Impulse on Rubber and Metal Hammers

[Ballbearing101]

Homework Statement

Between a metal or wooden hammer of equal mass, which is more effective at hammering a nail into the ground.

Relevant Equations

Impulse = Ft
a=f/m

The rubber hammer is more elastic so the time of contact will increase. Ft=m(v-u)
Does this mean it is more effective as less force is needed for the same change in momentum of the hammer (and the nail) so it requires less force from you?
Or does it mean it is less effective as it imparts less force on the nail and not move it as much?

 

[berkeman]

Homework Statement:: Between a metal or wooden hammer of equal mass, which is more effective at hammering a nail into the ground.
Relevant Equations:: Impulse = Ft
a=f/m

The rubber hammer is more elastic so the time of contact will increase. Ft=m(v-u)
Does this mean it is more effective as less force is needed for the same change in momentum of the hammer (and the nail) so it requires less force from you?
Or does it mean it is less effective as it imparts less force on the nail and not move it as much?

Rubber or wooden?

 

[haruspex]

Does this mean it is more effective as less force is needed for the same change in momentum of the hammer (and the nail) so it requires less force from you?
Or does it mean it is less effective as it imparts less force on the nail and not move it as much?

Which are you as user supplying, force or momentum?

 

[Ballbearing101]

Rubber or wooden?

Rubber

 

[berkeman]

Rubber

Thanks for the clarification.

So what is your intuition? And given that intuition, what do you think the quantitative difference is that makes it so much more ineffective to hammer nails with a rubber hammer?

 

[Ballbearing101]

My intuition went to bed at 11.

 

[haruspex]

My intuition went to bed at 11.

If it is awake now, please try to answer my question in post #3.

 

[Adesh]

The important points to be kept in mind:

1. Newton’s third Law will be followed. Nail will push on the hammer with same force.

2. The deformation caused in the rubber hammer would try to come at its origins shape.

 

[Adesh]

Try to think which ball bounces back higher: rubber/tennis ball or metal ball (when dropped from terrace).

 

[haruspex]

The important points to be kept in mind:
1. Newton’s third Law will be followed. Nail will push on the hammer with same force.
2. The deformation caused in the rubber hammer would try to come at its origins shape.

Try to think which ball bounces back higher: rubber/tennis ball or metal ball (when dropped from terrace).

No, as @Ballbearing101 surmised in post #1 it is time of contact that is key. But that has to be coupled with an appreciation of what is the same for both hammers.

 

[Delta2]

It turns out that the physics of hammering might not be so simple after all.

I am thinking that since the rubber hammer will bounce back more it will transfer more momentum to the nail, so seems to be more effective in that way, but of course the bouncing back will make harder the life and cause arm pain to the guy that hammers with it. Where am i wrong @haruspex cause we know i am wrong otherwise people would use rubber hammer from the middle ages...

 

[Adesh]

I am thinking that since the rubber hammer will bounce back more it will transfer more momentum to the nail, so seems to be more effective in that way,

I too think that, because the deformation that will be caused in the rubber hammer by the reaction force of the nail would try to come at its original shape and hence would apply force on the nail again.

 

[Delta2]

I too think that, because the deformation that will be caused in the rubber hammer by the reaction force of the nail would try to come at its original shape and hence would apply force on the nail again.

Not sure about that, i was thinking in terms of the momentum-impulse theorem, since the momentum of the rubber hammer is say MV before it hits the nail, after the hit it will bounce back with velocity -v, so the momentum impulse theorem says that $$-Mv-MV=J$$ where J is the impulse of the force from the nail to the hammer. By Newton's 3rd law the impulse of the force from the hammer to the nail will be $-J=M(v+V)$. The metal hammer will not bounce back rather it will continue with some smaller velocity v' towards the same direction so the impulse $-J'=M(V-v')$ (we assume before the hit metal hammer has the same momentum MV as the rubber hammer) which obviously is smaller than $-J=M(v+V)$.

 

[haruspex]

Not sure about that, i was thinking in terms of the momentum-impulse theorem, since the momentum of the rubber hammer is say MV before it hits the nail, after the hit it will bounce back with velocity -v, so the momentum impulse theorem says that $$-Mv-MV=J$$ where J is the impulse of the force from the nail to the hammer. By Newton's 3rd law the impulse of the force from the hammer to the nail will be $-J=M(v+V)$. The metal hammer will not bounce back rather it will continue with some smaller velocity v' towards the same direction so the impulse $-J'=M(V-v')$ (we assume before the hit metal hammer has the same momentum MV as the rubber hammer) which obviously is smaller than $-J=M(v+V)$.

As I wrote in post #10, this is not what is important. Please do not distract @Ballbearing101.

 

[Delta2]

As I wrote in post #10, this is not what is important. Please do not distract @Ballbearing101.

You are not saying that it is wrong, just that it isn't important. I wonder what is important then but ok i ll make a private conversation with you as to not reveal too much or distract the OP.

 

[Ballbearing101]

This is what evie and irene Curie must of felt like

 

[Ballbearing101]

@haruspex, your first post
What would be the difference? I assume your applying the force as your wielding the hammer and the nail is providing the change in momentum as its stopping the hammer.

