9702/May Jun/12/2015/Q14

A ladder is positioned on icy (frictionless) ground and is leant against a rough wall. At the instant
of release it begins to slide.
Which diagram correctly shows the directions of the forces P, W and R acting on the ladder as it
slides?

Solution:

Answer: B.

W is the weight and always acts downwards.

R is the normal reaction to the weight and acts upwards (since ground is frictionless).

For this question, you need to imagine this as a real case – how the ladder would move when it slides.

Before the ladder begins to slide, there is a horizontal force acting to the right at the point of contact of the ladder with the rough wall since the ladder itself exerts a force to the left on the wall due to its mass.

(Diagram A corresponds to this [case where no friction acts and the ladder is not sliding] – The angle of the weight with the ladder is not zero, so there is a component of the weight acting against wall. From Newton’s 3^rd law, there is a reaction from the wall – this is P before the ladder begins to slide).

As the ladder begins to slide, the point of contact of the ladder with the rough wall tends to move downwards. Since the wall is rough friction would act upwards, opposing the motion. So, at the point of contact, there is now a force to the right, along with a force acting upwards, the resultant of which is shown by P in diagram B.

The ground is frictionless, so there is no additional force opposing the motion.

Reference: PYQ - May/Jun 2015 Paper 12 Q14