# Calculating the speed of hammer to drive a nail in the wall

• ermcnoobphysics
In summary, the hammer needs to be moving at a speed of 19.365m/s in order to drive the nail in the wall in one stroke.
ermcnoobphysics
1. We know that we need 5000N to drive a nail 2.5 cm into a wall. How fast does a hammer of 500g mass have to be in order to drive the nail in the wall in one stroke?(look at the picture if it is unclear. The 2 cm in the picture should be 2.5cm)

2.
F=m*a
W=F*x
x=distance

3. I thought it would simply be 10m/s
since 5000N=10m/s*500g.
But my teacher said it is wrong. Now I have to get to the solution which is 19m/s and show him how I did it.

Last edited:
A picture has not been attached. Does the hammer strike perpendicular to the wall?

PWiz said:
A picture has not been attached. Does the hammer strike perpendicular to the wall?
Now it should be there. Sorry I thought I had uploaded it.

I presume that the graph extends all the way to s=2.5 cm ?

PWiz said:
I presume that the graph extends all the way to s=2.5 cm ?
Well the 2 cm should be 2.5cm. So 2.5 cm corresonds to the 5000N,

ermcnoobphysics said:
Well the 2 cm should be 2.5cm. So 2.5 cm corresonds to the 5000N,
That simplifies things considerably. You've been given the force and the displacement in the direction of the force. Does any conservation law come to your mind? How is this related to the velocity at which that 0.5kg hammer needs to be moving at?

PWiz said:
That simplifies things considerably. You've been given the force and the displacement in the direction of the force. Does any conservation law come to your mind? How is this related to the velocity at which that 0.5kg hammer needs to be moving at?
So the work is: 2.5cm*5000N =12500J
So then the work energy theorem says:
W=KEf-KE0
We can eliminate KE0 so it is
W=0.5*m*v^2
√(W/0.5*m)=v
So we get v=7.071m/s
This looks correct to me, but apparantely it is 19.0m/s

ermcnoobphysics said:
So the work is: 2.5cm*5000N =12500J
So then the work energy theorem says:
W=KEf-KE0
We can eliminate KE0 so it is
W=0.5*m*v^2
√(W/0.5*m)=v
So we get v=7.071m/s
This looks correct to me, but apparantely it is 19.0m/s
No, a constant force is not applied along the 2.5 cm displacement! The force increases linearly as can be seen in the F-s graph. Try calculating the area under the graph.

O
PWiz said:
No, a constant force is not applied along the 2.5 cm displacement! The force increases linearly as can be seen in the F-s graph. Try calculating the area under the graph.
Ohhhhh... I understand...
Area under graph is 9375N of course and then
9375N : 500g=18.75 m/s
Thanks a lot, now I get a bonus to my grade :)
Just one last (stupid)question. Why isn't it possible to calculate the 18.75m/s using W=0.5*m*v^2 to calculate the velocity?

ermcnoobphysics said:
O
Ohhhhh... I understand...
Area under graph is 9375N of course and then
9375N : 500g=18.75 m/s
Thanks a lot, now I get a bonus to my grade :)
Just one last (stupid)question. Why isn't it possible to calculate the 18.75m/s using W=0.5*m*v^2 to calculate the velocity?
Your procedure and answer is incorrect. Firstly, why will the area have the units of N? Also remember that the units along the x-axis are cm, not m. Do you know what the area represents?

I don't understand why you're using ##F=ma## over here: this expression will give you the average force that the hammer exerts on the wall as it decelerates to a stop (while hitting the nail). We are not interested in this result. In fact, the question itself mention the singular word "velocity," which should reveal to you that they are asking the constant speed at which the hammer must be moving to drive the nail in (constant velocity = 0 acceleration)!

The last part of your post is in fact using the correct approach. Try some energy calculations!

PWiz said:
Your procedure and answer is incorrect. Firstly, why will the area have the units of N? Also remember that the units along the x-axis are cm, not m. Do you know what the area represents?

I don't understand why you're using ##F=ma## over here: this expression will give you the average force that the hammer exerts on the wall as it decelerates to a stop (while hitting the nail). We are not interested in this result. In fact, the question itself mention the singular word "velocity," which should reveal to you that they are asking the constant speed at which the hammer must be moving to drive the nail in (constant velocity = 0 acceleration)!

The last part of your post is in fact using the correct approach. Try some energy calculations!
Okay area under graph is 93.75 J
I use
93.75J = 0.5*0.5kg*v^2
→v =19.365m/s
Okay now I am sure it is correct!
Haha thanks for helping an idiot like me..I make so many simple mistakes with units..I'll keep that in mind for the future.thanks again

ermcnoobphysics said:
Okay area under graph is 93.75 J
I use
93.75J = 0.5*0.5kg*v^2
→v =19.365m/s
Okay now I am sure it is correct!
Haha thanks for helping an idiot like me..I make so many simple mistakes with units..I'll keep that in mind for the future.thanks again
Don't call yourself an idiot; everyone overlooks some things at one point or another - just keep learning from your mistakes!

F(2.5cm) = 6250(N). Try again.

theodoros.mihos said:
F(2.5cm) = 6250(N). Try again.

## 1. What factors affect the speed of a hammer driving a nail into a wall?

The speed of a hammer driving a nail into a wall can be affected by several factors, including the weight and design of the hammer, the force applied by the person wielding the hammer, the material and thickness of the wall, and the condition of the nail.

## 2. How can I calculate the speed of a hammer driving a nail into a wall?

To calculate the speed of a hammer driving a nail into a wall, you can use the equation v = √(2Fd/m), where v is the velocity of the hammer, F is the force applied, d is the distance the nail is driven, and m is the mass of the hammer. You will also need to measure the time it takes for the hammer to reach its maximum depth in the wall.

## 3. Does the angle of impact affect the speed of a hammer driving a nail into a wall?

Yes, the angle of impact can affect the speed of a hammer driving a nail into a wall. A hammer that strikes the nail at a shallower angle will have a slower speed than one that strikes the nail at a steeper angle. This is because the force applied to the nail is spread out over a larger surface area at a shallower angle, resulting in less driving force.

## 4. How does the hardness of the wall material affect the speed of a hammer driving a nail?

The hardness of the wall material can affect the speed of a hammer driving a nail in two ways. First, a harder material will require more force to drive the nail, which can result in a slower speed. Second, a harder material may also be more resistant to denting, which can cause the hammer to bounce off the surface and reduce the speed of the nail being driven.

## 5. Can the speed of a hammer driving a nail be increased by using a heavier hammer?

Yes, using a heavier hammer can potentially increase the speed of a nail being driven into a wall. This is because a heavier hammer will have more mass, which means it can deliver more force to the nail. However, the person wielding the hammer must also be able to handle the weight and exert enough force to take advantage of the hammer's increased mass.

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