Does acceleration affect impact energy vs constant velocity?

[Ray033]

I do not have a good working knowledge of physics yet. I tried to piece this together but after researching this, I couldn’t figure out the correct laws of physics to combine to develop a formula to answer this question.

Ex. 1 - A moving object impacts a static object at a constant velocity.

Ex. 2 - A moving object impacts a static object at the same velocity but is accelerating at the moment of impact.

Assuming the mass of the objects is the same and the velocity at the moment of impact is the same in both examples.

Question - Does the acceleration component in example 2 increase the energy of the impact compared to the constant velocity used in example 1?

Any help in answering this question would be appreciated.

 

[PeroK]

Question - Does the acceleration component in example 2 increase the energy of the impact compared to the constant velocity used in example 1?

Any help in answering this question would be appreciated.

It depends whether the force producing the acceleration is maintained throughout the collision. For example, if you have a vertical pile driver, then the force of gravity continues to act while the object is being pile driven. And, indeed, you have to take this into account in your energy equations.

You might find a case where the accelerating force switches off at the moment of impact - and, in that case, the prior acceleration is irrelevant. In that case, only the speed at impact matters.

 

[Dale]

You might find a case where the accelerating force switches off at the moment of impact - and, in that case, the prior acceleration is irrelevant. In that case, only the speed at impact matters.

Or if the distance moved at the point of application of the external force is small, then the additional energy would be negligible.

 

[Ray033]

I do not have a good working knowledge of physics yet. I tried to piece this together but after researching this, I couldn’t figure out the correct laws of physics to combine to develop a formula to answer this question.

Ex. 1 - A moving object impacts a static object at a constant velocity.

Ex. 2 - A moving object impacts a static object at the same velocity but is accelerating at the moment of impact.

Assuming the mass of the objects is the same and the velocity at the moment of impact is the same in both examples.

Question - Does the acceleration component in example 2 increase the energy of the impact compared to the constant velocity used in example 1?

Any help in answering this question would be appreciated.

I do not have a good working knowledge of physics yet. I tried to piece this together but after researching this, I couldn’t figure out the correct laws of physics to combine to develop a formula to answer this question.

Ex. 1 - A moving object impacts a static object at a constant velocity.

Ex. 2 - A moving object impacts a static object at the same velocity but is accelerating at the moment of impact.

Assuming the mass of the objects is the same and the velocity at the moment of impact is the same in both examples.

Question - Does the acceleration component in example 2 increase the energy of the impact compared to the constant velocity used in example 1?

Any help in answering this question would be appreciated.

It depends whether the force producing the acceleration is maintained throughout the collision. For example, if you have a vertical pile driver, then the force of gravity continues to act while the object is being pile driven. And, indeed, you have to take this into account in your energy equations.

You might find a case where the accelerating force switches off at the moment of impact - and, in that case, the prior acceleration is irrelevant. In that case, only the speed at impact matters.

Thanks for the reply. So, acceleration can

I do not have a good working knowledge of physics yet. I tried to piece this together but after researching this, I couldn’t figure out the correct laws of physics to combine to develop a formula to answer this question.

Ex. 1 - A moving object impacts a static object at a constant velocity.

Ex. 2 - A moving object impacts a static object at the same velocity but is accelerating at the moment of impact.

Assuming the mass of the objects is the same and the velocity at the moment of impact is the same in both examples.

Question - Does the acceleration component in example 2 increase the energy of the impact compared to the constant velocity used in example 1?

Any help in answering this question would be appreciated.

It depends whether the force producing the acceleration is maintained throughout the collision. For example, if you have a vertical pile driver, then the force of gravity continues to act while the object is being pile driven. And, indeed, you have to take this into account in your energy equations.

You might find a case where the accelerating force switches off at the moment of impact - and, in that case, the prior acceleration is irrelevant. In that case, only the speed at impact matters.

