Writing something a few days ago, I came across this picture and was reminded that I meant to post it here and ask a question.
In the photo, I'm forcing a Wills Cattle Creep wall into a foam baseboard. By gently tapping it with a big hammer several times, I was able to shove it in to the foam without damaging the plastic part and with plenty of control.
Had I used a smaller hammer, I'd have had to whack it hard to get the same effect, smashing the plastic.
The question: Why is easier to give things a gentle tap with a big hammer than a small one?
Something to do with momentum? I can use the principle, but can't entirely get my head around why it works. That bothers me, which is why I'm asking you.
It might also have something to do with the area the force is transmitted through. (I think a larger surface area might mean a lower pressure - or something like that.)
ReplyDeleteAnother option might be to rest a block of wood on top of your bridge - then get out the "gentle persuader".
(While I think about it, I wonder if it might also be worth thinking about using a rubber or plastic mallet, instead of the precision instrument in your photo.)
Otherwise, I'm not really sure - it's rather a long time since I did physics in school!
I would guess that with a big hammer you are primarily using the hammer's weight rather than the velocity of the strike. A slower velocity means the shock waves spread more slowly from the impact point. Plus the size of the hammer's head means the impact is spread over a bigger area.
ReplyDeleteConsider that a person firing a gun will receive only a bit of a jolt to the hand and arm while the person receiving a bullet gets a bit dead.
Hi Phil, is it from F=ma, one of Einstein's theories from memory. The force you want is the same with both a large and a small hammer, but the larger hammer having a greater mass only needs a smaller acceleration, and thus less of a tap than a lighter hammer which needs more acceleration and thus a bigger tap.
ReplyDeleteI think the amount of energy is mass x velocity. So you get the same energy with a bigger hammer at a slower speed.
ReplyDeleteAnd the smaller hammer would pass the energy through a smaller area on the piece being pounded, creating extra stress.
Maybe smaller hammers need more speed to get the same impact, that means less control.
ReplyDeleteI'd use a bigger hammer because it offers me more control than a smaller one. The lighter the hammer the further you have to 'swing' it to deliver the same effect. I find a shorter movement with a bigger hammer is easier to control. But don't ask me to explain the physics (work =force x distance moved and all that stuff....)
ReplyDeleteLetter stamps always work best with a massive hammer. A mallett is standarx milling machine fare to seat things in vices.
ReplyDeleteHi Phil,
ReplyDeleteI'm no expert (studying electrical not mechanical engineering!) but I thought I'd try and explain my thoughts. There are several factors contributing for this:
Deformation to the plastic itself is easy, as it is a very soft material. The name for this deformation is strain. Stress is the measure of the pressure within the structure and is proportional to strain; so the more stress we put into the structure, the more it will deform.
As Stress = (force applied to the body) / (area the force is applied) , it is clear that a larger hammer head reduces the stress within the plastic.
Momentum is conserved during a collision. Think of a huge, heavy, moving truck colliding with a stationary car: they'll both be moving afterwards, but not as quickly as the truck did before. The relationship is: momentum (p) = the velocity (v) x the mass (m).
For your situation, we have a mass (the hammer, h), it's velocity (before collision, h1) and afterwards its mass and new velocity (h2) and the moving plastic piece (m(p) and v(p)).
This can be described as:
m(h) x v(h1) = m(h) x v(h2) + m(p) x v(p)
The exact ratio of the moving parts after the collision requires a material-dependant variable but for us this is enough.
The most important thing to realise is that the energy transferred to the plastic is kinetic energy, defined as E = 1/2 x m x v^(2).
The momentum required to move the plastic must be the same for both a small and a large hammer. That means that the small hammer has to move quicker in order to have the same value for the momentum (p = m x v). So long that we apply constant momentum, the kinetic energy is proportional to the velocity.
This means that our larger hammer, despite doing the same job, passes less kinetic energy into the plastic as the small hammer. More kinetic energy causes more stresses, heat, and so forth.
I hope this helps
It might help to visualise that momentum is related to mass. Imagine a football rolling down a sloped driveway and also your car. You can easily put your foot out to stop the football dead in its tracks, but try the same with your car! If you can stop the car it will push your quite a few feet before you do manage it. The small vs large hammer is the same. Your arm gives the hammer momentum and if each hammer's speed is the same then the small hammer is easily stopped in its tracks due to less momentum than the large hammer which shoves whatever it contacts further before coming to rest. What we don't really notice the amount of arm work needed is more on the large hammer to get it going. This is where the energy for the momentum comes from. It's why sledgehammers break things up so easily, but why they take a lot of effort to swing them.
ReplyDelete