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**Homework Statement**

The three blocks shown are relased at t=0 from the position shown in the figure. Assume that there is no friction between the table and M2, and that the two pulleys are massless and frictionless. The masses are:

M1 = 2.00 kg

M2 = 7.00 kg

M3 = 4.00 kg

Calculate the speed of M2 at a time 1.750s after the system is released from rest.

(Question and diagram attached)

**The attempt at a solution**

I followed the way my professor did a similar question in my notes, however the answer is not correct. My process was as follows:

For mass 1:

ƩFnet = M1a

T1 - M1g = M1a

T1 = M1(a+g)

T1 = 4(a+9.8)

For mass 2:

ƩFnet = M2a

T2-T1 = M2a

T2 = M2a - T1

T2 = 7a + 2a - 19.6

T2= 9a - 19.6

For mass 3:

ƩFnet = -M3a

T2 - W3 = -M3a

T2 = W3 - M3a

T2 = 39.2 - 4a

I then made the two T2 equations equal to find acceleration of the system:

9a - 19.6 = 39.2 - 4a

9a + 4a = 58.8

a = 58.8/13

a = 4.523 m/s^2(right)

Then I found velocity of M3

Vf = Vit + (1/2)at^2

Vf = (0)(1.750) + (1/2)(4.523)(1.750^2)

Vf = 6.926 m/s

Anyone know where I went wrong? I would seriously appreciate any help. I've tried this a bunch of times and have gotten different answers for acceleration every time, all of them wrong. I only have a few more tries left. Any guidance would bed a great help!