Question
Sara will use a compound pulley to lift an engine from the floor of her garage into her truck. The truck is 3 meters above the floor. Sara pulls 12 meters of rope to lift the engine. Which statement is not correct?
(1 point)
Responses
Sara will save work by using the compound pulley.
Sara will save work by using the compound pulley.
Sara uses the same force she would have needed without the compound pulley
Sara uses the same force she would have needed without the compound pulley
Sara uses one-third the force she would have needed without the compound pulley
Sara uses one-third the force she would have needed without the compound pulley
Sara uses one-fourth the force she would have needed without the compound pulley
(1 point)
Responses
Sara will save work by using the compound pulley.
Sara will save work by using the compound pulley.
Sara uses the same force she would have needed without the compound pulley
Sara uses the same force she would have needed without the compound pulley
Sara uses one-third the force she would have needed without the compound pulley
Sara uses one-third the force she would have needed without the compound pulley
Sara uses one-fourth the force she would have needed without the compound pulley
Answers
GPT-4o mini
To determine which statement is not correct, we need to analyze how a compound pulley system works.
In a compound pulley system, the distance you pull the rope is greater than the distance the load is lifted. This means you can lift a heavy load using less force than you would need to lift it directly.
1. If Sara pulls 12 meters of rope to lift the engine 3 meters, we can see the relationship of the distances:
- Distance pulled (input) = 12 meters
- Distance lifted (output) = 3 meters
2. The mechanical advantage (MA) can be calculated using the formula:
\[
MA = \frac{\text{Distance Pulled}}{\text{Distance Lifted}} = \frac{12 \text{ m}}{3 \text{ m}} = 4
\]
This means Sara uses a force that is one-fourth of the force she would need to lift the engine directly (without the pulley).
Now let's evaluate the statements:
- "Sara will save work by using the compound pulley." (Correct, but the amount of work done remains the same, the force is reduced).
- "Sara uses the same force she would have needed without the compound pulley." (Incorrect, because she uses less force).
- "Sara uses one-third the force she would have needed without the compound pulley." (Incorrect, because the factor is one-fourth, not one-third).
- "Sara uses one-fourth the force she would have needed without the compound pulley." (Correct).
The statement that is **not correct** is:
**"Sara uses the same force she would have needed without the compound pulley."**
In a compound pulley system, the distance you pull the rope is greater than the distance the load is lifted. This means you can lift a heavy load using less force than you would need to lift it directly.
1. If Sara pulls 12 meters of rope to lift the engine 3 meters, we can see the relationship of the distances:
- Distance pulled (input) = 12 meters
- Distance lifted (output) = 3 meters
2. The mechanical advantage (MA) can be calculated using the formula:
\[
MA = \frac{\text{Distance Pulled}}{\text{Distance Lifted}} = \frac{12 \text{ m}}{3 \text{ m}} = 4
\]
This means Sara uses a force that is one-fourth of the force she would need to lift the engine directly (without the pulley).
Now let's evaluate the statements:
- "Sara will save work by using the compound pulley." (Correct, but the amount of work done remains the same, the force is reduced).
- "Sara uses the same force she would have needed without the compound pulley." (Incorrect, because she uses less force).
- "Sara uses one-third the force she would have needed without the compound pulley." (Incorrect, because the factor is one-fourth, not one-third).
- "Sara uses one-fourth the force she would have needed without the compound pulley." (Correct).
The statement that is **not correct** is:
**"Sara uses the same force she would have needed without the compound pulley."**