An Atwood\'s machine consists of blocks of masses m1 = 10.1 kg and m2 = 22.2 kg

Question

An Atwood's machine consists of blocks of masses m1 = 10.1 kg and m2 = 22.2 kg attached by a cord running over a pulley as in the figure below. The pulley is a solid cylinder with mass M = 7.90 kg and radius r = 0.200 m. The block of mass m2 is allowed to drop, and the cord turns the pulley without slipping.

(a) Why must the tension T2 be greater than the tension T1? Explain

(b) What is the acceleration of the system, assuming the pulley axis is frictionless? __________m/s2

(c) Find the tensions T1 and T2.

T1 = _______N

T2 = ______N

Explanation / Answer

equations of motion to m1 and m2 are

for m1

T1-m1g = m1a

T1 = m1(a+g)

for m2

m2g-T2 = m2a

T2 = m2*(g-a)

since m2 >m1 we can say that T2>T1

B) net torque is Tnet = I*alpha

Tnet (T2-T1)*R = 0.5*M*R^2*(a/R)

T2-T1 = 0.5*M*a

m2g-m2a -m1a-m1g = 0.5*M*a

(m2-m1)*g = (0.5*M+m1+m2)*a

accelaration a = (m2-m1)*g/(0.5M+m1+m2) = ((22.2-10.1)*9.81)/((0.5*7.9)+10.1+22.2) = 3.27 m/s^2

C) T1 = m1(a+g) = 10.1*(3.27+9.81) = 132.15 N

T2 = m2*(g-a) = 22.2*(9.81-3.27) = 145.188 N

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