# Accelerating Cart Problem

1. Jun 24, 2011

### maff is tuff

1. The problem statement, all variables and given/known data

A block is placed against the vertical front of a cart as shown in the figure. (see attachment)

What acceleration must the cart have in order that block A does not fall? The coefficient of static friction between the block and the cart is $$u_s$$.

2. Relevant equations

$$f_s=u_sn$$

3. The attempt at a solution

Ok so if the box doesn't slide down that means that the friction force has to have the same magnitude as the weight of the box, right? I drew my force diagram in the attachment below. So here's my calculations:

$$f_s=mg$$
$$f_s=u_sn$$
$$n=ma$$

plug n into second equation and set first and second equation equal:

$$mg=u_s(ma)$$
$$a=\frac{g}{u_s}$$

This answer is wrong and I don't know why. I think I am missing something huge. Thanks for the help.

Also this is my first time using the LaTex and it took a quite a bit to type it all in so if you have any tips on that, that would be appreciated.

#### Attached Files:

• ###### Accelerating cart problem picture.jpg
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Last edited by a moderator: Jun 24, 2011
2. Jun 24, 2011

### Staff: Mentor

Your work looks good to me. Why do you think it's wrong?

3. Jun 24, 2011

### maff is tuff

It is online homework and it didn't accept it. The feedback said:The correct answer does not depend on the variable: u_s. Does that mean I should sub out u_s for something?
$$a=\frac{g}{u_s} = \frac{g}{f_s/n}= \frac{gn}{f_s}$$ ?

4. Jun 24, 2011

### Staff: Mentor

That makes no sense to me; of course the answer depends on u_s. (What if the surface was frictionless?)

5. Jun 24, 2011

### maff is tuff

If it is frictionless then no matter how hard it is accelerating, it will fall down right? Yeah this question is stumping me. How else do you think I could write it? The new way I wrote it up there is wrong right?

6. Jun 24, 2011

### Staff: Mentor

Right.
Your original answer is the one that makes sense to me. Online systems can be very picky, so be sure you are using the exact symbols that they gave you. (Trying to find ways to avoid writing μ does not make sense to me.)

7. Jun 24, 2011

### WatermelonPig

Is this MasteringPhysics? Haha, well I'll edit in a response.

Ok post a screenshot of the problem I can't see what you're doing wrong.

8. Jun 24, 2011

### maff is tuff

Yes it is MasteringPhysics. I think I entered it in correctly; I'll double check.

9. Jun 25, 2011

### maff is tuff

I'm so stupid I put "u" instead of "μ ". I was in the process of taking a screenshot and I noticed I didn't see a little tail on the "u" so I put a "μ" in there and it accepted it. Man all those points lost on a stupid error but at least I'm not as confused anymore. Anyway, thanks guys for the help. I'll try to think things through more next time but I always say that and still miss things. Thanks again :)

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