A certain lead-acid storage Battery has a mass of 34 kg. Starting from a fully c

Question

A certain lead-acid storage Battery has a mass of 34 kg. Starting from a fully charged state, it can supply 6 A for 24 hours with a terminal voltage of 12 V before it is totally discharged. If the energy stored in the fully charged Battery is used to lift the Battery with 100-percent efficiency, what height is attained? Assume that the acceleration due to gravity is 9.8 m/s2 and is constant with height. Express your answer to three significant figures and include the appropriate units. If the stored energy is used to accelerate the Battery with 100 percent efficiency, what velocity is attained? Express your answer to three significant figures and include the appropriate units. Gasoline contains about rho 1 = 4.5 times 10T J/kg. Compare this with the energy content per unit mass for the fully charged Battery (rho 2) Express your answer using three significant figures.

Explanation / Answer

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The energy content in the batter is given by

E = 6A * (24 * 3600 seconds) * 12V

   = 6220800 Joules

   = 6.22 * 10^(6) Joules

2 = 6220800/34 = 182964.71 J/kg

2/1 = (182964.71) / (4.5 *(107) )

          = 4.07 (10^(-3))

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