Atwood\'s machine is a system consisting of two objects connected by a string th

Question

Atwood's machine is a system consisting of two objects connected by a string that passes over a frictionless pulley, as shown in the figure below. Earlier in the course, we neglected the effect of the pulley, but now we know how to account for the pulley's impact on the system. The mass of the object on the left is M = 7.00 kg. The mass of the object on the right is m = 3.00 kg. The mass of the pulley is mp = 3.00 kg. Use g = 10.0 m/s2. What is the magnitude of the acceleration of the system?What is the tension in the part of the string that is connected to the block of mass M?What is the tension in the part of the string that is connected to the block of mass m?

Explanation / Answer

The acceleration of the system must be the acceleration of any one component of the

system therefore, Newton's second law should be applied to each of the three bodies.

For M:

Mg - T1 = Ma ..(1)

For m:

T2 - mg = ma ..(2)

For mP:

T1R - T2R = I(alpha) = I*a/R .. (3)

moment of inertia of dis I = mP*R^2/2

From (1),(2) and (3)

(Mg - M1)R - (mg -ma)R = mpR^2a/R

a = g(M-m)/(M+m+mp/2)

M = 7 kg , m = 3kg , mp = 3g , g =10 m/s^2

a = (7-3)*10/(7+3+1.5)

a = 3.476 m/s^2

(b) the tension in the string that is connected to M is T1 = M(g-a) = 7(10 -3.476) =45.668 N

(c) the tension in the string that is connected to m is T2 = m (g+a) = 3(10+3.476) = 40.428 N

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