The vertical forces that the ground exerts on a stationary van are shown. The van is 2.50 m long with the wheels at a distance of 0.600 m from the front of the van and 0.400 m from the rear of the van.

Question 8

The vertical forces that the ground exerts on a stationary van are shown.

The van is 2.50 m long with the wheels at a distance of 0.600 m from the front of the van and 0.400 m from the rear of the van.

What is the horizontal distance of the van’s centre of gravity from the front of the van?

A 0.540 m                   B 0.960 m                   C 1.14 m                     D 1.36 m

Reference: Past Exam Paper – March 2017 Paper 12 Q13

Solution:

Answer: C.

Consider the moments about the front wheel (acting as the pivot). The 16 000 N force does not cause any moment.

Let the centre of gravity W be at a distance of y from the front wheel.

Since the van is stationary, the resultant force on the van is zero.

(Downward) Weight W = sum of upward forces = 16 000 + 9 000 = 25 000 N

About front wheel,

Clockwise moment = W × y = 25 000 × y

Anti-clockwise moment = 9000 × 1.5

For equilibrium, sum of clockwise moment = sum of anticlockwise moment

25 000 × y = 9000 × 1.5

Distance y from front wheel = (9000 × 1.5) / 25 000 = 0.54 m

Distance from front of van = 0.6 + 0.54 = 1.14 m