Final answer:
Car batteries are rated in ampere-hours (Ah), which corresponds to charge capacity. The energy stored in a 50 ampere-minute, 12-volt battery is 36,000 Joules (J). Assuming 100% efficiency, the volume of water required from a 50 cm-high hydroelectric dam to charge the battery is 7200 liters.
Step-by-step explanation:
Car batteries are rated in ampere-hours (Ah), which corresponds to charge capacity. The energy stored in a battery can be calculated by multiplying the charge capacity (in Coulombs) by the voltage difference across the battery. In this case, the battery has a rating of 50 ampere-minutes (A·min) and a voltage of 12 volts (V).
To find the energy stored in the battery, we first convert the charge capacity from ampere-minutes to Coulombs:
50 A·min x 60 s/min = 3000 C
Then we calculate the energy using the formula:
Energy (E) = Charge (Q) x Voltage (V)
E = 3000 C x 12 V = 36,000 J
Therefore, the energy stored in a 50 ampere-minute, 12-volt battery is 36,000 Joules (J).
Secondly, presuming 100% efficiency, we can determine the volume of water required to charge the battery. Since 1 Joule of energy is equal to 1 liter of water lifted by 10 cm, we can calculate:
Volume of water = Energy / (Density x g x height)
where Density of water (ρ) = 1000 kg/m3 and g is the acceleration due to gravity (9.8 m/s2).
Using the given energy of 36,000 J and height of the hydroelectric dam of 50 cm:
Volume of water = 36,000 J / (1000 kg/m3 x 9.8 m/s² x 0.5 m) = 7200 liters
Therefore, the volume of water required from a 50 cm-high hydroelectric dam to charge the battery is 7200 liters.