Question

In: Physics

You attach a 100-g puck to a string and let the puck glide in a circle...

You attach a 100-g puck to a string and let the puck glide in a circle on a horizontal, frictionless air table. The other end of the string passes through a hole at the center of the table. You pull down on the string so that the puck moves along a circular path of radius 0.50 m. It completes one revolution in 6.0 s.

If you pull harder on the string so the radius of the circle slowly decreases to 0.40 m, what is the new period of revolution?

Tf =

Solutions

Expert Solution

Mass of the puck = M = 100 g = 0.1 kg

Initial radius of the circle = R1 = 0.5 m

Initial moment of inertia of the system = I1

I1 = MR12

I1 = (0.1)(0.5)2

I1 = 2.5 x 10-2 kg.m2

Initial time period of one revolution = T1 = 6 sec

Initial angular velocity of the puck = 1

1 = 1.047 rad/s

New radius of the circle = R2 = 0.4 m

New moment of inertia of the system = I2

I2 = MR22

I2 = (0.1)(0.4)2

I2 = 1.6 x 10-2 kg.m2

New angular speed of the puck = 2

By conservation of angular momentum,

I11 = I22

(2.5x10-2)(1.047) = (1.6x10-2)2

2 = 1.636 rad/s

New time period of one revolution = T2

T2 = 3.84 sec

New period of revolution = 3.84 sec

genius_generous answered 1 year ago
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