# Three hanging masses and two pulleys, why does m3 accelerate?

**1. The problem statement, all variables and given/known data**

Figure CP7.57 shows three hanging masses connected by massless strings over two massless, frictionless pulleys.

a) Suppose: m1 = 2.5 kg, m2 = 1.5 kg, and m3 = 4.0 kg. Find the acceleration of each.

b) The 4.0 kg mass would appear to be in equilibrium. Explain why it accelerates.

**2. Relevant equations**

Tension of Rope A = 4*m1*m2*m3*g / (4*m1*m2 + m2*m3 + m1*m3)

**3. The attempt at a solution**

I managed to solve a) using the above equation which I derived thru some lengthy algebra (5 equations involving 5 unknowns — a1, a2, a3, Tension of Rope A, and Tension of Rope B), and got the following answers: a1 = -2.21m/s^2, a2 = 2.85m/s^2, and a3 = -0.316m/s^2. These answers match up with the answer key.

But I’m kind of stuck at part (b) — even though I worked out mathematically in part (a) that box 3 does indeed accelerate, I’m unsure how to explain why it accelerates in a way that makes intuitive sense. There was no answer key for part (b), so I’d appreciate any helpful guidance. I’ve attached a picture illustration of the problem as well.

http://ift.tt/N3FkEZ

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