A car weighing 1400 kg is travelling up a hill at a speed of 54 km/h when its motor stops. If it is just able to reach the destination which is at a height of 10 m above the point, determine the work done against friction (the negative of the work done by friction). Assume g = 9.8 m/s ^2 .

Step-by-step solution

Mass of the car, m = 1400 kg Initial velocity, u = 54 km/h = 54 5 18 m/s = 15 m/s Final velocity, v = 0 Height, h = 10 m Initial kinetic energy, K_i = 1 2 m u^2 = 1 2 1400 (15)^2 = 157500 J Change in potential energy, U = mgh = 1400 9.8 10 = 137200 J By conservation of energy, the initial kinetic energy is used to increase the potential energy and do work against friction: K_i = U + W_ against friction 157500 = 137200 + W_ against friction W_ against friction = 157500 - 137200 = 20300 J