In the figure, block 1 has mass m_1 = 488 g, block 2 has mass m_2 = 554g, and th

Question

In the figure, block 1 has mass m_1 = 488 g, block 2 has mass m_2 = 554g, and the pulley in on a frictionless horizontal axle and has radius R = 5.48 cm. When released from rest, block 2 falls 75.8 cm in 5.49 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

Explanation / Answer

(A) Block 2 falls 0.758 m in 5.49s

y = v0t + a t^2 /2

0.758 = 0 + a (5.49^2) /2

a = 0.0503 m/s^2

(b) Applying Fnet = m a on block m2.

m2g - T2 = m2 a

T2 = 0.554 ( 9.81 - 0.0503)

T2 = 5.41 N .........Ans

(c) on m1:

T1 - m1 g = m1 a

T1 = (0.488) (9.81 + 0.0503) = 4.81 N ........Ans

(d) alpha = a / R

= (0.0503 / 0.0548)

= 0.918 rad/s^2

(e) Net torque = I alpha

R ( T2 - T1) = I alpha

(0.0548) (5.41 - 4.81) = I (0.918)

I = 0.0358 kg m^2 Or 35.8 x 10^-3 kg m^2

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