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A 30.0-g ball at the end of a string is swung in a vertical circle with a radius of 25.0 cm. the tangential velocity is 200.0 cm/s. find the tension in the string: (a) at the top of the circle, (b) at the bottom of the circle,

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Final answer:

The question from the student pertains to Physics, specifically the calculation of the tension in a string at various points when a ball is swung in a vertical circle, using principles of centripetal force and circular motion.

Step-by-step explanation:

The question involves determining the tension in a string when a ball tied to it is swung in a vertical circle. The tension differs based on the ball's position in the circle: at the top, at the bottom, and at an intermediate point. To calculate these, the concepts of centripetal force, gravity, and circular motion are utilized. The ball's mass and tangential velocity, as well as the radius of the circle, are critical for these calculations.

Typically, the tension in the string provides the centripetal force necessary to keep the ball in circular motion. At the top of the circle, gravity and centripetal force both act in the same direction, while at the bottom of the circle, the string tension must counteract both the centripetal force and gravity.

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