Experiment 08
WORK AND ENERGY-Simulation
PROCEDURE 1
Open up the work
energy.001.ip2 Interactive Physics link. You will see the inclined
plane set up that is described above. The measurement box gives four pieces
of data, the magnitude of the velocity (speed) of the block |v|,
the square of the velocity v2,
the horizontal position of the block x, and the vertical position
of the block y. The slider controls the height of the support at
the end of the incline. This will be varied to test the motion with different
slopes. To start, open up the Work Energy
Workbook and fill in the header data. Also, record the mass of
the block as indicated on the Interactive Physics simulation in cell E8,
and the Support Height for Trial 1 in cell E10.
1. With
the support height set at 1.0 units, RUN
the simulation and observe the relationship between the square of the speed
and the vertical height of the block. Rather than copying reams of data
down by hand, the simulation allows us to dump the data to a spreadsheet.
2. After
the simulation has run to your satisfaction, and has automatically stopped
before the block flies over the edge of the incline, in the FILE
menu, choose EXPORT DATA. Make
sure you hit the DESKTOP button in the save dialog box so that you
will know where to find the file later. The pertinent data will then be
saved as a text file suitable for importing into the work energy Workbook.
3. Go back
to the
Work Energy Workbook window and OPEN
the data file, which should appear in the dialog box as work energy.001
Data. Another dialog box will appear - simply hit FINISH
to dismiss it. A new data sheet will appear. With the new data window still
selected, choose EDIT.... MOVE OR COPY SHEET.
A Dialog box will appear. Select work energy workbook
as the Workbook, and Before Sheet 2 orBefore
(Move to the End) for the destination.
4. The
fourth column (column D) gives the vertical position of the block
y,
as it slides down the incline. Pick two values of y,
yA
and yB, respectively, for the block
after
it has moved about half-way down the plane, or for
x < 2.5
m, and enter the corresponding values of v2
and y from columns B and D, respectively, on
to Sheet 1 of the work energy Workbook in cells D13:E14.
The vertical distance h that the block falls is equal to the difference
in the y-values. Enter its value in cell E16. Evaluate the
acceleration of gravity using Equation(1) and compare your answer
with the known value of g.
HINT:
Take advantage of the spreadsheet by typing in cell E18 the following:
"= (D14
- D13)/(2 * E16)" . This formula takes the difference
between the squared velocities and divides it by twice the vertical height.
Enter the percent error in the appropriate box.
5. A
point-by-point analysis can be made by looking at the total variation of
v2
with y. In order to take advantage of all the data you have collected,
the best thing to do is to make a plot.
Before you can do this, you need
to prepare the data to be plotted in a side-by-side fashion. Move to the
2nd
(work energy.001) Sheet of the Workbook and select column B.
COPY,
then PASTE into column E. You
will now have the two data sets to be plotted side-by-side in columns D
and E. Select only the data in both of
these columns.
6. We want
to make a plot of v2 against h to
test the validity of Equation (1). Hit the Chart Wizard
button 
and follow the instructions below:
-
In the Chart Type dialog
window select X-Y (Scatter) from the Chart Types on the left
of the first window in the dialog
-
Select the very top Chart
Sub-type on the right (the one with points only-no lines or curves)
-
The second dialog window is Chart
Source Data and is fine as it stands.
-
The third dialog window is Chart
Options
a. Under the Title tab, fill in the title of the plot and
the captions for the variables along the (X) axis and the (Y) axis.
b. Under the Legend tab, make sure "Show Legend" is not checked.
-
The fourth dialog window is Chart
Location. Make sure that it is saved "As object in Sheet 1".
Use the mouse to size the chart
and to locate it.
7. Click
on any one of the data points. The points will change to a new exciting
color.
-
Choose Chart...Add Trendline
from the menu.
-
Under the Options tab, choose
Display
equation on chart. The equation of the best straight line fit to the
data will appear on the chart.
-
Move it to the top header of the plot
to make it readable.
-
The plot will now display the equation
for the best straight-line fit to the data. Record the Slope of
the line back on Sheet 1 of the Workbook in cell E22.
-
From the slope of the fitted line,
calculate the value of g using Equation (1) and enter the
value where indicated in cell E24.
HINT:
Use the spreadsheet calculator by entering in cell E24 the following:
"= E22/2".
8. Go
back to the work energy.001 simulation and RESET
the simulation. Using the slide control, change the support height to 0.8
units. Record this value as the Trial 2Support
Height in cell E28 in the work energy Workbook.
