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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.

Respuesta :

AL2006
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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