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Math Help - [SOLVED] Need help with pulley problem

  1. #1
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    [SOLVED] Need help with pulley problem

    Hi, i need help with the following question:

    The sprocket assembly for a
    0.800 m diameter bike wheel is
    shown here. If the rider can
    pedal at 50.0 rotations per
    minute, what speed will the bike
    be traveling? Express your
    answer in km/hr. The radius of
    the back sprocket is 0.050 m
    and the radius of the front
    sprocket is 0.150 m.

    Here is the picture for reference:
    [html]http://img191.imageshack.us/i/33012387.png/[/html]I don't know how to start this question, but i do know that the velocity of the pulley or sprocket is the same.
    Last edited by ogglock; April 22nd 2010 at 09:42 PM.
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  2. #2
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    If the pedal is attached to the larges sprocket, and the wheel to the smaller sprocket, one rotation of pedal of 0,150 m radius will produce 3 rotations of smaller sprocket of radius 0.05 m.So the wheel will also rotate 3 rotations during one rotation of pedal.
    Now proceed to find the speed of the bike.
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  3. #3
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    i understand how you got the three rotations but im stuck after that. The answer is suppose to be 22.6 but i can't even get close to it
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  4. #4
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    Quote Originally Posted by ogglock View Post
    i understand how you got the three rotations but im stuck after that. The answer is suppose to be 22.6 but i can't even get close to it
    In one rotation wheel travels π*D m,where D is the diameter of the wheel. In three rotation it will be moving 3π*D m.
    In one minute pedal rotates 50 revolutions.
    In one minute wheel rotates .........revolutions.
    In one minute wheel travel ........... m.
    In one hour wheel travel ........... m = ........km.
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  5. #5
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    Quote Originally Posted by sa-ri-ga-ma View Post
    In one rotation wheel travels π*D m,where D is the diameter of the wheel. In three rotation it will be moving 3π*D m.
    In one minute pedal rotates 50 revolutions.
    In one minute wheel rotates .........revolutions.
    In one minute wheel travel ........... m.
    In one hour wheel travel ........... m = ........km.
    sorry but could you explain what the symbols π and m stand for
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  6. #6
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    Quote Originally Posted by ogglock View Post
    sorry but could you explain what the symbols π and m stand for
    π is pi ......3.1416... m is meter.
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  7. #7
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    sorry to ask again but can you show me how you did it.
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  8. #8
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    Quote Originally Posted by ogglock View Post
    sorry to ask again but can you show me how you did it.
    Hi oddlock,
    You sure are having trouble here.
    pedal rotates 50 revs per min. or 3000 revs per hr
    rear sprocket rotates 3x3000 =9000 revs per hr= bike wheel revs per hr
    distance traveled in one hr =9000xpi x wheel dia =22,619 m perhr or 22.62 km per hr

    bjh
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  9. #9
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    thanks i was able to get it
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