# Converting potential energy to force

• assafwei
In summary, the conversation revolves around finding a way to convert potential energy to force on impact in an impact test where a metal ball falls on plastic. Various methods, such as using impact formulas and calculating energy by length, have been attempted but have not yielded accurate results due to difficulties in estimating the time interval of the impact. Suggestions have been made to search for equations in reference books and to measure the deflection of a beam under static load to estimate the impact force. However, it is acknowledged that without proper instrumentation, it is difficult to obtain accurate results. Assumptions and limitations of different methods have also been discussed. Ultimately, it is concluded that accurately measuring the deflection of the plastic case due to the impact force may be the most
assafwei
Hi,

I have an impact test (Metal ball falling on plastic) and i have a problem conveting the energy (i.e. height and mass) to the force apllied to the plastic upon impact.

I tried calculating with impact formulas but its difficult to estimate the time interval of the impact.
I tried derivating energy by length (F=dU/dx) but the results seems way off.

Any ideas?

Thanks,

Assaf.

Do a google search for force of falling objects. I'm 98% sure there are equation in the Roark handbook, but I'm not sure where my copy is at the moment. If I can find it, I'll post it.

Also try searching here, I'm pretty sure it's been discussed a couple of times here.

Timoshenko is the only one that I know of that talks about the deflection/force due to a dropped object, but it is on a simply supported beam. Everyone else seems to skip the load and go directly to calculating stresses. If you can arrange your set up to be just that, you can measure the deflection of the beam at the mid span and use

$$\delta = \sqrt{\frac{Wv^2L^3}{2g*24*EI}}$$

Where

W = weight of the falling object
L = span length
v = speed of the object at impact, i.e. $$v=\sqrt{2gh}$$

Calculate that and then go back and compare that to the static load required to bend the same beam under static, classical beam theory.

This does assume that all potential energy goes into the deflection of the beam. Of course we know that this is not going to be true. So this calculation would be a maximum.

Without instrumenting your set up with either strain gauges or accelerometers, getting an accurate result is very very difficult (as you have found out).

FredGarvin said:
Timoshenko is the only one that I know of that talks about the deflection/force due to a dropped object, but it is on a simply supported beam. Everyone else seems to skip the load and go directly to calculating stresses. If you can arrange your set up to be just that, you can measure the deflection of the beam at the mid span and use

$$\delta = \sqrt{\frac{Wv^2L^3}{2g*24*EI}}$$

Where

W = weight of the falling object
L = span length
v = speed of the object at impact, i.e. $$v=\sqrt{2gh}$$

Calculate that and then go back and compare that to the static load required to bend the same beam under static, classical beam theory.

This does assume that all potential energy goes into the deflection of the beam. Of course we know that this is not going to be true. So this calculation would be a maximum.

Without instrumenting your set up with either strain gauges or accelerometers, getting an accurate result is very very difficult (as you have found out).

From what i understood, you propose to calculate the deflection using your equation and then extract the force using regular beam deflection equations?
This could be feasble assumin I am trying to figure out the force exerted on a beam, unfortunatley this is not the case...

I was pretty sure there is a simple way of converting potential energy to force on impact...

assafwei said:
I was pretty sure there is a simple way of converting potential energy to force on impact...
There isn't. Force and energy are entirely different animals and not directly related. Impact force depends on the deformation and resulting deceleration. You may want to look up a charpy impact test and fracture toughness for more info. Ie, steel can handle a lot more force than aluminum, but breaks under impacts where aluminum won't due to the fact that it is less ductile and doesn't deflect when a force is applied.

assafwei: Is your metal ball falling on a plastic plate? Is it a structural component such that you could measure or calculate a static deflection? If so, measure or calculate the static deflection, delta, of your plastic plate when you place the metal ball on the plate. Then, assuming your plate remains in the elastic range during the impact, you can compute the impact force F = m*g*[1 + (1 + 2*h/delta)^0.5], where m = falling object mass, h = drop height, and delta = static deflection. This is an estimate.

nvn said:
assafwei: Is your metal ball falling on a plastic plate? Is it a structural component such that you could measure or calculate a static deflection? If so, measure or calculate the static deflection, delta, of your plastic plate when you place the metal ball on the plate. Then, assuming your plate remains in the elastic range during the impact, you can compute the impact force F = m*g*[1 + (1 + 2*h/delta)^0.5], where m = falling object mass, h = drop height, and delta = static deflection. This is an estimate.

Unfortunbatley i don't have the equipment to measure the deflection so this method is not applicable

FredGarvin,

Can you please tell in which book Timoshenko mentions this formula?

Can you tell the assumptions behind this? What is "span length"? And is there any assumption on the geometry of the falling object and the region on the beam at which it falls? And why does v = 0 lead to zero deflection (because even if we just place a weight W on the beam, it'll deflect at the midspan).

Srikant

I would do this. I would drop the ball on a cantilever beam. Then I would instrument the beam to tell me the deflections and strain it sees due to impact. I would then hit the beam with a force hammer until I got the same response as the ball caused. Bingo you're done.

I have put together the attached spreadsheet for calculating the impact force of a dropping object. You'll have to approximate the deflection of the plastic case due to impact force and you'll be able to calculate the impact force.

At the least you can get a range of forces starting from zero deflection-bigger force to maximum deflection smaller force.

I hope it helps.

Tudor Agapescu

#### Attachments

• Free Fall-Impact Calculation.xls
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## What is potential energy?

Potential energy is the stored energy an object possesses due to its position or configuration.

## What is force?

Force is a push or pull exerted on an object that causes it to change its state of motion or shape.

## How can potential energy be converted to force?

Potential energy can be converted to force through the process of work. When an object with potential energy is moved, work is done on the object which results in the conversion of potential energy to kinetic energy, which then causes a force to be exerted.

## What are some examples of converting potential energy to force?

Some examples of converting potential energy to force include stretching a rubber band, lifting an object, or compressing a spring. In all of these cases, potential energy is converted to force when the object is released and returns to its original state.

## What factors affect the conversion of potential energy to force?

The amount of potential energy an object possesses and the distance over which it is converted to force are the main factors that affect the conversion. The type of potential energy (gravitational, elastic, etc.) and the efficiency of the conversion process can also play a role.

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