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Using the formula for torque, how much force must be applied to a 40-inch-long torque wrench to achieve 400 foot-pounds of torque?

A. 120 lbs
B. 125 lbs
C. 135 lbs
D. 167 lbs

Answer :

To solve the problem of determining the force needed to apply 400 foot-pounds of torque using a 40-inch torque wrench, we can use the formula for torque:

[tex]\tau = r \times F[/tex]

where [tex]\tau[/tex] is the torque, [tex]r[/tex] is the lever arm length (in feet), and [tex]F[/tex] is the force applied (in pounds).

First, we need to convert the length of the torque wrench from inches to feet, since our torque is given in foot-pounds. There are 12 inches in a foot, so:

[tex]r = \frac{40 \, \text{inches}}{12 \, \text{inches/foot}} = \frac{10}{3} \, \text{feet}[/tex]

Next, we rearrange the torque formula to solve for the force [tex]F[/tex]:

[tex]F = \frac{\tau}{r}[/tex]

Substituting the known values into the formula gives us:

[tex]F = \frac{400 \, \text{foot-pounds}}{\frac{10}{3} \, \text{feet}}[/tex]

Carrying out the division:

[tex]F = \frac{400 \times 3}{10} = \frac{1200}{10} = 120 \text{ lbs}[/tex]

Thus, the force required to achieve 400 foot-pounds of torque using a 40-inch-long torque wrench is 120 pounds.

The correct answer is option A. 120 lbs.

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