1) In the figure, block 1 has mass m1 = 480 g, block 2 has mass m2 = 600 g, and

Question

1) In the figure, block 1 has mass m1 = 480 g, block 2 has mass m2 = 600 g, and the pulley is on a frictionless horizontal axle and has radius R = 5.1 cm. When released from rest, block 2 falls 74 cm in 5.5 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 pulleys 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/s2.

2) In the figure, two particles, each with mass m = 0.84 kg, are fastened to each other, and to a rotation axis at O, by two thin rods, each with length d = 5.9 cm and mass M = 1.0 kg. The combination rotates around the rotation axis with angular speed ? = 0.25 rad/s. Measured about O, what is the combination's (a) rotational inertia and (b) kinetic energy?

Explanation / Answer

a) a = 2h/t^2 = (2*0.74)/(5.5*5.5) = 0.0489 m/s^2

b) T2 = m2*(g-a)

T2 = 0.6*(9.81-0.0489) = 5.85666 N

c) T1 = m1*(g+a) = 0.48*(9.81+0.0489) = 4.732272 < -answer

d) alfa = a/R = 0.0489/0.051 =0.9588 rad/s

e) torque = I*alfa

(T2-T1) *R = I*alfa

I = ((5.85666 - 4.732272)*0.051)/(0.9588)

I = 0.059807 kg m^2

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I = Ir + m*d^2 + m*(2d)^2

I = (1/3)*2M*(2d)^2 + 4md^2

I = (1/3)*8M*d^2 + 4*m*d^2

I = ((8M/3) + 4m )*d^2

I = ((8/3) + (4*0.84))*(0.059*0.059)

i = 2.0978*10^-2 kg m^2

b) KE = 0.5*I*w^2 = 0.5*2.0978e-2*0.25*0.25

KE = 6.555625*10^-4 J

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