Studio Physics I
Introduction to Circular Motion
In order to receive credit for a written answer, it must be expressed as a complete sentence.
For this activity you will need a movie called “FerrisWheel”. You can get it off of the
CD (go to VideoPoint folder, then Movies, then look for it in the list). You can also
transfer it from the course webpage (Go to “class activities”, scroll down to the bottom of
the page, RIGHT CLICK on the movie, choose “save link as” and watch were the file
gets saved to.) Once you have the movie file, open the Videopoint software, chose open
movie and open FerrisWheel.
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1. The first thing that must be done is to calibrate our measurement tool. The diameter
of the Ferris wheel (shown on the first frame) can be used as the known length. It is
16.98 meters. (This is the diameter of the inside wheel, not the outside edge of the
carts.) Click on the ruler icon (#2 in the picture shown above) and follow the
instructions that appear on the computer screen. You will need to change the “known
length” field to match the diameter of the wheel. Do not change “scale origin” or
“scale type”.
2. Click on the icon #3 shown in the figure above. This will instruct the software to
leave a trail of markers at every location that you point the cursor to and click.
3. Center the cursor over a point on the wheel that you think you can keep track of. We
suggest that you choose a point in the lower left-hand portion of the picture. This is
because these points remain easy to see for many frames of the movie. They will not
be obstructed by anything as the frames advance. Click on the point on the wheel that
you have chosen. The movie will advance to the next frame and a small O should
appear at the location you clicked on. The spot on the wheel that you chose to keep
Copyright@1999, 2000, 2001 Cummings
track of should have rotated through some angle. Click on the spot in its new
location. Collect about 20 data points.
4. Based on the trail of circles left on the movie image, does the Ferris Wheel appear to
be rotating with a relatively constant speed? Explain your reasoning.
5. Use the software to plot the velocity in the x-direction. When you do this, there will
also be a column added to the data table (#6 in the picture on the first page) that
shows the values of the velocity at the different moments in time. (You may have to
scroll over to see it). Plot the velocity in the y-direction. Sketch the plots on your
activity sheet. Is the velocity in the x-direction relatively constant? Is the velocity in
the y direction relatively constant? Write down the range of values that you find for
each.
6. In addition to the x and y components of velocity that we looked at above, let’s
consider the magnitude of the total velocity of the wheel. In general, how does one
get the magnitude of the total velocity from Vx and Vy (the components)? Calculate
the magnitude of the total velocity from the x and y components in your data table for
the first two times listed in the table. Show all your work on your activity write-up
7. Use the software to plot the magnitude of the total velocity of the ferris wheel. This
is done in the same way as you have made other plots, except you must chose
MAGNITUDE (not x or y) from the pulldown menu where you would usually chose
x or y. Then chose “velocity” and click ok. Do the first couple of data points agree
with what you calculated above? (They should) Based on the graph, what is the
approximate value of the magnitude of average total velocity? What is the largest
difference between the average and one of the total velocities in the data table? What
is this difference as a percentage of the average? (This percent difference is a crude
indication of the uncertainty in your measurement.) Is the magnitude of the total
velocity (speed) relatively constant?
8. What is the magnitude and direction of the centripetal acceleration of a passenger on
this Ferris Wheel at the highest point? What is the magnitude and direction of the
centripetal acceleration of a passenger on this Ferris Wheel at the lowest point?
9.
What forces act on a person at the top of the Ferris wheel? (Note that the person is
upside down at the top. Hence, the normal force from the seat on the person points
downward). What forces act on a person at the bottom of the Ferris Wheel? What are
the directions of these forces? Draw a free-body diagram for the passenger at the
highest point. Draw a free-body diagram for the passenger at the lowest point. Show
the direction of acceleration off to the side of each of the free-body diagrams. Have
your TA (or professor) check your work on this question
before proceeding.
Copyright@1999, 2000, 2001 Cummings
10. Translate each of the two free body diagrams into an algebraic expression based on
Newton’s second law (F = ma). Make sure your signs (+/-) are consistent with the
directions of the forces and acceleration.
11. What value will you use in the equations above for acceleration?
12. Based on your experience on a Ferris wheel or elevator, is the normal force exerted
on the passenger greater than, less than or equal to the passenger’s weight (=mg) at
each of these points? (Hint, do you feel lighter or heavier) Make sure that your
answers to this question are consistent with the free-body diagrams that you drew in
step 10 and the resulting second law equations.
13. If we were to measure a person’s “apparent weight” on a Ferris Wheel (or in an
elevator or anywhere else), what we would actually be measuring is the normal force
exerted on the person. What is the apparent weight of a person with mass = 68 kg or
weight= 68*9.8= 666 N when he is at the highest point on the Ferris Wheel in the
video? What is the apparent weight of the person at the lowest point?
Copyright@1999, 2000, 2001 Cummings