In the figure, block 1 has mass m_1 = 470 g, block 2 has mass m_2 = 530 g, and t
ID: 1501169 • Letter: I
Question
In the figure, block 1 has mass m_1 = 470 g, block 2 has mass m_2 = 530 g, and the pulley is on a frictionless horizontal axle and has radius R = 4.7 cm. When released from rest, block 2 falls 73 cm in 5.0 s without the cord slipping on the pulley, What is the magnitude of the acceleration of the blocks? What are tension T_2 (the tension force on the block 2) and tension T_1 (the tension force on the block 1)? What is the magnitude of the pulley's angular acceleration? 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.Explanation / Answer
m1 = 470 g
m2 = 530 g
R = 4.7 cm
(a)
Acceleration of block 2,
s = u*t + 1/2at^2
0.73 = 0 + 1/2*a*5.0^2
a2 = 0.0584 m/s^2
As the rope is not sliiping, acceleration is same for both the blocks,
a = 0.0584 m/s^2
(b)
m2*g - T2 = m2*a
0.53 * 9.8 - T2 = 0.53 * 0.0584
T2 = 5.16 N
(c)
T1 - m1*g = m1*a
T1 - 0.47 * 9.8 = 0.47 * 0.0584
T1 = 4.63 N
(d)
Magnitude of pulley's angular acceleration, = a/r
= 0.0584/0.047
= 1.24 rad/s^2
(e)
(T2 - T1) * r = I *
(5.16 - 4.63) * 0.047 = I *1.24
I = 0.02 Kg m^2
Rotational Inertia, I = 0.02 Kg m^2