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Calculate velocity of a spring loaded object

Calculate velocity of a spring loaded object

Calculate velocity of a spring loaded object

(OP)
I am trying to calculate the velocity of a spring loaded object. So say I have a marble at rest and then I deflect and release a spring and the spring hits the marble I need to know the velocity that the marble will travel at. I do have a formula but the units I am a little unsure about. Also, I have 2 resources, one says to use the "deflected" dimension of the spring and the other says to use the "compressed lenth" of the spring. Big difference. Any insight would be appreciated.

-Bill

RE: Calculate velocity of a spring loaded object

1/2mv^2=1/2kx^2 assuming zero friction and a sliding (rather than rolling) marble.

-handleman, CSWP (The new, easy test)

RE: Calculate velocity of a spring loaded object

(OP)
That's what I have as well. Will the mass of the object be in kilograms? How about the spring.....is the "x" the deflected amount or the compressed length amount. meaning if I have a 1" lg spring and am deflecting it .25 would "x" be the .25 or the .75? THANK YOU!!!

-Bill, CSWP

RE: Calculate velocity of a spring loaded object

x is the amount of deflection from free length.

Units of mass are a matter for you to decide. g, kg, or lbm. Just be consistent. Just be sure to use mass and not weight.

In simple terms, the formula calculates the energy contained in the deflected spring and converts it to kinetic energy, assuming 100% of the spring energy is converted to the marble's kinetic energy.

RE: Calculate velocity of a spring loaded object

And to add to Tick's post, realize that the spring is not massless, and thus as parts of the spring are accelerated to push the marble, the spring itself gains some kinetic energy. I.e., you will never get 100% conversion of spring energy to marble kinetic energy.

RE: Calculate velocity of a spring loaded object

Hi Applico,

From your description I do not think you are compressing the spring, and releasing the spring while the marble is in contact with the spring from the beginning of its extension.

It sounds to me instead either:
1 - The spring is released from fully compressed, and spanks the marble before full extension while the base of the spring is still grounded.
2 - You compress the spring, then release it so it launches itself and strikes the marble.

RE: Calculate velocity of a spring loaded object

Frankly, from your description I don't think you are an engineer. This is high-school physics.

-handleman, CSWP (The new, easy test)

RE: Calculate velocity of a spring loaded object

applico,

Your description of your problem is ambiguous. Are you using the marble to compress the spring? F=ma, therefore, a=F/m. Are you causing the spring to strike the marble at some velocity? You are working out kinetic energy, and energy absorbed in impact.

I agree with handleman.

--
JHG

RE: Calculate velocity of a spring loaded object

he could be playing marbles in the office ...

but it's a sort of interesting question ...
you compress the spring, then release it. ok, it extends with a force F = kx; but this force is accelerating the small mass of the spring. i think that the spring will over-extend, and then retract, etc ... approaching it's original position as an undamped single degree of freedom dynamic system response. that imples that there's a difference between over-compressing the spring (ie past the marble) and releasing it (to strike the marble with some velocity) as opposed to pushing the spring back with the marble (so it's not over compressed) ... i think ...

Quando Omni Flunkus Moritati

RE: Calculate velocity of a spring loaded object

(OP)
handleman & drawoh

Although I do appreciate your input I never claimed to be anybody but someone with a question. No mud slinging required. I think you need to take it down a couple notches.

RE: Calculate velocity of a spring loaded object

Do lighten up, folks. The man is here for help.

Applico:
All due respect, your lack of knowledge is apparent. We will try to advise as best as possible. However, that may be difficult without a certain base level of knowledge that is usually assumed among engineering professionals.

RE: Calculate velocity of a spring loaded object

Yeah, I agree with Applico and TheTick. Manners have been horrible in this forum for quite some time now.

Anyway, toy cannon scenario. Load a marble and compress the spring, trigger release. How far will the marble go? The range is dependent on angle of trajectory and muzzle velocity off the compressed spring. Total energy of the spring equals total energy imparted to the marble of known mass. Assume potential energy during the compression of the spring is negligible, so you get HandleMan's solution for velocity, v=sqrt(k/m) for spring constant k and marble mass m.

