Hooke's Law derivation problem involving two blocks

[Emethyst]

Homework Statement

A block with mass M rests on a frictionless surface and is connected to a horizontal spring of force constant k, the other end of which is attached to a wall. A second block with mass m rests on top of the first block. The coefficient of static friction between the blocks is u. Find the maximum amplitude of oscilliation such that the top block will not slip on the bottom block.

Homework Equations

Hooke's Law (F = -kx), F = ma

The Attempt at a Solution

So far what I managed to do is get two F_net equations, setting the lefthand direction as the negative direction (this being the direction of the spring force and acceleration). The first F_net equation is (m + M)(a) = -F_spring and the second 0 = umg - F_spring, or umg = F_spring. After this I start encountering problems. I am supposed to end up with x =(ug(m + M))/k as the equation to find the maximum amplitude, but I end up with x = umg/k for in Hooke's Law I first found acceleration: a = -kx/m, then made m = m + M, and finally subbed all three equations together and solved for x. Can someone point out where I'm going wrong here and show me the correct way to derive the correct formula? Any help would be greatly appreciated.

 

[Oddbio]

Well, you said that you made m = m + M.. if you put that into your final equation then it is equivalent to what you said you should be getting.

 

[MaxL]

There are problems with your Fnet equations. For example, the first one is missing the force due to friction from the top block. And Fspring shouldn't be acting on the second block at all. Draw a picture and be very careful in labeling it!

I think you're going about this the wrong way. Start by figuring out what the condition is that makes the blocks slip. When they slip, that means one block is accelrating with respect to the other. So Fnet_topblock DOES NOT EQUAL Fnet_bottomblock.

Also, remember that Ffric doesn't have to equal u*Fnormal. It be less than that, just not more than that.

This is a great problem! Thanks for bringing it to my attention.

 

[Emethyst]

Ok, so there is then going to be only one F_net equation?

 

[MaxL]

Sort of. There are two Fnet equations (because there are two moving bodies) but the idea is to combine them into a single equation, then figure out what you have to do to break the equality.