Solving Pulleys and Tension Problems

[Bluesroo]

This is incredibly simple, but i cannot remember the formula for tension, which is a show stopper.

Homework Statement

Simple pulley. Two masses attached with a string running over a frictionless wheel. m1 is 8kg and m2 is 12kg. I need to find acceleration and tension over the string.

Homework Equations

F= ma
anet= (Fg2-Fg1)/(m1+m2)
T= Fnet1+Fg1 or T= Fnet2-Fg2 (I don't think these are right)

The Attempt at a Solution

F= ma
Fg1= 8kg* 9.8m/sec^2
Fg1= 78.4N

Fg2= 12kg* 9.8m/sec^2
Fg2= 117.6N

anet= (Fg2-Fg1)/(m1+m2) (at second glance this seems like a faulty equation as well...)
anet= (117.6N-78.4N)/(8kg+12kg)
anet= 1.96m/sec^2

Now I can't find tension because I'm not sure where Fnet comes from (the sum of Fg1 and Fg2?) nor do I have the formula for tension written down... I didn't take very good notes on this (surprise surprise )

 

[glueball8]

Draw Free Body diagram of a object. Then Fnet = ma.

 

[jegues]

Use your everday experience to reason this one out. Then after you get the base of the problem done the rest is simple math.

Two masses hanging on a frictionless pulley, which why is the system going to accelerate?

Which mass is going to move down, causing the other to move up?

Can you write equations to sum up all the forces on these two masses? F = ma

HINT: The tension is the same for both masses (frictionless pulley).

You should end up with two equations with 2 unknowns. You can solve for this.

What are some efficient ways of solving systems of equations?

Hope this helps, let me know if you're still stuck.

 

[Bluesroo]

@Bright Wang
I have a free body diagram drawn on my paper. I have the anet part figured out, I created that equation correctly... Thanks for the helping me verify that.

@Jegues
I don't see how I can create two equations... Because tension is the same throughout the string wouldn't there only be one equation that can be used to solve? They are solving for the same number...

The only things I can think of are:
T=(Fg2-Fg1)anet
and
T=(m1+m2)anet

In regards to efficiently solving equations, I think that's how I got myself in this... I don't think I understood the material well enough before I tried to simplify equations and combine things.

 

[glueball8]

What you did at the start, is looking at the rope, and the two boxes as a system. Now can you take the system apart, then you can calculate tension. You only need FBD of 1 object.
I'm going to draw it horizontally for one object

<----Tension---|BOX|--------Force of gravity on the one box------> while ~> accele

Now can you create a equation use "sum of Force" = ma. (Of one object). Just look at the FBD

 

[Bluesroo]

I think I got it (this is using m2):
Fg2= m*ag
Fg2= 12kg* 9.8m/sec^2
Fg2= 117.6N

Fnet= m*anet
Fnet= 12kg*1.96m/sec^2
Fnet= 23.5N

Fg2-Fnet= T
117.6N-23.5N=T
T= 94.1N

 

[glueball8]

Yes, that's what I got.