Can You Really Hit a Feather with 200 Newtons?

[gcarreau]

Homework Statement

My teacher puzzled me in the beginning of the year by saying that one cannot possible hit a falling feather with 200 Newtons because a falling feather doesn't have 200 Newtons to hit you back with. (Newton's Third Law)

Homework Equations

None

The Attempt at a Solution

I argued with her that yes, you can hit a feather with 200 Newtons because for example if I was to use all my strength and hit a brick wall and after that with the same amount of strength hit the air in the room both would have the same force, as the force my arm produces cannot just simply vanish. She still said I was wrong and I'd really like to know why if I am wrong as she was unable to clearly answer.

 

[ehild]

Try and observe. You don't need a feather, try to hit air. Do you feel the same when hitting a wall?

"With the same strength" you can accelerate your fist so it has both the same momentum (and velocity) and kinetic energy as it had when hitting the wall. The force is interaction with two bodies. During this interaction, your fist shares momentum and energy with the bodies it interacts. The velocity of your fist will change: it stops in a very short time when you hit the wall: Change of velocity is caused by force, this force is exerted by the wall, and according to Newton's third law, you exert the same force on the wall.

What happens when you just hit into empty air? Will air stop your fist?

ehild

 

[gcarreau]

No air will not stop my fist if I was punching the air. However Newton's third law states that every action has an opposite and equal reaction. When I hit the air I am hitting particles in the air and they are hitting me back. Since my body is it's own system and since force is F=ma I can always create a force using my mass and acceleration of my arm. I'm just trying to say that because one can hit a feather softly and have it move a little, one can also hit a feather with all their strength equaling x amount of Newtons. I don't know if what I'm saying makes much sense but I tried.

 

[ehild]

You do not create force : you "create" acceleration, by exerting force. Force can vanish. If acceleration stops, so does the force. When you exert force with your muscles, your hand will accelerate, it will gain speed. When you hit something, that other body will exert force on your hand, decreasing its speed. The deceleration multiplied by the mass is equal to the force the other body exerts on your hand, and equal to the force your hand exerts on the body. You yourself with all your strength can act only on your arm and hand, not on the other body.

ehild

 

[gcarreau]

Alright that makes a lot more sense now. Thank you ehild.