How Do You Calculate Acceleration of Multiple Connected Blocks?

[matajone]

I've been given the mass of 3 blocks connected by string. I know the force and the coefficient of friction and am asked to determine acceleration. The answer will be in a form something like this a=8ug. (Grrr...for not remembering how to change to scientific lettering.) Anyhow, my textbook hasn't been very helpful, and I simply can not remember how to get started on this. I know that I'm being stumped by the multiple, connected boxes. Any help you can throw my way would be appreciated.

Matt

 

[chroot]

I think you'll have to explain the problem a little more completely and precisely for us to be able to help.

In any case, problems like these usually are just exercises in drawing free-body diagrams and applying Newton's second law.

- Warren

 

[matajone]

I'll just give you the question verbatim.

Consider a force pulling 3 blocks along a rough horizontal surface, where the masses are a mulitple of a given mass m, as shown in the figure below. The coefficient of the kinetic friction is u. The blocks are pulled by a force of 84umg.


_______ _______ _______
| |T1 | |T2 | |
| 2m |---| 5m |---| 7m |
_______ _______ _______

Determine the acceleration.

 

[chroot]

Since the blocks move as one (the string connecting them is assumed to be ideal), the question is equivalent to just finding the acceleration of a single block with a total mass of 14m. Draw a free-body diagram and use Newton's second law.

- Warren

 

[matajone]

Thank you. I took some time away from the problem, and that is what I decided to try. Thanks for letting me know I wasn't just making something up to make myself happy.

Matt

 

[matajone]

Ok, now I'm confused.

I got to the next question and it is asking for something I don't even remember hearing about during any of the lectures and I can't find in the book. Just a simple nudge in the right direction would be great.

"The equation of motion for the central mass 5m is given by."

Then I'm give 9 different options and I have to identify the correct one.

I think it is:

T2 + T1 + 5umg = 5ma

However, I have no idea why I think that. Just looking at it makes me think it is.

Matt

 

[chroot]

Once again, you need to more precisely describe your problem if you wish us to help you.

T1 and T2, assuming they are the tensions in the strings to the left and right, are in opposite directions. Thus, you probably should add one and subtract the other, not add them both. Obviously, when the tensions are equal in magnitude but opposite in direction, there is no net force, and thus no movement at all.

- Warren