A rod PQ is attached at P to a vertical wall, as shown in Fig. 3.1. The length of the rod is 1.60 m. The weight W of the rod acts 0.64 m from P.

Question 42

A rod PQ is attached at P to a vertical wall, as shown in Fig. 3.1.

The length of the rod is 1.60 m. The weight W of the rod acts 0.64 m from P. The rod is kept horizontal and in equilibrium by a wire attached to Q and to the wall at R. The wire provides a force F on the rod of 44 N at 30° to the horizontal.

(a) Determine

(i) the vertical component of F,          [1]

(ii) the horizontal component of F.     [1]

(b) By taking moments about P, determine the weight W of the rod.           [2]

(c) Explain why the wall must exert a force on the rod at P.             [1]

(d) On Fig. 3.1, draw an arrow to represent the force acting on the rod at P. Label your arrow with the letter S.             [1]

Reference: Past Exam Paper – June 2015 Paper 22 Q3

Solution:

(a)

(i) Vertical component = 44 sin 30° = 22 N

(ii) Horizontal component = 44 cos 30° = 38(.1) N

(b)

{The vertical component of F acts at a distance of (0.64 + 0.96 =) 1.60m from the pivot.

Clockwise moment = Anti-clockwise moment}

W × 0.64 = 22 × 1.60

W = 55 N

(c) F has a horizontal component (not balanced by W)

{The horizontal component of F acts on the wall and this is not balanced by W. From Newton’s 3^rd law, there should be an equal and opposite force exerted by the wall on the rod.}

OR F has 38 N acting horizontally

OR 38 N acts on wall

OR vertical component of F does not balance W

OR F and W do not make a closed triangle of forces

(d) Line from P in the direction towards the point on wire vertically above W and direction up

{This force, along with F and W should form a system that is in equilibrium. For equilibrium, the resultant force and the resultant moment should be zero. If all the 3 forces pass through the same point, the resultant moment would be zero.

Moment = Force × perpendicular distance from line of action of force to pivot.

In this case, the pivot is that point where all the 3 forces pass. As they pass on the point, the ‘distance …’ is zero, and thus, the moment at that point is zero.}