Question
If W=F×d
, which of the following equations shows work being calculated using the correct units?(1 point)
Responses
113 J=(17.4 N)×(6.51 ft)
113 J=(17.4 N)×(6.51 ft)
113 J=(17.4 N)×(6.51 m)
113 J=(17.4 N)×(6.51 m)
113 N=(17.4 J)×(6.51 ft)
113 N=(17.4 J)×(6.51 ft)
113 N=(17.4 J)×(6.51 m)
, which of the following equations shows work being calculated using the correct units?(1 point)
Responses
113 J=(17.4 N)×(6.51 ft)
113 J=(17.4 N)×(6.51 ft)
113 J=(17.4 N)×(6.51 m)
113 J=(17.4 N)×(6.51 m)
113 N=(17.4 J)×(6.51 ft)
113 N=(17.4 J)×(6.51 ft)
113 N=(17.4 J)×(6.51 m)
Answers
GPT-4o mini
To determine which equation shows work being calculated using the correct units, we need to remember that work (W) is calculated using the formula:
\[ W = F \times d \]
where:
- \( W \) is the work measured in joules (J),
- \( F \) is the force measured in newtons (N),
- \( d \) is the distance measured in meters (m).
It's important to note that when calculating work, the distance should be in meters to keep the units consistent. Joules is defined as one newton-meter (1 J = 1 N·m).
Now let's analyze the given equations:
1. **113 J = (17.4 N) × (6.51 ft)**
- Units are inconsistent: feet are not in the SI system for work.
2. **113 J = (17.4 N) × (6.51 m)**
- This is correct: the distance is in meters (the correct SI unit).
3. **113 N = (17.4 J) × (6.51 ft)**
- Incorrect units: joules are used incorrectly with feet.
4. **113 N = (17.4 J) × (6.51 m)**
- Incorrect units: joules and meters multiply to give incorrect units.
The only equation that shows work calculated using the correct units is:
**113 J = (17.4 N) × (6.51 m)**.
\[ W = F \times d \]
where:
- \( W \) is the work measured in joules (J),
- \( F \) is the force measured in newtons (N),
- \( d \) is the distance measured in meters (m).
It's important to note that when calculating work, the distance should be in meters to keep the units consistent. Joules is defined as one newton-meter (1 J = 1 N·m).
Now let's analyze the given equations:
1. **113 J = (17.4 N) × (6.51 ft)**
- Units are inconsistent: feet are not in the SI system for work.
2. **113 J = (17.4 N) × (6.51 m)**
- This is correct: the distance is in meters (the correct SI unit).
3. **113 N = (17.4 J) × (6.51 ft)**
- Incorrect units: joules are used incorrectly with feet.
4. **113 N = (17.4 J) × (6.51 m)**
- Incorrect units: joules and meters multiply to give incorrect units.
The only equation that shows work calculated using the correct units is:
**113 J = (17.4 N) × (6.51 m)**.