What is the acceleration needed to prevent block A from sliding down the cart?

[maff is tuff]

Homework Statement

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 $$u_s$$.

Homework Equations

$$f_s=u_sn$$

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.

 

[Doc Al]

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

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

 

[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?
$$a=\frac{g}{u_s} = \frac{g}{f_s/n}= \frac{gn}{f_s}$$ ?

 

[Doc Al]

The feedback said:The correct answer does not depend on the variable: u_s.

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

 

[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?

 

[Doc Al]

If it is frictionless then no matter how hard it is accelerating, it will fall down right?

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?

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.)

 

[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.

 

[maff is tuff]

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

 

[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 :)