Bot GPT 4-o mini To determine the efficiency of the lever, we need to first calculate the useful work output and then use that to find the efficiency.
Step 1: Calculate the Work Output
The work output (useful work done) when lifting the box can be calculated using the formula:
\[ W = F \cdot d \]
where:
- \( W \) is the work done,
- \( F \) is the force applied,
- \( d \) is the distance moved.
Calculate the Force
The force required to lift the 35 kg box is equal to the weight of the box, which is given by:
\[ F = m \cdot g \]
where:
- \( m = 35 \) kg (mass of the box),
- \( g = 9.81 \) m/s² (acceleration due to gravity).
Plugging in the values:
\[ F = 35 , \text{kg} \cdot 9.81 , \text{m/s}^2 = 343.35 , \text{N} \]
Calculate the Work Done
Now, we can calculate the work done by lifting the box a distance of \( d = 18 \) m:
\[ W = 343.35 , \text{N} \cdot 18 , \text{m} = 6180.3 , \text{J} \]
Step 2: Calculate the Efficiency
Efficiency (\( \eta \)) is given by the ratio of useful work output to the energy input, expressed as a percentage:
\[ \eta = \left( \frac{\text{Useful Work Output}}{\text{Energy Input}} \right) \times 100 \]
We know from the problem:
- Energy Input = 10,000 J,
- Useful Work Output = 6180.3 J (calculated above).
Now we can substitute these values into the efficiency formula:
\[ \eta = \left( \frac{6180.3 , \text{J}}{10000 , \text{J}} \right) \times 100 \]
\[ \eta = \left( 0.61803 \right) \times 100 = 61.803% \]
Conclusion
The efficiency of the lever is:
\[ \eta \approx 61.8% \]
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