2 blocks, each on an inclined plane

[RonakPat]

Homework Statement

Two 2kg blocks are joined by a massless cord and pulley, ignoring friction, determine each block's acceleration using a free body diagram for each.

Picture for visual aid: http://img27.imageshack.us/img27/2653/86460048.png
or a link: http://img27.imageshack.us/img27/2653/86460048.png

The Attempt at a Solution

I did the free body diagrams and solved for the tension on the string to try to equate the two sides

for the first block i got: T - mgsin30 = ma(1) so T = ma(1) + mgsin30
for the second block i got: mgsin60 - T = ma(2) so T = mgsin60 - ma(2)

The problem is the fact that i have two variables that i am solving for. I can't figure it out

 

[tiny-tim]

Welcome to PF!

Hi RonakPat! Welcome to PF!

You're missing the obvious …

the length of the string is constant, so a₁ + a₂ = 0. ​

(some people call that a geometric constraint)

 

[RonakPat]

Hi RonakPat! Welcome to PF!

You're missing the obvious …

the length of the string is constant, so a₁ + a₂ = 0. ​

(some people call that a geometric constraint)

So should I still set the two things equal then substitute one of the accelerations(a2) out to find the other(a1) then use what you gave me to find the other(a2)?

 

[tiny-tim]

Equal and opposite, yes.

 

[RonakPat]

Well i solved it and it came out to be 1.79m/s². Does it matter which of them has the negative acceleration or do both have equal positive accelerations?

 

[tiny-tim]

Does it matter which of them has the negative acceleration or do both have equal positive accelerations?

hmm … well, you'd better say that one goes upward with acceleration 1.79m/s², and the other goes downward …

you'll have to make it clear you know which way they're going!