Two people pushing off each other

[azure kitsune]

Homework Statement

A father and his seven-year-old daughter are facing each other on ice skates. With their hands, they push off against one another. (a) Compare the magnitudes of the pushing forces tat they experience. (b) Which one, if either, experiences the larger acceleration?

Homework Equations

Newton's second and third laws

The Attempt at a Solution

Let the father be on the right and daughter be on the left. Let the right be the positive direction.

Then the force the father exerts on the daughter is -F_father while the force the daughter exerts on the father is +F_daughter

By Newton's third law, because the father is pushing on the daughter, the daughter exerts a +F_father force on the father. But the daughter is already exerting +F_daughter on the father. Are these values supposed to be added together to get the total value of force exerted on the father? I'm kind of confused how these forces would add up because I can imagine that if you push on someone, you move backwards because of the reaction force, but now that person is pushing too so there are all these forces and I'm not sure what to do with them.

(If that's the case, then the forces exerted on both people would be equal in magnitude and whoever has smaller mass would experience larger acceleration, right?)

 

[edziura]

"the forces exerted on bother people would be equal in magnitude and whoever has smaller mass would experience larger acceleration, right?"

This is correct.

The 3rd law has always been confusing. One way to deal with it is to keep in mind that the two forces involved, action and reaction, always act on different objects, and are always equal in magnitude (and of opposite direction).

The fact that both people are pushing adds confusion, but the 3rd law still holds; it just means that the magnitude of the forces is greater than it would be if only one person 'pushed' while the person didn't 'push back'.

 

[azure kitsune]

Thanks for the explanation! I think I understand it better. (But thinking about this too much still makes my head hurt...)