P7: In the figure shown, a 10 kg block hangs on the right, and a 4 kg block hang

Question

P7: In the figure shown, a 10 kg block hangs on the right, and a 4 kg
block hangs on the left. The pulley is a disk of radius 25 cm and
mass 2 kg. The string is ideal, the pulley turns without friction, and
the string does not slip on the pulley. The system is initially at rest,
then it is released.

P7: In the figure shown, a 10 kg block hangs on the right, and a 4 kg block hangs on the left. The pulley is a disk of radius 25 em and mass 2 kg. The string is ideal, the pulley turns without friction, and then it is released. a) What is the acceleration of the heavy block? b) What is the tension in the string attached to the light block?

Explanation / Answer

Given

m1 = 4 kg , m2 = 10 kg , m = 2 kg

R = 0.25 m

from free body diagram

tension in the string attached to the light block is  

T1 - m1*g = m1*a ==> T1 = m1(a+g)

tension in the heavy block is  

T2 - m2*g = -m2*a

T2 = m2g - m2a ===> T2 = m2(g-a)

now the net torque is T1*R - T2*R = -I *alpha

here I = 0.5*m*R^2 , and a = R*alpha

m1(a+g)*R -m2(g-a)*R = -(0.5*m*R^2)(a/R)

4(a+9.8)*0.25 - 10(9.8-1)*0.25 = - (0.5*2*0.25)(a)

a = 9.76 m/s2

now the tension in the light block is T1 = m1(a+g) = 4(9.76+9.8) N = 78.24 N

Acceleration of heavy block is a = 9.76 m/s2

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