Conservation of Energy Experiment (MJM)
- This experiment will use an air track, a cart, and a
mass connected over a pulley.
- This is the same setup as for Newton's second law experiment,
but ..
- We will not be using a sonic ranger. Instead we will
be using a shaft encoder.
- The string will go over the pulley of the shaft encoder,
and the encoder will record angle and time
- The software will calculate angle in radians and angular
velocity in rad/sec
Study conservation of energy.
- We will be converting angle information into distance.
For this you must measure the pulley radius.
- From the distance at a given time, you can calculate
the decrease of potential energy.
- From the velocity at that same time, you can calculate
the system kinetic energy.
- With a set of distance and velocity values you can calculate
the total system energy as time goes along.
Download and check the program
- Before the lab next Wednesday, download the program MJMEncoder.exe
from my web page
- Put it in the same directory as the lab software you
downloaded earlier.
- It should come up when you double-click it. Please check
that this is ok.
Be ready to use Excel. We will take data from the encoder
program and put it into Excel. Then you can massage the data as we go,
after each set of x,v values.
Determine the pulley radius R.
- Rig up the air track and shaft encoder at the end. Attach
the string to the cart and small mass on the paper-clip hanger.
- Figure out a way to determine the radius of the pulley
to high accuracy using the air track and the cart and the string and the
small mass. Determine the pulley radius R.
- s = R theta, where s is the length along the arc of a
circle of radius R and theta is the angle subtended by the arc. Use this
relation to convert your angle data in Excel to distance data. Then use
its big brother, v = omega R, to convert angular velocity to linear velocity
Data taking
- The small nuts are around 3.2 g each, and the large paper
clip mass is 1.5 g. Check this if you wish.
- Obtain the mass of your cart. This can be done before
or after your first set of x,v data.
- Go to Set Parameters and select every 4th point, 4000
points. Leave '2-channel' checked.
- Make sure the cart will travel for around 1 meter before
the small masses hit the ground.
- Be ready to catch the cart before it reaches the very
end of the track, since there will be no bumper there.
- Get the cart ready to be released and steady the small
masses. Press 'S' to start taking data, and right after that release the
cart.
- You should get a plot of theta vs. time showing up. It
will start with negative and go to positive values.
- Check that the angular velocity graph is ok. Check that
the data runs for 1.5 seconds or so.
- Save your data to a file, and write in your lab notebook
what the file is called, and what mass is used.
- In what follows you will want three columns, one for
time, one for angle, and one for angular velocity
- Bring up the angular velocity graph. Use the coordinate
tool ('+') to record the velocity and time at even intervals like every
0.20 sec or every 0.25 sec. Record at least 5 values. DO NOT TRY TO ZOOM
ON THE ANGULAR VELOCITY GRAPH. (I got zonked trying this; I don't know
why.) Write these v,t values by hand in your lab notebook. When you have
recorded all of these, go to the angle vs. time graph. [The reason saving
data and then angular velocity first is that you can later bring up the
saved file and it will have angle vs time, but not angular velocity vs.
time.]
- On the angle, time graph, first record the initial angle
value. [Feel free to zoom anywhere on this graph since if there is a crash
or a glitch, you can bring the angle, time data up again.]
- Use the same times as for angular velocity, and record
the angle and time. You should have at least 5 values.
Now you have at least 5 sets of x,v data. This is to go
in the spreadsheet.
Spreadsheet Analysis
- Use a cell for
- cart mass
- pulley radius
- small hanging mass
- You will want columns for
- angle
- angular velocity
- distance travelled
- potential energy with respect to initial height [ -mgR(
theta-theta_o)] {which m?}
- linear velocity in m/s
- kinetic energy
- total energy KE + PE
- Do the spreadsheet analysis of your first run before
anything else. You need to make sure it's going ok and that things are
making sense. [Would it make sense if the KE+PE were decreasing somewhat
with time? This is a point to check and discuss.]
Do a second run with 8 small masses instead of 4, and
repeat the analysis.
If time permits in the lab, do another run with your choice
of mass hanging off the end.
In writing the report, you may want to print out some
of the spreadsheet, and attach it to your lab book.
- Did you observe approximate conservation of mechanical
energy?
- How approximate was the 'conservation'?
- Was there evidence of energy not being entirely conserved?
If so, discuss this evidence.