Solving Pulley-Based Question: Tension & Mass Calculation | Step-by-Step Guide"

[Hunter King A]

Homework Statement

The problem states,
"A mass m1 = 5 kg is connected to another mass m2 over a frictionless pulley by a massless string. The acceleration of m2 is -3 m/s². Find the (a) tension in each strong and (b) the mass of m2

Homework Equations

W=mg
F=ma
...

The Attempt at a Solution

Alright, well my attempt goes a little like this:

I realized that the two masses are attached by the string, thus their acceleration must be the same, despite the fact that one weight might be larger than the other or vice-versa. I also realized that -3 can be interpreted as a means of saying m2 is going up, while m1 is going down. Thus the two accelerations are 3 (for m1) and -3 (for m2).

Here is where I get iffy, I drew a free-body diagram to represent the forces,

W= Mg
W= 5 (9.8)
W= 49 N

Thus there is a force of 49 N pulling the first box down. But NOW what do I do? The two boxes obviously cannot be the same weight otherwise there would not be an acceleration.

The obvious thing to do would be:

T(tension)
T= 49 - w2
T= 49 - (m2g)

m2g= ma
m2g= m(-3)

...

Or something like that.

I could really use some help, the solution is probably easy but I can't seem to wrap my head around what is going on.

 

[PhanthomJay]

Welcome to PF, Hunter King A!
The problem should have clarified what is meant by negative acceleration. You get different answers for the mass depending on whether the 5 kg mass is moving up or down. Conventionally, usually, negative implies the downward direction in this case, meaning that m1 moves down, while the 5 kg mass moves up. Rather than try to solve this problem in one full swoop, you should get used to drawing free body diagrams of each mass, identifying the forces acting on each, then applying Newton's laws. What 2 forces act on m1? What 2 forces act on the 5kg mass? What is the net force on each? You will get 2 equations with 2 unknowns, solve for T and m by the method of your choice.

 

[Hunter King A]

Thanks Phantom.

I actually figured it out when I buckled down and put my head to the problem.

Turns out that T= (m1+m2)a

and using another formula that I derived from finding the T via the weights of the two masses I was able to find the mass and than the tension.