Question
Sammy uses an inclined plane to load a forge into his truck. If he does 64 J of work, and the inclined plane is 3 m long, how much force does he expend? (round to the nearest whole number)
(1 point)
Responses
21 N
21 N
192 N
192 N
22 N
22 N
21.3 N
(1 point)
Responses
21 N
21 N
192 N
192 N
22 N
22 N
21.3 N
Answers
GPT-4o mini
To find the force exerted by Sammy when using the inclined plane, we can use the work formula:
\[
\text{Work} = \text{Force} \times \text{Distance} \times \cos(\theta)
\]
In this case, we can assume that the force is applied parallel to the inclined plane, so the angle \( \theta \) is 0 degrees, and \(\cos(0) = 1\). Thus, the formula simplifies to:
\[
\text{Work} = \text{Force} \times \text{Distance}
\]
Rearranging this to find the force:
\[
\text{Force} = \frac{\text{Work}}{\text{Distance}}
\]
Substituting the known values:
\[
\text{Work} = 64 \, \text{J}
\]
\[
\text{Distance} = 3 \, \text{m}
\]
Now, calculate the force:
\[
\text{Force} = \frac{64 \, \text{J}}{3 \, \text{m}} \approx 21.33 \, \text{N}
\]
Rounding to the nearest whole number, we find:
\[
\text{Force} \approx 21 \, \text{N}
\]
Therefore, the correct response is **21 N**.
\[
\text{Work} = \text{Force} \times \text{Distance} \times \cos(\theta)
\]
In this case, we can assume that the force is applied parallel to the inclined plane, so the angle \( \theta \) is 0 degrees, and \(\cos(0) = 1\). Thus, the formula simplifies to:
\[
\text{Work} = \text{Force} \times \text{Distance}
\]
Rearranging this to find the force:
\[
\text{Force} = \frac{\text{Work}}{\text{Distance}}
\]
Substituting the known values:
\[
\text{Work} = 64 \, \text{J}
\]
\[
\text{Distance} = 3 \, \text{m}
\]
Now, calculate the force:
\[
\text{Force} = \frac{64 \, \text{J}}{3 \, \text{m}} \approx 21.33 \, \text{N}
\]
Rounding to the nearest whole number, we find:
\[
\text{Force} \approx 21 \, \text{N}
\]
Therefore, the correct response is **21 N**.