There are two blocks connected by a rope which is wound over an ideal pulley. Th
ID: 1790550 • Letter: T
Question
There are two blocks connected by a rope which is wound over an ideal pulley. This is depicted in Figure 3. The blocks are released from rest. When the bottom block hits the ground, the top block is still to the left of the pulley.
(a) When the bottom block hits the ground, how fast is it moving? (b) What is the work done by gravity on the bottom block, as it moves from its initial position to the ground? What is the total work done by gravity on the top block during the same time? (c) What is the tension in the rope, as the bottom block falls? (d) Using the work-energy theorem, compute the velocity of the bottom block as it hits the ground. Make sure you obtain the same result as in part (a).
3 kg 2 kg 2 m InExplanation / Answer
a. let acceleration of the system be a, tension in the rope be T
from force balance on the two masses
2g - T = 2a
T = 3a
2g - 3a = 2a
5a = 2g
a = 2g/5 = 3.924 m/s/s
h = 2 m
so final speed = v
2*a*h = v^2
2*a*2 = v^2
v = 2*sqroot(a) = 3.96181 m/s
b. work done by gravity on the bottom block = 2*g*d = 39.24 J
work done by gravity on the top block = 0 J ( as its displacement is perpendicular to the gravitational force)
c. T = 2(g - a) = 11.6964 N
d. from work energy theorem
work done = gain in KE
39.24 = 0.5(2 + 3)v^2
v = 3.96181 m/s