Hammer & a nail -- Calculating penetration depth into wood for first strike

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Discussion Overview

The discussion revolves around calculating the penetration depth of a nail into wood when struck by a hammer. Participants explore the necessary parameters and equations, including the weight of the hammer, its velocity, friction forces, and other factors influencing penetration depth. The scope includes theoretical considerations and practical applications related to mechanics and material properties.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested
  • Mathematical reasoning

Main Points Raised

  • One participant suggests using momentum and energy equations to calculate penetration depth but expresses uncertainty about the role of friction forces.
  • Another participant proposes that fracture energy needed to propagate a crack in the wood is more relevant than friction, noting the complexities involved in determining this energy.
  • A different viewpoint highlights that the characteristics of the nail, such as diameter and surface, as well as the type of wood, significantly complicate the calculations.
  • One participant mentions that extraction resistance is similar to driving resistance but notes that driving requires more energy, referencing a source for further details.
  • Another participant suggests a method involving constant physical properties and using slow motion to measure penetration time, leading to a calculation of penetration distance based on retardation.

Areas of Agreement / Disagreement

Participants express various viewpoints on the factors affecting penetration depth, indicating that there is no consensus on the most relevant parameters or methods for calculation. Multiple competing views remain regarding the importance of friction versus fracture energy and the influence of nail and wood properties.

Contextual Notes

Limitations include the dependence on specific wood types, nail characteristics, and the assumptions made about forces acting on the hammer. The discussion highlights the complexity of the problem and the need for further exploration of the variables involved.

Lobotomy
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If you know the weight of the hammer, and the velocity it hits the nail. What would you need to know about friction forces, etc in order to calculate how far it is driven down into the wood? So assume the hammer weight 0,5kg and it is being swung at 50m/s when it hits the nail. Friction is (?). how far is the nail driven down?

I assume these two equations at least are needed.
  1. Impuls = p= m*v
  2. Energy = m*v^2/2
 
Physics news on Phys.org
What browser do you use to access the link?
It doesn't seem to work with either Chrome or Firefox.
 
The link works fine on Chrome for me.
 
Now it works for me too.
Maybe something temporary down on their side.
Thank you.
 
BvU said:
https://isaacphysics.org/questions/hammer_nail

Thanks.

How to solve the first one? I've tried using both the momentum and energy equations, calculating the v for the hammer+nail weight knowing the hammer weight and hammer initial velocity. i got something like 9,73 and 9,86 but it says incorrect for both of them.

second question uses the answer (velocity) of first questions, just multiplied by the weight i guess to get the impulse?

third not sure
 
Rather than friction, don't you need the fracture energy needed to propagate a crack? That, in turn, will depend on the energies needed to both separate and rupture wood fibers. Not sure how to get that information.
 
The nail's addition to the problem(especially diameter, surface, point, etc.) measured in terms of lateral extraction resistance and species of wood is a messier complication than you might like - from 1959 -
http://naldc.nal.usda.gov/naldc/download.xhtml?id=CAT88208690&content=PDF
See pp 35-39

Extraction resistance is approximately the same as resistance to driving, driving requires more. But this is as good as it gets. Otherwise you have to go to ASTM for particular applications.
 
Lobotomy said:
how far it is driven down into the wood?
which wood are you talking about
answer depends on type of wood , thinness of nail , material of nail , impact time ,etc too many variables
take all but one factor const and plot a graph
this might take you somewhere close to final expression
 
  • #10
suppose type of wood , type of nail, thinness of nail etc physical properties are const
assuming const force acts on hammer always
now clock time taken to penetrate by slow motion cam
u/t gives retardation (u is initial velo)
plug retardation a in-
(u^2)/(2.a) gives penetration distance
 

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