# Force of nail after being struck by a hammer

• unteng10
In summary, the problem involves a 5lb hammerhead traveling at 5.4ft/s that strikes a nail and comes to a stop in 0.00081s. The equation used is F=Pf-Pi/delta T, with Pf and Pi representing final and initial momentum respectively. The mass of the hammerhead is assumed to be 5/32, and based on the given acceleration of gravity, the resulting momentum is 0.84375. The calculated force is -1041.67 N, but this cannot be a negative force. There may be a need to consider the direction of the forces and clarify the question of what force the nail received.

## Homework Statement

A 5lb hammerhead, traveling at 5.4ft/s strikes a nail and is brought to a stop in .00081s. The acceleration of gravity is 32ft/s^2, What force did the nail recieve?

## Homework Equations

The equation I have is F=Pf-Pi/delta T. Both Pf and Pi have a arrow above them going to the right.

## The Attempt at a Solution

I know I have to find Pf and Pi, and P=mv. With that said would Pf be 0, since it comes to a stop, and Pi be (5lb)(5.4ft/s)? And I am guessing that delta T would .00081s?

unteng10 said:

## Homework Statement

A 5lb hammerhead, traveling at 5.4ft/s strikes a nail and is brought to a stop in .00081s. The acceleration of gravity is 32ft/s^2, What force did the nail recieve?

## Homework Equations

The equation I have is F=Pf-Pi/delta T. Both Pf and Pi have a arrow above them going to the right.

## The Attempt at a Solution

I know I have to find Pf and Pi, and P=mv. With that said would Pf be 0, since it comes to a stop, and Pi be (5lb)(5.4ft/s)? And I am guessing that delta T would .00081s?

Welcome to PF.

The real question here is what is the mass of the hammerhead? Since they give you acceleration of 32ft/s2, then this suggests to me this is how much it weighs. So I would say you need to determine your mass as 5/32 and then multiply by your 5.4 to get your momentum and then proceed as you were apparently intending.

LowlyPion said:
Welcome to PF.

The real question here is what is the mass of the hammerhead? Since they give you acceleration of 32ft/s2, then this suggests to me this is how much it weighs. So I would say you need to determine your mass as 5/32 and then multiply by your 5.4 to get your momentum and then proceed as you were apparently intending.

So, p=mv which would be p=(5/32)(5.4) which equals .84375.
Then, F=Pf-Pi/delta T, which would be (0)-(.84375)/(.00081)-(0), which would equal -1041.67 N, but you can't have a negative force can you? Am I doing this right, or am I missing something?

unteng10 said:
So, p=mv which would be p=(5/32)(5.4) which equals .84375.
Then, F=Pf-Pi/delta T, which would be (0)-(.84375)/(.00081)-(0), which would equal -1041.67 N, but you can't have a negative force can you? Am I doing this right, or am I missing something?

Which direction did you choose as + ?
And what is the question asking?
What force did the nail recieve?
So if the impact of the hammer resulted in a (-) force to the hammer that sounds like it received an upward force and the nail received a downward force.