In the figure, block 1 has mass m1 = 460 g, block 2 has mass m2 = 550 g, and the

Question

In the figure, block 1 has mass m1 = 460 g, block 2 has mass m2 = 550 g, and the pulley is on a frictionless horizontal axle and has radius R = 5.0 cm. When released from rest, block 2 falls 79 cm in 4.6 s without the cord slipping on the pulley. (a) What is the magnitude of the acceleration of the blocks? What are (b) tension T2 (the tension force on the block 2) and (c) tension T1 (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 rn/s^2.

Explanation / Answer

part a )

applying kinematics equation on block 2

d = 1/2 * a*t^2

0.79 m= 1/2 * a * (4.6)^2

a = 0.0745 m/s^2

part b )

tension in block 2

all force in block 2

m2g - T2 = m2a

T2 = m2(g-a)

T2 = 0.550 * ( 9.81 - 0.0745)

T2 = 5.35 N

part c )

force on block 1

T1 - m1g = m1a

T1 = m1(g+a)

T1 = 0.460 ( 9.81 + 0.0745)

T1 = 4.55 N

part d )

angular acceleration = a/r

alpha = 0.0745/5*10^-2m = 1.49 rad/s^2

part e )

torque = I*alpha

and we also know that = torque = r x F

I*alpha = T2 * r - T1*r

I = (T2 * r - T1*r)/alpha

I = 0.0268 kg-m^2

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