Thanks for the reply. So, acceleration can increase the energy at the moment of impact vs constant velocity assuming that the force producing acceleration is maintained at impact. So, would I have to use the formula for kinetic energy and combine it with a formula from Newtons Laws of Motion to incorporate the acceleration into the calculation?

 

[PeroK]

Thanks for the reply. So, acceleration can


Thanks for the reply. So, acceleration can increase the energy at the moment of impact vs constant velocity assuming that the force producing acceleration is maintained at impact. So, would I have to use the formula for kinetic energy and combine it with a formula from Newtons Laws of Motion to incorporate the acceleration into the calculation?

That's a specific calculation for each problem. The impact in a particle collision is usually assumed to be of a sufficiently short time that the external forces are neglected during the collision itself. This allows you to use conservation of momentum and (for an elastic collision) conservation of kinetic energy to study the collision itself. The external accelerating force is applied to the particles before and after the collision, but not during it.

That said, you have to be careful that this is a reasonable assumption. And, you also have to keep an eye on how an external force like gravity may affect the solution to a collision problem.

 

[Ray033]

I really appreciate the reply. At this point, I was trying to test this in its simplest form and figure out how to calculate if acceleration could increase impact energy compared to constant velocity at impact. Just to give you an idea, I've changed my examples by adding basic values so I can try to eliminate any complicated variables when trying to figure out the calculations.

Ex. 1 - A 5 lb steel ball impacts a steel plate at a constant velocity of 1000 mph.

Ex. 2 – A 5 lb steel ball impacts a steel plate at 1000 mph but is accelerating 50 mph/sec at the moment of impact and the force producing the acceleration is maintained at the moment of impact.

Assuming the mass of the objects is the same and the velocity at the moment of impact is the same in both examples.

From what you told me earlier acceleration can increase impact energy compared to a constant velocity impact. Now I have to figure out the calculations to prove it.

I think your help has me pointed in the right direction.

Thanks again.

 

[jbriggs444]

From what you told me earlier acceleration can increase impact energy compared to a constant velocity impact. Now I have to figure out the calculations to prove it.

You have had opinions offered both ways. Both opinions are accurate. It depends on the details. Primarily on the duration of the collision. Or, almost equivalently, on the depth of penetration.

Say that you have this 5 pound steel ball impacting a steel plate at 1000 mph.

That is a bit more than 2 kg of steel at a density of 8 grams per cubic centimeter. I make it about 280 cubic centimeters. The volume of a spherical ball is $V = \frac{4}{3}\pi r^3$. If we solve for $r$ in terms of $V$ we get $r = \sqrt[3]{\frac{3V}{4\pi}} \ = \ \sqrt[3]{\frac{284 \times 3}{4\pi}} \approx 4$ cm radius. About a three inch diameter sphere.

At 1000 mph or about 1500 feet per second that ball can traverse its own diameter 6000 times in one second. If we imagine bringing this to rest with a constant rate of deceleration within its own diameter (so it winds up nestled in its own crater) that would take 1/3000 of a second.

[If it is slowing down steadily to a stop, its average speed during the collision is half of its speed before the collision]

That is a deceleration rate of 1500 feet per second in 1/3000 of a second. Or about 4.5 million feet per second squared.

Meanwhile, you specified an external force producing an acceleration rate of about 73 feet per second squared. Compared to the 4.5 million feet per second squared from the collision, the added force is negligible.

 

[Ray033]

Thanks for explaining all of that to me and showing me the math. It’ll take a little while to absorb it.

With the random values I chose the result you got was negligible. However, if I understand the general principle that you showed me, by increasing only the rate of acceleration, the result would still be an increase in the impact energy even if it’s a very small amount.

When I get this figured out, I’ll try to find values that will result in a more measurable increase in impact energy compared to constant velocity.

Again, thank you for all of the information.

 

[jbriggs444]

With the random values I chose the result you got was negligible. However, if I understand the general principle that you showed me, by increasing only the rate of acceleration, the result would still be an increase in the impact energy even if it’s a very small amount.

