Circular motion of two wires and a ball

[flyguyd]

circular motion!

two wires are tied to a 200g ball. the ball revolves in a horizontal circle at a constant speed of 7.5 m/s. what is the tension in each wire.

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[Astronuc]

The top wire must support the ball, so there will be a vertical vector force in opposition to gravity.

The ball is rotation, so calculate the horizontal component \ifrac{mv^2}{r}. Each wire then provides half of the centripetal force, assuming they are of equal length.

The tension in each wire found by the vector sum of horizontal and vertical components.

 

[thepatientmental]

The tension in each wire can be calculated using the equation T = mv^2/r, where T is the tension, m is the mass of the ball, v is the speed, and r is the radius of the circle. Since the ball is moving at a constant speed, we can use the centripetal acceleration equation a = v^2/r to find the radius of the circle, which is equal to 7.5^2/9.8 = 5.76 meters. Plugging this value into the tension equation, we get T = (0.2 kg)(7.5 m/s)^2/5.76 m = 0.26 N. Therefore, the tension in each wire is 0.26 N. This means that both wires are equally supporting the weight of the ball and providing the necessary centripetal force to keep it moving in a circular motion.