If the cannon is inclined B to the horizontal, then the marble will have a range of R = v^2 sin2B / g, g = acceleration due to gravity.

We're talking a toy cannon here, small mass spring with negligible properties for inertia. I'm trying not to over think the problem and give buddy an answer to be used for his example.

Regards,
Cockroach

RE: Calculate velocity of a spring loaded object

I am curious that you use the term deflect rather than compress. It opens up the possibility that you have a spring which you are pulling sideways in an arc to then strike your marble, or whatever, at some unknown distance from the deflected position of the spring?? As opposed to compressing it axially along it's length.

I would go down the energy route to start with and then do some tests as it sounds quite complex with many variables.

A sketch or a drawing always goes down well in trying to explain your problem to others and can demonstrate that you are serious. It's very easy to upload by clicking on the link under the post box.

If I can mis interpret what you say then you can see how use of words without drawings can lead to errors in understanding.

My motto: Learn something new every day

Also: There's usually a good reason why everyone does it that way

RE: Calculate velocity of a spring loaded object

i thought it was like 'roach's answer, except that the spring was being compressed more than the marble's position, like launching a pin-ball (for those other old farts who can still remember)

Quando Omni Flunkus Moritati

RE: Calculate velocity of a spring loaded object

It doesn't look like you guys are getting anywhere with this and I too find the problem interesting when one takes into account the spring.

I looked on the internet and couldn't find the canned solution for handling the mass of the the spring.

I am going to solve this with my Mathcad. It is super simple if one assumes the mass is weightless but it isn't. It will just take a little calculus to find how the spring will accelerate. The rest will require some differential equations.
A spring also has internal resistance so it doesn't vibrate forever.

Also, if you simply compress the spring, like those in a ball point pen, then release it it will fly up for a distance. Also, the spring should vibrate while in the air or after pushing the marble.

I do have a question. Is the other side of the spring connected to something? I don't know if it will make any difference to the answer.

Peter Nachtwey
Delta Computer Systems
http://www.deltamotion.com

RE: Calculate velocity of a spring loaded object

Quote:

It doesn't look like you guys are getting anywhere with this and I too find the problem interesting when one takes into account the spring.

If we are ignoring losses due to friction and inelastic behaviour of the materials it's quite simple.

The spring will stay in contact with the marble so long as it has some compression. At the point where the spring returns to its original length the centre of mass of the spring will have a velocity of V/2, where V is the velocity of the marble, so the total kinetic energy will be:

(m(spring).(V/2)^2 + m(marble).V^2)/2 = Kx^2/2 where K is the spring stiffness and x is the spring compression.

So V = x.(K/(m(spring)/4 + m(marble)))^.5

Doug Jenkins
Interactive Design Services
http://newtonexcelbach.wordpress.com/

RE: Calculate velocity of a spring loaded object

The OP though says the spring "hits the marble". I'm with rb1957 on this, sounds like there is an impact of a moving spring on a stationary marble with all the consquential issues of re-bound, start distance of the marble away from the compressed position etc etc.

Sounds quite complex to me - I would go for some experiments my self as the position thing looks crucial to me plus the thing at the end of the spring - is it hard or soft? will the marble ricochet off the end of the spring or be carried along with it for a while as it acceperates??

Too many here seem to be assuming that the marble will be in contact with the spring at all times. Read the OP carefully = that's not what he said and he hasn't come back to correct / provide more details yet.

Simple sounding question, but in reality I think there are a lot of variables and quite complex.

My motto: Learn something new every day

Also: There's usually a good reason why everyone does it that way

RE: Calculate velocity of a spring loaded object

Quote:

The OP though says the spring "hits the marble".

Well he also says it is a "spring loaded" object, and that he has "1/2mv^2=1/2kx^2 assuming zero friction and a sliding (rather than rolling) marble" as well.

