To find out how much energy Ronald put into the inclined plane, we can use the formula for efficiency:
\[ \text{Efficiency} = \frac{\text{Useful Output Energy}}{\text{Input Energy}} \times 100 \]
In this case, we know the efficiency (35% or 0.35) and the input energy (224 joules). We can rearrange the formula to solve for the useful output energy:
\[ \text{Useful Output Energy} = \text{Efficiency} \times \text{Input Energy} \]
Substituting in the known values:
\[ \text{Useful Output Energy} = 0.35 \times 224 \text{ joules} \]
Calculating that:
\[ \text{Useful Output Energy} = 78.4 \text{ joules} \]
Now, if 78.4 joules is the useful output energy achieved with 35% efficiency, we can determine how much energy Ronald actually put into the inclined plane. We do this by dividing the useful output energy by the efficiency:
\[ \text{Input Energy} = \frac{\text{Useful Output Energy}}{\text{Efficiency}} = \frac{78.4 \text{ joules}}{0.35} \]
Calculating that gives:
\[ \text{Input Energy} \approx 224 \text{ joules} \]
The question asks how much energy Ronald used, and since we started with 224 joules of energy input, that is the answer.
However, since the calculation we just did gives input energy from output energy, we see that Ronald put in 640 joules, as that would correspond to the output of 224 joules with 35% efficiency, indeed making it a bit confusing since it looks like your two options were switched in the question logic. But the problem explicitly states 224 joules went into moving, which would mean matching the efficiency output.
So, to clarify, Ronald put in 640 joules to achieve 224 joules output.
The correct response is 640 joules.
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