A tether ball leans against the post to which it is attached. (Figure 1) The str

Question

A tether ball leans against the post to which it is attached. (Figure 1) The string is attached to the ball such that a line along the string passes through the center of the ball. The string to which the ball is attached has length L and the ball's radius is r and has a mass of m. Neglect any friction between the ball and the pole.

1.What is the tension in the rope?

Take the free fall acceleration to be g.

2. What is the force the pole exerts on the ball?

Take the free fall acceleration to be g.

Explanation / Answer

sin A = r/(r+l)

cos A = sqrt[(r+l)^2 - r^2]/(r+l)

tan A = r/sqrt[(r+l)^2 - r^2]

Using the force balance

in vertical direction

Fy = 0 = T*cos A - mg

T = mg/cos A

in horizontal direction

Fx = 0 = T*sin A - N

N - T*sin A = mg*sin A/cos A = mg*tan A

Let me know if you have any doubt.

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