Assume that your house uses an average of 16 kWh of electrical energy per day. If you could convert the mass of a 46 g golf ball into electrical energy, how many years' supply of energy would you have?

Note: 1 kWh = 3.6 x 10^6 J

Use the equation [tex]E = mc^2[/tex] to solve the question.

Please show your work.

Holy cow !
Before we do the mass-energy conversion, and then relate that to the household energy usage, we have to get some numbers in order, and massage some units etc.:
46 grams = 0.046 kg c = 3 x 10^8 m/s c² = 9 x 10^16 m²/s²
Household daily energy consumption:
(16 kilowatt-hour) = (16 x 1,000watt x hour) = (16 x 1,000 joule/sec x hour)
16,000 (joule-hour/sec) x (3,600 sec/hour) = (16,000 x 3,600) = 5.76 x 10^7 joule
I just noticed that the question GAVE us the joule equivalent of 1 kWh, so it wasn't necessary to derive it. I checked my figure here against that one, and got the same number ... 5.76 x 10^7 joule per day. So I'm OK so far. yay!
Now we have everything we need:
E = m c² = (0.046) x (9 x 10^16) = 4.14 x 10^15 joules in a golf ball of mass.
(4.14 x 10^15 joules) / (5.76 x 10^7 joules per day) = 71,875,000 days
That's roughly 196,783 years of typical household electrical energy use. (assuming that every year was, is, and shall always be 365-1/4 days.)

Answered by AL2006 | 2024-06-10

Using a 46 g golf ball, we can theoretically convert it to 4.14 x 10^{15} joules of energy. This amount of energy would last approximately 196,783 years for a household consuming 16 kWh per day. Therefore, the mass-energy conversion illustrates the substantial energy potential contained within even small amounts of matter.
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Answered by AL2006 | 2024-12-22