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

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.

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Dâu 4 years 2021-08-02T08:36:08+00:00 1 Answers 150 views 0

Answers ( )

  1. huyenthanh
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    2021-08-02T08:37:37+00:00
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    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

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