A small block on a frictionless, horizontal surface has a mass of 0.0245 kg. It
ID: 1359609 • Letter: A
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