# Forces - two objects in contact

## Homework Statement

Two objects, in contact with each other, are being pushed across a table. The masses are 113g and 139g. Friction is negligible. The applied horizontal force of magnitude 0.0538N is exerted on the more massive object. Determine the acceleration of the two object system and the magnitude of the force exerted by each of the two objects on the other.

Fnet = m*a

## The Attempt at a Solution

To find acceleration I use f=ma, with f being the applied horizontal force and m being the total mass:
a= 0.0538/ (0.113+0.139)
a=0.213 m/s^2

Now I'm confused about how the forces are acting between the two objects in the system. How is this calculated?

Write the Newton's 2nd law equation for one of the mass

F=smaller mass *a
F=0.113*0.213
F=0.241N

that's the correct answer ...but I don't understand why. Why is the force acting between the two objects caused by the mass of the smaller object only? Is it because it is the only thing pushing back on the system (like, against the applied force?)

: S

Okay, so what are the forces exerting on the more massive one? And what are the forces on the other?

On the larger mass, there is an applied force and also a force of contact (not sure what type of force this is called) from the smaller object.

Fapp <---- [larger object] ---> Fsmaller object on larger object

On the smaller mass, there is the force of contact from being pushed by the larger mass.

Flarger object on smaller object <-----[smaller object]

I think that's it. I'm confused because I would think that "Fsmaller object on larger object" and "Flarger object on smaller object" would be different in magnitude ...Since the masses of each object are different.

But then again, Newton's third law says for every action force, there's an opposite but equal reaction force. So this force should be equal right?

Hmm, I think the direction should be different:
Fapp ----> [larger object] <--- Fsmaller object on larger object
Flarger object on smaller object ----> [smaller object]
The problem states that the objects are pushed, right?

I think that's it. I'm confused because I would think that "Fsmaller object on larger object" and "Flarger object on smaller object" would be different in magnitude ...Since the masses of each object are different.

But then again, Newton's third law says for every action force, there's an opposite but equal reaction force. So this force should be equal right?

Yes

Thanks!