Two stacked blocks attached to a spring

[mintsnapple]

Homework Statement

Homework Equations

F_spring = kx, where x is the distance compressed
f_friction = uN

The Attempt at a Solution

Forces acting on m: N_1 up, mg down, f_friction to right
Forces acting on M: N_2 up, Mg+N_1 down, f_spring to the right

Block m will still be in equilibrium as long as the force exerted by the spring equals the force of friction:

kx = uN_1
The block isn't accelerating in y-direction so N_1 = mg
So kx = u*mg
x = u*mg/k

Does that look fine?

 

[Pythagorean]

Looks good to me, force balance between the friction and the spring gives the upper bound.

A small nitpick; I might have worded this differently:

"Block m will still be in equilibrium as long as the force exerted by the spring equals the force of friction:"

I would instead say "is equal to or less than".

 

[haruspex]

No, this is wrong. You've not taken into account that the spring also has to accelerate M, so the accelerating force on m will be less than kx.
Let the acceleration be a. Write out the horizontal ∑F=ma equations for both blocks. Don't forget that the horizontal friction force on m applies equally and oppositely to M.

A small nitpick; I might have worded this differently:

"Block m will still be in equilibrium as long as the force exerted by the spring equals the force of friction:"

I would instead say "is equal to or less than".

First, we're not asking for m to be in equilibrium - merely that it does not slip.
Secondly, the condition for not slipping is that the horizontal force required to accelerate it at the same rate as M does not exceed the maximum frictional force. The actual frictional force may be less than maximum.

 

[Pythagorean]

Ugh, thanks haruspex. I'm more disconnected from this stuff than I thought.