In the figure, block 1 has mass m_1 = 480 g, block 2 has mass m_2 = 570 g, and t

Question

In the figure, block 1 has mass m_1 = 480 g, block 2 has mass m_2 = 570 g, and the pulley is on a frictionless horizontal axle and has radius R = 4.51 cm. When released from rest, block 2 falls 73.3 cm in 5.03 s without the cord slipping on the pulley, (a) What is the magnitude of the acceleration of the blocks? What are (b) tension T_2 (the tension force on the block 2) and (c) tension T_1 (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/s^2. (a) Number Units (b) Number Units (c) Number Units (d) Number Units (e) Number Units

Explanation / Answer

Part A)-

S = ut + 1/2at2

0.733 = 0 + 1/2a(5.03)2

a = 0.058 m/s2

Part B)-

then for M2-

Fnet = Ma

(0.570)(9.81) - T2 = (0.570)(0.058)

T2 = 5.624 N

As we know that both have same acceleration then-

T1 - (0.480)(9.81) = (0.480)(0.058)

T1 = 4.74 N

For angular acceleration -

(alpha) = a/r

=0.058 / 0.0451

= 1.28 rad/s2

For rotational inertia -

Torque = I(alpha)

(T2 - T1) r = I (1.28)

( 5.624 - 4.74) (0.0451) = I (1.28)

I = 0.0311 kg.m2

Thank you !!! Have fun

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