Data for a potential and kinetic energy experiment

[Mr Davis 97]

I have performed an experiment testing how mechanical energy is conserved. I conducted this experiment by first creating a ramp. I gathered data by first calculating the gravitational potential energy of a marble on various points on the ramp (depending on height). Next I rolled the ball down the ramp, and when it hit the ground I started a stopwatch and timed how long it took to travel 1.17 m on a flat plane. I used this to find the average velocity. The mass of the marble is .0284 kg, so with all this data I was able to calculate the final kinetic energy (neglecting friction). Here is the data for four trials where each trial changes depending on the initial height the marble started at on the ramp:

Height (m):
0.05
0.06
0.07
0.08

Parallel component of weight (N):
.13
.13
.13
.13

Work (J):
.009
.014
.020
.023

Initial potential energy (J):
.014
.017
.019
.022

Final kinetic energy (J):
.002
.003
.004
.006I am confused about the last portion of the data. If the marble started with, say, .014 J of potential energy, why does it only have .002 J by the end of the 1.17 m it rolls on the ground? Does it lose .012 J of energy due to friction, or are my calculations incorrect?

 

[nasu]

How did you measure the time? You had photogates?

 

[Mr Davis 97]

How did you measure the time? You had photogates?

I used a stopwatch. So while the not the best method, I don't think I could have made that much error. I did many trials.

 

[nasu]

I think the problem is that you don't need that much error to get these results.
Let's take the first data set, for example.
Without friction and taking g=10m/s^2, the speed of the ball at the base of the inclined will be
[itex]v_1=\sqrt{2 g h}=\sqrt{2 10m/s^2 0.05m}=1 m/s[/itex]
The reaction time of the humans is of the order of 1/4 second.
The travel time of your ball over the 1.17 m is about 1 s, right?
You see the problem? Maybe they cancel out, you starte later and you stop later the stopwatch. If you are lucky, by the same amount.:)
And I don't know you setup but you may have some parallax error too. You cannot see both marks on your horizontal portion at right angle.
There is also the KE of the rotation around the CM of the ball. For a spherical ball this I think it will be 1/5 of the translation KE, for rolling without sliding.

Of course you have some friction too and it may be the main factor after all.

 

[Mr Davis 97]

I think the problem is that you don't need that much error to get these results.
Let's take the first data set, for example.
Without friction and taking g=10m/s^2, the speed of the ball at the base of the inclined will be
[itex]v_1=\sqrt{2 g h}=\sqrt{2 10m/s^2 0.05m}=1 m/s[/itex]
The reaction time of the humans is of the order of 1/4 second.
The travel time of your ball over the 1.17 m is about 1 s, right?
You see the problem? Maybe they cancel out, you starte later and you stop later the stopwatch. If you are lucky, by the same amount.:)
And I don't know you setup but you may have some parallax error too. You cannot see both marks on your horizontal portion at right angle.
There is also the KE of the rotation around the CM of the ball. For a spherical ball this I think it will be 1/5 of the translation KE, for rolling without sliding.

Of course you have some friction too and it may be the main factor after all.

Do the think that the discrepancy is too egregious to turn in, or would be better to just do the experiment again in order to get better results that coincide with the law of conservation of mechanical energy?

 

[jbriggs444]

The reaction time of the humans is of the order of 1/4 second.

Reaction time is not very relevant here. It is possible (and even easy) to stop a watch within a few tens of milliseconds of an event that can be anticipated. Humans can account for both the projected movement of the object and the latency in their clicking finger so that the watch is stopped as the object crosses the finish line.

 

[Mr Davis 97]

Reaction time is not very relevant here. It is possible (and even easy) to stop a watch within a few tens of milliseconds of an event that can be anticipated. Humans can account for both the projected movement of the object and the latency in their clicking finger so that the watch is stopped as the object crosses the finish line.

So do you think my results are due to a loss of energy by friction?