In the figure, block 1 has mass m 1 = 468 g, block 2 has mass m 2 = 563 g, and t
ID: 1605269 • Letter: I
Question
In the figure, block 1 has mass m1 = 468 g, block 2 has mass m2 = 563 g, and the pulley is on a frictionless horizontal axle and has radius R = 4.56 cm. When released from rest, block 2 falls 75.0 cm in 4.73 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 m/s2.
In 1111 1112Explanation / Answer
a) let a is the acceleration of the blocks.
use, y = voy*t + (1/2)*a*t^2
0.75 = 0 + (1/2)*a*4.73^2
==> a = 2*0.75/4.73^2
= 0.067 m/s^2
b) T2 = m2*g - m2*a
= 0.563*9.81 - 0.563*0.067
= 5.48 N
c)
T1 = m1*g + m1*a
= 0.468*9.81 + 0.468*0.067
= 4.62 N
d) alfa = a/R
= 0.067/0.0456
= 1.47 rad/s^2
e) net Torque = I*alfa
(T2 - T1)*R = I*alfa
==> I = (T2 - T1)*R/alfa
= (5.48 - 4.62)*0.0456/1.47
= 0.0268 kg.m^2