How to Calculate Acceleration, Time, and Tension in an Atwood Machine Problem

[K1rby]

Homework Statement

"Calculate the acceleration of an Atwood machine if one of the two weights is four times as heavy as the other. What is the tension in the string if the lighter body has a mass of 3kg? Find also the time for this mass to cover a distance of 0.45 meter."

So:

*Given:
m1=3kg (the lighter one)
m2=12kg(?) (four times heavier)
d=0.45m

*Find:
1)acceleration
2)time
3)tension

Homework Equations

I'm a little confused about this. First the formula for acceleration is F=ma--> a=F/m. But there are few things missing to complete it. Time meanwhile, I'm clueless on how to find it since there are quite a number of formulas to find time such as d=vt--> t=d/v but there aren't anything given about v. Tension meanwhile, is not that much of a problem for me.

The Attempt at a Solution

So I first tried solving for the acceleration. a=F/m. But there aren't any given about force. Meanwhile, a=dt^2. But d I think is displacement which is different from the other given d of mine which is distance. Second I solved for time. I've tried all formulas I know for solving time but then still won't work.

I need a little assistance about these. Thanks in advance.

 

[PhanthomJay]

You need to study Free Body Diagrams, Newton's laws , and the kinematic equations of motion for constant acceleration. First off, it's not F=ma, it's F_net= ma. F_net must be determined by drawing free body diagrams of each mass. For example, looking at the larger mass, its weight acts down and the tension acts up. Since the heavier mass is accelerating downwards, then F_net = mg-T =12g -T, and thus
12g-T =12a, per Newton 2. Now look at the lighter block and proceed in similar fashion, noting that tension on either side of an ideal pulley must be the same, and the magnitude of a must be the same. Then solve 2 equations with 2 unknowns. Then the time is not found by using d=vt...look up (and learn) the correct equation of motion for constant acceleration that relates distance with time and acceleration.
Welcome to PF!

 

[K1rby]

Thanks! I finally got it out of a number of tries and attempts.

Again, thanks a lot!