A 1400 kg car drives up a 16 m high hill. The car's speeds at the bottom and top are 21 m/s and 13 m/s, respectively. If the car's engine does 80 kJ of work then what is the work done by friction?

mass, m = 1400 kg

height, h = 16 m

initial velocity, u = 21 m/s

final velocity, v = 13 m/s

Work done by engine, We = 80 kJ

Let the work done by the friction force is Wf.

Use the work energy theorem

net work done = change in kinetic energy

work done by engine + work done by friction force + work done by the gravitational force = Change in kinetic energy

80000 + Wf - m x g x h = 0.5 m (v² - u²)

80000 + Wf - 1400 x 9.8 x 16 = 0.5 x 1400 x (169 - 441)

- 139520 + Wf = - 190400

Wf = 50880 J