A small block with mass 0.300kg is attached to a string passing through a hole i
ID: 1386018 • Letter: A
Question
A small block with mass 0.300kg is attached to a string passing through a hole in a frictionless, horizontal surface (see the figure(Figure 1) ). The block is originally revolving in a circle with a radius of 0.750m about the hole with a tangential speed of 3.60m/s . The string is then pulled slowly from below, shortening the radius of the circle in which the block revolves. The breaking strength of the string is 28.0N .
https://session.masteringphysics.com/problemAsset/1260516/2/YF-10-92.jpg
What is the radius of the circle when the string breaks?
Explanation / Answer
Apply conservation of angular momentum
m*v1*r1 = m*v2*r2
==> v2 = v1*(r1/r2)
let r2 is the radius when string breaks.
T = m*v2^2/r2
T*r2 = m*(v1*(r1/r2))^2
T*r2^3 = m*v1^2*r1^2
r2 = (m*v1^2*r1^2/T)^(1/3)
= (0.3*3.6^2*0.75^2/28)^(1/3)
= 0.427 m <<<<<<<<<<------------------ANswer