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Find Distance of Car, given Rest-Energy

  1. Apr 11, 2014 #1
    1. The problem statement, all variables and given/known data
    Suppose one gallon of gasoline produces 1.01×108 J of energy, and this energy is sufficient to operate a car for 18.2 miles. An aspirin tablet has a mass of 332 mg. If the aspirin could be converted completely into thermal energy, how many miles could the car go on a single tablet?

    2. Relevant equations



    3. The attempt at a solution

    1 gallon of gas= (1.01E8) J
    Distance of car(on gas)= 18.2 miles
    Mass(aspirin)= 332 mg
    Looking for
    Distance of car(on asprin)=???


    I converted the mass from grams to kilograms.
    332mg = (332E-3)g = (332E-6)kg

    *After this I'm not sure if I'm doing the right thing.*
    The problem says "converted completely into thermal energy" so I'm assuming that this means I need to find the rest energy.
    Erest=mc^2 [m=mass in kg; c=speed of light=(3E8)m/s]
    =(332E-6)(3E8)^2
    =(332E-6)(9E16)
    =(2.988E13) J​

    I then set up the energy of gas, distance on gas and the energy I found abvoe of the asprin, to solve for distance on asprin?
    (distance of gas)/(energy of gas)=(distance of aspirin)/(energy of aspirin)
    =(18.2 miles)/((1.01E8)J)=(?distace of asprin?)/((2.988E13)J)
    =[(18.2)(2.988E13)]/(1.01E8)
    =(5.43816E14)/(1.01E8)
    =5384316.832 miles = (5.38E6) miles​

    However that answer is incorrect and I'm not sure if I am even using the right formulas for this problem.

    Any help would be greatly appreciated!
     
  2. jcsd
  3. Apr 11, 2014 #2
    is the answer 0.001242742 miles?
    im not a guru btw
     
  4. Apr 11, 2014 #3
    The correct answer is (5.38E6)mi. My calculations were correct, I just had my units of measurement wrong.
     
  5. Apr 12, 2014 #4

    NascentOxygen

    User Avatar

    Staff: Mentor

    Hi blue_lilly. I'm pleased that the physics forums was able to help you to solve your problem on this occasion. :smile:
     
  6. Apr 13, 2014 #5
    errr so a gallon of gas get you 18 miles and an aspirin 5.38*10^6 miles ?

    i guess we been using the wrong fuel all this time...
     
  7. Apr 16, 2014 #6
    If only it really worked like that, we would saving a lot of money. C:
     
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