In the figure, block 1 has mass m1 = 460 g, block 2 has mass m2 = 576 g, and the
ID: 1782007 • Letter: I
Question
In the figure, block 1 has mass m1 = 460 g, block 2 has mass m2 = 576 g, and the pulley is on a frictionless horizontal axle and has radius R = 5.21 cm. When released from rest, block 2 falls 71.3 cm in 4.51 s without the cord slipping on the pulley. (a) What is the magnitude of the acceleration of the blocks? What are (b) tension T2 (the tension force on the block 2) and (c) tension T1 (the tension force on the block 1)? (d) What is the magnitude of the pulley’s angular acceleration? (e) What is its rotational inertia? Caution: Try to avoid rounding off answers along the way to the solution. Use g = 9.81 m/s2.
i1M ImExplanation / Answer
along vertical
initial velocity voy = 0
acceleration ay = -a
displacement y = -71.3 cm = 0.713 m
time t = 4.51 s
from equation of motion
y = voy*t + (1/2)*ay*t^2
-0.713 = 0 -(1/2)*a*4.51^2
acceleration a = 0.07 m/s^2
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(b)
for block 2
m2*g - T2 = m2*a
T2 = m2*g - m2*a
T2 = 0.576*9.81 - 0.576*0.07
T2 = 5.61 N
(c)
for block 1
T1 - m1*g = m1*a
T1 = m1*g + m1*a
T1 = 0.46*9.81 + 0.46*0.07
T1 = 4.545 N
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part (d)
angular acceleration alpha = a/R = 0.07/0.0521 = 1.343 rad/s^2
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part (e)
for the pulley
net torque = I*alpha
net torque = (T2-T1)*R
(T2 - T1)*R = I*alpha
(5.61-4.545)*0.0521 = I*1.343
moment of inertia I = 0.0413 kg m^2
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