2022-07-14

Non-Constant Acceleration due to Gravity
Recently, I had the first physics lab for my university physics course. This lab was fairly simple, as we were merely using a computer and a distance sensor to graph the position, velocity, and acceleration of a cart as it moved along a linear track.
One of the situations we captured data for involved starting the cart at the bottom of an inclined ramp and giving it a push upwards. As expected, it rolled up, came to a stop, and then came back down the track to its starting position. The position-vs-time graph was essentially parabolic, the velocity-vs-time graph was essentially linear, and the acceleration-vs-time graph was essentially linear. So far, so good.
At this point in the lab, the instructor pointed out that, if the data was examined closely, the acceleration of the cart was greater while the cart was traveling upwards than when the cart was traveling downwards (approximately $0.546\frac{m}{{s}^{2}}$ and $0.486\frac{m}{{s}^{2}}$, respectively), and asked us to determine why in our lab report.
Now, gravity was the only force acting upon the cart, and thus it's acceleration should be a constant, at least at the scale our experiment was conducted at, so these results are completely baffling my lab group. So far, we have proposed the following ideas, but none of them seem very plausible.
Doppler effect on the ultrasonic distance sensor
Friction
Air resistance
Human error
The first seems highly improbable, and the last three are more obfuscation and hand waving than actual theories.
Why does our experimental data show the acceleration due to gravity to change based on the direction the object is moving?

earendil666h1

Expert

That the numerical value of the resulting acceleration is greater upwards than downwards is likely due to friction. Uphill friction and gravity pull in the same direction, while downhill friction and gravity pull in opposite directions.
You can use the difference in acceleration to estimate the friction. The average is the (projected) gravitational acceleration, from which you can calculate the inclination angle (assuming a constant slope).

tripes3h

Expert

The ideal case must be symmetric in time. Off by 10.7% difference/average seems significant. If the cart is not symmetric in shape, including wheel mounts, air resistance is suspect re ballistic coefficient, Cd. Does the cart have an ultrasonic reflector only on one end? Doppler shift is testable by aiming the ultrasonic sensor at the other end of the cart. Is there an air current in the room from a heater? Is there an electromagnet under the track?
When the cart went down, could air loft under its leading end? Some mgh is feeding the spinning wheels. Are they patterned in any way that air will blow differently depending on their direction of spin?
If you only ran the experiment once, you have no statistics for systematic and statistical errors. Labwork begins with "the universe hates me." Then, start shaving away footnotes. It isn't paranoia if it happens.]

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