# Help with p.s.i. impact equation based on velocity, area and mass?

Help with p.s.i. impact equation based on velocity, area and mass????

Hey Everyone,

I am new to this forum, so I hope this is in the right format

## Homework Statement

Does anyone know the equation to calculate the pressure exerted on an object by another moving object?

i.e. If I swing a hammer whose head is x square inches, at y feet per second, weighing z pounds, then how many p.s.i. will be exerted when it hits?

## Homework Equations

No Idea, but if anyone knows of a website that outlines this I would also appreciate it very much. I tried googling "Impact equations" and got nothing relevant.

## The Attempt at a Solution

No Idea where to start.

-cds333

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Need help with simple impact equation based on area, mass & velocity...

Hey,

Does anyone know the equation to calculate the pressure exerted on an object by another moving object?

i.e. If I swing a hammer whose head is x square inches, at y feet per second, weighing z pounds, then how many p.s.i. will be exerted when it hits?

I know practically nothing about physics so any help please don't be too esoteric, anything appreciated though.

-cds333

ok so hopefully you can follow... with little physics knowledge im assuming you dont have much calculus knowledge... alright so your dropping the 10 lb weight from rest and your acceleration is constant due to gravity. a=32.3 ft/s integrate and you will have velocity V=32.2*t + 0 the zero is your initial velocity which is zero because it starts at rest. integrate again and you will have your position as a function of time S = 32.2t^2 + 10 the ten is your initial dropping point... so you wanna find when it will strike the ground so you set S = 0 and solve for t... this will give you the time when the object will hit the ground... i got .5573 seconds when the object hits. plug this into your second equation and get your velocity at that time which is 17.94 i believe... now that is your velocity at the time of impact... so at impact the object will come to a complete stop, exerting all of its energy into what it is striking. so as newton said F = m*a so you know your mass (10lb/32.2ft/s) [remember its mass not weight so you must divide by 32.2] and now you need to know how long the impact took... because you know that acceleration is change in velocity divided by change in time, so your change in velocity is from 17.94 to zero which is just 17.94 now divide that by how long the actual impact [which should be a very short amount of time hence the name impact/impulse] took which can depend on the material. then you will have the acceleration/deceleration...... multiply that by the mass and you will get the force from the impact...

can anybody confirm?

Hey thanks for the reply, shamrock.

Does the fact that it is not falling have any thing to do with it? The hammer in question would be swung, most likely parallel to the ground. I need to compute the amount of pressure exerted because I need to make sure what I am building is strong enough to withstand the force of an average adult male sledgehammer swing. The material is concrete, rated at 5000 psi, once I know the p.s.i. of my sledgehammer (at average velocity), I can go ask the concrete guy how much re-bar and other crap I need to load it up with to provide adequate structural integrity.

For the purposes of this equation the velocity would be constant, wouldn't it? I mean, technically it could never be absolutely constant I know, but I don't need to be exact, just to within +/- 250 p.s.i. end result. I plan to shoot video of me swinging it in front of a grid to get swing speed, and I would already know the mass and surface area of the hammer head. I just need to know how to compute it all together. You were right on BTW - no calculus exp.

Thanks again for helpin' me out, I have no idea who else to ask.

ok the fact that it is falling is not a big deal... i used that example because you can calculate the velocity at a given time preatty easily... in your case it might be a little easier because you dont need to calculate the velocity if you have a high speed camera.

So with a sledge hammer it could be pretty hard to calculate what kind of pressure you will be exerting because force is based on mass and acceleration. The head of the hammer will have a velocity right before impact, but it is hard to say whether it will still be accelerating or not based on a persons swing.

So this is how i would do it if you know that the head of the hammer is close to constant velocity at impact. Try and weigh just the head of your sledge hammer in pounds. Divide that by 32.2 to get the mass (remember to do this because lbs. are weight not mass). Next, use your camera to find out the velocity right before impact. You will probably have to zoom your camera in to the impact zone to determine exactly when the head is striking the concrete. Then you need to determine the amount of time from when the head starts to strike the concrete to when it comes to a complete stop (it will probably bounce back again so you might have to determine when the head changes directions from striking to bouncing back).

So your acceleration/deceleration is your velocity that you determined, divided by the time that you determine the impact took place (sould be a matter of milliseconds). Multiply that deceleration that you just calculated by the mass you attained in the beginning and you will have the force applied. Divide that force by the area of the hammer and you will have pounds per square inch.

This may not be as accurate as you may need because when the hammer is striking the concrete it is decelerating at different rates as the two materials compress slightly. So you are only getting an average force, instead of a maximum force. It will be close but not perfect. Also it is hard to say if the hammer head is still accelerating when it hits the concrete at impact depending on the persons swing.

Another way to do this would be to apply a "strain gage" to the concrete. When you hit the concrete with the hammer it can determine the amount of force that you are hitting it with based on the change in resistance it is experiencing. Then you can just divide that force (which you could then determine the actual maximum force) by the area of the hammer head to give you pressure.

Look up a strain gage and its theory and applications. Its a very useful tool but can be kind of tricky to use sometimes. It would be interesting to see your results from calculating and from the actual strain gage measurements to see how close you can get.

Lets hope someone else has some input as well haha
Good Luck!

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Alright ive been trying to find a simplified explanation of the strain gage and i seem to be finding alot of complex applications and equations... I would suggest doing it like this. Apply your strain gage to a piece of steel overhanging something fixed to the ground... so the steel would be like a diving board. make sure it is very stable since you will be hitting it with a sledge hammer... apply the strain gage correctly to the the steel. Now put some premeasured weights hanging on the piece of steel. Record the resistance that you are getting back with an ohm meter. Now keep doing this with many different weights and record the resistance. If you put weights with corresponding resistances into excel you can come up with an equation to predict the weight on the piece of steel based on the resistance that you are measuring with the strain gage. So now with that information you can strike the piece of steel and record the resistance. With your equation and that resistance from the hammer you can figure out the force applied by the hammer. Divide that force by the head area and get your pressure...

When looking up information on the strain gage, ignore extra circuitry like the wheatstone bridge and other circuitry (it is just used to get very accurate answers and i dont believe you will need to be that accurate) You will just need a strain gage and an ohm meter to measure resistance.

Make sure you do this part with steel as well just to get the force of the hammer because if you use conrete you will get very innacurate answers because the steel will flex from the impact to give you measurements on the strain gage... If you use concrete... it will just compress at the area of impact instead of flexing like the steel and will give you inaccurate readings on the strain gage... use the steel just to obtain the force from the hammer...

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id love to hear an update if you have gotten anywhere on this project

mgb_phys
Homework Helper
It's tricky to calculate an exact answer because it is dominated by the time the impact takes, which depends on details of the stiffness of the materials and their deformation at impact.

Somebody posted some rules of thumb from an old 1940s handbook for metal on metal, metal on wood etc but I can't find them in the search.
Hopefully someone bookmarked them

i see... that may be an easier way to find the force of the hammer... the way i explained with the strain gage is almost fool proof if you do it with harder materials because it will determine the actual force of the hammer that you are applying no matter what the material if you do it metal to metal... and that would be the maximum force that you could apply to any material

Motownman....check out this explanation... http://paws.kettering.edu/~drussell/bats-new/batw8.html [Broken] ...short story is bat speed is way more important that bat weight for hitting the ball outta the park.

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