# Pulley system

devanlevin
2 masses are tied in the followin configuaration, the 1st with a mass of m1 the 2nd mass of m2, pulleys and ropes have no mass or friction.

what is the acceleration of each mass, using only parameters g, m1, and m2

not too much i can see from this, i know that |a1|=2|a2|,
i think that
1 F=m1a=m1g-T
a1=g-T/m1

2 F=m2a=m2g-2T
a2=g-2t/m2

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looks right to me.

Doc Al
Mentor
So far, so good. But now you need to combine all three equations to solve for a1 & a2 in terms of the given parameters. Hint: Careful with signs. If a1 is down, a2 must be up.

devanlevin
a1=-2*a2,

a1=g-T/m1

a2=g-2t/m2
-------------------
T=m1(g-a1)=m1(g+2a2)

a2=g-[2m1(g+2a2)]/m2
m2a2=g-(2m1g)-(4m1a2)

a2(m2+4*m1)=g(1-2*m1)

a2=g*(1-2m1)/(m2+4m1)

is that correct,?? the answer in my textbook is similar, either a mistake on their behalf or im missing something,, their answer is

a2=g*(m2-2m1)/(m2+4m1)

Doc Al
Mentor
a2=g-[2m1(g+2a2)]/m2
m2a2=g-(2m1g)-(4m1a2)
You made an error in this step. Note how the terms in your last equation all have the same units--except one. (When you multiplied by m2, you did not do it completely.)

devanlevin
thanks