9709/Oct Nov/43/2011/Q4

ABC is a vertical cross-section of a surface. The part of the surface containing AB is smooth and A is 4m higher than B. The part of the surface containing BC is horizontal and the distance BC is 5m (see diagram). A particle of mass 0.8 kg is released from rest at A and slides along ABC. Find the speed of the particle at C in each of the following cases.

(i) The horizontal part of the surface is smooth.

(ii) The coefficient of friction between the particle and the horizontal part of the surface is 0.3.

Solution:

(i) 

mgh = 0.8 ×  10 × 4   = 32

For using ½ mv^2 = PE

[½ 0.8v^2 = 32]

Speed at C, v = 8.94 ms^–1

(ii) 

R = mg

= 0.8 x 10

8 N

Friction force, 

F = μ mg

   = 0.3 (8)

   = 2.4 N

Force from B to C = 2.4N (opposite direction of friction force)

Work done from B to C 

= 2.4 x 5

= 12 J

Conservation of Energy

½ mv^2 + 12 = PE

½ mv^2 = 32 - 12

Speed at C, v = 7.07 ms^-1

Reference: PYQ - Oct/Nov 2011 Paper 43 Q4

9709/Oct Nov/2002/4/Q4

Two particles A and B are projected vertically upwards from horizontal ground at the same instant.

The speeds of projection of A and B are 5ms^-1 and 8ms^-1 respectively. Find

(i) the difference in the heights of A and B when A is at its maximum height,

(ii) the height of A above the ground when B is 0.9m above A.

Solution:

Reference: PYQ - Oct/Nov 2002 Paper 4 Q4