As shown in the figure, block 1 has mass m 1 = 490 g, block 2 has mass m 2 = 524

Question

As shown in the figure, block 1 has mass m1 = 490 g, block 2 has mass m2 = 524 g, and the pulley, which is mounted on a horizontal axle with negligible friction, has radius R = 5.10 cm. When released from rest, block 2 falls 74.0 cm in 5.04 s without the cord slipping on the pulley.

1) What is the magnitude of the acceleration of the blocks?

2) What is tension T2?

3) What is tension T1?

4) What is the magnitude of the pulley's angular acceleration?

As shown in the figure, block 1 has mass m1 = 490 g, block 2 has mass m2 = 524 g, and the pulley, which is mounted on a horizontal axle with negligible friction, has radius R = 5.10 cm. When released from rest, block 2 falls 74.0 cm in 5.04 s without the cord slipping on the pulley. 1) What is the magnitude of the acceleration of the blocks? 2) What is tension T2? 3) What is tension T1? 4) What is the magnitude of the pulley's angular acceleration? 5) What is its rotational inertia?

Explanation / Answer

1)

y = 0.5*a*t^2

a = 2y/t^2 = (2*0.74)/(5.04*5.04) = 0.058 m/s^2

2)

m2*g - T2 = m2*a

T2 = m2*g - m2*a = m2*(g-a) = 0.524*(9.8-0.058) = 5.104808 N

3) T1 - m1*g = m1*a

T1 = m1*(g+a) = 0.49*(9.8+0.058) = 4.83042 N

4)

alfa = a/R = 0.058/0.051 = 1.137 rad/s^2

5) (T2-T1)*R = I*alfa

I = 1.23*10^-2 kg m^2

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