Consider two objects with m 1 > m 2 connected by a light string that passes over
ID: 1634028 • Letter: C
Question
Consider two objects with m1 > m2 connected by a light string that passes over a pulley having a moment of inertia of Iabout its axis of rotation as in the figure below. The string does not slip on the pulley or stretch. The pulley turns without friction. The two objects are released from rest separated by a vertical distance 2h. (Use any variable or symbol stated above along with the following as necessary: g and R.)
(a) Use the principle of conservation of energy to find the translational speeds of the masses as they pass each other.
(b) Find the angular speed of the pulley at this time.
Explanation / Answer
Applying energy conservation,
PEi + PEf = PEf + KEf
m1 g h - m2 g h + 0 = 0 + m1 v^2 /2 + m2 v^2 /2 + I w^2 / 2
m1 v^2 + m2 v^2 + I (v/R)^2 = 2 g h (m1 - m2)
v^2 ( m1 + m2 + I/R^2) = 2 g h (m1 - m2)
v = sqrt[ (2 g (m1 - m2)) / (m1 + m2 + I/R^2)] .....Ans
(B) w = v / R
w = sqrt[ (2 g (m1 - m2)) / (m1 R^2 + m2 R^2 + I)]