High speed camera projectile motion

[wjlancas]

We are trying to calculate the acceleration of gravity using a quarter inch ball bearing and a high speed video camera. The ball bearing it shot at 6 m/s across a grid .5 meters long. The high speed camera is 1.8 meters away and records the position of the ball at 250 frames per second. We thought that we could determine how fast the ball was accelerating downwards by analyzing the position of the ball bearing on each frame. However, we are systematically getting lower than usual results (9 m/s/s instead of 9.8 m/s/s). We have made sure that the set up is as precise as possible using laser levels. We have also checked the timing mechanism of the camera's clock. Does anyone have any suggestions?

 

[Domnu]

How exactly did the camera measure the ball bearing falling down? Is the camera a vertical column which has lasers (which I'm assuming you said... laser levels?) and at a particular point of time, it measures the height? Could you put your data here perhaps?

 

[mgb_phys]

I assume they take pictures on the falling ball and measure it's position on each frame.
By calibrating the lens (or havinga grid in the background) you can measure the absolute position of the ball on each frame.
A couple of details might give you problems, distortion in the lens means that a pixel isn't the same angle at the edge of the frames(and so is a different distance fallen)
I assume the laser levels are just to ensure the ball is falling perpendicular to the axis of the lens.

 

[wjlancas]

The laser levels were just being used to make sure the camera and the grid were aligned perpendicularly. We resolved the problem by running the camera at 500 frames per second instead of 250.

 

[DaveC426913]

The laser levels were just being used to make sure the camera and the grid were aligned perpendicularly. We resolved the problem by running the camera at 500 frames per second instead of 250.

I don't see how that would solve the problem but...

 

[wjlancas]

We think it was a pixelation problem. If the graph of the trajectory was off by a pixel during the first few frames then the acceleration of gravity generated would be less than expected. By increasing the number of frames, the error was reduced. Also, the software generated equation of the form at^2 + bt +c =y. The software would give values for the coefficients a,b,and c and from the value of a we could find would the acceleration was. We found that the value for c generated from the computer's curve fit did not match the y intercept from the initial point (x,y,t) (0,0,0). If we forced the curve fit to go through (0,0,0) then the acceleration generated was approximately -9.8 within uncertainty limits.

 

[Domnu]

So I'm assuming you use pixels on the screen to determine the height of the ball?

 

[wjlancas]

Yes that is correct.

 

[Domnu]

Hmm... okay, in that case, yes, a pixelation problem would throw off your measurements pretty crazily... not to mention that you would have to use a decent amount of optics to account for the object being closer/farther away from you... I'm not an expert with optics, so I wouldn't know much about it.

Well, another experiment that you could try is this: Shoot a marble/ball bearing from a launcher at a particular angle, A and see where it lands. Calculate the displacement of the landing, and using your angle, try to figure out g. Another experiment (with lesser accuracy) would be to just measure how much time it takes an object to reach the ground after dropping it. If you wanted to see real-time moving data, you can place a marble directly above a motion detector, start the motion detector and release the marble... of course you want to have someone catching the marble before impact :P Your setup seems to be a bit unnecessarily complicated... I don't think the work with pixels, frame rates, etc. will produce any more accurate results than any of the experiments delineated above (excepting maybe for the dropping of the ball and measuring time...).

 

[wjlancas]

Thank you for the suggestions, but the setup we have is necessary for what we want to do with it later. Measuring gravity was just something we had to verify before we proceeded any further. We are going to spin seeds using our launcher and compare the values of the accelerations for them to that which we obtained for gravity. The seeds are less than a 1/5 of an inch and will be traveling much faster than the ball bearing, but we hope that our setup will work for them as well.