Question
A moving company wants to lift a piano to the second story of a house and has these three pulley set ups to choose from (the piano would replace the weight pictured). Which would be the best choice and why?
(1 point)
Responses
Choice B would be the best, because you are pulling upwards using half of the force, so it would be easier.
Choice B would be the best, because you are pulling upwards using half of the force, so it would be easier.
Choice A would be the best because the pull motion is downward he will only use 1/2 of the force, so that will be easier.
Choice A would be the best because the pull motion is downward he will only use 1/2 of the force, so that will be easier.
Choice C because the pulley changes the directions of the pull and reduces the amount of force needed, even though the rope is pulled longer.
Choice C because the pulley changes the directions of the pull and reduces the amount of force needed, even though the rope is pulled longer.
Either A or B because the force will be the same (half) and the amount of rope pulled is the same and the directions does not matter.
Either A or B because the force will be the same (half) and the amount of rope pulled is the same and the directions does not matter.
Question 2
A man is using a pulley to raise a weight. He is applying 45 joules of energy to pull on that rope and 44.325 joules of energy are being used to lift the weight. What is the efficiency of the pulley?
(1 point)
Responses
98.5%
98.5%
.675 Joules
.675 Joules
98.325 joules
98.325 joules
1.015%
1.015%
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Answers
GPT-4o mini
For the first question regarding the best choice of pulley setup for lifting a piano, we should evaluate the options:
1. **Choice A**: This option indicates that the pull motion is downward, and the force required is halved. This suggests a simpler lifting process, but we need to verify if it indeed reduces the total effort more than the other choices.
2. **Choice B**: Similar to A, this choice states that pulling upwards would use half the force, making it easier. It seems appealing as well.
3. **Choice C**: States that while the pulley changes the direction of the force and reduces the effort needed, it requires pulling more rope length. This is a traditional feature of many pulley systems, focusing on the function over the effort.
4. **Either A or B**: This option notes that the effects are equivalent in force reduction and rope length.
**Best Choice: Choice C** would be the best choice. The main reason is that it underscores the effectiveness of a pulley in changing the direction of force and making lifting easier, despite the longer rope being pulled. It highlights a fundamental benefit of pulleys regarding ease of lifting heavier weights.
---
For the second question regarding the efficiency of the pulley:
Efficiency can be calculated using the formula:
\[
\text{Efficiency} = \left( \frac{\text{Useful Output Energy}}{\text{Input Energy}} \right) \times 100
\]
In this case:
- Useful Output Energy = 44.325 joules
- Input Energy = 45 joules
Substituting the values:
\[
\text{Efficiency} = \left( \frac{44.325}{45} \right) \times 100
\]
\[
\text{Efficiency} = 0.985 \times 100 = 98.5\%
\]
The answer is **98.5%**. This shows that the pulley setup is highly efficient, making the most of the energy input to lift the weight.
1. **Choice A**: This option indicates that the pull motion is downward, and the force required is halved. This suggests a simpler lifting process, but we need to verify if it indeed reduces the total effort more than the other choices.
2. **Choice B**: Similar to A, this choice states that pulling upwards would use half the force, making it easier. It seems appealing as well.
3. **Choice C**: States that while the pulley changes the direction of the force and reduces the effort needed, it requires pulling more rope length. This is a traditional feature of many pulley systems, focusing on the function over the effort.
4. **Either A or B**: This option notes that the effects are equivalent in force reduction and rope length.
**Best Choice: Choice C** would be the best choice. The main reason is that it underscores the effectiveness of a pulley in changing the direction of force and making lifting easier, despite the longer rope being pulled. It highlights a fundamental benefit of pulleys regarding ease of lifting heavier weights.
---
For the second question regarding the efficiency of the pulley:
Efficiency can be calculated using the formula:
\[
\text{Efficiency} = \left( \frac{\text{Useful Output Energy}}{\text{Input Energy}} \right) \times 100
\]
In this case:
- Useful Output Energy = 44.325 joules
- Input Energy = 45 joules
Substituting the values:
\[
\text{Efficiency} = \left( \frac{44.325}{45} \right) \times 100
\]
\[
\text{Efficiency} = 0.985 \times 100 = 98.5\%
\]
The answer is **98.5%**. This shows that the pulley setup is highly efficient, making the most of the energy input to lift the weight.