 

[jbriggs444]

Post #10 by @haruspex is a good hint. What thing (or things) are the same for both hammers? What thing (or things) are different about the impacts that ensue?

@haruspex has mentioned time of impact. How does that differ for the two hammers? What is the effect of that difference?

 

[Ballbearing101]

The time of impact will increase for the rubber hammer, so for the same change in momentum the force decreases. So if the force needed to change the hammers momentum is less, +considering Newtons 3rd law, therefore, the force on the nail is less.
But if the change in momentum remains the same, (m(v-u)) doesn't that mean the nail will be displaced the same distance regardless of the hammer's property.

 

[haruspex]

if the change in momentum remains the same, (m(v-u)) doesn't that mean the nail will be displaced the same distance regardless of the hammer's property.

You are not considering what opposes the advance of the nail. We are driving it into a fixed block. To make progress we have to overcome the resistive force.

 

[Ballbearing101]

How does that affect it if we're considering a closed system.

 

[haruspex]

How does that affect it if we're considering a closed system.

The nail is being hammered into the ground, and the question relates to the relative movement of the two, so it is not a closed system.

 

[hutchphd]

I think this is a very dubious pedagogical example. For one thing soil is often not a Newtonian fluid (nor for that matter are the fascia in wood with a nail).
Maybe one should be trying to crack a walnut instead? Just a comment..

 

[haruspex]

soil is often not a Newtonian fluid

Why does that make it unsuitable for such a question? I would model it in terms of static and kinetic friction, increasing somewhat as the nail is driven in.

 

[jack action]

I don't understand why the discussion revolves around impulse, force and momentum. From my point of view, this is all about energy. Momentum is conserved, but kinetic energy isn't. There are two ways to look at it:

1. Inelastic collision and coefficient of restitution
2. Model the hammer and the ground as springs and determine the amount of elastic energy necessary to deform them (either elastic or plastic deformation). Whatever energy is used to deform one, will not be used to deform the other.

 

[haruspex]

From my point of view, this is all about energy.

Not so; see post #24. If the peak force does not overcome the resistance of the ground the nail makes no progress. The ground will deform and spring back.

 

[jbriggs444]

Not so; see post #24. If the peak force does not overcome the resistance of the ground the nail makes no progress. The ground will deform and spring back.

Speaking as someone who has swung a hammer into a nail in a soft target (unbacked board) and a hard one (board backed with plank end-on), the difference is dramatic. The effect to which @haruspex refers applies. Nobody who has ever tried it would drive a nail with a rubber hammer. You want a sharp, well-backed impact.

In my mind's eye, I see an ideal impact of hammer on spike being driven into the work as an inelastic collision of hammer head with spike followed by a period of deceleration as the spike plus hammer head move slightly into the work.

 

[jrmichler]

The simple model of a nail being driven into anything is zero movement until a certain force on the nail, then continuous movement as long as that (constant) force is maintained.

Try breaking down the problem like this:

Step 1: What is the force vs time (qualitative plot - hand sketch) of rubber and steel hammers hitting a rigid, immovable object. If the two hammers have equal mass and velocity, how does the area under the two curves compare? How does the time in contact compare? And the peak force? Show us a pair of sketches on the same axes.

Step 2: Apply the knowledge from Step 1 to a nail that needs a certain force to start and keep moving. Look at two possibilities:
1) The hammer bounces off the nail because the peak force is not enough to move the nail.
2) The hammer contacts the nail with enough force to move, then stays in contact while moving the nail. The force is F = ma, where m is the mass of the hammer, and a is the hammer acceleration while in contact. The force F is the force to move the nail.

Speaking as a person who has used heavy, light, hard, and soft hammers. Also sledges, splitting mauls, baseball bats, and axes.

 

[hutchphd]

hy does that make it unsuitable for such a question? I would model it in terms of static and kinetic friction, increasing somewhat as the nail is driven in.

I guess I am thinking mostly about splitting firewood with a maul or wedges. It is not at all clear to me that simple static and moving friction model makes any sense for that process. In particular the resistance force often seems to rapidly increase with the speed of the maul or wedge so there seems a "natural speed limit" because this nonlinearity. Perhaps soil is a simpler system...I've not spent much time pounding in the dirt.
Seems breaking rocks (or walnuts) would provide a more straightforward idea.

 

[haruspex]

I see an ideal impact of hammer on spike being driven into the work as an inelastic collision of hammer head with spike

I don't think inelasticity is in itself an advantage. What matters is the stiffness. Treating the hammer as a massive spring, a high k during compression means a large force. If completely inelastic then there is zero k under decompression, whereas elasticity might give a sufficiently large k to achieve a bit more movement of the nail.

splitting firewood with a maul or wedges. It is not at all clear to me that simple static and moving friction model makes any sense for that process. In particular the resistance force often seems to rapidly increase with the speed of the maul or wedge so there seems a "natural speed limit"

I would have thought the resistance would increase as the split progresses (up to a point) and the same would be true for driving a nail into the ground or into a block of wood. Thus, the threshold force to be exceeded increases with each blow. But to address the question in the thread it suffices to consider a single blow.

breaking rocks (or walnuts) would provide a more straightforward idea.

It might be a simpler problem to analyse, but it is not the one in the thread.