Circular Motion of a Mass with Tension in a Rope

[d.tran103]

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.

 

[SammyS]

Draw a free body diagram for the ball.

The rope will not be horizontal.

 

[ashishsinghal]

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.

 

[deepthishan]

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)