1) A pulley with two different radii is constructed by welding two cylinders tog
ID: 2077043 • Letter: 1
Question
1) A pulley with two different radii is constructed by welding two cylinders together such that their symmetry axes align. The first cylinder has radius r r1 0.200 m and has a mass ma 2.00 kg. The second cylinder has a radius rb T2 0.300 m and has a mass mb 4.00 kg. Recall for a cylinder that I MR (a) What is the total moment of inertia of this combined pulley? This physical pulley is used in the setup depicted below, which we now consider. m2 (c) Take that the positive direction of motion is m2 sliding to the left, the pulley rotating counterclockwise, and mi falling. If the pulley is spinning with angular velocity w, what are the velocities of my and m2? (your answer will be completely symbolic: leave r2 symbolic at this stage)Explanation / Answer
1. (a) I1 = ma ra^2 /2 = 2 x 0.2^2 /2 = 0.04 kg m^2
I2 = mb rb^2 /2 = 4 x 0.3^2 /2 = 0.18 kg m^2
I = I1 + I2 = 0.22 kg m^2
(C) v1 = w r1
v2 = w r2
(d) a1 r1 = alpha
a1 = alpha / r1
and a2 = alpha / r2
(e) m1 g - T1 = m1 a1
m1 g - T1 = m1 alpha / r1
29.4 - T1 = 15 alpha
T1 + 15 alpha = 29.4 ......(i)
on m2:
T2 - f = m2 a2
T2 - uk m2 g = m2 alpha / r2
T2 - 24.5 = 16.67 alpha
T2 - 16.67 alpha = 24.5 ..... (ii)
now for pulley,
r1 T1 - r2 T2 = I alpha
0.2 T1 - 0.3 T2 = 0.22 alpha
0.2 T1 - 0.3 T2 - 0.22 alpha = 0 ..... (iii)
(F) Solviing,
T1 = 32.08 N
T2 = 21.52 N
alpha =- 1470 / 8221 = - 0.18 rad/s^2
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