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Answer :
To solve this problem, we start with the formula for torque:
$$
T = F \times r
$$
where
- $T$ is the torque,
- $F$ is the applied force, and
- $r$ is the length of the lever arm.
The problem gives the torque as $250$ foot-pounds and the wrench length as $24$ inches. First, we need to convert the wrench length to feet because the torque is given in foot-pounds. Since there are $12$ inches in a foot, we have:
$$
r = \frac{24 \text{ inches}}{12 \text{ inches/foot}} = 2 \text{ feet}
$$
Now, rearrange the torque formula to solve for the force:
$$
F = \frac{T}{r}
$$
Substitute the values:
$$
F = \frac{250 \text{ ft-lb}}{2 \text{ ft}} = 125 \text{ lbs}
$$
Thus, a force of $\boxed{125 \text{ lbs}}$ must be applied to achieve $250$ foot-pounds of torque.
$$
T = F \times r
$$
where
- $T$ is the torque,
- $F$ is the applied force, and
- $r$ is the length of the lever arm.
The problem gives the torque as $250$ foot-pounds and the wrench length as $24$ inches. First, we need to convert the wrench length to feet because the torque is given in foot-pounds. Since there are $12$ inches in a foot, we have:
$$
r = \frac{24 \text{ inches}}{12 \text{ inches/foot}} = 2 \text{ feet}
$$
Now, rearrange the torque formula to solve for the force:
$$
F = \frac{T}{r}
$$
Substitute the values:
$$
F = \frac{250 \text{ ft-lb}}{2 \text{ ft}} = 125 \text{ lbs}
$$
Thus, a force of $\boxed{125 \text{ lbs}}$ must be applied to achieve $250$ foot-pounds of torque.
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