Mass, Power, Potential Energy….

Gentiana Spahiu

February 28^th, 2011

Mass, Power, Acceleration, Battery Discharge, Time, Potential Energy…

Please for a detailed lab blog follow this link lab-21 For some technical reason I was unable to enter the scattered graphs in the blog, but the word format has the complete lab write-up.

Thank you for your understanding.

How inter-related are the above concepts?

In the last two science classes we explored important concepts like, mass, power, and energy and we ran basic experiments to measure how one affects the other. The students were provided with the appropriate tools, like the Pulleys and the weights, the Lego Mindstorm motor, and of course the LabView application which made it that much easier to record and process the data.

We were divided in groups and we were given specific instructions on how to conduct the experiments, what and how to measure the data, the respective formulas for each of the tests. These experiments require us to identify the variables that we are measuring:

Independent variables (the variables we are manipulating): mass, power levels

Dependent variables (the va

riables that are affected by manipulation): acceleration, battery discharge, potential energy, power used.

How would we execute the experiment?

We would attach the pulley to the Lego Mindstorm motor through a USB cable so that the data would be recorded in the LabView application. Then we would attach the different weights in the hook of the pulley and ran the motor so that the weights would be lifted. The recorded measurement would be recorded in the LabView. Through this application we would be able to later manipulate the power level so that we can trace its outcome on the acceleration variable.

After performing the experiments we should be able to conclude based on data the different correlations of mass, force, power levels and power used, time, acceleration, battery discharge, and potential energy.

The following are the experiments that my group and I conducted. We also build scattered charts with the data collected, which makes the relation between what we are measuring more understandable.

Acceleration vs. Mass

In the first experiment, we changed the mass variable to three different measurements: 0.05 kg, 0.13 kg, and 0.25 kg while keeping all the other variables constant to see how the acceleration was affected. In order to gather as accurate of data as possible we executed the test nine times, three times per each mass. This way we would be able to derive consistent results on how the mass change affects the acceleration. Observing the result we can conclude that change of mass indeed affects the acceleration of the motor: the heavier the weight the smaller the acceleration.

Speed (RPM)	Battery disch (mV)	Mass (kg)	Power level	Time (s)	Acceleration(RPM/s)	MASS	Ave Acceleration
87.873192	56	0.25	75	3.249	27.046227	0.25	22.12013
56.13612	14	0.25	75	3.732	15.041833
71.846847	56	0.25	75	2.96	24.272583
87.722965	70	0.13	75	2.392	36.673481	0.13	31.51186
74.822819	97	0.13	75	2.869	26.079756
83.39685	69	0.13	75	2.624	31.782336
81.468841	69	0.05	75	2.637	30.894517	0.05	31.56166
86.405229	41	0.05	75	2.55	33.884403
80.836108	83	0.05	75	2.703	29.90607

Power level	Acceleration(RPM/s)		Average Acceleration
30	2.92634		3.008051
30	2.672375
30	3.425438
50	12.364987		12.18651
50	11.641745
50	12.552812
80	35.650478		33.876445
80	31.80605
80	34.172807

Acceleration vs. Power

The above experiment was performed again, but this time instead of changing the weight we kept it constant and we manipulated the power in three different levels: 30, 50, 80. Then again we watched how the acceleration was affected because of the induced change. We noticed that the change of power with all the other variables virtually constant (weight constant at 0.2 kg) had quite an impact on the acceleration. We concluded that: the lower the power the lower the acceleration of the motor. Following is a simplified table and also the accompanying graph:

Mass (kg)	Battery discharge (mV)	Acceleration(RPM/s)		Average Battery discharge
0.05	69	30.894517		64.333
0.05	41	33.884403
0.05	83	29.90607
0.13	70	36.673481		78.666
0.13	97	26.079756
0.13	69	31.782336
0.25	56	27.046227		42
0.25	14	15.041833
0.25	56	24.272583

Mass vs. Battery Discharge

The third expe-riment consisted running the motor with different weights on the pulley: 0.05 kg, 0.13 kg, 0.25 kg and watch how the battery discharge levels were changing, if they were. Again, we kept all the other variables virtually constant. Looking at the data gathered we noticed that there is some correlation between mass and battery discharge, but it seems like it is not that strong. The R² of this equations is a merely 0.4785.

Power used vs. Power Levels

The last experiment was a little more elaborated because we had to manually enter certain formulas to calculate Potential Energy before we would graph the Power used vs. levels and see how they were correlated. Initially we use the formula:

Potential Energy = m * g * h

Then, to calculate the Power used we divided the above by the time it required for the motor to lift the weights.

Power used= m*g*h/  t

We noticed that the higher the power level the higher the energy used to lift the weights which was confirmed by the R²= 0.8358. The following are the graph and the simplified table of the experiment.

Mass (kg)	Power level	Time (s)	GRAVITY	HEIGHT	m*g*h	Power used	Power level
0.2	50	4.186	9.8	0.24	0.4704	0.11237458	50
0.2	50	4.264	9.8	0.23	0.4508	0.10572233	50
0.2	50	4.028	9.8	0.26	0.5096	0.1265144	50
0.2	80	2.47	9.8	0.2	0.392	0.15870445	80
0.2	80	2.609	9.8	0.19	0.3724	0.14273668	80
0.2	80	2.518	9.8	0.28	0.5488	0.21795075	80
0.2	30	8.184	9.8	0.25	0.49	0.05987292	30
0.2	30	8.651	9.8	0.25	0.49	0.05664085	30
0.2	30	7.545	9.8	0.27	0.5292	0.07013917	30

In conclusion, this experiment almost objectively showed us how correlated mass, power levels and power outcomes through power used and battery discharge are correlated. This was quite a learning experience for me because it made it that much easier to visualize some theories that we all know and take them ‘as is.’