Question
If W=F×d , which of the following equations shows work being calculated using the correct units?(1 point)
Responses
113 N=(17.4 J)×(6.51 m)113 N=(17.4 J)×(6.51 m)
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 J=(17.4 N)×(6.51 ft)
Responses
113 N=(17.4 J)×(6.51 m)113 N=(17.4 J)×(6.51 m)
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 J=(17.4 N)×(6.51 ft)
Answers
GPT-4o mini
To identify the correct equation for calculating work using the correct units, we need to consider the formula for work:
\[ W = F \times d \]
Where:
- \( W \) is work measured in joules (J).
- \( F \) is force measured in newtons (N).
- \( d \) is distance measured in meters (m) or feet (ft).
From the formula, we can see that:
- The units of work (J) are equivalent to newtons (N) multiplied by meters (m): \( 1 \, \text{J} = 1 \, \text{N} \cdot 1 \, \text{m} \).
Now, let's evaluate the provided options:
1. **113 N = (17.4 J) × (6.51 m)** → Incorrect; ends up equating force to joules times meters, which does not match the work formula.
2. **113 J = (17.4 N) × (6.51 m)** → Correct; this equation properly uses the formula \( W = F \times d \) with appropriate units leading to work being in joules.
3. **113 N = (17.4 J) × (6.51 ft)** → Incorrect; again, it does not correctly apply the formula.
4. **113 J = (17.4 N) × (6.51 ft)** → Incorrect; although the result is in joules, using feet in this context changes the dimensional analysis, as 1 J = 1 N·m, not N·ft.
Therefore, the correct response is:
**113 J = (17.4 N) × (6.51 m)**
\[ W = F \times d \]
Where:
- \( W \) is work measured in joules (J).
- \( F \) is force measured in newtons (N).
- \( d \) is distance measured in meters (m) or feet (ft).
From the formula, we can see that:
- The units of work (J) are equivalent to newtons (N) multiplied by meters (m): \( 1 \, \text{J} = 1 \, \text{N} \cdot 1 \, \text{m} \).
Now, let's evaluate the provided options:
1. **113 N = (17.4 J) × (6.51 m)** → Incorrect; ends up equating force to joules times meters, which does not match the work formula.
2. **113 J = (17.4 N) × (6.51 m)** → Correct; this equation properly uses the formula \( W = F \times d \) with appropriate units leading to work being in joules.
3. **113 N = (17.4 J) × (6.51 ft)** → Incorrect; again, it does not correctly apply the formula.
4. **113 J = (17.4 N) × (6.51 ft)** → Incorrect; although the result is in joules, using feet in this context changes the dimensional analysis, as 1 J = 1 N·m, not N·ft.
Therefore, the correct response is:
**113 J = (17.4 N) × (6.51 m)**