Question

In the figure below, block 1 has mass m_1 = 460 g, block 2 has mass m_2 = 500 g, and the pulley, which is measured on a horizontal with 2.5200 s without the cord slipping on the pulley. (Do not treat the pulley as a uniform disk Give your answers to three significant figures. Use these rounded values in subsequent calculations) What is the magnitude of the acceleration of the blocks? What is the tension T_2? What is the tension T_1? What is the magnitude of the angular acceleration? What rotational inertia?

Answer 1

(A) d = u t + a t^2 / 2

0.811 = 0 + a (2.52^2 / 2)

a = 0.255 m/s^2

(b) m2g - T2 = m2 a

0.500 x 9.81 - T2 = 0.500 x 0.255

T2 = 4.777 N

(c) T1 - m1g = m1 a

T1 = 0.460 ( 9.81 + 0.255) = 4.62 N

(d) alpha = a / R = 0.255 / 0.05 = 5.10 rad/s^2

(e) net torque = R( T2 - T1) = 7.85 x 10^-3 N m

net torque = I alpha

7.85 x 10^-3 = I ( 5.10)

I = 1.54 x 10^-3 kg m^2