As shown in the figure below, blocks A and B are connected by a massless string
ID: 1368462 • Letter: A
Question
As shown in the figure below, blocks A and B are connected by a massless string that passes over the outer edge of a pulley that is a uniform solid disk. Block A has a mass of 8.00 kg. Block B has a mass of 7.00 kg. The pulley has a mass of 3.00 kg. When the system is released from rest, it experiences a constant (and non-zero) acceleration. There is no friction between block A and the surface. Use g = 10.0 m/s2.
(a) What is the acceleration of the system?
(b) What is the tension in the part of the string that is connected to block A?
(c) What is the tension in the part of the string that is connected to block B?
Explanation / Answer
net force on A is TA = mA*a
net force on B is mB*g - TB = mB*a
for pulley net torque is T = I*alpha
(TB-TA)*R = I*alpha = I*(a/R) = (0.5*mp*R^2)*(a/R) = 0.5*mp*R*a
TB-TA = 0.5*mp*a
mB*(g-a) - mA*a = 0.5*mp*a
mB*g - (mB+mA)*a = 0.5*mp*a
accelaration a = mB*g/[(0.5*mp) +(mB+mA)]
a = (7*10)/[(0.5*3)+(8+7)] = 4.24 m/s^2
B) TA = mA*a = 8*4.24 = 33.93 N
C) TB = mB*(g-a) = 7*(10-4.24) = 40.32 N
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