9709/Oct Nov/2003/4/Q6

One end of a light inextensible string is attached to a fixed point A of a fixed vertical wire. The other end of the string is attached to a small ring B, of mass 0.2 kg, through which the wire passes.

A horizontal force of magnitude 5N is applied to the mid-point M of the string. The system is in equilibrium with the string taut, with B below A, and with angles ABM and BAM equal to 30◦ (see diagram).

(i) Show that the tension in BM is 5N.

(ii) The ring is on the point of sliding up the wire. Find the coefficient of friction between the ring and the wire.

(iii) A particle of mass m kg is attached to the ring. The ring is now on the point of sliding down the wire. Given that the coefficient of friction between the ring and the wire is unchanged, find the value of m.

Solution:

Reference: PYQ - Oct/Nov 2003 Paper 4 Q6

9709/Oct Nov/2003/4/Q5

Particles A and B, of masses 0.4 kg and 0.1 kg respectively, are attached to the ends of a light inextensible string. Particle A is held at rest on a horizontal table with the string passing over a smooth pulley at the edge of the table. Particle B hangs vertically below the pulley (see diagram). The system is released from rest. In the subsequent motion a constant frictional force of magnitude 0.6N acts on A. Find

(i) the tension in the string, 

(ii) the speed of B 1.5 s after it starts to move.

Solution:

 
Reference: PYQ - Oct/Nov 2003 Paper 4 Q5

Mechanics 1 Modelling with Friction Question 11

A chute at a water sports centre has been designed so that swimmers first slide down a steep part which is 10 m long and at an angle of 40° to the horizontal. They then come to a 20 m section with a gentler slope, 11° to the horizontal, where they travel at constant speed.

(i) Find the coefficient of friction between a swimmer and the chute.

(ii) Find the acceleration of a swimmer on the steep part.

(iii) Find the speed at the end of the chute of a swimmer who starts at rest.

(You may assume that no speed is lost at the point where the slope changes.)

An alternative design of chute has the same starting and finishing points but has a constant gradient.

(iv) With what speed do swimmers arrive at the end of this chute?

Solution:

Mechanics 1 Modelling with Friction Question 9

In each of the following situations a brick is about to slide down a rough inclined plane. Find the unknown quantity.
(i) The plane is inclined at 30° to the horizontal and the brick has mass 2 kg: find μ.
(ii) The brick has mass 4 kg and the coefficient of friction is 0.7: find the angle of the slope.
(iii) The plane is at 65° to the horizontal and the brick has mass 5 kg: find μ.
(iv) The brick has mass 6 kg and μ is 1.2: find the angle of slope.

Solution: