Re:The Cole-Bar Hammer, a 7-year old Kickstarter that is sti...
by tzs on Monday January 11, 2021 @10:04PM
(#25741736)
It's probably too late for anyone to see this, but I think momentum is what matters for a hammer. Here is my argument.
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.
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.