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practice_prelim1_ws_fa07

# practice_prelim1_ws_fa07 - b The hill the biker is climbing...

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Practice Workshop style question: A bicycle rider is climbing a giant hill. We would like to help her calculate how much work she can transfer to the bicycle per pedal rotation. The result will suggest an advisable gear ratio for the biker. As she rides, the bicycle rider is pushing straight down on her pedal with force F = 100 N . a). The energy due to torque for a small angle is ∆ E = T θ . If the torque applied by the rider is T = 1 4 sin θ , find the energy she uses to rotate the pedal for half a cycle. Since she is pedaling with both feet, how much energy is used in a full cycle?
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Unformatted text preview: b). The hill the biker is climbing is 100m high and 1000m long (hypotenuse). If her mass is, m=50kg, and potential energy is P e = m g h , how much energy will she need to get up the hill? (let g=10m/s 2 ) c). If the bicycle has a wheel diameter of d=2 =π , how many rotations will the wheel require to climb the slope? How much energy is needed for each ro-tation? d). What should the gear ratio be to be sure she makes it up the hill? Hint: how many pedal rotations are required to give the bike enough energy to rotate the wheel once? 4...
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