A small block on a frictionless, horizontal surface has a mass of 0.0245 kg. It

Question

A small block on a frictionless, horizontal surface has a mass of 0.0245 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 0.280 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 0.140 m. Model the block as a particle.

(a) Is angular momentum of the block conserved?

Yes or No     

Why or why not?

(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

here,

mass of the block , m = 0.0245 kg

initial radius , r0 = 0.28 m

initial angular speed , w0 = 1.8 rad/s

final radius , r = 0.14 m

(a)

as there is no torque acting on the block
the angular mometum is conserved

(b)

let the new angular speed be w

use conservation of angular monetntum

m * r0^2 * w0 = m * r^2 * w

0.28^2 * 1.8 = 0.14^2 *w

w = 7.2 rad/s

the angular speed is 7.2 rad/s

(c)

change in kinetic energy of the block , KE = 0.5 * m* (v^2 - v0^2)

KE = 0.5 * 0.0245 * (( 0.14 * 7.2)^2 - (0.28 * 1.8)^2 )

KE = 9.34 * 10^-3 J

the change in kinetic energy is 9.34 * 10^-3 J

(d)

work done = change in kinetic energy of block

the change in kinetic energy of the block is 9.34 * 10^-3 J

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