What are the angles for static equilibrium in a board supported by a rope?

[Oomair]

Homework Statement

A uniform board of length 2.4 m and mass m = 5.1 kg has one end on the ground. With the aid of a horizontal force applied at the upper end by means of an attached horizontal rope, the board is held at an angle θ with respect to the vertical The coefficient of static friction between the end of the board and the ground is µs = 0.36.

What is the range of angles the board can make with the vertical and still be in static equilibrium?
How does the tension in the rope vary with the angle within the angle's possible range?

Homework Equations

The Attempt at a Solution

Ok they want the minimum angle, i found the max angle and the tension at the max angle, my question is that doesn't Tension stay the same since the length of the board is constant and normal force has to be present and equal to Mg? wouldn't the tension be the same at any angle?

 

[Nick89]

I haven't fully read your question but the normal force is NOT always equal to Mg!

Consider a block lying on a slope. The normal force is directed perpendicular (not entirely vertical) to the slope and it's magnitude is only a part of the weight Mg.

 

[Oomair]

i know that normal force is not always equal to mg, but in this situation the board is touching the ground at all time, and the normal force must be equal to the weight of the board so the system can stay in static equilibrium

 

[alphysicist]

Hi Oomair,

Homework Statement

A uniform board of length 2.4 m and mass m = 5.1 kg has one end on the ground. With the aid of a horizontal force applied at the upper end by means of an attached horizontal rope, the board is held at an angle θ with respect to the vertical The coefficient of static friction between the end of the board and the ground is µs = 0.36.

What is the range of angles the board can make with the vertical and still be in static equilibrium?
How does the tension in the rope vary with the angle within the angle's possible range?

Homework Equations

The Attempt at a Solution

Ok they want the minimum angle, i found the max angle and the tension at the max angle, my question is that doesn't Tension stay the same since the length of the board is constant and normal force has to be present and equal to Mg? wouldn't the tension be the same at any angle?

No, the tension will not be the same. For example, if the pivot for calculating torques is at the ground, then the torque from the weight force will change (since the moment arm is changing). The tension will have to adjust so as to keep the torques in balance.