# I What is the Mass of a Piston?

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1. Oct 20, 2018

### InebriatedScientist

I am trying to teach myself Physics, so I can use it in engineering for my own devices. The project I am working on right now is a very simple spring based launcher. This is frustrating me to no end.

Here is my objective. I want to lunch a golf ball about 10 or so feet.
I know that I need to calculate the springs energy. I also know that the springs energy is approximately equal to kinetic energy. All I am doing is transforming spring energy into kinetic energy.

The equation is like so.. 1/2ks2 approx = 1/2(Mball + Mpiston)V2

The ball is about 0.101lb. In order for me to proceed, I need to know the mass of the piston. I have the other information I can work that out, however...

How the hell would I do that if I have not constructed the piston yet? I looked up how to find the mass. The information I found goes on and on about density and so on. The piston is going to be made out of Metal, more than likely steel. The head is going to be steel and the rod is going to be steel.

Now I am following a tutorial on how to go about constructing this device. Problem is, his measurements are different than mine. Because I have something else in mind for my luncher. For example, my spring is going to be 9.5in long with a maximum weight capacity of 27lb. Obviously, I assume, I am going to overshoot the 10-foot mark. His is half that or so.

I need to know the mass of the piston. How would I find that, if I have not constructed it? Do I just "estmate"

Last edited: Oct 20, 2018
2. Oct 20, 2018

### olgerm

⇔$M_{piston} \approx \frac{k \cdot s^2}{V^2} - M_{ball}$

$\frac{M_{ball}*V^2}{2}=M_{ball}\cdot h\cdot g$

3. Oct 20, 2018

### Staff: Mentor

Or you could calculate backwards from what you know of the mass of the ball and the characteristics of the spring to calculate an upper bound on the mass of the piston, then consider whether it is possible to construct a piston that will work with that spring.

4. Oct 20, 2018

### sophiecentaur

It sounds like stating the obvious but, once you have designed the piston, you will know its volume so you can work out its mass. You can easily get a typical value for the density of steel.
There is also some kinetic energy in the moving spring at the point where the ball is launched. I seem to remember that the ke of a spring of mass m when the free end is moving at v is mv2/6. (i.e. 1/3 of a mass m at speed v) Whether this is significant or not will depend on the mass of the spring compared with the rest of the moving parts. If it's a strong spring then it is likely to have mass comparable with the piston ( which will be as light as possible, consistent with being strong enough.)
Does your tutorial mention the ke of the spring?

5. Oct 20, 2018

### jrmichler

You sketch up a piston that looks like it will do the job, then calculate the volume and multiply by density to get the mass. Then you calculate velocity. If it does not work, change something (piston material, piston design, different spring) and try again. It's an iterative problem. The approach of @Nugatory also works.

Also, add half the mass of the spring to the mass of the piston when you do your calculations.

Do you really need a piston? Can the spring push the ball directly?

6. Oct 20, 2018

### sophiecentaur

I am not sure you are right there. If you integrate the ke along the length of the spring, I think you get 1/3.

7. Oct 20, 2018

### Staff: Mentor

If ever there was an application that suggested aluminum.....

8. Oct 20, 2018

### jrmichler

You are correct. It's right there in the SMI Handbook of Spring Design.

9. Oct 21, 2018

### sophiecentaur

Spoilsport. What's wrong with Titanium?

10. Oct 21, 2018

### InebriatedScientist

Right, so, then "estamte"?

11. Oct 21, 2018

### InebriatedScientist

I actually changed the design. Working with steel would be much harder. I thought I would make this to be mounted on a platform so I would need a longer spring. However, I changed my mind. The budget was supposed to be about 20-30\$ but the spring I needed that I estimated for 9 3/5in was too expensive and I am trying to follow constraints that I imposed on myself. At least where I was shopping for it.

So on that note, I am going to just make a "handheld" version and use aluminum. It will be easier to work with anyway.
Maybe when I have more precision tools, I would be able to construct a "turret" size.

Last edited: Oct 21, 2018
12. Oct 21, 2018

### InebriatedScientist

Yes, it does, he uses steel compression spring. Well, I am not sure. The equation he uses is 1/2ks2. k= stiffness s= change in length. It makes sense to do that since all we are doing is converting spring energy to kinetic energy. What do I remember is that the lengths of the spring produce more force. That is, the longer it is the father the ball will go.

The problem I had, was...Do I make an estimated piston and then measure the mass or do I just look up the density of a steel and or aluminum piston shaft? I most of the time overthink things. I overthink about things that do not need to be and under think at times for what is important.

Unrelated Rant..sorry.
At one time I decided to just make the spring thinking that I could use any old steel wire. I first thought that this was not possible since I assumed it needed special steel material that is springy. This halted my project. I ask for an advice about my "overthinking" and I was told that I don't need to worry about it, that I should not over think. However when I then directly asked, can I make a spring out of any steel wire and they said no. Obviously, I was annoying since I knew the answer but doubted myself. Only to be told the same exact thing that I knew already. Really sucks, it took up my time. I would rather overthink from now on than underthink.

