B Resistive force that a nail will have to overcome to penetrate a piece of wood

[Keelr9]

TL;DR Summary

Can you calculate the resistive force a nail will have to overcome to penetrate a piece of wood?

lets say a hammer of 0.5kg strikes a nail at 10m/s. The nail penetrates into the wood by 1cm. The reason why the nail stops is because friction has eventually overcome the nails momentum.
The retardation of the nail can be worked out, but Can you calculate the force that stops the nail if you have its dimensions?

i apologise if I've missed something out.

 

[jrmichler]

A good question, and welcome to PF. The problem statement gives you enough information to solve the problem if you assume constant deceleration force.

If, on the other hand, you wish to try to estimate that force from nail dimensions and wood properties, I suggest getting a copy of Wood Handbook, Wood as an Engineering Material. This book is available as a free download at: https://www.fpl.fs.fed.us/documnts/fplgtr/fpl_gtr190.pdf.

Look in Chapter 8, where they discuss the withdrawal resistance of nails. Study the part where they discuss the immediate vs time delayed withdrawal resistance, and use that as an estimate of the force to drive the nail. I suggest adding to that force an additional force representing the force to drive the tip of the nail into the wood. A rough estimate of that force would be the cross sectional area of the nail multiplied by the compressive strength of the wood.

Do not expect the calculated force to match the force from the problem statement. If you were to video an actual hammer hitting a nail, you could get the actual hammer velocity. That plus a measurement of nail depth per hit would give actual numbers that could be compared to the force calculated from wood properties. And it would be an interesting experiment.

 

[Keelr9]

A good question, and welcome to PF. The problem statement gives you enough information to solve the problem if you assume constant deceleration force.

If, on the other hand, you wish to try to estimate that force from nail dimensions and wood properties, I suggest getting a copy of Wood Handbook, Wood as an Engineering Material. This book is available as a free download at: https://www.fpl.fs.fed.us/documnts/fplgtr/fpl_gtr190.pdf.

Look in Chapter 8, where they discuss the withdrawal resistance of nails. Study the part where they discuss the immediate vs time delayed withdrawal resistance, and use that as an estimate of the force to drive the nail. I suggest adding to that force an additional force representing the force to drive the tip of the nail into the wood. A rough estimate of that force would be the cross sectional area of the nail multiplied by the compressive strength of the wood.

Do not expect the calculated force to match the force from the problem statement. If you were to video an actual hammer hitting a nail, you could get the actual hammer velocity. That plus a measurement of nail depth per hit would give actual numbers that could be compared to the force calculated from wood properties. And it would be an interesting experiment.

Hi Jrmichler,

Thank you for your reply, I will look at the book you provided, I'm planning on doing experiment with various wood species to find if there is a correlation between the density of the timber, young modulus and the force needed to drive the nail into the wood.

 

[Herman Trivilino]

lets say a hammer of 0.5kg strikes a nail at 10m/s.

The product of those two numbers gives you 5 Ns of impulse. If you had a force sensor you could produce a graph of force versus time and the area under the graph would be 5 Ns.

The reason why the nail stops is because friction has eventually overcome the nails momentum.

I'm not sure what you mean by "overcome" but certainly you can't say whether either is greater than the other. In physics friction is a force, and since force and momentum have different dimensions it makes no sense to compare them. Why not just say the nail stops because of friction?

 

[sophiecentaur]

. In physics friction is a force, and since force and momentum have different dimensions it makes no sense to compare them.

Mixed dimensions account for half the non-Scientists' questions on PF. The language used by all of us in everyday life has this sort of problem built in.

We are left with the response "That's the wrong question. This is the right question and here is the answer." That can be construed as clever clogs and just too smart. People are usually not prepared to start with basics unless they were instilled in that when they first learned things in School so what can one do?