__Experiment 8__

Conservation of Energy

Objective:

Experimental verification of the law of conservation of mechanical energy

Equipment:

A computer with Internet connection, a calculator (The built-in calculator of the computer may be used.), paper, and pencil

Theory:

Consider an object of mass **M** moving at constant velocity
V
on a horizontal and frictionless surface**.** Its
K**.**E**.** is
0**.**5MV^{2}. If this object climbs up an incline, its velocity keeps decreasing as its elevation increases.
This means that it loses K.E.
as it gains
P.E. **.** The amount of **K.E. loss** is equal to the amount
of **P.E. gain.** This is according to the Law of
**Conservation of Energy**.
**Its total energy remains constant **(in the absence of energy losses due to
friction). The applet to be used in this experiment is a car with a
certain amount of initial K.E.**.** The energy balance for the car may
be written as**:**

**
K.E.
**
at the bottom of the incline** **
**
= P.E. at the top of the incline where it
comes to stop**

This can mathematically be written as:

0**.**5MV^{2} = Mgh

In the absence of frictional forces, we may cancel
M from both sides and solve
for h, the highest elevation it can reach**.**

h = V^{2}/2g
(Verify this)

Note: If the car is not at zero elevation to begin with, then its initial P.E. is not zero and its initial P.E. must be added to its initial K.E. The formula for final height calculation, in this case, becomes:

Mgh_{i }+_{ }0**.**5MV^{2} = Mgh_{f}

where h_{i} and
h_{f}
are its initial and
final heights or elevations**.**

__
Procedure:__

Click on this link:
http://www.mhhe.com/physsci/physical/giambattista/roller/roller_coaster.html
**.** The applet has a screen with a grid**.** The distance
between every two neighbor points in the vertical direction is the equivalent of
20m. The zero in the
vertical direction is not on
the lowest row of dots. Each dot on the lowest row has a y-value of 20m.
If you want to start from zero potential energy (or a zero height), you need to
start from below the first row of dots. As a quick practice, below where
it says "Construction Tools", click on "Straight." Then place the
mouse on the first row at the leftmost dot and draw a straight line (uphill
road) all the way to the right and end it at the 4th dot from the bottom.
Set the initial speed at 32**.**5 m/s and let the mass be at 500kg.
Then click on "Start." You will see that a car appears at the lower left
and goes up the incline. On the information bar, you will notice an
initial height of 20m. This is because the lowest row has an elevation of
20m in this applet. This elevation gives an initial potential energy to
the car. If you want the initial potential energy to be zero, you need to
start the car from zero elevation. Zero Elevation, is 20m lower. It
is the borderline of the grid. Now click "Reset," and then
click on the incline you just drew. It will turn red. It means
it is "selected." Then click on the "Delete Selection" button. The
incline will disappear.

Now, try to start another incline from the leftmost point on the borderline (0,0) and extend it to the rightmost point that has an elevation of 100m. An elevation of 100m means the fifth point from the lowest point ( 5 spaces from the borderline).

If you click "Reset," you will see an initial height of (0 m) on the information bar. Select a mass of 500kg and an initial speed of 40m/s, and calculate the initial K.E.. Run the applet and double-check your result with the value shown on the information bar and assure its correctness. If you start the applet, you will see that the car climbs the incline until it runs out of K.E. energy. If you look at the value of P.E. on the information bar, you will see a P.E. greater than expected. This applet has some glitches in it. The P.E. can not be more than the initial K.E. You can also change the simulation speed for easier and slower tracking. The "pause" key allows you to stop the simulation momentarily for taking or recording your readings.

You may try some examples of your own before starting the actual experiment. This will help you explore what the applet can do. We will not use the curved path options in this experiment because the applet is not bug free and results in wrong values. We will use the straight line option only.

Experiment:

The matrix of dots in the applet
is a (20 rows) by (29 columns)-matrix. Note that the lowest row of dots is
the bottom borderline itself. The leftmost column of dots is the left
borderline itself as well. In each case,
select the path (as determined by the given coordinates), mass,
initial velocity, and the initial height according to the values in
Table 1**.** Also, have the
simulation speed at its slowest setting and read the highest elevation (Height)
the car reaches as the applet runs in each case. The highest elevation may
be read from the information bar of the applet.
This reading will be your measured value of the
Height, each case. The accepted value is what
you calculate and expect it to happen each case.

__
Data:__

**
**Given
and Measured:

Trial | Straight or Zigzag Path
Coordinates (20m, 20m) |
Mass (kg) |
Initial Speed (m/s) |
Initial Height (m) |
Measured Final Height (m) |
Calculated
Final Height (m) |
%
Error |

1 | (0,0 - 24,5) | 500. |
20.0 |
0.0 | |||

2 | (0,0 - 18,5) | 500. | 20.0 | 0.0 | |||

3 | (0,0 - 12,5) | 500. | 20.0 | 0.0 | |||

4 | (0,0 - 06,5) | 500. | 20.0 | 0.0 | |||

5 | (0,0 - 24,5) | 500. |
40.0 | 0.0 | |||

6 | (0,0 - 18,5) | 500. | 40.0 | 0.0 | |||

7 | (0,0 - 12,5) | 500. | 40.0 | 0.0 | |||

8 | (0,0 - 06,5) | 500. | 40.0 | 0.0 | |||

9 | (0,0 - 24,5) | 500. |
44.3 | 0.0 | |||

10 | (0,0 - 18,5) | 500. | 44.3 | 0.0 | |||

11 | (0,0 - 12,5) | 500. | 44.3 | 0.0 | |||

12 | (0,0 - 06,5) | 500. | 44.3 | 0.0 | |||

13 | (0,5 - 24,11) | 500. |
25.0 | 100. | |||

14 | (0,5 - 18,11) | 500. | 25.0 | 100. | |||

15 | (0,5 - 12,11) | 500. | 25.0 | 100. | |||

16 | (0,5 - 06,11) | 500. | 25.0 | 100. | |||

17 | (0,5 - 24,11) | 500. |
35.0 | 100. | |||

18 | (0,5 - 18,11) | 500. | 35.0 | 100. | |||

19 | (0,5 - 12,11) | 500. | 35.0 | 100. | |||

20 | (0,5 - 06,11) | 500. | 35.0 | 100. | |||

21 | (0,5 - 24,11) | 500. |
48.5 | 100. | |||

22 | (0,5 - 18,11) | 500. | 48.5 | 100. | |||

23 | (0,5 - 12,11) | 500. | 48.5 | 100. | |||

24 | (0,5 - 06,11) | 500. | 48.5 | 100. | |||

25 | (0,5 - 5,2 - 24,11) | 500. |
45.0 | 100. | |||

26 | (0,5 - 5,2 - 18,11) | 500. | 45.0 | 100. | |||

27 | (0,5 - 5,2 - 12,11) | 500. | 45.0 | 100. | |||

28 | (0,5 - 5,2 - 06,11) | 500. | 45.0 | 100. |

Table 1 **
**

__Comparison
of the results:__

Provide the percent error formula used as well as the % error in each case according to the Table..

__Conclusion:__

State your conclusions of the experiment.

__
Discussion:__

Provide a discussion if necessary.