Finding Velocity and Force of a projectile

[Mr Timn]

1. So first off, this isn't a homework problem but I figured this would be the best place to post this kind of question. I have an air powered cannon that can shoot potatoes. It is basically a beefed up version of those little potato guns you can buy at FredMyers. You pump up a chamber with air so it is compressed, and then manually turn a valve that releases the pressure through the barrel, firing whatever is inside of the barrel. So I need to find out how fast the muzzle velocity of the potato is, and how much force it is exerting on a target from the distance of point blank (about a foot long.) I don't have a chronograph so I need to use the method of the ballistic pendulum, which I believe boils down V=[(mb+mp)*√(2*g*h)] /mb for the velocity, but I have no Idea how to find the force of the bullet upon impact.

2. What I know is that my projectile is about 0.17kg in weight (I say about because I have an old scale and haven't gotten a more precise scale yet so I'm just rounding the best I can.)(mb)
My pendulum will be 4 pounds which is about 1.8kg.(mp)
And since I haven't actually tested this, for sake of example, I'll say the pendulum moves a total of 4 inches upwards. I think I'm supposed to measure in inches but I'm not sure so I need help there. (h)
And gravity which is 9.8 m/s^2. (g)
The equation I'm using is V=[(mb+mp)*√(2*g*h)] /mb which I got from wiki on the ballistic pendulum and in the book 'Back Yard Ballistics'.

3. Now with the numbers plugged in I get: V=[(0.17+1.8)*√(2*9.8*4)] /0.17 which comes out to be 102.6 m/s which is about 229 mph. I think this doesn't seem right, so I thought maybe the height (h) is suppose to be in feet? So if I divide h by 12 I get 0.34. If I plug this into the same equation with same other variables it comes out to be 29.61 m/s which seems about right which is about 66 mph.
For the force of impact, I could use E=1/2 mv^2 but that would give the result in joules which confuses me. If I want to find the force of impact, wouldn't I want to find the force in Newtons?

So to wrap things up, I need help in finding the velocity of a potato fired from an air powered potato cannon using a ballistic pendulum and I also need to find the amount of force the potato is exerting on the target upon impact. As you can probably tell from reading all of this, I am not great at physics but would love to be able to understand it so any help and correction is appreciated. Thanks!

 

[Simon Bridge]

1. So first off, this isn't a homework problem but I figured this would be the best place to post this kind of question. I have an air powered cannon that can shoot potatoes.

COOL!

It is basically a beefed up version of those little potato guns you can buy at FredMyers. You pump up a chamber with air so it is compressed, and then manually turn a valve that releases the pressure through the barrel, firing whatever is inside of the barrel. So I need to find out how fast the muzzle velocity of the potato is, and how much force it is exerting on a target from the distance of point blank (about a foot long.)

You pretty much have to measure it - too many variables.

I don't have a chronograph...

... someone in the 21st century does not have a stopwatch?
Borrow a phone.

... so I need to use the method of the ballistic pendulum, which I believe boils down V=[(mb+mp)*√(2*g*h)] /mb for the velocity, but I have no Idea how to find the force of the bullet upon impact.

... Ah, you fire a potato into a bucket on a swing and measure how high it swings?
That's tell you the impact energy. Impact force is distributed over time, and area ... so impacts have a varying pressure.
A high peak pressure over a short time is a more damaging impact.

However, you can fire into the bucket at point blank, and, hopefully, the distances and speeds are too small for much air resistance ... and losses from heat and sound will be small fingers crossed, so solving 2(M+m)gh = mv^2 for v will be pretty good for muzzle velocity (M is the bucket mass, m is the potato mass, and h is how high the bucket rises above it's initial height). You'll want to adjust the apparatus to minimize losses and fire off a lot of shots to get an average.

 

[haruspex]

so solving 2(M+m)gh = mv^2 for v will be pretty good for muzzle velocity (M is the bucket mass, m is the potato mass, and h is how high the bucket rises above it's initial height).

Surely the height will only tell you the velocity after potato and bucket merge. You must then use momentum conservation to find the muzzle velocity.

 

[Mr Timn]

I don't have a chronograph...
... someone in the 21st century does not have a stopwatch?
Borrow a phone.

I have thought about that. I was talking about one of those fancy chronographs that people use to measure paintball and airsoft velocity. So with a stop watch though, I don't have reflexes as fast as superman so I can't be shooting at point blank. This means maybe 50 to 100 feet away I could have someone else fire the cannon and then time the potato until it hits the target. This would not measure the muzzle velocity but if done multiple times at different distances I think I could graph the results and create a function with the results. Would that work well though?
And as far as force goes, I still haven't grasped how to measure that. Thanks for the great replies! I never expected to get such great replies that make sense to anybody.

