How far does a 0.5kg hammer at 50m/s drive a nail into wood?

[Lobotomy]

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

 

[BvU]

https://isaacphysics.org/questions/hammer_nail

 

[nasu]

What browser do you use to access the link?
It doesn't seem to work with either Chrome or Firefox.

 

[The Bill]

The link works fine on Chrome for me.

 

[nasu]

Now it works for me too.
Maybe something temporary down on their side.
Thank you.

 

[Lobotomy]

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

 

[marcusl]

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.

 

[jim mcnamara]

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.

 

[hackhard]

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

 

[hackhard]

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