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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
T2T1 = 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!
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
T2T1 = 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!
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