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

• B
• Lobotomy
In summary, If you know the weight of the hammer, and the velocity it hits the nail, you can calculate how far it is driven down into the 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

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:

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

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

## 1. How do you calculate the penetration depth of a hammer and nail?

The penetration depth can be calculated by dividing the force applied by the area of the nail's head. This will give the pressure exerted on the wood, which can then be used to estimate the depth of penetration.

## 2. What factors affect the penetration depth of a hammer and nail?

The factors that can affect penetration depth include the hardness and density of the wood, the size and shape of the nail, and the force applied by the hammer.

## 3. Can the penetration depth of a hammer and nail be accurately predicted?

While there are formulas that can be used to estimate the penetration depth, it may vary depending on the variables involved. Factors such as the condition of the wood and the angle at which the nail is struck can also affect the penetration depth.

## 4. Is the penetration depth the same for all types of wood?

No, the penetration depth can vary depending on the type of wood. Harder and denser woods will require more force to penetrate than softer and less dense woods.

## 5. Are there any safety precautions to consider when using a hammer and nail?

Yes, it is important to wear protective eyewear and gloves when using a hammer and nail to avoid any potential injuries. It is also important to use the appropriate size and type of nail for the specific project to ensure proper penetration and stability.