# Impulse on Rubber and Metal Hammers

## 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?

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berkeman
Mentor
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
Homework Helper
Gold Member
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?

Rubber or wooden?
Rubber

berkeman
Mentor
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?

My intuition went to bed at 11.

haruspex
Homework Helper
Gold Member
My intuition went to bed at 11.
If it is awake now, please try to answer my question in post #3.

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).

haruspex
Homework Helper
Gold Member
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
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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...

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
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Gold Member
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)##.

Last edited:
haruspex
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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
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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.

This is what evie and irene Curie must of felt like

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
Homework Helper
2019 Award
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?

Lnewqban
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
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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.

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

haruspex
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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.

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
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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