OpenResponse Homework Problem 272 Imagine that you have a so

Open-Response Homework Problem 27.2 Imagine that you have a solid cylinder (M = 2 kg, R = 0.1 m, I = 1/2MR^2 ) and have wound a very light wire around it many times. The cylinder can turn freely about its axis, which is held in place horizontally (imagine, basically, a toilet paper roll!) You then attach a block of mass m = 1 kg to the end of the wire, and allow the block to fall (starting from rest), unwinding the string, which causes the cylinder to rotate. What is the block’s speed just as it reaches the ground, 2 m below from where it started?

Solution

change in potential energy of block = change in KE of block + change in KE of cylinder

mgh = 1/2*mV^2 + 1/2*IW^2 ( W = v/R

=> 1*9.8*2 = 1/2*1*V^2 + 1/2*2/2*V^2

=> V = 4.42 m/s