A car weighing 1400 kg is moving at a speed of 54 km/h up a hill when the motor stops. If it is just able to reach the destination which is at a height of 10 m above the point, calculate the work done against friction (negative of the work done by the friction).
Mass of the car, m = 1400 kg
Height covered by the car, h = 10 m
Work done on the car by gravity = -mgh
= -1400×9.8×10
= -137200
(negative sign indicates that the displacement is opposite to the gravitational force)
Initially, speed of the car = 54 km/h = 15 m/s
Initial kinetic energy of the car at given speed = 1/2 × mass × (speed of the car)2
= 0.5 × 1400 × 15 × 15
= 157500 J
Final kinetic energy of the car (it eventually stops) = 0 m/s
Change in kinetic energy of the car = 0 – 157500 = - 157500 J
Also, this change in kinetic energy of the car = Work done by friction + work done by gravity
⇒ Work done by friction = Change in kinetic energy – work done by gravity
= -157500 – (-137200)
= -157500 + 137200
= -20300 J
⇒ Work done against friction = 20300 J