Science doc - Curriculum Support

Conservation of energy:
Computer acquisition and analysis
of data
Overview
This snapshot demonstrates how data acquisition and analysis technology can be used to enhance
a traditional physics experiment. Demonstrating conservation of energy for a falling object can be
difficult. Measuring gravitational potential energy (GPE) is straightforward. However
measurement of kinetic energy (KE) is more difficult.
The experiment is performed by using a computer and an interface to determine final velocity and
verify that mechanical energy is conserved for a falling object. In addition, analysis of the data can
be performed using a spreadsheet, either at home or on school computers.
Why do it?
Students can rapidly achieve results without becoming confused and distracted by complex
methods for determining kinetic energy, allowing them to focus on the aim of the experiment and
the methods of analysis.
Students perform their own data analysis, which can be compared with that performed by the
computer.
Which computer-based technologies are needed?
Data capture and analysis software (The Physics Computerlab is used here)
Spreadsheet (Microsoft Excel is used here).
Computer-based technologies in the Science KLA, NSW DET © 1997
101
Making it happen
Verifying conservation of mechanical energy
for a falling object.
Aim
To verify that the total mechanical energy of a falling body is conserved.
Theory
The total mechanical energy of a falling body is equal to the sum of its kinetic energy (KE) and its
gravitational potential energy (GPE).
When an object is raised to a certain height it gains gravitational potential energy. When released
the object falls, and its gravitational potential energy is converted to kinetic energy. In this way the
total mechanical energy remains constant.
At the bottom the GPE will be completely converted to KE.
Mathematically this can be expressed as:
KE (at bottom of swing) = GPE (at top of swing)
∴ 1 mv 2 = mgh
2
∴ v 2 = 2gh
The aim of the experiment is to verify this last equation.
Note that it is not necessary to measure the mass of the bob to show that the gravitational potential
energy is converted to kinetic energy. We only have to measure the velocity and the height and
verify the equation.
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Computer-based technologies in the Science KLA
Method
The equipment consists of a bi-filar (two-string) pendulum and The Physics Computerlab as
shown below. Set up this equipment, ensuring that the pendulum bob passes cleanly through the
timing gate.
Step 1:
Start The Physics Computerlab software and select the “Timer” option.
Step 2:
Pull the pendulum bob back so that its centre of mass is five centimetres above its
rest position (see diagram above).
Step 3:
Step 4:
Click on the “Do Experiment” button.
Step 5:
Repeat the experiment for the values of height shown in the “Results” table.
Release the pendulum bob and allow it to pass through the timing gate. The
computer will measure the time for each swing and record it in a table on the
screen.
Results
Width of pendulum bob (W) =
To determine the velocity of the bob, measure its width and substitute in the equation below, where
t = time for the bob to cross the timing gate beam (as measured by the computer).
Velocity = W
t
Height (m)
Time (s)
Velocity (ms-1)
v2
2gh
0.05
0.10
0.15
0.20
0.25
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Discussion
Discuss any experimental errors that may have arisen. Suggest ways in which the experiment may
be improved. You may, for example, consider recording several values of time for each height and
averaging these values.
Conclusion
Write your own conclusion, ensuring that it relates to the aim as stated above. You should compare
the results for v2 and 2gh. Has your experiment verified that the GPE was converted to KE, that is,
that total mechanical energy is conserved?
Extensions: Using a spreadsheet to assist with data analysis
1. Copy your time and height data into your spreadsheet.
2. Construct appropriate formulas to find velocity, velocity squared and 2gh as you did in your
results above.
3. Compare your results for v 2 with those for 2gh.
Conservation of energy: finding the value of ‘g’
Aim
To find the value of the acceleration due to gravity (g) using conservation of mechanical energy.
Theory
The total mechanical energy of a falling body is equal to the sum of its kinetic energy (KE) and its
gravitational potential energy (GPE).
When an object is raised to a certain height, it gains gravitational potential energy. When released,
the object falls and its gravitational potential energy is converted to kinetic energy. In this way the
total mechanical energy remains constant.
At the bottom the GPE will be completely converted to KE.
Mathematically this can be expressed as:
KE (at bottom of swing) = GPE (at top of swing)
∴ 1 mv 2 = mgh
2
∴ v 2 = 2gh
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Computer-based technologies in the Science KLA
The aim of the experiment is to find the value of g by plotting a graph of velocity (v) vs the square
root of the height (h).
Method
The equipment consists of a bi-filar (two-string) pendulum and The Physics Computerlab as
shown below. Set this equipment up, ensuring that the pendulum bob passes cleanly through the
timing gate.
Step 1:
Start The Physics Computerlab software and select the Timer option.
Step 2:
Pull the pendulum bob back so that its centre of mass is five centimetres above its
rest position (see diagram above).
Step 3:
Click on the “Do Experiment” button.
Step 4:
Release the pendulum bob and allow it to pass through the timing gate.The
computer will measure the time and record it in a table on the screen.
Step 5:
Repeat the experiment for the values of height shown in the Results table.
Results
Width of pendulum bob (W) =
To determine the velocity of the bob, measure its width and substitute in the equation below,
where t = time for the bob to cross the timing gate beam (as measured by the computer).
Velocity = W
t
Height (m)
Time (s)
Velocity (ms-1)
0.05
0.10
0.15
0.20
0.25
Computer-based technologies in the Science KLA
105
On graph paper plot a graph of
v vs h.
Is this graph a straight line?
This is not a straight line. Students go on to plot v vs √h and find it is a straight line. It may be useful
to discuss with students how the second graph is more valuable than the first as it allows the
determination of a mathematical relationship to explain the motion of the pendulum.
On a separate sheet of graph paper plot a graph of
v vs √h
From the slope of the line of best fit of this graph, determine the value for g using the equation.
Slope = √2g
Discussion
Discuss any experimental errors that may have arisen. Suggest ways in which the experiment may
be improved. You may, for example, consider recording several values of time for each height and
averaging these values.
Conclusion
State your experimental value for acceleration due to gravity.
Extensions: Using a spreadsheet to determine and construct the line of
best fit.
1. Copy your height and velocity data into your Excel spreadsheet
Extension exercise 2
2. Use the “Chart Wizard” to construct:
should indicate to
(i) a graph of velocity vs height, and
students that being
(ii) a graph of velocity vs square root of height,
able to find a straight
line relationship is
useful to scientists.
The first graph,
velocity vs height,
does not produce a
straight line and so
3. Use the “Function Wizard” to determine the slope of the line of best fit for your second graph.
You will need to use is the “Slope” function. Microsoft Excel uses linear regression to achieve
this. Write a brief description of this technique.
4. Use the “Function Wizard” to determine the Y Intercept of the line of best fit. The function you
will need to use the “Intercept” function.
5. Create a line of best fit using the “Insert Trend Line” option from the “Chart” menu and select
“linear”.
has limited value. The
other graph allows
Finding the Y intercept is useful to evaluate
the relationship to be
experimental values. Theoretically, the Y intercept
expressed. This
should be the origin (0,0). If not, it may be due to
models the way
such things as the friction of the system.
scientists work, i.e.
searching for
relationships to assist
the explanation of
observed phenomena.
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Computer-based technologies in the Science KLA

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