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Variation with a Bicycle

Variation with a Bicycle. Investigate the direct and inverse variations between gear selection and wheel speed on a multispeed bicycle. This is a one-gear bicycle that contains one set of gears on the pedal and one at the wheel.

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Variation with a Bicycle

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  1. Variation with a Bicycle Investigate the direct and inverse variations between gear selection and wheel speed on a multispeed bicycle.

  2. This is a one-gear bicycle that contains one set of gears on the pedal and one at the wheel.

  3. This is a one-gear bicycle that contains one set of gears on the pedal/wheel.

  4. Penny-farthing or High-wheeler bicycle In a penny-farthing bicycle, the pedals and the front wheel are directly connected just like they are on a kid's tricycle. That means that when you turn the pedals one time, the wheel goes around one time. http://en.wikipedia.org/wiki/Sprocket

  5. Penny-farthing or High-wheeler bicycle The front wheel was 53 inches in diameter. That means that each time a person rotated their pedals one revolution, the bicycle wheel rotated one circumference or 53* 3.14 ≈ 166 inches. If you are moving the pedal at 60 rpm, or one revolution per second the bike would move 166 inches per second or 999,600 inches per hour or 16 miles per hour. http://en.wikipedia.org/wiki/Sprocket

  6. http://videos.howstuffworks.com/science-channel/37724-deconstructed-bicycle-drive-train-video.htmhttp://videos.howstuffworks.com/science-channel/37724-deconstructed-bicycle-drive-train-video.htm Multi-geared bicycles change the relationship between the pedal and wheel rotations. Let’s study the relationship.

  7. The Wheels Go Round and Round • Shift the bicycle into its lowest gear using the smallest front sprocket and the smallest rear sprocket. • Count the number of teeth on the front and rear sprockets in use. Record them in table 1 on the template. • Line up the air value on the tire of the rear wheel with part of the bike frame. This is the starting point. Rotate the pedal through one complete revolution and stop the wheel immediately. Estimate the number of wheel revolutions to the nearest tenth and enter it in the table.

  8. The Wheels Go Round and Round • Shift gears so the change moves onto the next rear sprocket. Do not change the front sprocket. Repeat the last two steps. • Continue to change the rear sprocket and repeat the data collection.

  9. 13 3.7 48 48 15 3.2 48 17 2.9 2.5 48 19 48 21 2.4 48 23 2 34 48 1.5

  10. Describe how the number of teeth on the rear sprocket affects how the wheel turns. • What kind of variation is this?

  11. Plot the data in your calculator to confirm the relationship. • Define the variables as R(L1) and W(L2). • Create a list L3 to confirm the relationship. • Write an equation that relates the two variables. • Explain the meaning of the constant in the equation.

  12. Shift the bicycle into its lowest gear again. • Using the second table, record the number of teeth on the sprockets used.

  13. Record the number of wheel revolutions for one revolution of the pedals. • Keep the chain on the same rear sprocket and shift the chain to the next front sprocket. Collect the data for each front gear sprocket.

  14. 27 2.2 13 38 2.9 13 47 3.7 13 • Describe how the number of teeth on the front sprocket affects the turning of the wheel. • What type of variation models this relationship?

  15. Place the data in your graphing calculator. • L4= Front Wheel (F) • L5 =Revolutions (W) • Plot the data in your calculator to verify your answer. • Define the variables as F and W. Write an equation that relates the gears in the front gear and the number of wheel revolutions.

  16. Create a list L6 to find the value of k. • What is the meaning of the constant in this equation?

  17. Find a proportion relating • Number of front teeth • Number of rear teeth • Number of wheel revolutions • Number of pedal revolutions

  18. Use your proportion to predict the number of wheel revolutions for a gear combination you have not tried. Test your prediction.

  19. Explain why different gear ratios result in different numbers of rear wheel revolutions. Why is it possible to go faster in a high gear? • Find the circumference of the rear wheel in centimeters. How far will the bicycle travel when the wheel makes one revolution? How many revolutions will it take to travel 1 kilometer without coasting? • For the lowest and highest gear, how many times do you need to rotate the pedal for the bike to travel 1 kilometer? 1,200 km race?

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