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 of a 46g golf ball into electrical energy, how many years supply of energy would you have? Note: 1 kWh = 3.6 x 10^6 JUse the equation E = mc^2 to solve the question. Please show your work. Thanks in advance for your help!

Question

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 of a 46g golf ball into electrical energy, how many years supply of energy would you have? Note: 1 kWh = 3.6 x 10^6 JUse the equation E = mc^2 to solve the question. Please show your work. Thanks in advance for your help!

AL2006 · Accepted Answer

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 kgc = 3 x 10^8 m/sc² = 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 jouleI just noticed that the question GAVE us the joule equivalent of 1 kWh, so itwasn'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 daysThat'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.)

Subject: Physics - Page 305

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