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Saturday, July 27, 2019

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)

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