Yes.

It is sometimes helpful to consider what happens when one takes the scenario to extremes.

Suppose that we have this same 5 pound ball. But instead of travelling at 1000 miles per hour, it is travelling at one mile per hour. It is being pushed three inches into the steel plate by a hydraulic press under a force of twenty tons.

This time the impact energy is negligible. It is the hydraulic press that contributes essentially all of the energy to the ensuing collision. We can do the calculations for energy.

The kinetic energy of the ball is given by $KE = \frac{1}{2} mv^2$. We want to shift to metric units. English engineering units could be used but we do not want to be dealing with slugs, poundals or missing factors of 32.17. So we have a 2 kg ball moving at about 0.5 meters per second. $KE = \frac{1}{2}mv^2 \approx \frac{1 \times 2 \times {0.5}^2}{2} = 0.25$ Joules.

So about a quarter of a Joule of impact energy.

We are pushing this ball 6 centimeters into a steel plate encountering a hypothetical resistance of twenty tons. [I have no idea if this is the right order of magnitude force for pressing a steel ball into a steel plate]

20 tons (imperial units) is tolerably close to 20 metric tons. Or 200,000 Newtons. Work is force multiplied by distance. Multiply 200,000 Newtons by 6 cm (0.06 meters) and we get about 12,000 Joules.

As expected, this time the impact energy from the ball's pre-existing motion is dwarfed by the work done by the hydraulic press over the duration of the interaction.

 

[Ray033]

This explanation was very helpful. It gave me a completely different way to look at the problem and made it a bit easier to understand overall. I'll be careful with choosing extreme values to test a result thinking that larger numbers will produce larger results or discrepancies for comparison and I'll stick to the metric system for everything, even a simple example from now on.

I'm going to think about the info you gave me for a bit and then start trying to tackle the calculations needed to see what the results are when comparing the 2 different scenarios

I can't thank you enough. The information that you shared with me was great and I appreciate all of the time that you spent on this.

 

[Ray033]

I posted this question earlier but didn’t present it well with my limited knowledge, so I revised it and hopefully made things a bit clearer. However, I did receive some good information that was helpful. Thanks!

I do not have a good working knowledge of physics yet. I tried to piece this together but after researching this, I haven’t yet figured out the correct laws of physics and associated formulas to use in developing the calculations to answer this question.

I’m trying to determine if acceleration can increase impact energy compared to the impact energy at a constant velocity, assuming that all other values are the same. At this point, I am trying to test this in its simplest form. Just the energy created at the moment of impact and eliminating any variables associated with complex events after the moment of impact.

I just picked random for values for now and created the 2 examples below as a starting point to make the comparison. Once I have this figured out, I’ll substitute different values and see how it affects the results.

Ex. 1 - A moving object (m=3kg) impacts a static object (m=0.25kg) at a constant velocity of 240m/s.

Ex. 2 - A moving object (m=3kg) impacts a static object (m=0.25kg) at a velocity of 240m/s but is accelerating at the moment of impact and the force producing the acceleration is maintained through the moment of impact.

The mass of the objects is the same and the velocity at the moment of impact is the same in both examples.

Question : Can the acceleration component in example 2 increase the impact energy compared to the constant velocity used in example 1?

At this point, I don’t know if acceleration will have greater energy at impact than constant velocity assuming everything else is equal. That’s what I’m really trying to solve.

Any help in answering my question or pointing me in the right direction would be greatly appreciated.

 

[256bits]

Any help in answering my question or pointing me in the right direction would be greatly appreciated

All the answers given are really quite good to point you in the right direction, especially noting that the consequences of including an acceleration is problem dependent.

The one thing you have to do is define the impact. Is it to be considered elastic and rigid, plastic with deformation. How long is the impact to last.

