A pulley consists of a uniform disk of mass 5 kg and radius 0.12 m. A cord wound
ID: 1780284 • Letter: A
Question
A pulley consists of a uniform disk of mass 5 kg and radius 0.12 m. A cord wound around the pulley (like the figure above) is pulled with force 45 N. The pulley is initially stationary; there is no frlction. Find (a) the torque, (b) the angular acceleration. At t = 4 s, flnd (c) the angular velocity [600 rad/s], (d) the angular momentum. Find also (e) the work done in one complete revolution, and (f) the angular velocity when the rotational kinetic energy is 50 J.
equation(s) for the unknown(s) te to determine if your answer is fr 0 33.0 cm e FIGURE 10-21 Example 10-9 nsExplanation / Answer
Given:
F = 45N
M = 5kg
R = 0.12m
So, Inertia I = 1/2* M * R^2 = 0.036 kg-m2
a) Torque T = F*R = 5.4 N-m
b) We know,
T = I*alpha, where alpha = angular acceleration. So,
alpha = T/I = 5.4/0.036 = 150 rad/s2
c) Angular velocity w = alpha * t = 150*4 = 600 rad/s
d) Angular momentum L = I*w = 21.6 kg-m2/s2
e) angular displacement th = 1rev = 2pi rad
So, work done W = T*th = 5.4* 2pi = 33.93 J
f) KErot = 1/2 * I * w2 = 50 J(given)
=> w = sqrt(2*50/I) = sqrt (100/0.036) = 52.7 rad/s
Hope this helps :)
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