Q62. - Algebra 1

Question

ENERGY Matter can be converted completely into energy by using the formula at the left. Energy is measured in joules, mass in kilograms, and the speed of light is about 300 million meters per second.

a. Complete the calculations to convert 3 kilograms of gasoline completely into energy.

b. What happens to the energy if the amount of gasoline is doubled?

Step-by-Step Solution

Answer

a. 3 kilograms of gasoline converts to $\mathbf{270}\mathbf{,}\mathbf{000}\mathbf{,}\mathbf{000}\mathbf{,}\mathbf{000}\mathbf{,}\mathbf{000}\mathbf{,}\mathbf{000}$ joules of energy. 

b. If the amount of gasoline doubled, then the energy is also doubled.

Part a. Step 1. Write relation between energy and matter.

The matter can be converted completely into energy using formula, $E=m{c}^2$

Part a. Step 2. Replace variables with given values.

Replace m with 3 and c with $300000000$ in $E=m{c}^2$.

$$\begin{gathered} E=3\times {\left(300000000\right)}^2 \\ =270,000,000,000,000,000 \end{gathered}$$

Part a. Step 3. Write a conclusion.

Therefore, 3 kilograms of gasoline converts to $270,000,000,000,000,000$ joules of energy. 

Part b. Step 1. Write relation between energy and matter.

The matter can be converted completely into energy using formula, $E=m{c}^2$

Part b. Step 2. Replace variables with given values.

The amount of gasoline is doubled, that is, $m\to 2m$.

Replace m with 6 and c with $300000000$ in $E=m{c}^2$.

$$\begin{gathered} E=6\times {\left(300000000\right)}^2 \\ =540,000,000,000,000,000 \end{gathered}$$

Part b. Step 3. Write a conclusion.

Therefore, if the amount of gasoline doubled, then the energy is also doubled.