8. A torque wrench reads 25 lb ft.
a. If its length is 1.0 ft, what force is being applied to the wrench?
b. What is the force if the length is doubled?
well, torque = radius * force
T = rF
if the radius is doubled, the new torque is
T' = (2r)F = 2rF = 2T
Torque
To find the force being applied to the torque wrench, we can use the formula for torque:
Torque = Force × Distance
where torque is measured in lb ft (pound-feet), and distance is measured in feet.
a. If the length of the torque wrench is 1.0 ft, and the torque reading is 25 lb ft, we can rearrange the formula to solve for force:
Torque = Force × Distance
25 lb ft = Force × 1.0 ft
To find the force, we divide both sides of the equation by the distance:
Force = 25 lb ft / 1.0 ft
Force = 25 lb
So, if the length of the torque wrench is 1.0 ft and the torque reading is 25 lb ft, then the force being applied to the wrench is 25 pounds.
b. If the length of the torque wrench is doubled, i.e., 2.0 ft, we can again rearrange the formula to solve for force:
Torque = Force × Distance
25 lb ft = Force × 2.0 ft
Dividing both sides of the equation by the distance:
Force = 25 lb ft / 2.0 ft
Force = 12.5 lb
So, if the length of the torque wrench is doubled to 2.0 ft and the torque reading remains 25 lb ft, then the force being applied to the wrench is 12.5 pounds.