The two blocks in the figure ( Figure 1 ) are connected by a massless rope that
ID: 2245361 • Letter: T
Question
The two blocks in the figure(Figure 1) are connected by a massless rope that passes over a pulley. The pulley is 12cm in diameter and has a mass of 2.7kg . As the pulley turns, friction at the axle exerts a torque of magnitude 0.50N?m .
If the blocks are released from rest, how long does it take the 4.0 kg block to reach the floor?
Explanation / Answer
For the 2 kg mass, the forces involved are Weigt and T1
T1 - mg = ma
T1 - (2)(9.8) = 2a
T1 - 19.6 = 2a
T1 = 19.6 + 2a
For the 4 kg mass, look at force and weight again
mg - T2 = ma
(4)(9.8) - T2 = (4)a
39.2 - T2 = 4a
T2 = 39.2 - 4a
For the pulley, the two tensions creat a torque
(T2 - T1)r is that torque, but we also have a frictional torque that will act against that
(T2 - T1)(r) - .5 = I(alpha)
I for the pulley = .5mr^2 and alpha = a/r, so substitute
[(39.2 - 4a) - (19.6 + 2a)]r - .5 = (.5)(2.7)(r^2)(a/r)
(19.6 - 6a)(.06) - .5 = 1.35a(.06)
1.176 - .36a - .5 = .081a
.676 - .36a = .081a
a = 1.53 m/s^2
Finally apply d = vot + .5at^2
1 = 0 + (.5)(1.53)(t)^2
t = 1.14 sec
Related Questions
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.