In the figure, block 1 has mass m1 = 490 g, block 2 has mass m2 = 520 g, and the
ID: 1455610 • Letter: I
Question
In the figure, block 1 has mass m1 = 490 g, block 2 has mass m2 = 520 g, and the pulley is on a frictionless horizontal axle and has radius R = 5.0 cm. When released from rest, block 2 falls 72 cm in 5.0 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.
Explanation / Answer
Here ,
m1 = 0.490 Kg
m2 = 0.520 Kg
R = 5 cm
d = 72 cm = 0.72 m
t = 5 s
a)
let the acceleration is a
Using second equation of motion
d = 0.5 * a * t^2
0.72 = 0.5 * a * 5^2
a = 0.0576 m/s^2
magnitude of acceleration of the blocks is 0.0576 m/s^2
b)
Now , for the tension T2
m2 * g - T2 = m2 * a
0.52 * 9.8 - T2 = 0.52 * 0.0576
T2 = 5.066 N
the tension T2 is 5.066 N
c)
for the tension T1
T1 - m1 * g = m1 * a
T1 - 0.490 * 9.8 = 0.490 * 0.0576
T1 = 4.83 N
the tension T1 is 4.83 N
d)
for the angular acceleration of pulley is alpha
as a = R * alpha
0.0576 = 0.05 * alpha
alpha = 1.152 rad/s^2
the magnitude of the pulley’s angular acceleration is 1.152 rad/s^2