Question

What is ft, the magnitude of the tangential force that acts on the pole due to the tension in the rope?

Answer 1

The magnitude of the tangential force that acts on the pole due to the tension in rope is given as

T= weight x tan (theta) /2

Answer 2

Ft = tangential force = mg sin θ / 2

Further explanation

The force acting on a system with static equilibrium is 0

$\large {\boxed {\bold {\sum F = 0}}$

(forces acting as translational motion only, not including rotational forces)

$\displaystyle \sum F_x = 0 \\\\\sum F_y = 0$

For objects undergoing rotation, the equilibrium must be met

$\large {\boxed {\bold {\sum\tau = 0}}$

The force acting on the rod is the tension in the rope (T)and the weight of the rod

(w)

Because the sum of torques must be zero (objects in equilibrium) then  : (use point A as the pivot point)

(Ft = tangential force)

Στ = 0

Ft. L - w sin θ. 1/2 L = 0

Ft = T cos θ, and w = mg, such that

T cos θ. L - mg sin θ. 1/2 L = 0

T cos θ. L = mg sin θ. 1/2 L

T cos θ = mg sin θ. 1/2

$\rm Ft=T\:cos\:\theta=\dfrac{mg\:sin\:\theta}{2}$

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