An example:
You should be aware that gravity provides an acceleration for objects moving around the vicinity of the earth. A meteor impacting the earth suffers the gravitational acceleration of 9.8 m/s.s the whole time from encountering the upper atmosphere until the time it hits the surface. Depending upon its size, the meteorite will either burn up in the atmosphere, break up due to internal forces subjected upon it, reach terminal velocity, or have a continuously changing velocity on its trip from top of the atmosphere to the surface.
If one considers the impact of the meteor with the earth to be at the top of the atmosphere, then the gravitational attraction adds energy to the meteorite during the long impact duration through the atmosphere.
If one considers the impact of the meteor with the earth to be at the surface, then the gravitational attraction adds little energy to the meteorite during this short impact duration of crater formation, or bouncing around.

 

[sophiecentaur]

Ex. 1 - A moving object impacts a static object at a constant velocity.

Ex. 2 - A moving object impacts a static object at the same velocity but is accelerating at the moment of impact.

Not straightforward because you seem to assume that the impact is instantaneous. Most practical situations involve a finite time of contact during which there may be motion of object and target or distortion of one or both.

Very often a suitable method would be based on Energy, rather than forces. Often. Kinetic energy converted to work done, for instance. it's only the before and after situations that count and the dynamics of the collision may not be too important. There are a million such questions, involving vehicle impacts and sporting acts (punches and throws) and you usually have to make do with reasonable estimates of the quantities involved. You often have to be quite inventive.

 

[PeroK]

Question : Can the acceleration component in example 2 increase the impact energy compared to the constant velocity used in example 1?

What is your definition of impact energy? The kinetic energy of the 3kg mass is defined as $\frac 1 2 mv^2$. That depends only on speed, not acceleration. In what way does impact energy differ from kinetic energy?

 

[Ray033]

To clarify, maybe I should have used the term “impact force” instead of “impact energy”. When I said that I wanted to compare constant velocity to acceleration, I meant that the rate of acceleration is increasing over time for example 2.

I already have the results for example 1 in both the kinetic energy of the moving object and the impact force of the two objects colliding to use for comparison. When I calculated impact force, I assigned a value for the collision distance. Now I want to see if I can replace constant velocity for either result with an increasing rate of acceleration while keeping the impact velocity the same and see if it produces a larger result.

 

[PeroK]

To clarify, maybe I should have used the term “impact force” instead of “impact energy”.

The force of an impact depends on the elascticity of the materials, as this significantly affects the time of the collision. For hard materials the force will be relatively high, active for a relatively short duration. For soft/rubbery materials, the force will be relatively low.

When I said that I wanted to compare constant velocity to acceleration, I meant that the rate of acceleration is increasing over time for example 2.

As has been mentioned before, the external force is likely to be small compared to the maximum force of impact.

I already have the results for example 1 in both the kinetic energy of the moving object and the impact force of the two objects colliding to use for comparison. When I calculated impact force, I assigned a value for the collision distance. Now I want to see if I can replace constant velocity for either result with an increasing rate of acceleration while keeping the impact velocity the same and see if it produces a larger result.

The collision distance is usually unknown, although it will generally be quite short.

By pursuing this issue of acceleration at the point of a collision, I feel you are wandering around in the dark, as it were. The physics of elastic and inelastic collisions has a lot of material available. You would be better studying that than following your own ideas which are leading to confusion in this case.

 

[Ray033]

Thank you for the previous replies and info.

Earlier when I said “I meant that the rate of acceleration is increasing over time. That was a typo. It should have read “the rate of acceleration is NOT increasing over time.” The statement was just an attempt at clarification.

Again, I’m relatively new to the study of the subject so I’m working with a limited knowledge of physics. Maybe I’m trying to bite off more than I can chew at this point but the answer to this question is something I want to try to solve.

So, I’m going revisit this from the beginning, starting with a method used to calculate impact force at a constant velocity.

I am trying to test this in its simplest form and eliminate any variables that I can from the calculations. (e.g. force of gravity, friction, etc.) The objective is to see how acceleration influences impact force.

