Your artist friend is designing a kinetic sculpture and asks for your help since

Question

Your artist friend is designing a kinetic sculpture and asks for your help since she knows that you have had physics. Part of her sculpture consists of a 8.72 kg object (you can't tell what it is supposed to be, but it's art) and a 3.60 kg object which hang straight down from opposite ends of a very thin, flexible wire. This wire passes over a smooth, cylindrical, horizontal, stainless steel pipe 3.0 meters above the floor. The frictional force between the rod and the wire is negligible. The 8.72 kg object is held 2.0 meters above the floor and the 3.60 kg object hangs 0.50 meters above the floor. When the mechanism releases the heavier object, both objects accelerate and one will eventually hit the floor -- but they don't hit each other. To determine if the floor will be damaged, calculate the speed of the object which hits the floor.

m/s

Explanation / Answer

First find the work done on the falling object by gravity, then find velocity from that value.
The net gravitational force is 9.8(8.72-3.6) = 50.16 N, so the acceleration is 50.16/(8.72+3.6) = 4.07 m/s/s. The distance fallen by the mass is 2 m, so the work done is Fd = (m)(4.07)(2) =8.14m. From the kinetic energy equation, 8.14m = 1/2mv2;  v2/2= 8.14; v = 4.03 m/s.

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