# Converting potential energy to force

1. Jan 21, 2009

### 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.

2. Jan 21, 2009

### minger

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.

3. Jan 21, 2009

### FredGarvin

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).

4. Jan 21, 2009

### assafwei

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...

5. Jan 21, 2009

### Staff: Mentor

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.

6. Jan 21, 2009

### nvn

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.

7. Jan 24, 2009

### assafwei

Unfortunbatley i dont have the equipment to measure the deflection so this method is not applicable

8. Feb 15, 2009

### srikant1987

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

9. Feb 16, 2009

### Cyrus

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.

10. Feb 18, 2009

### TudorAgapescu

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

#### Attached Files:

• ###### Free Fall-Impact Calculation.xls
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Last edited: Feb 18, 2009