Maximum oscillation amplitude for block

[CoasterGT]

Problem:

A 1.0 kg mass is riding on top of a 5.0 kg mass as it oscillates on a frictionless surface. The spring constant is 50 N/m and the coefficient of static friction between the two blocks is 0.50.

What is the maximum oscillation amplitude for which the upper block does not slip?


I don't know where to start. I have looked at trying to do it by looking at the total mechanical energy, but there are too many unknown variables. Any hints to help me get started would be appreciated.

 

[nrqed]

Problem:

A 1.0 kg mass is riding on top of a 5.0 kg mass as it oscillates on a frictionless surface. The spring constant is 50 N/m and the coefficient of static friction between the two blocks is 0.50.

What is the maximum oscillation amplitude for which the upper block does not slip?


I don't know where to start. I have looked at trying to do it by looking at the total mechanical energy, but there are too many unknown variables. Any hints to help me get started would be appreciated.

The max friction force on the top block is $\mu_s n$ where "n" is the normal force on that block, right? (in this case n is simply mg). Using Newton's second law, the force is maximu when th acceleration is maximum. The acceleration is maximum at the extremities of the motion. In shm, the maximum acceleration is $a_{max} = A \omega^2$, right? So find the maximum friction force on the top block, use that to find its maximum acceleration so that it does not slip and then use that to find the maximum amplitude A.

Hope this helps

Patrick

 

[CoasterGT]

It did. Thank you very much!

 

[lostie100]

I don't quite understand this problem. I know the formulas to use, but I'm confused as to which mass I should use in the w=root (k/m) equation. Also, the force of friction is around 4.9N, would that also be the block's acceleration? what would that do?