10/4/00

GOAL: To investigate the physics of circular motion on a ride at the state fair. To determine the centripetal acceleration of a ride by two different methods and to determine the ratio of a rider's apparent weight to true weight.

You will be provided with a set of accelerometers for data-taking at the state fair. The accelerometers will be used to measure

a) horizontal and vertical accelerations

b) angles

c) distances

Each person measures her/his own value(s) for all timings, angles, distances, and accelerations. In addition, you need to bring with you

a) pencil and the state fair data sheet

b) a watch (preferably one with a sweep second hand or a digital

watch with stop/start capabilities)

The above apparatus will be used to collect sufficient data in order to determine as many of the following as possible/relevant:

a) ride period (time/revolution)

b) physical dimensions of the ride (perhaps horizontal and vertical)

b) speed of the ride (in m/s)

c) centripetal acceleration

d) ratio of apparent weight of (i.e., the normal force felt by) a rider

to the rider's true weight

Practice using your horizontal accelerometer on the bus ride to the fair!!!

One possible way of organizing your results follows. You need not necessarily do it this way, although any complete lab report should include these as a minimum. Be as creative as you can.

A) A picture and a word description of the ride; direct measurements (period, radius,

height, etc.) should be incorporated in the picture and/or description

B) All relevant force diagram(s) and net force equations

C) Comparison of directly measured and indirectly determined centripetal accelerations

D) Ratio of Apparent Weight to True Weight of rider

E) Physiological sensations of rider

F) Miscellaneous

G) Conclusion

Describe briefly what your ride did. Draw a large diagram of the ride you experienced, and label it with relevant length measurements. Describe briefly how you determined these distances. Describe briefly how the ride period was obtained. Always start with symbols representing the raw data measured, show how it will be used to derive or calculate other quantities, and then put in the numbers.

Some rides may require only one force diagram (i.e., the same force diagram applies throughout the ride). Other rides (especially ones that involve both vertical and horizontal motion) may require different force diagrams for different parts of the ride.

Draw the relevant force diagram(s) for your ride.

Write the appropriate net force equations for your ride.

For most rides, you should be able to determine the centripetal acceleration in at least two ways:

(1) by calculating it using a_c = v²/r , where v and r are the linear speed and radius of the ride, respectively.

(2) by measuring it directly using the appropriate accelerometer.

Use your net force equations to solve for the ratio of a rider's apparent weight to true weight (in terms of the centripetal acceleration a_c and any important ride parameters, such as the angle of tilt). Then, using your formula and the values for centripetal acceleration calculated or measured previously, calculate the ratio of the rider's apparent weight to true weight. Your apparent weight might be exerted by a floor, a wall, or a seat. Some rides may have more than one normal force; for example, a normal force due to a seat and a normal force due to the back of the seat.

Describe the physiological sensations that you experienced on the ride and how they did or did not match what was expected purely from Newton's first law, the force diagram, and the net force equation analysis. For example, did you feel heaviest (and lightest) where you expected to? did the ride make you dizzy or sick to your stomach? Why? if, at some point during the ride you were upside down, could you tell?

Use the ride problems in Cutnell & Johnson [chapter 5(19, 58)] and on the sheet titled "Circular Motion Problems at the State Fair" as examples of other things you might do. It might be appropriate to determine a friction coefficient, the ride speed for which you would feel weightless, etc.

G) CONCLUSION