Two crates of mass m1= 50 kg and m2 = 25 kg are connected by a rope that passes
ID: 2133778 • Letter: T
Question
Two crates of mass m1= 50 kg and m2 = 25 kg are connected by a rope that passes over a massless, frictionless pulley as shown in the figure as below. The crates start from rest. Assume the rope has a mass of 2 kg. If the tops of the crates start at the same inital height and the rope has a length of 10 m, what is the final speed after the crates have moved a distance of 2.5m ?
??? m/2
Two crates of mass m1= 50 kg and m2 = 25 kg are connected by a rope that passes over a massless, frictionless pulley as shown in the figure as below. The crates start from rest. Assume the rope has a mass of 2 kg. If the tops of the crates start at the same inital height and the rope has a length of 10 m, what is the final speed after the crates have moved a distance of 2.5m ? ??? m/2Explanation / Answer
Solution: The free-body diagrams are shown. The governing
equations are
Fy left : T ? 2(9.81) N = (2 kg)a
Fy right : T ? 5(9.81) N = ?(5 kg)a
Solving, we find
T = 28.0 N, a = 4.20 m/s2.
To find the velocity, we integrate the acceleration
v = at = (4.20 m/s)(0.5 s) = 2.10 m/s.
v = 2.10 m/s.
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