Hit the RUN
button and observe the simulation. Repeat the steps in section 1
above
to export the data and to make a plot in the work energy Workbook.
In this case, the data should again be entered as before (Move
to the End) in the EDIT.... MOVE OR
COPY SHEET Dialog
box.
PROCEDURE 2
Open up the work-energy.002
Interactive
Physics file. The two blocks have fixed masses, and in this simulation
the idea is to vary the speed with which the horizontal block passes through
the fixed points along the track. You will do this by adjusting the initial
velocity of the blocks using the slider control.
1. Start
with the initial velocity set equal to zero. RUN
the simulation.
2. After
the simulation has run to your satisfaction, and has automatically stopped
before the block flies over the edge of the horizontal plane, in the FILE
menu, choose EXPORT DATA. Make
sure you hit the DESKTOP button in the save dialog box so that you
will know where to find the file later. The pertinent data will then
be saved as a text file suitable for importing into a spreadsheet application
such as the work energy Workbook.
3. Switch
to the Workbook window and record the initial velocity and the two
mass values in cells C48 and F48:F49.
4. OPEN
the data file, which should appear in the dialog box as work energy.002
Data. Another dialog box will appear-simply hit FINISH
to dismiss it. A new data sheet will appear. With the data window still
selected, choose EDIT.... MOVE OR COPY SHEET.
A dialog box will appear. Select work energy workbook
as the Workbook, and Before Sheet 4or
Before (Move to the End) for the destination.
-
A point-by-point analysis can be made
by looking at the total variation of the square of the velocity v2of
mass
#2 , with the vertical distance it has fallen, d. In order
to take advantage of all the data you have collected, the best thing to
do is to make a plot. Before making the plot, go to Sheet 1 of the
Workbook and answer
Questions 1 and 2:
-
Next, you need to prepare the data
to be plotted in a side-by-side fashion. Move to the 3rd (work energy.002)
Sheet of the Workbook and select column A. COPY,
then PASTE into column D. Select
column C. COPY, then PASTE
into column E. You will now have the two data sets to be plotted
side-by-side in columns D and E. Select both of
these columns.
5. We
want to make a plot of v2 against d to
test the validity of equation (2). Hit the Chart Wizard button
and follow the instructions below:
-
In the Chart Type dialog
window select X-Y (Scatter) from the Chart Types on the left
of the first window in the dialog
-
Select the very top Chart
Sub-type on the right (the one with points only-no lines or curves)
-
Hit the Next button
-
The second dialog window is Chart
Source Data and is fine as it stands.
-
Hit the Next button
-
The third dialog window is Chart
Options
a. Under the Title tab, fill in the title of the plot and
the captions for the variables along the (X) axis and the (Y) axis.
b. Under the Legend tab, make sure "Show Legend" is not checked.
-
Choose Chart...Add Trendline
from the menu.
-
Under the Options tab, choose
Display
equation on chart. The equation of the best straight line fit to the
data will appear on the chart.
-
Move it to the top header of the plot
to make it readable.
-
The plot will now display the equation
for the best straight-line fit to the data. Record the Slope of
the line back on Sheet 1 of the Workbook in cell E72.
7. From
the Slope of v2 vs. d
determined from Equation (2), use the measured slope and the mass
values to calculate a value for g in
cell E74.
HINT:
Use
the spreadsheet to do this calculation. The mass values are entered in
cells F48 and F49, respectively. The value of g is
half the Slope times the sum of the masses divided by mass #2. Therefore
in cell E74 enter: " =
(E72/2) * (F48 + F49)/F49
".
8.
Finally, determine the percentage
error and enter into cell E76.
9. Return
to the Interactive Physics Simulation Window. Set the initial velocity
to —5.0 m/s. RUN the simulation
and
repeat steps 2 through 6 for this case, except there
is no need to answer
Questions 1 and 2 again. Be sure to
enter the new initial velocity in cell C79.
10. From the
Slope
of v2 vs. d determined from
Equation
(2), use the measured slope and the mass values to calculate a value
for g in cell E84.
HINT:
Use
the spreadsheet to do this calculation. The mass values are entered in
cells F79 and F80, respectively. The value of g is
half the Slope times the sum of the masses divided by mass #2. Therefore
in cell E84 enter: " =
(E82/2) * (F79 + F80)/F80
".
11. Finally,
answer Question 3, check over and print out your Worksheet
and use it to develop your lab report.