Finding x: Block Sliding on Spring SHM

[physicsss]

A block of mass m is attached to a horizontal spring with constant k. resting on top of this block is another block of mass m. a coefficient of static friction mu exists between the two blocks. now suppose the spring is initially at equilibrium length, and someone gives it a push. the block moves in SHM in response. At a certain distance from equilibrium, the top block starts wo slide off the bottom one, find the x in terms of the given quantities and g.

So with the the moment when the top block slides off the block is when umg=ma? and where do I go from here?

 

[futb0l]

$$\mu mg = kx$$

The spring force = the frictional force.

 

[Doc Al]

So with the the moment when the top block slides off the block is when umg=ma?

Right. So this tells you the maximum acceleration that the top block can withstand before it starts sliding. So find the acceleration of the system as a function of distance from the equilibrium postion. (You know the force on the system from the spring, and you know the mass of the system.)

 

[Skomatth]

Hey futb0l,

Are you sure about that? I could be wrong but for the top block $$ma <_= \mu m g$$ (couldn't figure out less than or equal sign) . So when it isn't slipping $$kx = 2ma$$