A ball is attached to one end of a wire, the other end being fastened to the cei

Question

A ball is attached to one end of a wire, the other end being fastened to the ceiling. The wire is held horizontal, and the ball is released from rest (see the drawing). It swings downward and strikes a block initially at rest on a horizontal frictionless surface. Air resistance is negligible, and the collision is elastic. The masses of the ball and block are, respectively, 1.6 kg and 2.39 kg, and the length of the wire is 1.27 m. Find the velocity (magnitude and direction) of the ball (a) just before the collision, and (b) just after the collision.

(a) v =
(b) v =

Explanation / Answer

(a)

speed of ball immediately before collision is found by conservation of energy

initial PE of ball = final KE of ball

m* g *h = (1/2) *m* v1^2

v1 = sqroot(2*g*h)

= sqroot(2*9.8*1.27)

= 4.98 m/s

(b)

Since we have an elastic head-on collision, we know that

the relative velocity of approach = relative velocity of separation, or

4.98 m/s = v - u

v = 4.98 + u

where v, u are the post-collision velocities of the block, ball respectively

Conserve momentum

initial p = final p

1.6 * 4.98 = 1.6kg * u + 2.39kg * v

substitute for v from above

7.968 = 1.6u + 2.39(4.98 + u)

= 11.90 + 3.99u

- 3.93 = 3.99u

u = -0.98 m/s

it is equal to u = -1.0 m/s

v = 4.98 + u

= 4.1 - 1.0

= 3.98 m/s

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