Question
A construction crew needs to utilize a lever to elevate a boulder. The lever has a mechanical advantage of 6, and it exerts a force of 1600 N on the rock. What force must the construction crew apply to the lever?
Use the Formula Chart below.
Calculating Mechanical Advantage ...
(1 point)
Responses
380 N
380 N
267 N
267 N
534 N
534 N
134 N
Use the Formula Chart below.
Calculating Mechanical Advantage ...
(1 point)
Responses
380 N
380 N
267 N
267 N
534 N
534 N
134 N
Answers
GPT-4o mini
To determine the force that the construction crew must apply to the lever, we can use the formula for mechanical advantage (MA):
\[
MA = \frac{F_{\text{output}}}{F_{\text{input}}}
\]
Where:
- \( MA \) is the mechanical advantage,
- \( F_{\text{output}} \) is the force exerted on the boulder (1600 N),
- \( F_{\text{input}} \) is the force applied by the construction crew.
Given that the mechanical advantage is 6, we can rearrange the formula to find the input force:
\[
F_{\text{input}} = \frac{F_{\text{output}}}{MA}
\]
Substituting the values:
\[
F_{\text{input}} = \frac{1600 \, \text{N}}{6} \approx 266.67 \, \text{N}
\]
Rounding this to a reasonable precision gives us approximately 267 N.
Therefore, the force that the construction crew must apply to the lever is **267 N**.
\[
MA = \frac{F_{\text{output}}}{F_{\text{input}}}
\]
Where:
- \( MA \) is the mechanical advantage,
- \( F_{\text{output}} \) is the force exerted on the boulder (1600 N),
- \( F_{\text{input}} \) is the force applied by the construction crew.
Given that the mechanical advantage is 6, we can rearrange the formula to find the input force:
\[
F_{\text{input}} = \frac{F_{\text{output}}}{MA}
\]
Substituting the values:
\[
F_{\text{input}} = \frac{1600 \, \text{N}}{6} \approx 266.67 \, \text{N}
\]
Rounding this to a reasonable precision gives us approximately 267 N.
Therefore, the force that the construction crew must apply to the lever is **267 N**.