Inertial Forces: Is Force Same From Heavy/Light Body?

[olga11]

Homework Statement

If I act a force on a system consisting of a heavy and light body in
contact with each other from the side of the heavy body and then I act
the same force from the side of the light body, the inertial force
between the two bodies would be the same?

Homework Equations

The Attempt at a Solution

I know from experience that the inertial force is bigger in the first case
Does friction has to do with the proof?

 

[Dick]

The contact force between the objects has to accelerate the body that you are not pushing on directly. So if you push on the lighter one, the contact force is greater than if you push on the heavier one. Nothing to do with friction.

 

[olga11]

Thank you for your immediate answer.

Let me see if I got it right.

If the masses m (the light one) and M (the heavy one) are a system of bodies, then no matter on which side I act the force F, the acceleration will be the same, i.e. a.
If I act the force F on the mass m, the contact force F΄ must accelerate the mass M to a.
If I act the force F on the mass M, the contact force F΄΄ must accelerate the mass m to a.
Since a is the same and M>m, then F΄>F΄΄

If there is friction, the only difference is that I will have another acceleration, i.e. a΄

 

[Dick]

Right, exactly. Where a=F/(m+M). I couldn't have put it better myself.

 

[olga11]

You have been very helpful. I would dare to ask another question. I will put it here,too.

A bubble m(t) is in a spaceship with zero gravity.
It seems that the bubble's motion is due to a force F=k.m^2, where k is a constant.
Could this force be due to the acceleration of the spaceship?

My answer:
Let us suppose tha the spaceship moves with acceleration a in regard to an inertial system whose the observer says that no force is acted on the bubble because of zero gravity.
The observer in the spaceship would find a pseudo force on the bubble which would pull it down, just as gravity does. But the pseudo forces are always proportional to the masses. So the answer is NO.
I cannot figure out if the variable mass of the bubble has to do with the answer

 

[Dick]

Your answer is right. Another way to say the same thing is that the acceleration of two objects feeling your 'force' would be the same independent of the mass. The question is asking you to use the converse. If F=km^2=ma, then a=km. So a is not independent of mass and the force can't be purely due to acceleration (or gravity).