Question
A car applies a force of 36.8 Newtons for a 668-meter loop; what was the work done?(1 point)
Responses which is the correct answer and why
24,600 J
24,600 J
705 J
705 J
18.2 J
18.2 J
0 J
Responses which is the correct answer and why
24,600 J
24,600 J
705 J
705 J
18.2 J
18.2 J
0 J
Answers
GPT-4o mini
To determine the work done when a force is applied over a distance, we can use the formula for work:
\[ \text{Work} = \text{Force} \times \text{Distance} \times \cos(\theta) \]
where:
- \(\text{Work}\) is measured in Joules (J).
- \(\text{Force}\) is measured in Newtons (N).
- \(\text{Distance}\) is measured in meters (m).
- \(\theta\) is the angle between the force and the direction of motion.
In this scenario, if we assume that the force is being applied in the direction of motion (along the loop), \(\theta = 0^\circ\) and \(\cos(0^\circ) = 1\). Therefore, the formula simplifies to:
\[ \text{Work} = \text{Force} \times \text{Distance} \]
Now substituting the values provided:
- \(\text{Force} = 36.8 \, \text{N}\)
- \(\text{Distance} = 668 \, \text{m}\)
Calculating the work done:
\[ \text{Work} = 36.8 \, \text{N} \times 668 \, \text{m} \]
\[ \text{Work} = 24,606.4 \, \text{J} \]
Rounding this to three significant figures gives approximately:
\[ \text{Work} \approx 24,600 \, \text{J} \]
Therefore, the correct answer is:
**24,600 J**
This is because it represents the work done by the 36.8 Newton force over a distance of 668 meters in the same direction, resulting in the total energy transferred as work done.
\[ \text{Work} = \text{Force} \times \text{Distance} \times \cos(\theta) \]
where:
- \(\text{Work}\) is measured in Joules (J).
- \(\text{Force}\) is measured in Newtons (N).
- \(\text{Distance}\) is measured in meters (m).
- \(\theta\) is the angle between the force and the direction of motion.
In this scenario, if we assume that the force is being applied in the direction of motion (along the loop), \(\theta = 0^\circ\) and \(\cos(0^\circ) = 1\). Therefore, the formula simplifies to:
\[ \text{Work} = \text{Force} \times \text{Distance} \]
Now substituting the values provided:
- \(\text{Force} = 36.8 \, \text{N}\)
- \(\text{Distance} = 668 \, \text{m}\)
Calculating the work done:
\[ \text{Work} = 36.8 \, \text{N} \times 668 \, \text{m} \]
\[ \text{Work} = 24,606.4 \, \text{J} \]
Rounding this to three significant figures gives approximately:
\[ \text{Work} \approx 24,600 \, \text{J} \]
Therefore, the correct answer is:
**24,600 J**
This is because it represents the work done by the 36.8 Newton force over a distance of 668 meters in the same direction, resulting in the total energy transferred as work done.