A small block with mass of 0.0600 kg is attached to a cord passing through a hol
ID: 1596257 • Letter: A
Question
A small block with mass of 0.0600 kg is attached to a cord passing through a hole in a frictionless horizontal surface (see figure on the right). The block is originally revolving at a distance of 0.40 m from the hole with a speed of 0.70 m/s. The cord is then pulled from below, shortening the radius of the circle in which the block revolves to 0.10 m. At this distance, the speed of the block is 2.80 m/s. What is the tension in the cord in the original situation, when the block has speed v = 0.70 m/s? What is the tension in the cord in the final situation, when the block has speed v = 2.80 m/s? How much work was done by the person who pulled the cord?Explanation / Answer
a)
vi = 0.70 m/s
ri = 0.40 m
m = mass of block = 0.06 kg
Ti = tension in the string = centripetal force = m vi2/ri = 0.06 (0.70)2 /0.40 = 0.0735 N
b)
vf = 2.80 m/s
rf = 0.10 m
m = mass of block = 0.06 kg
Tf = tension in the string = centripetal force = m vf2/rf = 0.06 (2.80)2 /0.10 = 4.704 N
c)
work done = change in KE = (0.5) m (vf2 - vi2) = (0.5) (0.06) (2.802 - 0.702) = 0.2205 J