I’ll assume that these collisions are perfectly elastic and I also reduced the values I chose earlier to avoid extreme results.

Ex. 1 - Object A (m=1.3kg) impacts a static object (m=0.24kg) at a constant velocity of 12m/s.

Ex. 2 - Object B (m=1.3kg) impacts a static object (m=0.24kg) at a velocity of 12m/s but is accelerating at the moment of impact and the force producing the acceleration is maintained through the moment of impact.

I’ll keep researching but finding a correct method is the issue. I’m not sure which law or principle to use for the starting point and the following steps. In other words, I need to start with this formula from Principle A to solve for “x”, then insert “x” into this formula from Principle B to solve for “y” and so on.

Once I’m satisfied that I have the correct result for Example 1, I want to use a calculation for Example #2 that replaces “constant velocity” with “acceleration” and see if the calculation produces a larger impact force as a result.

Any info to help answer my question or point me in the right direction would be greatly appreciated.

 

[Dale]

The principle that you would use here is Newton’s 2nd law: $$\Sigma \vec F =m\vec a$$ where $\Sigma \vec F$ is the net force, and $\vec a$ is the acceleration.

If the external force is producing a given acceleration immediately before the collision, then you can use that to calculate the amount and direction of that force. Once you know that, then that force will simply be added to the collision force to find the net force during the collision.

To approximate the collision force, especially for elastic collisions, you could use the principle of Hookes law $$ F=-kx$$ where $k$ is the stiffness and $x$ is the extension from equilibrium.

 

[sophiecentaur]

Ex. 1 - Object A (m=1.3kg) impacts a static object (m=0.24kg) at a constant velocity of 12m/s.

Ex. 2 - Object B (m=1.3kg) impacts a static object (m=0.24kg) at a velocity of 12m/s but is accelerating at the moment of impact and the force producing the acceleration is maintained through the moment of impact.

There is no meaningful answer to the the questions posed in Ex1 and Ex2. There is not even a 'quick and dirty' answer unless you just assume that KE is converted to Work during the impact and calculations eat Energy involved.. That could be well worth knowing, of course but it's not a simple matter of SUVAT formulae and says nothing about the dynamics of the event.

BTW There's little point in putting actual values into this question until the theory has been sorted.

IMO you need to define what's going on much more than is contained in Ex1 and Ex2. You are making a huge assumption about 'constant velocity' because every impact is extended in time and that is what effects, for example the damage done or distortion. Two car passengers travelling in a car have a frontal collision. They are both travelling at the same speed which may have been increasing or decreasing immediately before impact. One has a seatbelt and an air bag, the other just has a hard walnut facia to hit. They end up stationary. Same initial conditions and your Ex1 does not differentiate between them. One of them gets out of the car, a bit shaken and the other is rushed to A and E.

In Ex2, you need to define much more about the conditions, particularly if the driver keeps a foot on the accelerator or the brake during impact.

 

[Ray033]

IMO you need to define what's going on much more than is contained in Ex1 and Ex2. You are making a huge assumption about 'constant velocity' because every impact is extended in time and that is what effects, for example the damage done or distortion. Two car passengers travelling in a car have a frontal collision. They are both travelling at the same speed which may have been increasing or decreasing immediately before impact. One has a seatbelt and an air bag, the other just has a hard walnut facia to hit. They end up stationary. Same initial conditions and your Ex1 does not differentiate between them. One of them gets out of the car, a bit shaken and the other is rushed to A and E.

Thanks for the feedback.

I defined these collisions as perfectly elastic. If my understanding of this type of collision is correct, deformation would not be involved. Neither object has an air bag so to speak.

My definition of constant velocity in Example 1 is that the driver is keeping their foot on the gas pedal to maintain a constant speed at the moment of impact. Neither accelerating nor decelerating at the moment of impact.

