Pulley Question - Are the axes wrong?

[cipotilla]

Pulley Question - Are the axes wrong??

Homework Statement

Please see problem # 2 in the attached document.

Homework Equations

Newtons second Law

The Attempt at a Solution

See the two last pages of the attachment, I have attempted a complete solution but my answer is incorrect, I have reviewed the math and I don't think I made a mistake there, is the axes system wrong??

 

[hage567]

I think you have the frictional force acting in the wrong direction on each of your free body diagrams. It will act in the opposite direction of motion, right? So looking at the system, which way to you think the blocks will move when they are released?

By the way: It's no big deal if you pick the wrong direction for the motion of the blocks. You will just end up with a negative acceleration. The important thing is to make sure all of your forces are consistent with whatever coordinate system you choose.

 

[cipotilla]

Block A would move down and B would move up. But if I assume its the otherway around, shouldn't the calculations still work out as long as I am consistant? By consistant I mean, that I say instead that A moves up and B moves down and I place all the forces in the directions according to this assumption instead. Why doesn't it work out this way?

 

[hage567]

"Block A would move down and B would move up. But if I assume its the otherway around, shouldn't the calculations still work out as long as I am consistant? By consistant I mean, that I say instead that A moves up and B moves down and I place all the forces in the directions according to this assumption instead. Why doesn't it work out this way?"

Yes, I just finished editing my post to mention that. LOL

If you assume Block A is going to move downwards, your direction for the friction in your diagram is incorrect. Friction acts in the opposite direction to what you have drawn. (since it opposes motion)

 

[hage567]

OK wait, I just looked harder at your diagram, and I see the arrows you have there showing the direction of motion. They look right. Let me look at it some more...

 

[Doc Al]

Block A would move down and B would move up. But if I assume its the otherway around, shouldn't the calculations still work out as long as I am consistant? By consistant I mean, that I say instead that A moves up and B moves down and I place all the forces in the directions according to this assumption instead. Why doesn't it work out this way?

As long as you have the forces acting in the correct directions, your initial choice of acceleration direction is arbitrary: if you guess wrong, your answer will come out negative. But things aren't so simple when friction is involved, since the direction of friction depends on the direction of motion. If you choose the wrong initial direction of motion, then your friction forces are not in the correct direction and you'll get a wrong answer.

Think about a simpler problem: A block sliding on an incline with friction. It makes all the difference in the world whether the block is going up or down. The acceleration will be totally different in each case, not just off by a sign.

In your problem, you tacitly assumed that block A goes up. When you found a negative acceleration, that should tell you that your original assumption of direction of motion was incorrect and inconsistent with your assumed direction of friction forces.

 

[cipotilla]

I see, thank you. I'll redo the problem now that I've learned that when friction is involved one cannot arbitrarily choose the direction of motion.