A small block on a frictionless, horizontal surface has a mass of 0.0290 kg. It
ID: 1517486 • Letter: A
Question
A small block on a frictionless, horizontal surface has a mass of 0.0290 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 0.310 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 0.155 m. Model the block as a particle. (a) Is angular momentum of the block conserved? Yes 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?
Explanation / Answer
a) Yes
b) Apply conservation of angular momentum
If*wf = Ii*wi
m*r2^2*wf = m*r1^2*wi
wf = (r1/r2)^2*wi
= (0.31/0.155)^2*1.8
= 7.2 rad/s
c) change in kinetic energy = KEf - KEi
= 0.5*If*wf^2 - 0.5*Ii*wi^2
= 0.5*(0.029*0.155^2)*7.2^2 - 0.5*(0.029*0.31^2)*1.8^2
= 0.0135 J
d) Workdone = change in kinetic energy
= 0.0135 J