General Physics 1Circular MotionSiena College Fall 2012
Ferris Wheel Analysis
In this lab, you will analyze a movie of the famous Cyclops Ferris Wheel at Hershey Park (this ride has since been replaced). Simply click on the movie to take data. Follow the directions and answer the questions on a separate sheet.
- Open Logger Pro, then go to File Open. In the first window, choose the file called FerrisWheel.cmbl.
- The first thing that must be done is to calibrate our measurement tool (we need to tell Logger Pro how to convert from pixels in the movie to meters). The diameter of the Ferris wheel, which is shown on the first frame, can be used as the known length. It is 16.98 meters. Note that this is the diameter of the inside wheel, not the outside edge of the carts. Click on the ruler icon (#1 in the picture shown above). Then pick a point on the rim of the wheel and click and drag across the diameter. In the window that pops up, make sure you change the “known length” field to match the diameter of the wheel.
- Click on the icon #2 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.
- Center the cursor over a point on the wheel that you think you can keep track of, perhaps between two of the carts (at the end of one of the spokes). We suggest that you choose a point in the lower left-hand portion of the picture. This is because these points 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 dot should appear at the location you clicked on. Determine where the spot has advanced to and click on it again. Collect as many data points as you can (until your spot is obscured by something in the movie).
Analysis (Answer on a separate sheet of paper)
- 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.
- In Logger Pro look at the velocity in the x and y directions vs. time How do these velocity components seem to be varying? Hint: the velocity components in circular motion vary in a specific way. Try to figure out how they are varying (how do vxand vy vary in your plots) and provide an explanation.
- 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?
- In Logger Pro, calculate the magnitude of the total velocity from the x and y components. Produce a plot of this total speed vs. time. Is the magnitude of the total velocity (speed) relatively constant? Does this imply that the acceleration of the point you clicked on is zero?
- 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?
- What forces act on a person at the top of the Ferris wheel? (Note that the person is upside down at the top. What forces act on a person at the bottom of the Ferris Wheel? Draw free-body diagrams for the passenger at both the highest and lowest points.Show the direction of the net acceleration off to the side of each of the free-body diagrams.
- 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. In each case, calculate the normal force exerted on a 65 kg passenger. Is the normal force less than, equal to, or greater than the gravitational force (mg) on the person? This normal force is referred to as the person’s “apparent weight.” This is how heavy a person actually “feels”. So at the highest and lowest points, does a person feel heavier, lighter, or the same as they would feel standing still?