A small block on a frictionless horizontal surface has a mass of 0.0300 kg . It

Question

A small block on a frictionless horizontal surface has a mass of 0.0300 kg . It is attached to a massless cord passing through a hole in the surface. (See the figure below (Figure 1) .) The block is originally revolving at a distance of 0.285 m from the hole with an angular speed of 1.65 rad/s . The cord is then pulled from below, shortening the radius of the circle in which the block revolves to 0.100 m . You may treat the block as a particle.

a.) Find the change in kinetic energy of the block in Joules

b.) How much work was done in pulling the cord in Joules?

Explanation / Answer

angular momentum about the center is conserved

=> I1W1 = I2W2

m*(0.285)^2*1.65 = m*(0.100)^2*W2

=> W2 = 13.40 rad/s

change in kinetic energy = KEi - KE

= (1/2*0.0300*(0.100))^2*(13.40)^2) - 1/2*0.0300*(0.285)^2*(1.65)^2 = 0.0029 J

b)  work done in pulling the cord = change in kinetic energy  = 0.0029 J

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