A small block on a frictionless, horizontal surface has a mass of 2.50×10 2 kg .

Question

A small block on a frictionless, horizontal surface has a mass of 2.50×102 kg . It is attached to a massless cord passing through a hole in the surface (Figure 1) . The block is originally revolving at a distance of 0.300 m from the hole with an angular speed of 2.89 rad/s . The cord is then pulled from below, shortening the radius of the circle in which the block revolves to 0.150 m. Model the block as a particle.

Part A

Is angular momentum of the block conserved?

Part B

What is the new angular speed?

Part C

Find the change in kinetic energy of the block.

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Part D

How much work was done in pulling the cord?

Express your answer with the appropriate units.

Explanation / Answer

a) angular momentum is always conserved wthout the influence of external force

b) I1 w1= I2w2

( 2.5 x 10^-2) (0.3)^2 (2.89) = ( 2.5 x 10^-2) (0.15)^2 w

w= 11.56 rad/sec

c)Change in KE = 1/2 I1w1^2 - 1/2 I2^2 w2^2 = 0.5 ( 0.225 x 10^-2 ) (2.89)^2 -0.5 ( 0.05625 x 10^-2) ( 11.56)^2 =0.028 J

d) Work = 0.028 J

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