13. Oct 21, 2018

### InebriatedScientist

huh, interesting, is dividing by 2 the same as using 1/2? Also, I am not sure I understand, it looks like you are solving for the piston mass? I seem to follow this fine. So then I can use mass of the ball and the other variables to actually find the mass of the piston with out ever constructing a piston? That is to say, I want to make the piston out of aluminum shaft and wooden or plastic head. However, I don't know the denstiy of any of those object. Can I still find the mass of the piston by working backwards like that?

14. Oct 21, 2018

### InebriatedScientist

I replied this to someone else. However I will just make a quick note here. I cam to the same conclusion using aluminum. The reason I used steel in this example is because the device was going to be much larger, about 3x2x2ft.

15. Oct 21, 2018

### sophiecentaur

The equation for what? That looks like the potential energy stored in the spring. There are three elements with KE in this model and the PE is shared.

You have to think all the relevant things. The really important thing is the design of the spring and the energy it can store. You don't seem to have mentioned any maximum for this. If you used a car suspension spring and could manage to compress it, you could send the golf ball the whole length of a football field or further. That would be ridiculous of course so you need to decide on whether you can make one or buy one. Making a 'good' spring is difficult. You can buy a range of springs on eBay etc. Perhaps an airgun spring would suit you. They store around 16J max in the UK (the regs) and they can be compressed by more than 100mm, which requires fairly open coils.
Frankly, the mass of the piston wouldn't be very critical. It only needs to be strong enough to act as a pad between the end or the spring and the actual projectile.

16. Oct 23, 2018

### InebriatedScientist

What I am calculating is KeneticEnergy, Gravitational Potential Energy, and Spring Energy. I personally would start with the Spring I guess. I got a spring, I am still not sure how far this ball will go. It seems what I got was much stronger Maximum Load Capacity. Which I think Max Load 110.74lb rate 49.79lb/in. Don't tell me the answers or anything, I want to calculate this my self. What I will do is update and show you my results for some the equations. Once that happens I would like some input if I am going in the right direction.

By the way, I have not said this yet it seems, but I appreciate this help. Thanks a lot.

17. Oct 23, 2018

### Staff: Mentor

Golf balls are pretty light and 10 ft or so is not that much range. Forces will not be that large. Why not construct your piston from wood or plastic? You might be able to re-purpose some existing object.

18. Oct 23, 2018

### InebriatedScientist

Well, I decided to use an aluminum tubing of 0.049" walls thickness, 1/4' OD, 1/2ft long.

19. Oct 24, 2018

### sophiecentaur

That looks like the cylinder, you're describing.
The piston is what the spring drives forwards and pushes the golf ball. That should be a light as you possible, consistent with being strong enough.

20. Oct 24, 2018

### InebriatedScientist

I give up, this is not helping me. I cannot do the math it seems or Physics. I don't understand any of this. All the problems I am given to solve are hypothetical or they just give you the answers. Then you just copy and paste things like a damn monkey.

I don't understand how ANYONE knows how fast an object moves. For example, I am given a situation. A cheetah is crouched in an ambush 20m to the east of an observer's blind. At time t=0 the cheetah charges an antelope in a clearing of 50m east of the observer. The cheetah runs along a straight line; the observer "ESTIMATES" that during the first 2s of the attack the cheetah's coordinate x varies with time according to the equation x=20m+ (5m*s-2)t2

This is simple to solve. This is a hypothetical concept. What I don't understand is, how the hell would you ever know you are 20m away? Or it charges in a clearing of 50m? WHERE ARE YOU GETTING THIS INFORMATION?. I mean, HOW would you even COUNT the seconds? How would you know you are counting according to how time passes? What if you are a slower counter or fast counter? <Sentence deleted by mentor>There are so many factors that I don't understand how people are accurate. I feel like I can just eye things and do them that way, by trial and error.

Let me put it this way. Suppose that you saw a dog chasing a ball that was thrown. You don't know how far away you are from the person that is throwing the ball, you "estimate" that you are maybe mid-lengths. You have no idea how far or fast the ball is since you are just observing this. You don't know how fast the dog is. AND NO you did not bring a watch to count out the seconds. YOU KNOW NOTHING! Because this is just a "split second" observation. HOW would you EVER able to calculate this or even began to? I don't understand how people do physics without using a calculator are have a nice classroom environment.
I HATE hypothetical equations. IN real life, you would not know ANY of this information.

Let me give you a second situation. Suppose you were climbing a mountain, and you slipped and landed in a tight hole. HOW would you know how far you fell? Since you had no idea how far up you were? There is just no way you can do any of these calculations. I don't understand how people just come up with the damn numbers.

And yes, this still relates to the ball launcher that I would like to make. Let me make it clear. I CAN MAKE THE BALL LAUNCHER without calculating ANYTHING. I could just eye the damn thing. Do we as humans just guess? The only way I can see myself ever "estimating" the numbers to make a projectile launcher is if I just go and do an assumed walk out "10ft" Then take an assumed mid-size stone and throw it, but as soon as I threw it, I start counting at an assumed rate. The problem with this is that there is so much unreliable info and assumed info. How the hell would you ever be accurate? IF all we do is trial and error, why would anyone spend an hour doing pointless equations when you can just "eye" and "estimate" things, To which we do anyway. I need some help explaining to me, how you approuch problems with no information. Also, I am still trying to calculate the mass of the piston. I looked up the density of aluminum and it said 2.7 grams. I am just going to use that.

Last edited by a moderator: Oct 27, 2018