How Do You Calculate the Tangential Force on a Pole?

[jumbogala]

Homework Statement

A pole is attached to a pivot point on the wall, making an angle x with the wall.

A piece of rope holds the other end of the rope to the wall.

The pole has length L, and the tension in the rope is T. Find the tangential force.

Homework Equations

The tangential force method involves finding the component of the applied force that is perpendicular to the displacement from the pivot point to where the force is applied. This perpendicular component of the force is called the tangential force.

The Attempt at a Solution

I thought it would be tangential force = T/cos x, because the angle the tangential makes with T will be x. So therefore, cos x = T/tangential force. But apparently that's wrong. Help?

 

[LowlyPion]

I'd suggest examining the moments about the pivot point.

Won't the projection of the Tangential force at length L have to balance the center of mass force at L/2?

 

[thomate1]

I would like to clarify a few things before providing a response. Firstly, it is important to specify the type of pole and rope being used in this scenario, as different materials and shapes may affect the calculation of the tangential force. Additionally, the pivot point and angle x should also be clearly defined for accuracy.

Assuming that the pole and rope are rigid and the pivot point is fixed, the tangential force can be calculated using the equation F_tan = T*sin x, where T is the tension in the rope and x is the angle between the pole and the wall. This is because the perpendicular component of the tension force (T*cos x) is equal in magnitude but opposite in direction to the normal force acting on the pole, which cancels out. Therefore, the only remaining force acting tangentially is T*sin x.

It is also important to note that the tangential force may vary depending on the position of the rope along the pole. If the rope is attached at the end of the pole, the tangential force will be equal to the tension in the rope (F_tan = T), but if the rope is attached closer to the pivot point, the tangential force will be less than the tension (F_tan = T*sin x).

In conclusion, the tangential force can be calculated using the equation F_tan = T*sin x, where T is the tension in the rope and x is the angle between the pole and the wall. It is also important to consider the position of the rope along the pole in order to accurately calculate the tangential force.