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12 October, 07:33

A car requires 1x10^8J of energy to drive 30km. calculate how many kilometers you could hypothetically drive using the energy contained in the rest mass of 100mg of fuel.

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  1. 12 October, 09:54
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    Ah hah! I spy a question about E = m c².

    OK, here we go. Fossen your seat belt, mon,

    it's going to be eh boompy rade!

    E = energy equivalent of mass

    m = the mass of the mass

    c = the speed of light

    E = (m) (c) ²

    = (100 mg) (3 x 10⁸ m/s) ²

    = (1 x 10⁻⁴ kg) (9 x 10¹⁶ m²/s²)

    = 9 x 10¹² (kg-m²/s²)

    = 9 x 10¹² (kg-m/s²) (m)

    = 9 x 10¹² (newton) (m)

    = 9 x 10¹² joules.

    The car can go 30 km on 10⁸ J of energy.

    How far can it go on 9 x 10¹² J?

    (9 x 10¹² J) x (30 km / 10⁸J)

    = (9 x 10⁴) x (30 km) = 2,700,000 km

    = roughly 7.3 times the distance to the moon.
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