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Math Help - Belt & pulley problem

  1. #1
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    Belt & pulley problem

    Hi everybody, I require assistance in solving this problem:

    A transmission belt passes tightly around 2 pulleys and crosses itself between them. The radii of the pulleys are 3m and 2m respectively, and their centres are 13m apart. Calculate:

    a) the length of the belt
    b) the total area enclosed by the belt.

    Answers
    a) 43.65m
    b) 56.75m^2

    I would like to know the working out required for these questions.

    I have also attached a simple diagram of the problem to aid in visualisation. Any assistance would be much appreciated.
    Attached Thumbnails Attached Thumbnails Belt & pulley problem-belt-pulley-problem.gif  
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  2. #2
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    Quote Originally Posted by Xyrios View Post
    Hi everybody, I require assistance in solving this problem:

    A transmission belt passes tightly around 2 pulleys and crosses itself between them. The radii of the pulleys are 3m and 2m respectively, and their centres are 13m apart. Calculate:

    a) the length of the belt
    b) the total area enclosed by the belt.

    Answers
    a) 43.65m
    b) 56.75m^2

    I would like to know the working out required for these questions.

    I have also attached a simple diagram of the problem to aid in visualisation. Any assistance would be much appreciated.
    I've attached a sketch of the construction of the 2 interior tangents of 2 circles.

    Use the greyed right triangle to calculate the tangent segments and the central angles which you have to use to calculate the 2 arcs of the circles.
    Attached Thumbnails Attached Thumbnails Belt & pulley problem-inneregemeins_tangkrse.png  
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