A post is driven perpendicularly into the ground and serves as the axis about which a gate rotates. A force of 12N is applied perpendicular to the gate and acts parallel to the ground. How far from the post should the force be applied to produce a torque with a magnitude of 3.0 Nm?
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To determine the distance from the post where the force should be applied to produce a torque of 3.0 Nm, we can use the equation:
Torque = Force × Distance
Rearranging this equation gives:
Distance = Torque / Force
First, we need to convert the given force from Newtons (N) to Newton-meters (Nm) since torque is measured in Newton-meters.
Given: Force = 12 N
Therefore, the torque is:
Torque = 3.0 Nm
Now we can substitute the values into the equation:
Distance = 3.0 Nm / 12 N
Dividing the torque by the force, we get:
Distance = 0.25 m
So, the force should be applied 0.25 meters (or 25 centimeters) from the post to produce a torque with a magnitude of 3.0 Nm.