3-Problem Lab 1: Electrical and Mechanical Energy
Problem Description:
Determining how the transfer of energy from electrical energy in a capacitor, to mechanical
energy is dependent on the capacitance of the capacitor.
Prediction:
The distance the block travels will increase as the values will increase with the voltage and the
capacitance of the capacitor. This relationship is demonstrated by the equation:
x = cv22mg
Our experiment will vary the capacitance of the capacitor used and will show positive relationship
between value of capacitance and distance the block travels.
*The derivation of the equations can be found in the data section.
Procedure:
First we gained access to necessary materials, which include: a set of masses, an electric motor with
a spool attached, string, a 6V battery, a 1F capacitor, a 0.47F capacitor, a 0.22F capacitor, a track, and a
digital multimeter. First we set up the track and place the block on the track. Then we tied the string
(attached to the spool at the other end) to one end of the block. For three trial with each of the
capacitors we used the battery to charge the capacitor, measured the voltage with the multimeter, the
discharge the capacitor through the motor. The motor then pulled the block a certain distance, which
we measured. This process transferred the electric potential energy in the capacitor into work which
was done on the block. In the three trials using the 1F capacitor we added 80g of mass to the 122g
block.
Set-up Diagram:
Data/Calculations:
Variable and constants used in equations:
Wf = work done by friction
x = distance travelled by block
= coefficient of kinetic friction = 0.275
m = combined mass of block and added masses
g = acceleration of gravity = 9.81 m/s
= efficiency of the system
v = measured voltage
Ee = electric potential energy
c = capacitance
Equations used + derivation
Wf = mgx
Ee = cv2
We then can take the efficiency percentage to be the ratio of the work done by
friction over the electric potential energy times 100:
= mgxcv2 x 100
We can also solve the equation for efficiency, for x, resulting in:
x = cv22mg
Table of results and efficiencies and graphs of prediction and results:
Trial 1
Trial 2
Trial 3
Aver.
Predict
C = 1F m = 202g
Volts Distance Efficienc
5.65
29 cm
0.99%
(x)
5.69
36.3 cm y %
1.22%
5.7
25.3 cm 0.85%
5.68
30.2 cm 1.02%
5.68
29.6 m
100%
C = .47F m = 122g
Volts
Distance Efficienc
5.65
17.4 cm
0.76%
y%
5.67
17.7 cm
0.77%
5.72
21.5 cm
0.92%
5.68
18.87 cm 0.82%
5.68
23.04 m
100%
C = .22F m =
Volts Distance
5.55
1.7 cm
5.59
1.6 cm
5.61
1.7 cm
5.58
1.67 cm
5.58
10.41 m
122g
Efficiency
0.17%
%
0.15%
0.16%
0.16%
100%
.
Graph 2
Analysis:
Several 1
Graph things can be observed from the data we gathered during the experiment. The predicted
value for distance (x) is the distance the block would travel if the energy was transferred from electric
potential to mechanical with perfect efficiency. By comparing the predicted values with the actual
values shows very clearly that this transfer of energy is far from efficient. If our data is correct this
means that electric motors, like the one we used in our lab, are very inefficient in moving objects. We
also can use the graphical comparison of the average predicted and average actual values to show that
the x values are in similar proportions. Our average efficiency values are 1.02% for the 1F capacitor,
0.82% for the 0.47F capacitor, and 0.16% for the 0.22F capacitor. These results tell us that capacitors
with higher capacitance are more efficient and, therefore, will move an object farther for their size.
This correlates with our average distance (x) results of 30.2cm for the 1F capacitor, 18.87cm for the .
47F capacitor, and 1.67cm for the .22F capacitor. The smaller efficiencies of the smaller capacitors
might be caused in part by a larger portion of the energy going to getting the block moving (static
friction).
Possible errors in this experiment could exist in several areas. One possible source of error is
the possibility of bad equipment, which could cause false voltage readings or a failure of the capacitors
to discharge properly. There is also the possibility that the capacitors simply dont discharge fully.
Another source of error could be inaccurate measurements of the distance travelled by the block. Also,
if the string wasnt parallel with the track as it pulled the block, not all of the force would go to moving
the block down the track. All of these possible errors might result in inaccurate x values and inaccurate
efficiency calculations.
Conclusion:
The data we acquired draws a few conclusions. One is that the system is a very inefficient way
to transfer energy from electric potential to mechanical. Even our best results gave an efficiency of
only 1.22%. We can also conclude that the efficiency of a capacitor is decreased when the capacitance
is decreased. Even if errors have given us data that is somewhat different than what it should be, it
would take an unrealistically large amount of error to change the conclusion of this experiment. The
inefficiency of this system means it should not be used in real life applications, when efficiency is
important. Overall, we can conclusively say, capacitors are very inefficient in converting energy
through an electric motor.