Maximum Acceleration of Stacked Blocks on Vertical Spring

[fiziksfun]

An 5 kg block is fastened to the top of a vertical spring (perpendicular to the floor) with a spring constant of 1000 N/m. A 3 kg block sits on top of the 5 kg block.

The springs are pushed down so that they oscillate.

I need help finding the magnitude of the maximum acceleration the blocks can obtain while still remaining in contact. I have no idea where to begin.

Any suggestions!? Help please!

 

[Hootenanny]

HINT: Consider the forces acting on the 3kg block, which force will be zero when the blocks lose contact?

 

[fiziksfun]

Ok so when the blocks lose contact, the force of the spring-mass will be equal to the force of gravity on the 3 kg block.

M(3)*a=-2mg, is this correct?

 

[Hootenanny]

You've still not answered my first question. What are the forces acting on the top block?

 

[fiziksfun]

The forces acting on the block are gravity and the force of the spring, correct? Or friction??

 

[Hootenanny]

The forces acting on the block are gravity and the force of the spring, correct?

Correct, but what I was trying to get at is that the force of the spring acts through the normal force exerted on the block. Hence, the net force acting on the block is $N - mg$. Can you now use this information to write an equation using Newton's second law?

 

[fiziksfun]

ma = N - mg

but what is the magnitude of the normal force ??!? kx !?

 

[Hootenanny]

ma = N - mg

Correct! And what do you know about the normal force when the block leaves the surface of the 5kg block?