In the figure below, a hanging mass is attached to a massive pulley (not massles
ID: 1987518 • Letter: I
Question
In the figure below, a hanging mass is attached to a massive pulley (not massless) by a string which is wrapped around the pulley. Using energy conservation principles, please solve the below. (Tip: solve with variables.)
(a) If the radius of the pulley R = 12 cm, M = 350 g, and m = 70 g, find the speed of the block after it has descended 50 cm starting from rest.
m/s
(b) Repeat (a) with R = 5.0 cm.
m/s
Explanation / Answer
K + P = 0
1/2 I w^2 + 1/2 mv^2 - mgh = 0
0.5 [ 0.5 M R^2 ] w^2 + 0.5 m v^2 - mgh = 0
0.5 [ 0.5 M R^2 ] [ v/ r ]^2 + 0.5 m v^2 - mgh = 0
0.5 [ 0.5 M ] [ v ]^2 + 0.5 m v^2 - mgh = 0
0.5 [ 0.5 * 0.350 ] [ v ]^2 + 0.5 * 0.07 * v^2 - 0.07 * 9.8 * 0.5 = 0
v = 1.67332 m /s <---------ans
b.
0.5 [ 0.5 * 0.350 ] [ v ]^2 + 0.5 * 0.07 * v^2 - 0.07 * 9.8 * 0.5 = 0
v- 1.67332 m /s