Blocks of mass m1 and m2 are connected by a massless string that passes over the
ID: 1293793 • Letter: B
Question
Blocks of mass m1 and m2 are connected by a massless string that passes over the pulley in the figure (Figure 1) . The pulley turns on frictionless bearings, and mass m1 slides on a horizontal, frictionless surface. Mass m2 is released while the blocks are at rest.
Suppose the pulley has mass mp and radius R. Find the acceleration of m1. Verify that your answers agree with part A if you set mp=0.
Find the tension in the upper portion of the string. Verify that your answers agree with part B if you set mp=0.
Explanation / Answer
Force on m2
m2g - T = m2a
T = m1 a
m2g - m1a = m2a
a = m2g/(m1 + m2)
Tupper = m1a = 2m1m2g/(2m1 + 2m2 + mp)
When we put mp = 0 then Tupper = m1m2g/(m1 + m2)
Tlower = m2g - m2a = m2g - 2m2*m2g/(2m1 + 2m2 + mp) = m2g(2m1 + 2m2 + mp - 2m2)/(2m1 + 2m2 + mp) = (2m1m2g + mp m2 g)/(2m1 + 2m2 + mp)
if we put mp =0 it will be same Tlower = m1m2g/(m1 + m2)