Frying Pans vs. Hammers: Which Drives Nails Farther with Same Mass and Velocity?

[z0rn dawg]

Someone asked me this question today (this isn't homework, so don't worry):

If a hammer and frying pan both having the same mass and same velocity hit a nail, which will drive the nail in farther? COR is assumed to be the same. Masses are the same, velocities are the same.

Since everything is the same, I said it wouldn't matter as long as the nail is hit by the dead center of the hammer or frying pan. Is this correct?

 

[mgb_phys]

The only exception I can think of is if the centre of the frying pan deflects (like the middle of a tennis racket) and so provides less force.

 

[lightarrow]

Someone asked me this question today (this isn't homework, so don't worry):

If a hammer and frying pan both having the same mass and same velocity hit a nail, which will drive the nail in farther? COR is assumed to be the same. Masses are the same, velocities are the same.

Since everything is the same, I said it wouldn't matter as long as the nail is hit by the dead center of the hammer or frying pan. Is this correct?

It's not correct because the way in which force and/or energy is transferred from a body to another one in a collision, depends on a lot of things, for example their elasticity (even if there isn't any macroscopic deformation), the speed of sound in the two bodies (which things also depends on the kind of materials), the way elastic waves propagate (and/or dissipate into heat) through the materials/structures, ecc. I don't think it's so immediate to understand which is better between the two, in general. In some cases, I wouldn't be surprised if a frying pan were more effective than a hammer.

 

[Bob S]

As long as the coefficient of restitution (COR) is the same, the total impulse transferred to the nail is the same. However, the duration of the impulse is shorter, and hence the instantaneous force is higher with the hammer. This would probably drive the nail further. A low instantaneous peak force is less likely to overcome static friction of the nail in the wood.

 

[cjl]

It's not correct because the way in which force and/or energy is transferred from a body to another one in a collision, depends on a lot of things, for example their elasticity (even if there isn't any macroscopic deformation), the speed of sound in the two bodies (which things also depends on the kind of materials), the way elastic waves propagate (and/or dissipate into heat) through the materials/structures, ecc. I don't think it's so immediate to understand which is better between the two, in general. In some cases, I wouldn't be surprised if a frying pan were more effective than a hammer.

Since the coefficient of restitution is assumed as the same, rebound and elasticity and such are taken care of. Because of that, I would say no difference in this case.

 

[z0rn dawg]

Thanks for all the answers. I didn't know it was this complicated!

As long as the coefficient of restitution (COR) is the same, the total impulse transferred to the nail is the same. However, the duration of the impulse is shorter, and hence the instantaneous force is higher with the hammer. This would probably drive the nail further. A low instantaneous peak force is less likely to overcome static friction of the nail in the wood.

Why would the duration of impulse be longer with the hammer? Are there any equations for this kind of stuff relating COR, time, mass, etc.? I searched google and couldn't find a thing.

 

[turbo]

Why would the duration of impulse be longer with the hammer? Are there any equations for this kind of stuff relating COR, time, mass, etc.? I searched google and couldn't find a thing.

Kind of complicated, because the problem as posed ignores practicalities like the geometries of the tools. When I was framing regularly, I could sink an 8-penny nail with a stroke of a framing hammer. I'd hate to try to do that all day with a cast-iron frying pan, assuming you could find one that only weighed 20 oz or so.

Another thing that your problem does not address is the surface area of the striking surface. Framing hammers are pretty big compared to regular light-duty claw-hammers, but when used with some degree of skill (and some fitness on the part of the user), they can sink a framing nail or spike pretty convincingly. A frying pan could not do this because it would contact the wood as soon as the head of the nail was at the level of the wood, and would stop with a joint-jarring deceleration. With dry, seasoned softwood and a framing hammer, every single nail will be seated lower than that level, because the head of that hammer seats the nail and decelerates only gradually, leaving every nail-head in a hammer-head-shaped depression. I don't know if this is what you're looking for, but I hope it helps.

