Why Is Tension 3mg at the Lowest Point?

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The tension in the rope at the lowest point of the object's movement is calculated to be 3mg due to the combination of gravitational force and the centripetal force required for circular motion. Using conservation of energy principles, the velocity of the mass at the lowest point can be determined based on its initial height and potential energy conversion. The radial acceleration at this point is derived from the velocity and the radius of the circular path. A free body analysis reveals that the radial component of the force balance at the lowest point consists of the tension in the rope minus the weight of the object. Understanding these concepts is crucial for analyzing forces in circular motion dynamics.
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Homework Statement


An object with mass m is attached to a fixed structure with a rope with dimension R like in the figure. The object is dropped. Why is the tension in the lowest point of the movement 3mg?
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Using conservation of energy, what is the velocity of the mass at the lowest point? What is the radial acceleration at the lowest point? Treating the mass as a free body, what is the radial component of the force balance at the lowest point?
 
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