Katy pushes a box up an inclined plane with an efficiency of 38%. If 460 joules of energy went into moving the box, how much energy did Katy put into the inclined plane? (Show your work, and report your answer in the correct unit). (3 points)

Answer 1

To calculate the energy Katy put into the inclined plane, we need to use the concept of efficiency.

Efficiency is defined as the ratio of useful work output to the total energy input, expressed as a percentage:

\[ \text{Efficiency} = \left( \frac{\text{Useful Work Output}}{\text{Energy Input}} \right) \times 100% \]

Given that the efficiency is 38% and the useful work output is 460 joules, we can rearrange the equation to find the energy input (the total energy Katy put in):

\[ \text{Energy Input} = \frac{\text{Useful Work Output}}{\text{Efficiency}} \]

First, we need to express the efficiency as a decimal:

\[ \text{Efficiency} = 38% = 0.38 \]

Now we can substitute the values into the equation:

\[ \text{Energy Input} = \frac{460 \text{ joules}}{0.38} \]

Calculating this gives:

\[ \text{Energy Input} = \frac{460}{0.38} \approx 1210.53 \text{ joules} \]

Thus, the total energy that Katy put into the inclined plane is approximately:

\[ \boxed{1210.53 \text{ joules}} \]