If, instead, the ball is revolved so that its speed is 3.7 m/s, what angle does the cord make with the vertical?

Complete Question:

A 0.50-kg ball that is tied to the end of a 1.5-m light cord is revolved in a horizontal plane, with the cord making a 30° angle with the vertical.

(a) Determine the ball’s speed. (b) If, instead, the ball is revolved so that its

speed is 3.7 m/s, what angle does the cord make with the vertical?

(Check attached image for the diagram.)

(a) The ball’s speed, v = 2.06 m/s

(b) The angle the cord makes with the vertical is 50.40⁰

Explanation:

If the ball is revolved in a horizontal plane, it will form a circular trajectory,

the radius of the circle, R = Lsinθ

where;

L is length of the string

The force acting on the ball is given as;

F = mgtanθ

This above is also equal to centripetal force;

(b) when the speed is 3.7 m/s

Therefore, the angle the cord makes with the vertical is 50.40⁰

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explanation: