Einstein saud that the amount of energy in matter is given by E=mC^2 where if m is in kilograms and c=3x10^8 which is the speed of light. The energy is E is given in Joules. Assuming that is takes an average of 1x10^11 Joules to heat your house during the year, calculate how many years you could heat your house with the energy contained in 1 kilogram of rotten bananas.

Question

Einstein saud that the amount of energy in matter is given by E=mC^2 where if m is in kilograms and c=3x10^8 which is the speed of light. The energy is E is given in Joules. Assuming that is takes an average of 1x10^11 Joules to heat your house during the year, calculate how many years you could heat your house with the energy contained in 1 kilogram of rotten bananas.

Answer 1

To answer this question, we need to calculate the energy contained in 1 kilogram of rotten bananas using Einstein's equation, E = mC^2.

Given:
m (mass of rotten bananas) = 1 kilogram
c (speed of light) = 3 x 10^8 meters per second

First, we need to convert the speed of light from meters per second to Joules. Knowing that the speed of light is a constant, we can use the conversion factor:

1 meter = 1 kilogram ⋅ (meters per second)^2

Thus, if we substitute the units into the equation, we can solve for Joules:

1 meter = 1 kilogram ⋅ (3 x 10^8 meters per second)^2
= 1 kilogram ⋅ 9 x 10^16 meters^2 per second^2

Now, we can calculate the energy contained in 1 kilogram of rotten bananas by multiplying the mass by the converted speed of light value:

E = 1 kilogram ⋅ 9 x 10^16 meters^2 per second^2
= 9 x 10^16 kilogram ⋅ meters^2 per second^2

We need to express the energy in terms of Joules. To convert from kilogram ⋅ meters^2 per second^2 to Joules, we use the conversion factor:

1 Joule = 1 kilogram ⋅ meters^2 per second^2

So, the energy contained in 1 kilogram of rotten bananas is:

E = 9 x 10^16 kilogram ⋅ meters^2 per second^2
= 9 x 10^16 Joules

Now that we know the energy contained in 1 kilogram of rotten bananas, we can calculate the number of years you could heat your house using this energy.

Energy required to heat house for a year = 1 x 10^11 Joules
Number of years you can heat your house = Energy contained in 1 kilogram of rotten bananas / Energy required to heat house for a year

Number of years = (9 x 10^16 Joules) / (1 x 10^11 Joules)
= 9 x 10^16 / 1 x 10^11
= 9 x 10^5 years

Therefore, you could heat your house for approximately 900,000 years with the energy contained in 1 kilogram of rotten bananas.