A small block with mass 0.250 kg is attached to a string passing through a hole in a frictionless, horizontal surface (see Fig). 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? Figure:

Solution 96P Step 1: Given data: Mass of block m = 0.250 kg Radius of circle r = 0.800 m Tangential speed v = 4.00 m/s The breaking strength of the string T = 30.0 N Step 2: Tension T of the string is radial so that it gives no torque on the block.angular momentum is therefore conserved 2 2 T = m(v /r) = m/r(L/mr) 2 3 T = L /mr L = mvr = 0.250 kg × 4.00 m/s × 0.800 m) = 0.800