A boy on a bicycle starts from rest and rolls down a hill inclined at 30°to the horizontal.

Question 24

A boy on a bicycle starts from rest and rolls down a hill inclined at 30°to the horizontal.

The boy and bicycle have a combined mass of 25 kg.

There is a frictional force of 30 N, which is independent of the velocity of the bicycle.

What is the kinetic energy of the boy and the bicycle after rolling 20 m down the slope?

A 1850 J                      B 2450 J                      C 3050 J                     D 3640 J

Reference: Past Exam Paper – June 2016 Paper 12 Q17

Solution:

Answer: A.

As the boy rolls down the slope on his bicycle, the gravitational potential energy is converted into kinetic energy (due to motion) and work done against friction.

GPE at top - - - > KE at bottom + Work done against friction

The slope is inclined at 30° to the horizontal and the length of the inclined slope of 20 m.

Vertical height of boy at top of slope = 20 sin 30°

GPE at top = mgh = 25 × 9.81 × 20 sin 30°

Work done against friction = F × d = 30 × 20 = 600 J

GPE at top = KE + Work done against friction

25 × 9.81 × 20 sin 30° = KE + 600

 
KE = 1852.5 = 1850 J