A car of mass 500 kg is at rest at point X on a slope, as shown. The car’s brakes are released and the car rolls down the slope

Question 12

A car of mass 500 kg is at rest at point X on a slope, as shown.

The car’s brakes are released and the car rolls down the slope with its engine switched off. At point Y the car has moved through a vertical height of 30 m and has a speed of 11 m s^-1.

What is the energy dissipated by frictional forces when the car moves from X to Y?

A 3.0 × 10⁴ J                        B 1.2 × 10⁵ J                        C 1.5 × 10⁵ J            D 1.8 × 10⁵ J

Reference: Past Exam Paper – November 2015 Paper 12 Q16 & June 2018 Paper 12 Q19

Solution:

Answer: B.

As the car rolls down the slope, its gravitational potential energy is being converted to kinetic energy AND work done against friction.

Loss in GPE = Gain in KE + Work down against friction

mgh = ½ mv² + Work down against friction

Work down against friction = mgh – ½ mv²

Work down against friction = (500×9.81×30) – (½ × 500 × 11²)

Work down against friction = 116 900 J = 1.2 × 10⁵ J