2 blocks, each on an inclined plane

AI Thread Summary
Two 2kg blocks connected by a massless cord and pulley are analyzed to determine their acceleration on inclined planes, with friction ignored. The user created free body diagrams and derived equations for tension and acceleration but faced challenges due to having two variables. A key insight was provided that the length of the string is constant, leading to the relationship a1 + a2 = 0. After resolving the equations, an acceleration of 1.79 m/s² was calculated, with clarification needed on the direction of acceleration for each block. The discussion emphasizes the importance of clearly indicating the direction of motion in such problems.
RonakPat
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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
 
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Welcome to PF!

Hi RonakPat! Welcome to PF! :smile:

You're missing the obvious …

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

(some people call that a geometric constraint)
 


tiny-tim said:
Hi RonakPat! Welcome to PF! :smile:

You're missing the obvious …

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

(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)?
 
Equal and opposite, yes. :smile:
 
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?
 
RonakPat said:
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! :wink: :biggrin:
 
Kindly see the attached pdf. My attempt to solve it, is in it. I'm wondering if my solution is right. My idea is this: At any point of time, the ball may be assumed to be at an incline which is at an angle of θ(kindly see both the pics in the pdf file). The value of θ will continuously change and so will the value of friction. I'm not able to figure out, why my solution is wrong, if it is wrong .
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