 

[haruspex]

And as far as force goes, I still haven't grasped how to measure that. .

See section 2 at https://www.physicsforums.com/insights/frequently-made-errors-mechanics-momentum-impacts/

 

[Simon Bridge]

I have thought about that. I was talking about one of those fancy chronographs that people use to measure paintball and airsoft velocity. So with a stop watch though, I don't have reflexes as fast as superman so I can't be shooting at point blank.

The pendulum method does not involve timing. Probably best not to try timing if the gun is so powerful... unless you can film it fast enough.

You could fire the potato directly upwards near a ruler (maybe lines marked on a wall), with a bit of trial and error you will be able to see how high it fires.
You hope air resistance is not too strong there too.

 

[Mr Timn]

Thank you for clearing that up haruspex. So I think I could use the kinetic energy equation of F=1/2 mv^2? That would give results in joules which I also have troubles understanding since joules measures how much force is needed to move an object (correct me if I'm wrong there)? I've heard Mythbusters and other sciencie people use joules to describe the force of an object but I have also heard them use Newtons. So for example to my question, an average guy can punch with about 150 joules of force. Would I measure my projectile in joules and then be able to compare the force to a punch? It would be kind of funny to say that an air cannon's projectile could throw a punch 4 times as hard as I can, but it would allow others to be able to visualize how much force the projectile is carrying.

P.S. To Simon Bridge, I don't know if you thought maybe the cannon was small because I compared it to the mechanics of the toy potato guns in stores, but it is about a 3 foot tall U with a butterfly valve on one side and a bike pump nozzle on the other side for pumping in the air. It can shoot 100 meters easily so I don't think I could measure it up against a wall. The idea did spark another idea in my mind of using the angle and known distance from the cannon to see how high the potato went and then have it timed as well. I'd have a person fire it 100 feet away from me and then I'd build a little protractor thing with a string and a straw and look through it from 100 feet away and see how much the angle was to look at. This allows you to use cos (I think. It may be sin) to figure out how high the potato went.

 

[haruspex]

So I think I could use the kinetic energy equation of F=1/2 mv^2? That would give results in joules which I also have troubles understanding since joules measures how much force is needed to move an object (correct me if I'm wrong there)? I've heard Mythbusters and other sciencie people use joules to describe the force of an object but I have also heard them use Newtons.

There is a difference between everyday usage of 'force' and its definition in physics.
In physics, there is force, momentum and energy, and these are all different entities. In standard units, force is in Newtons, energy in Joules, and momentum in kg m/s.
Ignoring the niceties of vectors versus scalars, force is mass x acceleration, energy is force x distance = mass x speed²/2, momentum is force x time = mass x speed.
How hard is it to stop a moving mass? The question is unanswerable unless you specify some distance or time within which it is to be stopped. It cannot be stopped instantly, and if you have all the time in the world then you can stop anything with a tiny force.

 

[Mr Timn]

OOOOK. That really cleared things up. Thanks!
I'd probably use mass x acceleration for the projectile, but the only problem is finding acceleration. Velocity I think I can find either with the ballistic pendulum or just timing it repeatedly but for acceleration, do I multiply the velocity by itself to get acceleration? I just would like to find out how to find the acceleration in any way so I can find force. Looking at your definitions, I don't want to find momentum and energy would be interesting to find out but isn't my goal.

 

[haruspex]

OOOOK. That really cleared things up. Thanks!
I'd probably use mass x acceleration for the projectile, but the only problem is finding acceleration. Velocity I think I can find either with the ballistic pendulum or just timing it repeatedly but for acceleration, do I multiply the velocity by itself to get acceleration? I just would like to find out how to find the acceleration in any way so I can find force. Looking at your definitions, I don't want to find momentum and energy would be interesting to find out but isn't my goal.

Then I'm not sure what you are trying to achieve. In the OP, you wrote that you wanted to find the force of impact. Unless you can specify a time or distance within which the projectile is to be stopped, that is unanswerable. Your other choices are to find the momentum of the projectile or its energy.

 

[Mr Timn]

If the force of impact is unanswerable, then I guess I can't answer it! :)
What I want to able to do is compare the projectile to a similar action ie. a punch, an arrow, a Nerf dart, ect. Since I am not a physics teacher or science genius I would have no idea how to achieve that. This means I am totally up for suggestions!

