9709/May June/2011/42/Q6

A small smooth ring R, of mass 0.6 kg, is threaded on a light inextensible string of length 100 cm. One end of the string is attached to a fixed point A. A small bead B of mass 0.4 kg is attached to the other end of the string, and is threaded on a fixed rough horizontal rod which passes through A. The system is in equilibrium with B at a distance of 80 cm from A (see diagram).

(i) Find the tension in the string. 

(ii) Find the frictional and normal components of the contact force acting on B. 

(iii) Given that the equilibrium is limiting, find the coefficient of friction between the bead and the rod.

Solution:

Reference: PYQ - May/Jun 2011 Paper 42 Q6

9709/May June/2011/42/Q3

The velocity-time graph shown models the motion of a parachutist falling vertically. There are four
stages in the motion:
• falling freely with the parachute closed,
• decelerating at a constant rate with the parachute open,
• falling with constant speed with the parachute open,
• coming to rest instantaneously on hitting the ground.

(i) Show that the total distance fallen is 1048m.
The weight of the parachutist is 850N.
(ii) Find the upward force on the parachutist due to the parachute, during the second stage.

Solution:

Reference: PYQ - May/Jun 2011 Paper 42 Q3

9709/May June/2011/42/Q2

An object of mass 8 kg slides down a line of greatest slope of an inclined plane. Its initial speed at the top of the plane is 3ms−1 and its speed at the bottom of the plane is 8ms−1. The work done against the resistance to motion of the object is 120 J. Find the height of the top of the plane above the level of the bottom.

Solution:

Reference: PYQ - May/Jun 2011 Paper 42 Q2