A wrench 0.4 meters long lies along the positive y-axis, and grips a bolt at the origin. A force is applied in the direction of ⟨0,1,5⟩ at the end of the wrench. Find the magnitude of the force in newtons needed to supply 100 newton-meters of torque to the bolt.
To find the magnitude of the force needed to supply 100 newton-meters of torque to the bolt, we can use the formula for torque:
Torque = force * lever arm
The lever arm is the perpendicular distance between the line of action of the force and the axis of rotation. In this case, the lever arm is the length of the wrench.
Given that the length of the wrench is 0.4 meters and the torque is 100 newton-meters, we can rearrange the formula to solve for force:
Force = Torque / lever arm
Substituting the values:
Force = 100 N∙m / 0.4 m
Simplifying:
Force = 250 N
So, the magnitude of the force needed to supply 100 newton-meters of torque to the bolt is 250 newtons.