Force of nail after being struck by a hammer

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Homework Help Overview

The problem involves a hammer striking a nail, where the hammer's mass and velocity are given, along with the time taken to come to a stop. The objective is to determine the force experienced by the nail as a result of the impact.

Discussion Character

  • Exploratory, Assumption checking, Mathematical reasoning

Approaches and Questions Raised

  • Participants discuss the calculation of momentum and the application of the force equation, questioning the definitions of initial and final momentum. There is also a focus on determining the mass of the hammerhead from the given weight and gravitational acceleration.

Discussion Status

Some participants have provided calculations for momentum and force, while others are questioning the assumptions made regarding directionality and the interpretation of negative force values. There is an ongoing exploration of the implications of these calculations.

Contextual Notes

Participants note the potential confusion regarding the direction of forces and the implications of negative values in the context of the problem. There is also a mention of the need to clarify the mass of the hammerhead based on the provided weight and gravitational acceleration.

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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 receive?



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?
 
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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 receive?

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 receive?
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.
 

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