Using a wrench 0.4 m long, a force of at least 100 N is needed to turn a
nut. (a) How large a torque is required? (b) How large a force is needed
to turn the nut using a wrench 0.15 m long?
Answer (b) is 267N
To calculate the torque required to turn a nut using a wrench, we can use the formula:
Torque = Force × Distance
(a) Given that a force of at least 100 N is needed to turn the nut and the length of the wrench is 0.4 m, we can calculate the torque as follows:
Torque = 100 N × 0.4 m
= 40 N·m
Therefore, a torque of 40 N·m is required to turn the nut using a wrench 0.4 m long.
(b) Now, let's calculate the force needed to turn the nut using a wrench 0.15 m long. We know that the torque required is 40 N·m, and the length of the new wrench is 0.15 m. We can rearrange the torque formula to solve for force:
Force = Torque / Distance
Force = 40 N·m / 0.15 m
≈ 266.67 N
Therefore, a force of approximately 266.67 N is needed to turn the nut using a wrench 0.15 m long.
To solve this problem, we need to understand the concept of torque. Torque is the rotational equivalent of force and is defined as the product of the force and the perpendicular distance (lever arm) from the force to the axis of rotation.
(a) To find the torque required using a wrench 0.4 m long, we can use the formula for torque:
Torque = Force x Lever Arm
Given that the force required is at least 100 N and the lever arm is 0.4 m, we can substitute these values into the formula:
Torque = 100 N x 0.4 m
= 40 N⋅m
Therefore, a torque of at least 40 N⋅m is required to turn the nut using a wrench 0.4 m long.
(b) To find the force required to turn the nut using a wrench 0.15 m long, we can rearrange the formula for torque to solve for force:
Force = Torque / Lever Arm
Given that the torque required is 40 N⋅m and the lever arm is 0.15 m, we can substitute these values into the formula:
Force = 40 N⋅m / 0.15 m
= 266.67 N (rounded to 3 significant figures)
Therefore, a force of approximately 267 N is needed to turn the nut using a wrench 0.15 m long.