10. A cylindrical pulley (M= 3.0 kg, r =.50 m) is free to rotate around its cent
ID: 1370356 • Letter: 1
Question
10. A cylindrical pulley (M= 3.0 kg, r =.50 m) is free to rotate around its central axis. A load of mass m = 6.0 kg is attached to a light cable the other end of which is wrapped around the pulley as shown below. If the load starts descending from rest: a. Draw the force diagrams for the pulley and the load. b. Write the equations for motion for both the pulley and the load. c. Find the acceleration of the load. d. What is the angular acceleration of the pulley? e. What is the speed of the load as it traveled a distance 8.0 m? f. Find the travel time of the load. g. What is the angular speed of the pulley at that instant?Explanation / Answer
a) on pulley there is force T - tension due to string along striing downwards
Mg - weight force donwards at centre of pulley
ON mass. T - tension upwards along string
mg - weight force downwrads
b) on pulley ,
torque = moment of inertia x angular acceleration
r x T = ( M r^2 /2 ) ( a/r)
T = Ma/2 ... (i)
On mass,
mg - T = ma ..... (ii)
c) from (i) a nd (ii)
mg - Ma/2 = ma
a = (6 x 9.81) / ( 6 + (3/2)) = 7.85 m/s^2
d) angular acc. = a/r = 7.85 / 0.50 =15.70 rad/s^2
e) using v^2 - u^2 = 2ad
v^2 - 0 = 2 x 7.85 x 8
v = 11.21 m/s
f) v = u + at
11.21 = 0 + 7.85t
t = 1.43 sec
g) w = v /r = 11.21/0.5 = 22.42 rad/s
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