Download Pendulum Lab

Name: ______________________
Partners: _______________________________________
Date: __________
Period: ________
Cut Short & Conservation of Energy Lab
There are 2 different lab setups at your table. One for each section of this lab.
A pendulum swinging to and fro illustrates the conservation of energy. Raise the pendulum bob to give it potential energy.
Release it and the potential energy is converted to kinetic energy as the bob approaches its lowest point. Then, as the bob
swings up on the other side, kinetic energy is converted to potential energy. Back and forth, the forms of energy change
while their sum is constant. Energy is conserved.
Part 1: Cut Short
What happens if the length of the pendulum is suddenly changed? How does the resulting motion illustrate energy
conservation?
Procedure
Step 1: At your lab station you will find a pendulum attached to a cross bar. Measure the length of the pendulum with a
meter stick from the top of the string to the center of mass of the pendulum bob. Record this value as the length of the
pendulum. Then measure from the bottom of the table to the center of mass of the pendulum bob. Record this as the
'height above the table'.
Length of the pendulum (L): _______
Height above the table (h.a.t.): _______
Step 2: Multiply the length of the pendulum by 2/3 and record below. Then, add this value to the height above the table.
This will tell you how high you should start your pendulum swinging in each trial in the lab. Don't forget the units!
2/3 X Length of the pendulum:
+
Height above the table (h.a.t.):
Start height of pendulum:
Step 3: You will find a second cross bar below the cross bar that the pendulum hangs from. Adjust this second bar to the
same height as the start height of the pendulum.
Predict height.
Step 4: Predict what height the pendulum bob will reach if the pendulum is released at your calculated start height, and
the pendulum string is stopped by the rod. Will the pendulum go higher, the same height, or not as high?
Release pendulum.
Step 5: Use your meter stick to place your pendulum bob at the proper start height. Have one of your teammates
positioned on the opposite side of where the pendulum is released to observe how high the pendulum swings. Release the
pendulum! Did the pendulum go higher, the same height, or not as high? (THINK! Think in 'experimental' terms.)
Raise rod.
Step 6: Predict what would happen if the rod were attached higher than the starting height. Perform the experiment as
above, with the second cross bar raised above the start height of the pendulum to confirm or deny your prediction.
Prediction: ______________________________________________________
Observation: ____________________________________________________
Lower rod.
Step 7: Predict what would happen if the rod were moved lower than the start height of the pendulum bob. Perform the
experiment again to confirm or deny your prediction.
Prediction: ______________________________________________________
Observation: ____________________________________________________
Step 8: Perform a few more trials until the cross bar is JUST BARELY LOW ENOUGH to the point where the pendulum
bob completely loops around. Be sure the cross bar is low enough to where the string stays taut until the top of the loop.
Sketch the arrangement below, along with your measurements.
What is the Total Energy of the system?
What is the PEgrav of the pendulum bob when it's at the top of its loop (starting to go around the bar)?
What must the rest of the energy be? What is the value of this energy?
From the above energy, calculate the velocity of the pendulum bob at the top of the loop.
From the velocity, calculate the centripetal acceleration of the pendulum bob at the top of the loop. How close is it to g?
Conclusions
1. Explain your observations in terms of potential and kinetic energy and the conservation of energy. Does the height
that the pendulum bob swung to support the Law of Conservation of Energy?
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2. Is there an upper limit on how high the rod can be and still loop around smoothly? If so, explain why you think there
are limits.
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3. Below, calculate where the cross-bar would need to be located in order for the pendulum to have just enough energy
to swing up and spin around the bar. Find the location of the bar relative to the original height (from the zeroreference point) of the pendulum.
Part 2: Conservation of Energy
Purpose
To determine if total energy in a pendulum is conserved by comparing potential and kinetic energies.
In the first part of the lab, you saw that the height to which a pendulum swings is related to its initial height. The work
done to elevate it to its initial height becomes stored as potential energy in relation to the
bottom of the swing. At the top of the swing, all the energy of the pendulum is in the form
of potential energy. At the bottom of the swing, all the energy of the pendulum is in the
form of kinetic energy.
The total energy of a system is the sum of its potential and kinetic energies. If energy is
conserved, the sum of the potential and kinetic energy at one moment will equal the sum
at any other moment.
Your goal is to demonstrate that total energy in a pendulum system is conserved. You must prove that this is a general rule
(not just for a particular starting height). The equipment you have to work with is:
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Pendulum suspended from ring stand. NOTE: Diameter of the pendulum bob = 2.8 cm.
Meter stick
Photogate timer and computer
Procedure:
Step 1: At your lab station you will find a pendulum attached to a cross bar. Measure the length of the pendulum with a
meter stick from the top of the string to the center of mass of the pendulum bob. Record this value as the length of the
pendulum. Then measure from the bottom of the table to the center of mass of the pendulum bob. Record this as the
'height above the table'.
Length of the pendulum (L): _______
Height above the table (h.a.t.): _______
Step 2: In the table below, chose and record 3 heights from which you will release the pendulum. Keep in mind that when
you perform the experiment you will have to include the h.a.t. to release your pendulum bob from the correct height. To
improve accuracy, do not use a Pendulum Height greater than half your pendulum length.
Pendulum Height ( )
Photogate Time ( )
Distance (m)
Trial 1
0.028
Trial 2
0.028
Trial 3
0.028
Pendulum Velocity (
Step 3: Open the file found in the 'Thawspace' of the computer named 'Pendulum Lab Settings.' You should see a data
table with columns for 'Time' and 'Gate State.' The 'Gate State' column records values for when the space between the
photogate is first blocked and then a second time for when the photogate is again open.
)
Step 4: Hold your pendulum bob at your first release height. Press the 'Collect' button to start the photogate sensor.
Release your pendulum bob so that it passes through the photogate. Stop the photogate and pendulum. Subtract the
Opening time of the gate from the closing time of the gate. Record this value in the 'Time' column of your data table.
NOTE: If you allow your pendulum to swing past your photogate more than once, you will have extra values for opening
and closing of the sensor. IGNORE THESE EXTRA VALUES! Only use the first two values of time.
Step 5: Repeat the above procedure for your other two heights. Use the diameter of the pendulum bob as the distance for
each of your trials. Using v=d/t, calculate the velocity of the pendulum bob as it passes the photogate. Be careful with
units!
Step 6: Calculate the gravitational potential energy for each of your heights, and the kinetic energy for the pendulum as it
passed the photogate. When performing calculations, remember that mass is measured in kilograms. Finally, calculate the
percent difference. Show your work for one trial, and complete the data table below.
Useful Equations:
P.E.top = mgh
K.E.bottom = (1/2)mv2
SHOW ONE SAMPLE CALCULATION HERE:
Potential Energy ( )
Kinetic Energy ( )
% Difference
Trial 1
Trial 2
Trial 3
Conclusion
Was the energy of the pendulum the same at the initial height and as it passed the photogate? NOTE: if your percent
difference was less than 10%, you had a successful lab! If not, discuss possible sources of error.
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