Let's assume for a moment that your house uses an average of 16kWh of electrical energy per day. If you could covert the mass o
f a 46g 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 E = mc^2 to solve the question. Please show your work. Thanks in advance for your help!
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) = <u>71,875,000 days</u>
That's roughly <em><u>196,783 years</u></em> of typical household electrical energy use. (assuming that every year was, is, and shall always be 365-1/4 days.)