Question

SOMEONE HELP ME PLS
Einstein's equation relating mass and energy is given by the formula E = mc,where m is the mass of an object and C = 3x108 ms-1, the speed of light.

1. Find how much energy is present in a 1 kg mass. (1 kg ms-1 = 1 joule)

2. Given that a standard light bulb uses 60 joules of energy every second, calculate how long (in years) such a light bulb could be powered by a 1 kg mass, if all the mass was converted to energy.

Answer 1

Using proportions, it is found that:

1. $\mathbf{3 \times 10^8J}$ are present in a 1 kg mass.

2. Such a light could be powered for 0.16 years.

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The energy is given by:

$E = mc = 3\times 10^8m$

• m is the mass.

Item 1:

• Mass of 1 kg means that $m = 1$, thus:

$E = mc = 3\times 10^8(1) = 3 \times 10^8$

$\mathbf{3 \times 10^8J}$ are present in a 1 kg mass.

Item 2:

• Applying the rule of three:

1 second - 60J

x seconds - $3 \times 10^8J$

$60x = 3 \times 10^8$

$x = \frac{3 \times 10^8}{60}$

$x = 5000000$

One year has 31536000 seconds $365 \times 24 \times 60 \times 60 = 31536000$. How many years are 5000000 seconds?

1 year - 31536000 s

x years - 5000000s

$3153600x = 5000000$

$x = \frac{5000000}{3153600}$

$x = 0.16$

Such a light could be powered for 0.16 years.

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