Forces misconception hammer and nail

[Ken G]

I made the assumption that kg*m/s² are transferable from one body to another just as kg*m/s are. If body A exerts force to accelerate B, B now has the force to accelerate something else. A, it seemed, must have lost some force. A must now not have the ability to produce as much acceleration as it did before. This seems logical.

The problem is, that extra "s" in the denominator makes a big difference. Force is momentum imparted per time, so if a body acquires some momentum in time t₁, it can impart that momentum into something else, but if it does so in a different time t₂, then it will be imparting a different force than what it received. The forces must be the same for action/reaction pairs only, because only then must the times be the same-- it's the same interaction, so it has to take the same time, so involves both the same momentum imparted and the same force, except for the opposite direction.

 

[Dale]

I realize I'm on shaky ground suggesting something like "conservation of force". It seemed to make sense when I wrote it if I thought of force in terms of Newtons. It seemed that any agent of force must lose as many Newtons as it succeeds in imparting to something else.

Your hand may exert a force of only one Newton over a second on a hammer, but the hammer can exert a force of a thousand Newtons over a millisecond on the nail. If force were conserved then the hammer could never have generated more than one Newton of force on the nail because that was all the force that was imparted to it. A hammer would be useless because it could not generate any more force than you could already generate with your hand.

 

[zoobyshoe]

The problem is, that extra "s" in the denominator makes a big difference. Force is momentum imparted per time, so if a body acquires some momentum in time t₁, it can impart that momentum into something else, but if it does so in a different time t₂, then it will be imparting a different force than what it received. The forces must be the same for action/reaction pairs only, because only then must the times be the same-- it's the same interaction, so it has to take the same time, so involves both the same momentum imparted and the same force, except for the opposite direction.

Yes. You're alluding to impulse, I believe: F (Δt)=Δρ. The longer the time over which a force acts the greater the change in momentum it produces. And I see what you mean in the whole final sentence.

Your hand may exert a force of only one Newton over a second on a hammer, but the hammer can exert a force of a thousand Newtons over a millisecond on the nail. If force were conserved then the hammer could never have generated more than one Newton of force on the nail because that was all the force that was imparted to it. A hammer would be useless because it could not generate any more force than you could already generate with your hand.

This suggests the quantity that is conserved I was grasping for each time I said "force" is Impulse. If the hammer generates a thousand Newtons it is only because it acts on the nail over a proportionately shorter time than the one Newton arm acts on the hammer. That latter sentence is correct, right? The multiplication of the force has to come at the expense of the amount of time over which the larger force can be applied, just as with distance and force in the same case of leverage? The distance over which the magnified force of the short arm of a lever can work is inversely proportional to the distance over which the smaller force has to work on the long arm of a lever. F (Δt) = -F (Δt) as F (d) = -F (d). (d = distance)