Question

A 15-lb block B starts from rest and slides on the 25-lb wedge A, which is supported by a horizontal surface. Neglecting friction, determine (a) the velocity of B relative to A after it has slid 3 ft down the inclined surface of the wedge, (b) the corresponding velocity of A.

Answer 1

The angle of the wedge is 30°.

Answer:

5.88 ft/s

Explanation:

a) The block will slide down due to it's weight.

initial velocity u= 0

final velocity, v

acceleration, a = g sin 30° = 32 ft/s²× sin 30° = 16 ft/s²

Sliding displacement, s = 3ft

Use third equation of motion:

$v^2-u^2 = 2as$

substitute the values and solve for v

$v^2-0 = 2\times 16 \times 3 =96 ft^2/s^2\\v = 9.8 ft/s$

b) Use conservation of momentum:

Initial momentum of the system  = 0

final momentum = (15) ( 9.8)+ (25)(v')

v' = 5.88 ft/s