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Kinetics/Motion in 2D/Energy question

  1. Jan 15, 2015 #1
    1. The problem statement, all variables and given/known data
    A 12V car battery is capable of storing 3.51 kWh of electric energy. For a certain electric car to maintain a speed of 48.3 km/hr, it must develop 10.7 kW of power. If this car is run by 11 batteries which are 90.5% efficient, how far can this car travel, at the desired speed, between recharges?
    V= 48.3 m/s (yes constant motion)
    P=10700W
    efficiency= 90.5%
    Each battery capacity= 3510W
    Uses 11 batteries
    2. Relevant equations
    E= (Wo / Wi ) *100

    E= .5 * m * v^2
    W= P*t
    3. The attempt at a solution
    1. Since its going at a constant velocity, i can find the mass. Using the Energy kinetic formula.
    2.Finding the mass i can plug it into the efficiency formula to get its work output.
    3. its using 11 batteries that are 90.5% efficient. So on the denominator of the efficiency formula it would be 11* 3510W because each capacity is 3.51kWh.
    5.the numerator would be the Energy kinetic formula * 100 and then the efficiency would be 90.5%
    6. Getting the time i could multiply it with the velocity to get its distance?
     

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  2. jcsd
  3. Jan 15, 2015 #2

    haruspex

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    Since it's at constant velocity, the KE is constant. The energy from the batteries is not being used to add to KE, so it won't tell you the mass. Neither KE nor the mass are of interest here.
    You are told how much power it needs to supply to the wheels, and you know the efficiency, so how much power must be drawn from the batteries?
    How long can the batteries supply that power for?
     
  4. Jan 16, 2015 #3
    Okay ignoring the kinetic formula, my bad wasnt thinking straight. Re doing the effieciency formula it would be 90.5%= (10700W*100%/ (11* (3.51kWh*3.6E6)t)
     
  5. Jan 16, 2015 #4
    Using this formula we're able to calculate how long the batteries will last at the power to run the car.?
     
  6. Jan 16, 2015 #5

    haruspex

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    Close, but if you check the dimensions you'll find it doesn't make sense. You have power/(energy*time).
     
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