Maybe they'll make it out of titanium and go after the ultralight tool enthusiast market? It'll never get used, but damn it's light!
But these multi taskers are pretty much good at nothing.
I reckon a lighter hammer swung faster is more likely to end up with a bent nail.
Also, exponential would be 2^v. v^2 is quadratic.
(And you need to sub in the F=ma part as well to demonstrate your point, so your gain from the lighter hammer should be less than quadratic. Exercise left to the reader.)
Seems that way; if you're using a hammer, the goal is for all parts of the system to come to a stop. You're trying to deform the material you're hammering the nail into; isn't that measured in energy transfer?
Intuitively, I feel like weighty hits tend to drive the nail into the wood, whereas fast hits just bash the nail about. That might be more about accuracy though?
(Also my anecdote confirmed by someone with practical experience, see other comment.)
Yes, if you're using your arm, there's a tradeoff between speed and accuracy. If you're using a nail gun, not so much.
I was just saying that it looks to me like measuring what happens in energy seems correct, and measuring in momentum looks like a conceptual mistake.
I'm assuming that when you swing a hammer, your arm applies a constant force to the hammer. Let's say that force is F, and we are swinging the hammer a distance of d, and the mass of the hammer is M.
Then the acceleration is a = F/M. The distance traveled in time t is 1/2 a t^2 = 1/2 F/M t^2. We want that to be d.
That happens at time t = sqrt(2dM/F). The velocity at time t is a t, so the velocity when the hammer hits the nail is v = sqrt(2dF/M).
That gives a momentum of M v = sqrt(2dFM).
The kinetic energy is 1/2 M v^2 = 1/2 M 2dF/M = d F.
Note that the momentum at distance d depends on the mass. It goes up as the square root of mass. Kinetic energy at distance d, on the other hand, does not depend on mass.
When I've hit hammers with nails, the heavy hammers have always seemed to drive the nail deeper per hit than the light hammers, which suggests that hammer mass does matter, suggesting that it is not kinetic energy that determines how deep the nail is driven.