OK so far.terryds said:
For static equilibrium Στ = 0 about any point. So, you can pick any convenient point for setting up Στ = 0.
I'm not sure what you mean here.
In order to determine the value of tan θ in an equilibrium problem, you must first identify all the forces acting on the object and their respective magnitudes and directions. Then, using the principles of equilibrium, you can set up a system of equations to solve for the unknown values, including tan θ.
Tan θ represents the ratio of the perpendicular component of a force to the parallel component of the force. In an equilibrium problem, determining tan θ can help you understand the balance of forces acting on an object and whether or not it will remain in equilibrium.
No, tan θ cannot be negative in an equilibrium problem. This is because the tangent function is defined as the ratio of two sides of a right triangle, and therefore cannot have a negative value. In cases where the value of tan θ appears to be negative, it actually represents a force acting in the opposite direction.
One common mistake is incorrectly identifying the direction of forces, which can lead to incorrect values for tan θ. It is also important to remember to include all forces acting on the object, including any forces of friction or tension. Lastly, not properly setting up and solving the equations can also lead to mistakes when determining tan θ.
While there are no shortcuts, it can be helpful to draw a clear and accurate diagram with all the forces labeled and their directions indicated. This can help you visualize the problem and make it easier to set up and solve the equations. It is also important to double check your work and make sure all values and directions are correct before determining tan θ.