 

[pallidin]

I would choose the hammer.
My assumption is that more mass directly in-line with an impact point has more effect on the nail than an impacting mass that is laterally spread.

I would suppose that the ideal scenario would be if the diameter of the hammer matches that of the nail. But, oh boy, would you have to be a good aim!

Just my thoughts...

 

[Bob S]

Why would the duration of impulse be longer with the hammer? Are there any equations for this kind of stuff relating COR, time, mass, etc.? I searched google and couldn't find a thing.

The impulse duration with the hammer is much shorter, because the hammer head does not flex like the bottom of the fry pan. Because the coefficient of restitution is the same for both the fry pan and the hammer, the instantaneous forces are higher.

 

[lightarrow]

Since the coefficient of restitution is assumed as the same, rebound and elasticity and such are taken care of. Because of that, I would say no difference in this case.

Ah, ok, infact I was wondering what "COR" could mean Thank you.

 

[lightarrow]

The impulse duration with the hammer is much shorter, because the hammer head does not flex like the bottom of the fry pan.

Hmmm, I don't get it very well; I understand it if there is a collision hammer-nail without other bodies, but since the nail is inserted in another body (wood or what it is) which makes a considerable friction on the nail, the time of contact between nail and hammer should be determined by the total movement of the nail, presumably.

 

[flatmaster]

Are the hammer and frying pan being swung linerally or rotationally? What about moment of inertia?

 

[Topher925]

As long as the masses, velocities, and COR's are the same, then there will be no difference.

 

[Bob S]

Hmmm, I don't get it very well; I understand it if there is a collision hammer-nail without other bodies, but since the nail is inserted in another body (wood or what it is) which makes a considerable friction on the nail, the time of contact between nail and hammer should be determined by the total movement of the nail, presumably.

We agree that the total impulse is the same for the frying pan and the hammer, because in both cases the coefficient of restitution is the same. The impulse is the integral of force over time. The frying pan base flexes during impact and stores energy, and later releases it. Hence the integration time is longer than for the hammer impulse, and therefore the instantaneous force from the frying pan is lower. Static friction of the nail in the wood is higher than sliding friction, so a higher peak impulse force is better to overcome static friction. Take the hammer and hit the center of the frying pan. Do you hear a ringing sound (ding)? That is the resonant frequency of the frying pan flexing.

 

[Topher925]

The frying pan base flexes during impact and stores energy, and later releases it. Hence the integration time is longer than for the hammer impulse, and therefore the instantaneous force from the frying pan is lower.

Think about what you are saying. Do you think the frying pan can store and release that energy isentropically? Of coarse not, meaning that your frying pan will be absorbing energy from the impact which implies that there will be a loss in energy during the collision as heat. If you assume the hammer is inelastic, how could it then possibly have the same coefficient of restitution as the pan assuming the same initial impulse?

 

[csprof2000]

For my money, if you have two identical rigid bodies striking identical nails with identical speeds and on identical trajectories, and if the same amount of energy is transferred in both cases, over the same amount of time and by the same function with respect to time...

how could it be any different?

If you're talking about real hammers and real frying pans and real nails, and approximately similar conditions and actually swinging these things around, my guess is the hammer works better. Otherwise, carpenters would use frying pans.

 

[rahmatkat]

I think youre wrong, though the pan and the hammer have the same mass, the hammer will drive the nail futher.

 

[csprof2000]

What's your basis for saying this?

 

[Phrak]

When I was framing regularly, I could sink an 8-penny nail with a stroke of a framing hammer.

You soaked your nails in wax and gasoline! I saw you do it! Back in the day when I was framing with a 12 oz. skillet this was a no-no.

 

[Dadface]

A most important factor to consider is the ergonomics of the two designs.Has anybody tried to use a frying pan to drive in a nail?Your bacon,eggs mushrooms, tomatoes and fried bread end up on the floor.Um,I fancy a fry up now.Where's the hammer?

 

[rahmatkat]

Sorry, i was anwering someones question, maybe i got on the wrong side of the track.
By the way, What is the formula for Centripital Force? it new to me.