts on the car during the descent.