A child on a sledge slides down a hill with acceleration a. The hill makes an angle θ with the horizontal.

Question 17

A child on a sledge slides down a hill with acceleration a. The hill makes an angle θ with the horizontal.

The total mass of the child and the sledge is m. The acceleration of free fall is g.

What is the friction force F ?

A m(g cosθ – a)

B m(g cosθ + a)

C m(g sinθ – a)

D m(g sinθ + a)

Reference: Past Exam Paper – June 2015 Paper 11 Q12

Solution:

Answer: C.

The resultant force is down along the slope.

Resultant force = ma

The weight may be resolved into 2 components: one along the slope and one perpendicular to the slope.

Component of weight along the slope = mg sinθ

Resultant force = Component of weight along slope – Friction force

ma = mg sinθ – F

F = mg sinθ – ma

F = m (g sinθ – a)