Masses Over Pulley: Finding Acceleration and Tension

[benny74]

Homework Statement

A mass m1 = 5.9 kg rests on a frictionless table. It is connected by a massless and frictionless pulley to a second mass m2 = 2.5 kg that hangs freely.

Homework Equations

1)What is the magnitude of the acceleration of block 1?
2)What is the tension in the string?
3)Now the table is tilted at an angle of θ = 75° with respect to the vertical. Find the magnitude of the new acceleration of block 1.
4)At what “critical” angle will the blocks NOT accelerate at all?
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5)Now the angle is decreased past the “critical” angle so the system accelerates in the opposite direction. If θ = 38° find the magnitude of the acceleration.
6)Compare the tension in the string in each of the above cases on the incline:
Tθ at 75° = Tθcritical = Tθ at 38°
Tθ at 75° > Tθcritical > Tθ at 38°
Tθ at 75° < Tθcritical < Tθ at 38°

The Attempt at a Solution

It looks like you assumed the tension in the string was m2g. However, this cannot be true since it is accelerating down! Try using Newton's Second Law for both masses and then add the equations together (note that BOTH masses have acceleration).

 

[benny74]

I found the answer to question on which is 2.92m/s^2.
And the answer to question 2 is 17.2N.
If anyone has any suggestions for the rest it would be greatly appreciated, Thanks!