Circular Motion of a Mass with Tension in a Rope

AI Thread Summary
The discussion revolves around calculating the rotational speed in rpm of a 25.0 kg ball swung in a near-horizontal arc with a rope length of 2.00 m and a constant tension of 100 N. The key equations involve centripetal force and tension, with the participant noting that tension must balance the weight of the ball while providing centripetal force. A free body diagram is suggested to clarify the forces acting on the ball. The conclusion drawn is that with the given tension, the ball's speed is approximately 2.82 m/s, leading to an estimated rotation speed of 13.5 rpm. The analysis highlights the complexities of balancing forces in circular motion.
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Hey can someone help me with this question? Thanks

Homework Statement


Goferd is getting buff by swinging a 25.0 kg ball in a near - horizontal arc. If the length of the rope that is attached to the ball is 2.00 m, and Goferd maintains a constant tension of 100. N in that rope, how many rpm does this ball rotate with?

A 9.55 rpm

B 13.5 rpm

C 4.63 rpm

D 17.7 rpm


Homework Equations


EFr = Fc = fsmax = UN = MsMg = mac = mv^2/r


The Attempt at a Solution


I tried to work with mv^2/r and mac but need a mass or velocity to find the RPM. I keep getting stuck with two unknowns.
 
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Draw a free body diagram for the ball.

The rope will not be horizontal.
 
I am confused. Tension will balance the weight of the body and also provide centripetal force. But tension is even less than mg of the ball! This means that the ball is accelerating downwards. Hence this is not a near horizontal motion.
 
Assuming a rigid and light rope

since it's near horizontal m*v^2/r=100 --> v≈2.82m/s ----> B) 13.5rpm

(The ball has a vertical acceleration downwards of g-4sin(alpha). Since it's near-horizontal, alpha is approx 0, therefore sin(alpha)≈0 --> downward acceleration ≈ g)
 
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