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
-Bill





RE: Calculate velocity of a spring loaded object
-handleman, CSWP (The new, easy test)
RE: Calculate velocity of a spring loaded object
-Bill, CSWP
RE: Calculate velocity of a spring loaded object
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
RE: Calculate velocity of a spring loaded object
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
-handleman, CSWP (The new, easy test)
RE: Calculate velocity of a spring loaded object
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
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
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
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
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 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
Quando Omni Flunkus Moritati
RE: Calculate velocity of a spring loaded object
TTFN

FAQ731-376: Eng-Tips.com Forum Policies
Need help writing a question or understanding a reply? forum1529: Translation Assistance for Engineers
RE: Calculate velocity of a spring loaded object
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
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
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
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
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
That was not from the OP.
TTFN

FAQ731-376: Eng-Tips.com Forum Policies
Need help writing a question or understanding a reply? forum1529: Translation Assistance for Engineers
RE: Calculate velocity of a spring loaded object
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
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.
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
-handleman, CSWP (The new, easy test)
RE: Calculate velocity of a spring loaded object
RE: Calculate velocity of a spring loaded object
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
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
-handleman, CSWP (The new, easy test)
RE: Calculate velocity of a spring loaded object
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
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
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
Quando Omni Flunkus Moritati
RE: Calculate velocity of a spring loaded object
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
-handleman, CSWP (The new, easy test)
RE: Calculate velocity of a spring loaded object
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
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
New here? Try reading these, they might help FAQ731-376: Eng-Tips.com Forum Policies http://eng-tips.com/market.cfm?
RE: Calculate velocity of a spring loaded object
What does 0.1% mean?
Peter Nachtwey
Delta Computer Systems
http://www.deltamotion.com
RE: Calculate velocity of a spring loaded object
Cheers
Greg Locock
New here? Try reading these, they might help FAQ731-376: Eng-Tips.com Forum Policies http://eng-tips.com/market.cfm?
RE: Calculate velocity of a spring loaded object
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
RE: Calculate velocity of a spring loaded object
Cheers
Greg Locock
New here? Try reading these, they might help FAQ731-376: Eng-Tips.com Forum Policies http://eng-tips.com/market.cfm?