Spring force required to overcome friction between two blocks

[MenchiKatsu]

Homework Statement

In Fig. 15-37, two blocks (m=1.8 kg and M=10. Kg) and a spring (k=200 N/m) are arranged on a horizontal frictionless surface. The coefficient of static friction between the two blocks is 0.40. What amplitude of simple har-monic motion of the spring–blocks system puts the smaller block on the verge of slipping over the larger block?

Relevant Equations

Friction= coefficient of friction x Normal force
Spring force = -kx
W=mg

200 x amplitude= 0.4 x 1.8 x 9.81
But the answer includes the big mass as well. Why ? Isn't it frictionless ? Doesn't friction depend on the weight of the small block ?

 

[MenchiKatsu]

 

[kuruman]

But the answer includes the big mass as well. Why ?

Because when the top mass is on the verge of slipping, the two masses accelerate as one. Begin by finding the maximum common acceleration of the two masses when the amplitude is A. Can you see what the next step is?

 

[MenchiKatsu]

W^2 x A ?

 

[kuruman]

That is incorrect. You already defined W = mg in your relevant equations. Also, please write an equation, not just an expression, and include a few words explaining what that equation expresses mathematically. We are not mind readers.

 

[MenchiKatsu]

Okay I will use small w for angular frequency. w^2 x A= is the acceleration the block undergoes when it is pulled by the string at amplitude A

 

[kuruman]

OK. Can you find the horizontal force acting on the top mass $m$?

 

[MenchiKatsu]

Isn't that just friction ? The spring is attached to the mass on the bottom. The spring pulls the bigger block and the top mass receives a force in the other direction due to friction.

 

[haruspex]

Isn't that just friction ? The spring is attached to the mass on the bottom. The spring pulls the bigger block and the top mass receives a force in the other direction due to friction.

In post 1 you calculated the maximum force from the spring then treated at as acting on the top mass. Clearly it does not.
Yes, the force on the top mass is static friction, but what is the maximum value it can take? So what is the maximum acceleration $m$ can have?

 

[MenchiKatsu]

It would be equal to the frictional force divided by m.

 

[haruspex]

It would be equal to the frictional force divided by m.

You skipped this question: what is the maximum value of that friction? You found that in post 1. You can then divide it by m to get the maximum acceleration, as you say.
The next step is to relate the maximum acceleration to the spring and its amplitude.