 

[haruspex]

If the force of impact is unanswerable, then I guess I can't answer it! :)
What I want to able to do is compare the projectile to a similar action ie. a punch, an arrow, a Nerf dart, ect. Since I am not a physics teacher or science genius I would have no idea how to achieve that. This means I am totally up for suggestions!

Now you are allowing the mass to vary. This makes the distinction between momentum and energy more significant.
A bullet, having low mass and high speed, has high energy but not a lot of momentum. It can do you a lot of damage without knocking you over.
A car, rolling slowly on a level road, in neutral, has a lot of momentum, but not much energy. Pushing on it, it will take you a while to stop it, but you can stop it in a fairly short distance.

 

[Mr Timn]

So I would have to use something that has a mass that is pretty close to my actual projectile. So if my potato is has a mass of 1 killogram and a first has 1 killogram (I actually have no idea what either really are) I could calculate the energy and momentum of the projectile and compare it to a punch? I'm getting a lot of great information here which will help me with future tests but I really want to go out and test the cannon out and figure out how it is relative to other acting objects. So could you give me an example with the potato as the projectile compared to something else? Maybe have an example problem so I can see how it works better?

 

[haruspex]

So I would have to use something that has a mass that is pretty close to my actual projectile. So if my potato is has a mass of 1 killogram and a first has 1 killogram (I actually have no idea what either really are) I could calculate the energy and momentum of the projectile and compare it to a punch? I'm getting a lot of great information here which will help me with future tests but I really want to go out and test the cannon out and figure out how it is relative to other acting objects. So could you give me an example with the potato as the projectile compared to something else? Maybe have an example problem so I can see how it works better?

If you want to compare them in an experiment then you need to define the experiment.

 

[Simon Bridge]

What I want to able to do is compare the projectile to a similar action ie. a punch, an arrow, a Nerf dart, ect.

How you do the comparison depends on the reason you need the data in the first place.
What is the question you want answered?

 

[Mr Timn]

My question is not very crazy but just: How bad would this *insert projectile name* hurt?

 

[Mr Timn]

I guess I should also clarify that none of the projectiles would be sharp (ie. bullets, metal tipped darts, bolts, ect.). Most objects would be pretty blunt and the only real differences would probably weight and therefor also velocity and anything derived from those measurements. So again just to restate my question:
How bad would this projectile hurt? (not cutting wise or piercing but purely how bad would the brute force hurt.)

 

[haruspex]

I guess I should also clarify that none of the projectiles would be sharp (ie. bullets, metal tipped darts, bolts, ect.). Most objects would be pretty blunt and the only real differences would probably weight and therefor also velocity and anything derived from those measurements. So again just to restate my question:
How bad would this projectile hurt? (not cutting wise or piercing but purely how bad would the brute force hurt.)

Pain is subjective, so maybe think in terms of physical damage to a specified part of the body.
The damage is even then a complicated question, but peak force will come into it. This will depend on the characteristics of the materials. A raw egg hitting the forehead will shatter, absorbing the energy. The peak force will be quite low. A rock at the same mass and speed will deliver a much greater peak force.
A superball hurts more than a lump of clay of the same mass and speed because of its extreme elasticity. The rebound means that the transferred momentum is greater.

 

[Simon Bridge]

What you want to investigate is a tad on the complicated side for what you have to hand. It is enough to start narrowing the question down to something you can investigate though. What is it for? You are considering hurting people like this?

Perhaps you just want an idea of how much to expect something will hurt, rather than an exact measurment ... so you know how much a punch hurts, so compared to that?

I'd suggest getting something deformable, like soft clay, and punching it as hard as you can ... look at the damage done.
Now you can shoot it with your potato gun from different distances ... using a potato about the same size as your fist.
You can qualitatively compare the two results.

Similar test would be to find out how many this sheets of wood you can punch through, compare with the impact from the gun.

This is not going to be precise for reasons in post #18, but it may give you the idea you need.

 

[Mr Timn]

Ok, that makes sense. It's kind of like all those YouTube channels that see what gun can shoot through the most iPhones.
And to answer your first question, this is purely for fun. I have other cannon type things like the classic potato gun and a tennis ball mortar and would like to eventually build a trebuchet. Then for your second question, no I'm considering hurting people like this (although I did one time stuff paintballs into the airgun and it shot my someone else at myself to see if it would make a paintball motor/shotgun thing. It didn't work well though since the velocity was so low.)
Thanks for the responses!