Download Lab 1500-7 - Otterbein University

Otterbein University Department of Physics
Physics Laboratory 1500-7
EXPERIMENT 1500-7
WORK & ENERGY
NAME:
INTRODUCTION
In this lab we will be rolling a cart down a ramp. In class, we have already analyzed this
system in terms of forces, but today we wish to look at the system in terms of energy.
Moving objects possess energy in various forms. An object that can fall has
(gravitational) potential energy (PE). An object that is moving possesses kinetic energy
(KE). A fundamental principle of physics is that the total energy in an isolated system is
neither created or destroyed - energy is conserved. As a cart rolls down a ramp, it loses
PE and gains KE. If the system were frictionless, we would expect that the total energy
of the cart would be constant:
PE + KE = Etotal
However, we know that the track isn’t completely frictionless. The cart rubs a little,
losing some energy due to friction of the track and air resistance. Thus, the total PE +
KE will decrease slightly.
Question: Where does the lost energy go?
You will need to remember the basic formulae for calculating energy in terms of the
velocity v and the height above a ground level h of an object:
KE = ½ mv2
PE = mgh
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Otterbein University Department of Physics
Physics Laboratory 1500-7
PART A: SETTING UP THE TRACK
Set up the track as shown in the diagram. Put a book under the one set of track supports
to lift it up distance d above the table. The motion sensor should be on the raised end. Put
a barrier on the lower end to make sure the cart doesn’t fall off track or
table.
Measure the height of the track in two places (d1 and d2 in the diagram above) and the
distance between those two places (not shown) to find θ, the angle of the track. Include a
diagram to help.
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Otterbein University Department of Physics
Physics Laboratory 1500-7
Find a formula to get h, the height of the cart, from x, the distance between the cart and
the motion sensor. Note that you can set h=0 wherever you like. In the diagram above,
it shows h=0 to be at the height of the table, but you may find it easier to set zero at the
height of the motion sensor. Draw another diagram to help you with this.
PART B: MEASURING THE MOTION OF THE CART
Weigh your cart on a scale and record the mass.
m = _______________
Start the Logger Pro software. It should show you two graphs and a mini spreadsheet
showing the time, position, and velocity of the cart. Set up the cart at the top of the ramp.
Start collecting a data run with the green button in the right part of the top bar. Let go of
the cart when you hear the motion sensor start to buzz. Select a region of time where the
motion sensor was working correctly to find the position and velocity. (The motion
sensor works badly if the car is too close or too far away from the sensor.) Select four
different times in this region (beginning, 1/3 of the way through, 2/3 of the way through,
and the end) and copy the values for time, position, and velocity in the first three columns
below.
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Otterbein University Department of Physics
t (s)
x
(m)
v
(m/s)
Physics Laboratory 1500-7
h
(m)
PE
(J)
KE
(J)
PE+KE (J)
Use the formulae found earlier to find the height of the cart, the potential energy, the
kinetic energy, and the total of potential + kinetic energy. Remember that your PE might
be negative, depending on how you chose h=0. If you’ve done this correctly, the PE+KE
numbers should be almost the same. Comment on how the PE+KE total changes over
time.
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Otterbein University Department of Physics
Physics Laboratory 1500-7
PART C: ANALYZE THE MOTION
Use the mouse to copy the data from the “good” region of your graph into an Excel
spreadsheet, as shown in the figure below. Use the control-C and control-V shortcuts to
copy and paste the data. Make sure to label your columns in the spreadsheet.
Let the computer repeat the exercise you did above, but using more values. Create
columns for h, PE, KE, and PE+KE. Use the included Excel “cheat sheet” to create
equations to fill out these values. Make sure everyone at the table sees how this is done.
Have the computer create a plot of x vs PE, KE, and PE+KE all on the same plot,
carefully labeling each trend. Title the plot “Run 1”. Hints: in Excel you create plots in
the following way. Highlight the values of the independent variable (position x in our
case), then hold down the “Control” button while highlighting all three dependent
variable columns (PE, KE, E=PE+KE). Then go to “Insert” and add a scatter plot. Next,
go to “Add Trendline” and check the box to display the equation of the straight fit line on
the chart for all three dependent quantities. Move them around in the plot so that all
information is visible.
PART D: DETERMINING FRICTION
The cart has minimal friction on the track, so we will increase friction by sliding blocks
down a much steeper incline. Set up the track as in Part A, but aim for an angle of about
20 degrees by using the heavy steel rods and cross bars. Recalculate the angle with the
method used previously.
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Otterbein University Department of Physics
Physics Laboratory 1500-7
Mark the top side of one of the black weights before you repeat the experiment by sliding
down the block down the incline. Make sure to catch the weight before it falls off the
track.
m2 = ______________________ (Mass of one weight)
Create a new table in the spreadsheet, but don’t delete the old one! Create the graphs of
PE, KE, and PE+KE as you did before. Label this graph ‘Run 2’.
Tape a second black weight onto the first one, and repeat the experiment. Label this
graph ‘Run 3’.
m3 = ______________________ (Mass of the two weights and tape)
In each case, you will probably find that the total PE+KE was decreasing, indicating that
energy was “leaking out” of the system. As we discussed above, this is because of
friction, which is pushing back on the object as it runs down the ramp.
The work-energy theorem says that the change in energy of an object is equal to the force
applied multiplied by the distance over through which the force was exerted on the
object:
ΔE = F Δx
Because the force of friction is causing our PE+KE total to change, we call this a ‘nonconservative’ force. That doesn’t mean energy isn’t being conserved, it just means that
PE+KE isn’t being conserved.
For each run (1,2, and 3) above, have the computer find the best-fit line to the total
PE+KE curve. For each run, use the best-fit line to find the force of friction. Make sure
you state how you got this value, and why it is the correct
one.
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Otterbein University Department of Physics
Physics Laboratory 1500-7
How is friction changing as you go from one weight to two weights? Does this make
sense, given what we know about friction? Be honest and imaginative.
How does the final velocity change as you go from one weight to two weights? Since it is
hard to compare two runs, let’s ask the simpler question: How does the acceleration
change? Fit the velocity curves with a straight line to determine the slope aka
acceleration.
What does this result say about the change in final velocity? How do the changes in
kinetic energy in Run 2 and 3 compare? Is this surprising? (Hint: Think about the
dependence of friction, potential and kinetic energy on mass.)
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Otterbein University Department of Physics
Physics Laboratory 1500-7
Do the experiment one more time. (You don’t need to include graphs of this run.) This
time, start the weights at the bottom and fling it up the ramp. How does the slope of the
PE+KE change? Explain what’s happening.
Make sure every lab partner has a copy of all 3 graphs (runs 1, 2, and 3), correctly
labeled and annotated!
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