What Forces Act on a Ball Suspended from the Ceiling?

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SUMMARY

The discussion focuses on the forces acting on a 1.7-kg ball suspended from the ceiling at an angle of 33.9°. The force holding the ball in position is not simply the weight of the ball (mass times gravity), which is 16.66N. Instead, the tension in the string must be analyzed in terms of its vertical and horizontal components to ensure that the sum of all forces acting on the ball equals zero. The vertical component of the tension balances the gravitational force acting on the ball.

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A 1.7-kg ball tied to a string fixed to the ceiling is pulled to one side by a force to an angle of 33.9° from the ceiling. Just before the ball is released and allowed to swing back and forth, (a) how large is the force that is holding the ball in position and (b) what is the tension in the string?



The Attempt at a Solution



I tried 16.66N for the force part a because I thought it would be the mass*gravity, but that's not right.
 
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The sum of all the forces of the ball must be 0. This is true for both the vertical and the horizontal components. There is the force of gravity (vertical), the force that´s pulling the ball aside (horizontal) and the tension in the string which has both a vertical and a horizontal component.
Answer (b) first. The vertical component of the tension of the string should balance the gravitational force on the ball
 

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