At the instant r = 1.5 m , the 7-kg disk is given a speed of v = 5 m/s , perpend

Question

At the instant r = 1.5 m , the 7-kg disk is given a speed of v = 5 m/s , perpendicular to the elastic cord. The disk slides on the smooth horizontal plane. Neglect its size. The cord has an unstretched length of 0.5 m .
(Figure 1)

Part A

Determine the speed of the disk at the instant r = 1.2 m .

Express your answer to three significant figures and include the appropriate units.

Part B

Determine the rate of shortening of the elastic cord at the instant r = 1.2 m .

Express your answer to three significant figures and include the appropriate units.

Explanation / Answer

Given Data:

r1 = 1.5m;

m = 7 kg;

r2 = 1.2 m;

v1 = 5 m/s;

v2 = ?

Part A:

From conservation of angular momentum;

r1mv1 = r2mv2

r1v1 = r2v2

v2 = r1v1 / r2 = 1.5*5/1.2

v2 = 6.25 m/s

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