A small block with mass 0.330 Kg is attached to a string passing through a hole
ID: 1463373 • Letter: A
Question
A small block with mass 0.330 Kg is attached to a string passing through a hole in a frictionless, horizontal surface (Figure1.). The block is originally revolving in a circle with a radius of 0.800 m about the hole with a tangential speed of 4.00 m/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 30.0 N. What is the radius of the circle when the string breaks? Express your answer with the appropriate units.Explanation / Answer
apply net force = tension in the string = centripetal force
T = mv^2 /r
where m is mass and v is velocity
r is raidus
so
30 = 0.33 * V^2/r
V^2 = 30 * r/0.33
V = sqrt(91 r )
ANgular momentum will be conserved, L1 = L2
m v r1 = m v2r2
0.33 * 4 * 0.800 = 0.33 * v * r
v r = 3.2
r = 3.2/(sqrt 91 r)
r^2 = 3.2^2 /91.r
r^3 = 3.2^2/91
r = 0.482 m or 48.2 cm