To tighten a bolt, you push with a force of 90 N at the end of a wrench handle that is 0.45 m from the axis of the bolt.
(a) What torque are you exerting?
Enter a number.
1 N·m
(b) If you move your hand inward to be only 0.15 m from the bolt, what force do you have to exert to achieve the same torque?
Enter a number.
2 N
(c) Do your answers depend on the direction of your push relative to the direction of the wrench handle? (Why or why not?)
3
To solve this problem, we can use the formula for torque:
Torque = Force x Distance
where the force is perpendicular to the rotation axis.
(a) The torque you are exerting can be found by multiplying the force you apply by the distance from the axis.
Therefore, the torque is:
Torque = 90 N x 0.45 m = 40.5 N·m
So, the answer to part (a) is 40.5 N·m.
(b) To find the force required to achieve the same torque when your hand is 0.15 m from the bolt, we can rearrange the formula:
Torque = Force x Distance
Force = Torque / Distance
Substituting the values:
Force = 40.5 N·m / 0.15 m = 270 N
So, the force required to achieve the same torque when your hand is 0.15 m from the bolt is 270 N.
The answer to part (b) is 270 N.
(c) No, the answers for torque and force do not depend on the direction of your push relative to the direction of the wrench handle. The torque only depends on the perpendicular distance from the axis and the force applied. The force required to achieve the same torque would be the same regardless of the direction of your push, as long as it is perpendicular to the wrench handle.