So why not first sort out how it works for the simple situation, before worrying about scenarios that may not be applicable, and which in any case would need more information?

Doug Jenkins
Interactive Design Services
http://newtonexcelbach.wordpress.com/

RE: Calculate velocity of a spring loaded object

How about it applico?? Tell us which supposition is correct.

Are you bending or compressing the spring ?

Is the marble in contact with the spring all the time or does it hit it like snooker cue?

Don't think this post is going to go much further without some response / input from you.

My motto: Learn something new every day

Also: There's usually a good reason why everyone does it that way

RE: Calculate velocity of a spring loaded object

Quote:

"1/2mv^2=1/2kx^2 assuming zero friction and a sliding (rather than rolling) marble" as well"

That was not from the OP.


True.

What do you deduce from that fact?

Doug Jenkins
Interactive Design Services
http://newtonexcelbach.wordpress.com/

RE: Calculate velocity of a spring loaded object

Quote:


What do you deduce from that fact?
I don't know except it is apparent that the OP and many on this forum don't understand the problem. This is not an easy problem. It is way outside the math skills of most unless it is dumbed down to simple STUDENT problem where a lot of parameters are assumed to be 0. I doubt there is a perfect solution but a very good iterative solution can be found.

I am still plugging away at this like a big jig saw puzzle. I know the last part will be using Runge-Kutta 4 to iteratively solve the equation. That part is easy. The problem is the spring which is the part that interests me. I haven't found a good solution except to divide the spring in the small length wise pieces so each piece is the the mass of the spring divided by the number of pieces. Obviously the answer gets better as I divide the spring up into more pieces but that requires addition differential equations. Someone must of worked out how a spring expands with no load before but I can't find it.

Quote:


Is the marble in contact with the spring all the time or does it hit it like snooker cue?

I am assuming the spring is a coil type of spring because that is what I am interested in.

Peter Nachtwey
Delta Computer Systems
http://www.deltamotion.com

RE: Calculate velocity of a spring loaded object

There are reasons why this problem is always simplified to the student level and why you aren't finding a cookbook solution... Solving it has very, very little benefit. Heck, if you want to get super-accurate, why not go ahead and take into account the internal material damping of the spring wire as it deforms elastically? As you are finding, the math is pretty complex, but I think you'll find that all the stuff you are calculating add up to have about as much effect as the variation in spring rate across two different batches of raw wire. The mass of the spring is pretty negligible to the final velocity on any reasonably-sized spring. That is, until you get up into heavy springs at a really high oscillation rate, like the valve springs on a 10k rpm indy car engine. As an academic exercise, I applaud your efforts and hope you enjoy the math, but if your answer ends up more than 20% different from the energy balance method I would be surprised.

-handleman, CSWP (The new, easy test)

RE: Calculate velocity of a spring loaded object

Ah, but handleman, don't you think it's fun to send the sparky's down the calculus trail to the complexity morass?

RE: Calculate velocity of a spring loaded object

PNachtwey,

I do not understand the problem because it has not been clearly explained. If the marble is pushed down on the spring and then released, the problem is easy to solve. If the spring is compressed separately and shot at the marble, we need to make assumptions about the mechanism. We need to account for friction. We need to account for the possibility that the spring will rotate as it hurtles, and not act like a spring when it contacts the marble.

--
JHG

RE: Calculate velocity of a spring loaded object

I think there is a quick and dirty analysis.

If you know the spring rate and the compression distance, you know the strain energy of the spring as you get ready to release it. If you assume 100% efficiency of your mechanism, you use the mass of the marble to work out velocity. Then all you have to do is guess at all the efficiencies.

Fmax = kδ

E = Fmaxδ/2 = kδ2/2

Also, E = mv2/2 = (w/g)v2/2

You need the spring rate k, the spring compression δ and the marble mass m. Work out velocity v.

You are on your own, working out efficiency.

--
JHG

RE: Calculate velocity of a spring loaded object

Umm, that's what I said in the first reply to this thread.

