In the figure, block 1 has mass m 1 = 450 g, block 2 has mass m 2 = 510 g, and t
ID: 1460137 • Letter: I
Question
In the figure, block 1 has mass m1 = 450 g, block 2 has mass m2 = 510 g, and the pulley is on a frictionless horizontal axle and has radius R = 4.6 cm. When released from rest, block 2 falls 75 cm in 4.6 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 ,
let the acceleration of the blocks is a
a) using second equation of motion
d = u*t + 0.5 * a * t^2
0.75 = 0.5 * a * 4.6^2
a = 0.071 m/s^2
the magnitude of acceleration is 0.071 m/s^2
----------------------------------------
b) let the tension is T1
T1 - m1 * g = m1 * a
T1 = 0.45 *(9.8 + 0.071)
T1 = 4.44 N
the tension T1 is 4.44 N
c)
let the tension is T2
m2 * g - T2 = m2 * a
0.51 * 9.8 - T2 = 0.51 * 0.071
T2 = 4.962 N
the tension T2 is 4.962 N
d)
for the angular acceleration is alpha
alpha = a/R
alpha = 0.071/.046
alpha = 1.543 rad/s^2
the magnitude of the pulley’s angular acceleration is 1.543 rad/s^2