One end of a meter stick is pinned to a table, so the stick can rotate freely in a plane parallel to the tabletop. Two forces, both parallel to the tabletop, are applied to the stick in such a way that the net torque is zero. The first force has a magnitude of 2.00 N and is applied perpendicular to the length of the stick at the free end. The second force has a magnitude of 6.00 N and acts at a 22.0o angle with respect to the length of the stick. Where along the stick is the 6.00-N force applied? Express this distance with respect to the end of the stick that is pinned.

To find the distance along the stick where the 6.00 N force is applied, we need to analyze the torques caused by the two forces.

Torque is a measure of how effectively a force rotates an object. The torque caused by a force is given by the formula:

Torque = Force x Perpendicular Distance

Let's consider the torques caused by each force individually.

1. The torque caused by the 2.00 N force (applied perpendicular to the length of the stick at the free end) will be zero. This is because the force is applied at the pivot point (pinned end), so the perpendicular distance between the force and the pivot point is zero.

2. The torque caused by the 6.00 N force (applied at a 22.0° angle with respect to the length of the stick) will not be zero. Let's call the distance along the stick where this force is applied as "x" (with respect to the pinned end).

To calculate the torque caused by this force, we need to find the perpendicular distance between the force and the pivot point (pinned end). This distance can be calculated using trigonometry. The perpendicular distance is given by:

Perpendicular Distance = x * sin(22.0°)

Now, we can calculate the torque caused by the 6.00 N force:

Torque = Force x Perpendicular Distance
Torque = 6.00 N * (x * sin(22.0°))

Since the net torque is zero, the torque caused by the 6.00 N force must be equal in magnitude but opposite in direction to the torque caused by the 2.00 N force. Since the torque of the 2.00 N force is zero, we can set up the equation:

6.00 N * (x * sin(22.0°)) = 0

To solve for x, we divide both sides of the equation by 6.00 N * sin(22.0°):

x = 0 / (6.00 N * sin(22.0°))

Since anything divided by zero is undefined, the distance along the stick where the 6.00 N force is applied cannot be determined.