Finding acceleration of a three-object pulley system

AI Thread Summary
The discussion focuses on calculating the acceleration of a three-object pulley system with given masses and a coefficient of kinetic friction. The user has set up equations based on Newton's second law but is struggling with the correct signs for the forces involved. A key point raised is the need to ensure that the direction of acceleration for each mass is accurately represented in the equations. Specifically, the upward acceleration of the third mass (m3) must be correctly accounted for to avoid sign errors in the calculations. Correcting these signs is crucial for determining the accurate magnitude of acceleration for each block.
kathyt.25
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Homework Statement


"Three blocks are connected on a table as shown in the figure below.
http://i4.photobucket.com/albums/y111/kathy_felldown/sb-pic0550.png

The table is rough and has a coefficient of kinetic friction of 0.360. The three masses are m1 = 3.74 kg, m2 =1.39 kg, and m3 = 1.86 kg, and the pulleys are frictionless. Determine the magnitude of the acceleration of each block."

I think I've figured out how to do it, but I keep on getting the wrong answer. I denoted left to be the POSITIVE x-direction, and down to be the POSITIVE y-direction, since that's the direction of movement. Can someone check my equations to see if I have them right?


Homework Equations


Fnet=ma
f(k)=u*n (where u=coefficient of friction)


The Attempt at a Solution


For m1, the 3.74kg mass:
Fnet(y) = m1*g - T1 = ma
Therefore, T1 = m1*g - m1*a --> EQUATION #1

For m2, the 1.39kg mas on the table:
Fnet(y) = m2*g - n = 0
Therefore, n = m2*g

Fnet(x) = T1 - T3 - f = ma
Therefore, T1 - T3 - u*n = ma --> EQUATION #2

For m3, the 1.86kg mass:
Fnet(y) = -T3 +m3*g = ma
Therefore, T3 = m3*g - m3*a --> EQUATION #3


I then substituted equations #1 and #3, into equations #2, and isolated for acceleration "a".
 
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kathyt.25 said:
For m3, the 1.86kg mass:
Fnet(y) = -T3 +m3*g = ma
Therefore, T3 = m3*g - m3*a --> EQUATION #3
You've made a sign error. The acceleration of m3 is upward and must have the appropriate sign.
 
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Likes MegaJoules
If m1 has acceleration a downwards, the acceleration of m3
is a upwards (or -a downwards if you prefer)
 
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