The three objects in the drawing are connected by strings that pass over massles

Question

The three objects in the drawing are connected by strings that pass over massless and friction-free pulleys. The objects move, and the friction between the middle object and the surface of the table is so small it can be ignored. (Assume m1 = 11.5 kg and m2 = 25.0 kg.) there are many similar problems posted here, but I cannot figure out how to do it without friction, if you want to see a picture, just search for this question, it will be 3 blocks, 2 hanging off of a table and one resting on the table.

Explanation / Answer

for m2

m2*g - T2 = m2*a=====> T2 = m2*(g -a)

for m1

T1 - m1*g = m1*a ====> T1 = m1*(g+a)

for m3

T2 - T1 = m3*a

m2*(g-a) - m1*(g+a) = m3*a

m2*g - m2*a - m1*g - m1*a = m3*a

a = (m2 - m1)*g/(m1+m2+m3)

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