A uniform diving-board is held by two fixed rods at points P and Q. A person stands at end R of the diving-board, as shown.

Question 32

A uniform diving-board is held by two fixed rods at points P and Q. A person stands at end R of the diving-board, as shown.

The forces exerted by the rods on the board are vertical. The board remains in equilibrium as the person slowly moves towards point Q from end R.

Which row describes the changes to the forces exerted by the rods on the board?

force at P                    force at Q

A         decreases                   decreases

B         decreases                   increases

C         increases                     decreases

D         increases                     increases

Reference: Past Exam Paper – June 2018 Paper 12 Q13

Solution:

Answer: A. 

For the board to remain in equilibrium, the resultant moment on it should be zero. That is, clockwise moment = anticlockwise moment.

The person’s weight acts downwards, causing a clockwise moment about the rods.

The rod at P exerts a downward force while the rod at Q exerts an upward force. Both of the forces causes a moment (in opposite direction) which balance the moment caused by the weight of the person.

We may take the pivot to be either at P or Q. When the pivot is taken to be at P, then the moment caused by the force at P is zero (as the perpendicular distance is zero). Similarly if the pivot is taken at Q, then the moment due to the force at Q is zero.

If the pivot is at P, the upward force at Q causes an anticlockwise moment. In the same way if the pivot is at Q, the downward force at P again causes an anticlockwise moment.

As the person moves towards the rods, the moment of the person’s weight at both P and Q decreases, and therefore the forces exerted by the rods at both P and Q must also decrease.