A ladder rests in equilibrium on rough ground against a rough wall.

Question 27

A ladder rests in equilibrium on rough ground against a rough wall.

Its weight W acts through the centre of gravity G. Forces also act on the ladder at P and at Q.

These forces are P and Q respectively.

Which vector triangle represents the forces on the ladder?

Reference: Past Exam Paper – November 2011 Paper 11 Q13 & Paper 13 Q14

Solution:

Answer: A.

For equilibrium,

-          The resultant torque is zero.

-          The resultant force is zero.

For the resultant force to be zero, the forces should form a closed triangle, all the vectors having the same orientation (all clockwise or all anticlockwise). This eliminates B and C.

Now, consider the forces acting on the system.

The weight of the ladder acts vertically downward. [D is incorrect as the weight is NOT downward.]

Both the ground and the wall are rough. This means that the force of friction will be present on both the wall and the ground.

Recall that the contact force acts perpendicularly to a surface.

At P, there is a horizontal contact force to the left as well as the force of friction which is upwards (this opposes the direction of motion if the ladder was to move (motion would then be downwards)). The resultant of these 2 forces is in the direction of P as shown in choice A.

Similarly, at, Q, the contact force is vertically up while friction is horizontally to the right (opposing the direction of tendency of motion (which would be to the left when the ladder moves)). The resultant of these 2 forces is indicated by Q in choice A.