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?
A. 534 N
B. 134 N
C. 380 N
D. 267 N
A. 534 N
B. 134 N
C. 380 N
D. 267 N
Answers
GPT-4o mini
To find 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:
- \( F_{\text{output}} \) is the force exerted on the rock (1600 N),
- \( F_{\text{input}} \) is the force applied by the construction crew.
We can rearrange this formula to solve for the input force:
\[
F_{\text{input}} = \frac{F_{\text{output}}}{MA}
\]
Given that the mechanical advantage is 6 and the output force is 1600 N, we can substitute these values into the formula:
\[
F_{\text{input}} = \frac{1600 \, \text{N}}{6}
\]
Calculating this gives:
\[
F_{\text{input}} = \frac{1600}{6} \approx 266.67 \, \text{N}
\]
Rounding to the nearest whole number, we get approximately 267 N.
Thus, the force that the construction crew must apply to the lever is:
**D. 267 N**
\[
MA = \frac{F_{\text{output}}}{F_{\text{input}}}
\]
Where:
- \( F_{\text{output}} \) is the force exerted on the rock (1600 N),
- \( F_{\text{input}} \) is the force applied by the construction crew.
We can rearrange this formula to solve for the input force:
\[
F_{\text{input}} = \frac{F_{\text{output}}}{MA}
\]
Given that the mechanical advantage is 6 and the output force is 1600 N, we can substitute these values into the formula:
\[
F_{\text{input}} = \frac{1600 \, \text{N}}{6}
\]
Calculating this gives:
\[
F_{\text{input}} = \frac{1600}{6} \approx 266.67 \, \text{N}
\]
Rounding to the nearest whole number, we get approximately 267 N.
Thus, the force that the construction crew must apply to the lever is:
**D. 267 N**