How Does Newton's Third Law Apply When One Block Pushes Another?

[aeromat]

Problem Type: Derivation

Homework Statement

2 blocks of mass m1 and m2 are placed in contact with each other on a smooth, horizontal surface as in the figure below. A constant force F is applied to m1 as shown.

(a) find the acceleration of the system

Homework Equations

Newton's Laws

The Attempt at a Solution

Picture of the problem:

F
-------> [ m1 ][m2]
=================================

Frictionless surface assumed.


FBD Sketch (are the action and reaction forces equal in magnitude?)

For m1:

Applied force -----> [ m1 ] <----- Reaction force by M2?
Fn and Fg are present.

For m2:

Applied force by m1-----> [m2]
Fn and Fg are present.

Is the reaction force received by m1 pushing m2 equal in magnitude but opposite in direction to the applied force on m1?

 

[NJJ289]

Because the problem is only asking you the acceleration of the system, you can safely consider m1 and m2 the "same" block.

Remember, don't confuse yourself with free-body-diagrams. Usually only consider a force for calculation if it results in acceleration. In this case, the only force causing acceleration is the push (or friction, if it specifies).

 

[aeromat]

But wait, the picture of my diagram states that the m1 mass is much bigger than the m2 mass. So, how would this work out? I am getting really confused with the action/reaction forces, and I don't know how I would work without them.

 

[SammyS]

The force exerted by m₂ on m₁ is equal (in magnitude) but opposite (in direction) to the force m₁ exerts on m₂.

I would call this the reaction force.

I would call this the action force.