Maximum Force for Block on Bracket Friction?

[Proximity]

Homework Statement

A 10kg block is resting on a 5kg bracket, which rests on a frictionless surface. The coef. of static and kinetic friction between the block and bracket are .4 and .3, respectively. Find out a) the max force that can be applied to the block without the block sliding on the bracket and b) the acceleration of the 5kg bracket.

http://img114.imageshack.us/img114/1958/56qe9.jpg

Homework Equations

Fnet = m * a

The Attempt at a Solution

This seems like a very simple question but I'm just having an issue with it (plus the book calls it a "challenging" problem so it just seems too easy).

Finding a) was pretty simple, just do 10 * .4 * 9.81 (Normal Force * $$\mu$$_k). I came up with 39.24N as the answer.

To find b I thought it would just have to apply Newton's second law.

39.24N = (5kg + 10kg) * a
a = 2.62m/s

But since this seemed too easy so I thought that I was wrong. Since the bracket exerts a frictional force on the block, do I have to include the force of the block on the bracket as given by Newton's third law? That seemed logical to me but then it would obviously negate the force of the string which would mean no acceleration, and it seems extremely obvious that there would be acceleration.

Any help would be great, thanks.

 

[Doc Al]

Finding a) was pretty simple, just do 10 * .4 * 9.81 (Normal Force * $$\mu$$_k). I came up with 39.24N as the answer.

What you found is the maximum value of static friction, which is not the same thing as the applied force F. (If F simply equaled the max friction force then the block would be in equilibrium.)

So it's not that simple. Apply Newton's 2nd law to the block and to the system as a whole.

 

[Proximity]

That is what F equals though, isn't it? The question asks the max force that can be applied to the block so it doesn't slide. The max force that the static friction can apply is 39.24N, and so the max force on the string that can be applied is also 39.24N.

 

[Doc Al]

That is what F equals though, isn't it?

No.

The question asks the max force that can be applied to the block so it doesn't slide. The max force that the static friction can apply is 39.24N, and so the max force on the string that can be applied is also 39.24N.

That would be true if it wasn't accelerating. But it is. Apply Newton's 2nd law.