Circular Motion (finding speed)

  1. 1. The problem statement, all variables and given/known data
    A ball of mass 0.23 kg is attached securely to a string, then whirled at a constant speed in a vertical radius of 0.75 m. Calculate the minimum speed of the ball at the top of the path if it is to follow a complete circle.


    2. Relevant equations
    F = mv(squared)/R


    3. The attempt at a solution
    I first solved for Fc when the ball is at the top of the circle with F=mv(squared)/R - mg and it equals 1.7 N. I then rearranged the equation to solve for V using V = the square root of FR/m and got the answer 2.35 m/s. My sheet says the answer is 2.7, which is pretty close to what I got, but I may have done something wrong. Any thoughts?
     
  2. jcsd
  3. This is what i think, right so the forces acting on the mass are gravity and the tension of the string, it's best to draw a diagram.
    T = tension.
    Defining positive direction to be downwards.


    At the top of the circle: F = mg + T

    As you say F= (mv^2)/r for circular motion. So equate these.

    Now can you figure out how to find the minimum speed?
     
  4. Yes, I've figured it out now, thanks!
     
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