Time (t) the duration of the collision isn’t a variable that I used. I did calculations using a formula for Elastic Impact – Conservation of Momentum that gave me the values for final velocity after impact of (V1ϝ = 8.26m/s), (V2ϝ = 20.26m/s) so I know the change in velocity of both objects after the collision with both going in the same direction. This was based on the impact velocity of 12m/s from my examples.

 

[Dale]

I defined these collisions as perfectly elastic. If my understanding of this type of collision is correct, deformation would not be involved.

Deformations may still be involved, just elastic deformations. That is the type of deformation given by Hookes law in my post above.

Time (t) the duration of the collision isn’t a variable that I used. I did calculations using a formula for Elastic Impact – Conservation of Momentum

This won’t work for your purpose. You want to know the additional energy due to an external force that is applied during the collision. The conservation of energy formula assumes that is 0. You will have to do some more complicated work for the more complicated scenario.

 

[PeroK]

Thanks for the feedback.

I defined these collisions as perfectly elastic. If my understanding of this type of collision is correct, deformation would not be involved.

Your understanding is not correct.

 

[Ray033]

Okay… I clearly started out on the wrong track, but I learned something about collisions.

From the replies, Hookes law and Newtons second law are part of the equation for the solution. What other laws or principles should I be looking at to solve the problem? …or any other direction that you would give me. Thanks

 

[Dale]

I haven’t calculated it directly myself, but I think that you will need the following:

Newton’s 2nd law $$\Sigma \vec F= m \vec a$$

Hooke’s law $$\vec F=-k \vec x$$

The definition of work $$dW = \vec F \cdot d\vec x$$

The definition of kinetic energy $$E_K=\frac{1}{2}mv^2$$

The definition of elastic potential energy $$E_P=\frac{1}{2}k x^2$$

 

[sophiecentaur]

A few 'impossibilities' here which were the way people started off thinking about the way forces work with objects. Newton and his chums sorted this out and showed that things down on earth do, in fact, follow the same rules as things out in space. You have to think in terms of the very basic situations and move on to practical situations like real collisions later.

deformation would not be involved.

Example 1 is that the driver is keeping their foot on the gas pedal to maintain a constant speed at the moment of impact.

I’ll assume that these collisions are perfectly elastic

You cannot assume that.

If there is no deformation then there has to be infinite acceleration with an instantaneous change in velocity. Where would the Energy go?

Time (t) the duration of the collision isn't a variable that I used.

Neither the duration of the collision nor the distance travelled during the collision can be zero or the calculations can't work.

No Deformations may still be involved, just elastic deformations.

There must be some permanent deformations and energy loss or the 'car' or whatever will bounce back the way it came from.

The OP can't get a proper answer until he actually takes on board the basic realities and discards his intuition. Boring but the first few pages of a mechanics text book have to be learned or you get nonsense results. Maybe I am overestimating the quality of many text books which plough on without mentioning the apparent paradoxes which the student will bump into with no help.

 

[Frabjous]

Maybe I am overestimating the quality of many text books which plough on without mentioning the apparent paradoxes which the student will bump into with no help.

Do you have a good reference for these paradoxes?

 

[Dale]

There must be some permanent deformations and energy loss or the 'car' or whatever will bounce back the way it came from

Yes, elastic collisions are bouncy. I don’t think that is a problem here.

 

[sophiecentaur]

Yes, elastic collisions are bouncy. I don’t think that is a problem here.

Except that the OP quotes car collisions and requires that the final velocity is zero. A fundamental difference which is a bit muddled reasoning.

 

[sophiecentaur]

Do you have a good reference for these paradoxes?

Not explicitly but I have talked with students for years and 'they' produce a whole collection of 'strange' models of what happens in these situations. Terms like 'the force of a moving car' and the implication in this thread that the time derivatives are relevant during an instantaneous process. Where are they dealt with in your average school text book?

 

[Dale]

and requires that the final velocity is zero.

That can happen momentarily in an elastic collision.