A rigid cross-shaped structure having four arms PO, SO, QO and RO, each 1.00 m long, is pivoted at O. Forces act on the ends of the arms and on the midpoints of the arms as shown.

Question 44

A rigid cross-shaped structure having four arms PO, SO, QO and RO, each 1.00 m long, is pivoted at O. Forces act on the ends of the arms and on the midpoints of the arms as shown.

What is the magnitude of the resultant moment on the structure about O?

A 45 N m                     B 90 N m                     C 120 N m                  D 190 N m

Reference: Past Exam Paper – November 2016 Paper 12 Q17

Solution:

Answer: C.

In this question, we need to carefully identify the forces that cause a clockwise moment and those that cause an anticlockwise moment.

Consider RS.

Consider the two 70 N forces. Both of them cause anticlockwise moments. They are each 1.00 m from the pivot.

As for the two 20 N forces, the one on arm OS cause a clockwise moment while that one arm RO cause an anticlockwise moment. But since they are at equal distances from the pivot, they cancel out each other. Thus, they can be neglected.

The 30 N force on arm OS is at 0.50 m from the pivot and also causes an anticlockwise moment.

Consider PQ.

The two 50 N forces cause clockwise moments. They are at 0.50 m from the pivot.

The 30 N force on arm PO is at 0.50 m from the pivot and causes an anticlockwise moment.

Sum of clockwise moments = (50 × 0.5) + (50 × 0.5) = 50 Nm

Sum of anticlockwise moments = (70 × 1) + (70 × 1) + (30 × 0.5) + (30 × 0.5)

Sum of anticlockwise moments = 170 Nm

Resultant moment = 170 – 50 = 120 Nm