Circular Motion Question?

Question

A ball that is .2kg is attached to a 0.75 m string and swung in a vertical plane.

a) At what is the speed must the ball travel so that its "weight" at the top of the swing is zero?

b) What is the tension in the string at the bottom of the swing?

c)If the rock is now moved into a horizontal swinging motion, what is the angle of the string to the horizontal?

Answer 1

A) for the weight to be zero, the force of gravity and the circular force must cancel each other out. Fg=Fc. force of gravity is mass times the accelaration of gravity (8.91m/s^2). Fc expands to mv^2/r. expand both sides to get mg=mv^2/r. "m" cancels each other out on both sides. g=v^2/r. Now just solve for v=(square root)(g times r). Ive lost my calculator, so you're gonna have to do that. just type (square root) (9.81x0.75) and you get the answer.

B) The tension at the bottom would be a sum of the force of centripital force and gravitation. Fc+Fg..... mg+mv^2/r.... you know m, you know g, you know r, and v is your answer from the previous question. Just plug in and you get an answer. (0.2 times 9.81)+(0.2 times answer from previous question^2 devided by 0.75)

C. if the rock is swinging horizontally, the rope is either straight up or down, so the angle is 90 degrees.

Its been a while since i took this stuff, so if i made any mistakes i apologize. If you need more help, just add me to your yahoo and open an instant messenger chat with me. My name is [e-mail]