A small block on a frictionless, horizontal surface has a mass of 0.0280 kg. It

Question

A small block on a frictionless, horizontal surface has a mass of 0.0280 kg. It is attached to a massless cord passing through a hole in the surface (see figure below). The block is originally revolving at a distance of 0.400 m from the hole with an angular speed of 1.80 rad/s. The cord is then pulled from below, shortening the radius of the circle in which the block revolves to 0.200 m. Model the block as a particle.

(b) What is the new angular speed?
_____rad/s

(c) Find the change in kinetic energy of the block.
______L

(d) How much work was done in pulling the cord?
________J

Explanation / Answer

1. r1^2w1= r2^2w2 :

w2= r1^2w1/r2^2 :

w2= 5.4rad/s

2. change in kinetic energy = 1/2*m(V1^2-V2^2) = 1/2 * m( r1w1)^2 - 1/2*m(r2w2)^2 = m( 0.5184-1.1664) = 0.009072 = 0.01 J

3. work done by pulling the cord = change in kinetic energy = 0.01J

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