# Deceleration and forces

• furor celtica

## Homework Statement

ok i just need an explanation for one tiny thing.

a drop-forge hammer of mass 1500kg falls under gravity on to a piece of hot metal which rests in a fixed die. from the instant the hammer strikes the piece of metal until it comes to rest, the hammer is decelerating at 1.5 ms^2.
find the magnitude of the force exerted by the hammer on the piece of metal while (a.) the hammer is decelerating (b.) after the hammer has come to rest.

## The Attempt at a Solution

of course b. was easy, 15000N
for a. I'm not sure, i know it has something to do with Newton's third law. the answer is 17500 N but why would the force be greater while the hammer is decelerating? isn't deceleration just the difference between opposing forces divided by weight? in this case i would have answered that the force was 15000N as well.

The same way that there is a normal force on the hammer when it is sitting stationary there is also a force that causes the hammer to decelerate and a force that is normal to this that acts on the material being struck by the hammer.

You are given that it decelerates at 1.5 m/s^2. Determine the force due to this in addition to the force from the hammer.

Not sure why the answer came up as 17500N as it seems to me it should be 17250N.

yes that is the correct answer. where does the decelerating force come from?

where does the decelerating force come from?

F = ma

'a' here being the deceleration of the hammer; i.e. the metal pusing back on it.

You can think of it a few different ways. The point is that the hammer and the piece of metal don't merge so there is a force pushing the two apart. The important thing to note for this problem is that for every action there is an equal but opposite reaction...
What you call the forces is irrelevant since it could be modeled multiple ways. I imagine it is actually an electromagnetic force that repulses the two objects.

I imagine it is actually an electromagnetic force that repulses the two objects.

It's not electromagnetic. The question doesn't state the either the hammer or the metal are charged and they should therefore both be assumed to be electrically neutral.

The force that causes two objects to repel is electromagnetic. Why don't the two objects pass through each other? Electrically neutral just means that the average charge is equal. An electron and a proton together are electrically neutral but that doesn't mean they don't cause an electromagnetic force on each other.

That's why I said you can call it what you want but that's what I think the fundamental force keeping them apart is.

The force that causes two objects to repel is electromagnetic. Why don't the two objects pass through each other? Electrically neutral just means that the average charge is equal. An electron and a proton together are electrically neutral but that doesn't mean they don't cause an electromagnetic force on each other.

That's why I said you can call it what you want but that's what I think the fundamental force keeping them apart is.

This is at best misleading and at worst just wrong.

Of course if one brings two atoms close together there will be an induced electric dipole due to the electron clouds and nuclei repelling/attrcting each other. Whilst this may be a small force for individual atoms there are of course many of them in your average lump of metal.

However, the actual reason why solids don't pass through each other is due to the pauli exclusion principle - two fermions (spin 1/2 particles) cannot exist in the same quantum state simultaneously. Quantum mechanically one would say that the closer together you bring two fermions the more their anti-symmetric wavefunctions overlap and thus keep them appart. This is the reason solids on the macroscopic scale appear rigid (putting special relativity aside for clarity.) This phenomenon has been reliably prooved some time ago by Freeman Dyson, a theoretical physicist from Prinston - Hence, I'm afraid, you were wrong (about the predominant cause at least.)

Returning to the scope of the original question - it is clearly posed at an pre-university level where no consideration of quantum mechanics (or molecular structure for that matter) is either expected or necessary. Hence my former comment regarding the fact that both the hammer and metal should be assumed electrically neutral unless otherwise specified. The question should instead be answered using nothing more than Newtonian mechanics. Hence why I said your answer is misleading.

Isn't that just the approach from a particle physics standpoint? How is that any more valid than the electromagnetic repulsion overcoming the strong force?
I don't know anything about Freeman Dyson and am not going to pretend that I know everything but my understanding is that the electromagnetic repulsion exceeds the strong force as it approaches an infinite repulsion as the particles come together.

I'm not to sure about the pauli exclusion principle as the root cause since a fermion pair can become a boson. I'm not saying that I'm correct but to my best understanding it seems reasonable. Hopefully I'll learn more depth in grad school but I don't see why you are so adamant about the particle approach.

Either way I agree it is irrelevant to the homework problem. I wasn't trying to solve the problem via the electromagnetic force, I was just trying to answer the question about where the decelerating force comes from which I interpreted as a theoretical question and like I said before there are multiple ways of thinking about it.

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hi furor celtica! for a. I'm not sure, i know it has something to do with Newton's third law. the answer is 17500 N but why would the force be greater while the hammer is decelerating? isn't deceleration just the difference between opposing forces divided by weight? in this case i would have answered that the force was 15000N as well.

It's more to do with Newton's second law …

the forces on the hammer have to satisfy Ftotal = ma …

when the hammer has stopped, that's N - mg = 0

before then, N - mg = a, so N is bigger 