-handleman, CSWP (The new, easy test)

RE: Calculate velocity of a spring loaded object

what's the difference between ...
a) compressing the spring d1 with the marble in contact with it, and
b) compressing the spring d1, but the marble rests (on some catcher) ahead of the spring.

in both cases the spring energy is the same, you've done the same work on the spring, so you'd expect the results (on the marble)would be the same (ok, very similar 'cause the losses are slightly different). i guess the biggest difference is that if the marble's motion is wrt some fixed datum, then it's starting point will be different in the two scenarios.

Quando Omni Flunkus Moritati

RE: Calculate velocity of a spring loaded object

As I mentioned before, any reasonably sized spring relative to a marble will have pretty negligible mass w.r.t. the marble. In rb's "b" scenario, most of the spring's kinetic energy will, upon impact, be dissipated in much the same way as it would if the marble were fixed. The marble will travel only slightly farther than it would if the spring were released exactly at the marble's position.

Energy transfer from a coil spring directly to a marble is going to be horribly inefficient. Add a "striker" to the end of the spring to try to increase this efficiency and suddenly you have an entirely different problem. However, in either case the contribution of the spring's mass to the problem is pretty negligible.

-handleman, CSWP (The new, easy test)

RE: Calculate velocity of a spring loaded object

This is a first year physics problem, you do it in one of those lab seminars on springs. It is not complex, finding iterative solution sets because there is a worry about standing waves translating through the spring. For God's sake man, this was solvable in Newton's day without computers!

DrawOH got it. A few before that post too. RB1957 let buddy know how to get his spring constant. This problem is over.

Regards,
Cockroach

RE: Calculate velocity of a spring loaded object

"buddy" can look that up for himself

Quando Omni Flunkus Moritati

RE: Calculate velocity of a spring loaded object

Quote:


Ah, but handleman, don't you think it's fun to send the sparky's down the calculus trail to the complexity morass?
I do a lot of modeling using systems of differential equations. I have had to learn how to do it because the hydraulic and mechanical can't.
I know the answer to how to model the spring now. Do you?

Peter Nachtwey
Delta Computer Systems
http://www.deltamotion.com

RE: Calculate velocity of a spring loaded object

So... Now that you know... How different was the result from the simple energy calc?

-handleman, CSWP (The new, easy test)

RE: Calculate velocity of a spring loaded object

Quote:


So... Now that you know... How different was the result from the simple energy calc?
No different. It did take some calculus but I expected that.
Now there needs to be something for the internal resistance of the spring. A spring doesn't oscillate forever.
I don't see internal damping specifications anywhere.
There is actually a lot of information on springs on the web but one must dig for it. I found info on cantilever springs too.



Peter Nachtwey
Delta Computer Systems
http://www.deltamotion.com

RE: Calculate velocity of a spring loaded object

In cases where the internal behaviour of the spring matters the intrinsic damping of the spring is very small compared with that added to the system by the contacts at the end of the spring, etc.

Typical damping factor for a pure steel homogenous structure in isolation is around 0.1%. Very easy to measure approximately using the logarithmic decrement method.

Cheers

Greg Locock


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RE: Calculate velocity of a spring loaded object

Quote:


Typical damping factor for a pure steel homogenous structure in isolation is around 0.1%. Very easy to measure approximately using the logarithmic decrement method.
Damping factors are not expressed in percent.
What does 0.1% mean?

Peter Nachtwey
Delta Computer Systems
http://www.deltamotion.com

RE: Calculate velocity of a spring loaded object

Quote:


% critical damping.
So 0.1% is a damping factor of 0.001.
If so then a spring alone with a natural frequency of 100Hz would have a time constant of 1/(2*PI*100*0.001)=1.59 seconds. It takes about 5 time constants for an oscillation to decay with 1% so that would be almost 8 seconds. I don't see where spring oscillate for that long. The damping factor of most springs must be be much higher.

Peter Nachtwey
Delta Computer Systems
http://www.deltamotion.com

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