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Stair climbing

  1. Feb 22, 2006 #1
    I worked this out but I must of gone wrong somewhere

    Energy is conventionally measured in Calories as well as in joules. One Calorie in nutrition is one kilocalorie, defined as 1 kcal = 4186 J. Metabolizing 1 g of fat can release 9.00 kcal. A student decides to try to lose weight by exercising. She plans to run up and down the stairs in a football stadium as fast as she can and as many times as necessary. Is this in itself a practical way to lose weight? To evaluate the program, suppose she runs up a flight of 100 steps, each 0.150 m high, in 61.5 s. For simplicity, ignore the energy she uses in coming down (which is small). Assume that a typical efficiency for human muscles is 20.0%. Therefore when your body converts 100 J from metabolizing fat, 20 J goes into doing mechanical work (here, climbing stairs). The remainder goes into extra internal energy. Assume that the student's mass is 56.0 kg.

    (a) How many times must she run the flight of stairs to lose 1 lb of fat?
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    First off, we have to convert. When 1 lb of fat is burned that is 453.592 g. Each gram of fat burned requires 9.00 kcal as the problem states which is equivalent to 37674 J. So to burn 1 g of fat you need to work off 37674 J so to burn 453.592 g of fat one must burn (453.592)(37674)=17088625 J.

    Ok so to the physics:
    W=Fd
    The distance is the vertical distance going up the stairs which is 100(.15m)=15m.

    I got confused on what the force should be, is it the force of gravity which would be 56(9.8)?

    If so W=fd = (560)(15) = 8400 but only 1/5 of that work goes towards metabolizing fat so 1680 J per time up the stairs. Then you take the total amount of joules needed to be burned / 1680 and get a huge, unreasonable number..any help is appreciated
     
  2. jcsd
  3. Feb 22, 2006 #2
    The force of gravity is 9.8 and not 56
     
  4. Feb 22, 2006 #3
    Its not the persons weight, mg? So the force per flight of stairs is W=fd=(9.8)*(15)

    So the work to go up 1 flight of stairs = 29.4 J, and you need to burn17088625 J so 17088625/29.4 is the number of times she must go up the stairs, which equals 581,245?
     
  5. Feb 22, 2006 #4
    1/5 of that work goes towards mechanical work not metabolizing fat.
     
  6. Feb 22, 2006 #5
    The total fat used up is 5 times the energy used in doing mechanical work. This is coz 20% of used fat is used to generate energy to do mechanical work. So even the other 80% is also lost from the body.
     
  7. Feb 22, 2006 #6
    So the energy used in work going up the stairs * 5 is the amount of energy burnt on each run of the stair flight? So is the total amount she needs to burn in order to burn a lb of fat 17088625 J?
     
    Last edited: Feb 22, 2006
  8. Feb 22, 2006 #7
    :surprised OUCH! w=mg. If m=56 kg, then w=56*9.8 N.

    -Dan
     
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