What Calculations Determine the Dynamics of a Ball in Vertical Circular Motion?

[thugg]

Circular Motion...

Ok, you have a ball being swung vertically in a circle. Mass=0.1kg, radius=0.8m, speed at top = 6m/s , and this occurs 0.2m off the ground. using the floor as the zero point for gravitational potential energy, what is the total energy. Determine the speed at the lowest point. Determine the tension at the top and bottom. The ball reaches the top of the circle once before the thread breaks, when the ball is at the lowest point of the circle. Determine the horizontal distance it travels before hitting the floor.

Any help would be great.


Edit: to make it not appear as though I just want some answers...i have tried this and got these answers, maybe you can tell me where i went wrong...


total energy = pe + ke = .5*.1*36 + 9.8*.1*1.8= 3.564

speed at lowest point... 0.2*9.8*0.1 + 0.5*0.1*v squared = 3.564 v = 8.2

tension at top... 0.1*36/0.8 - 0.1*9.8 = 3.52
tension at bottom... 0.1*36/0.8 + 0.1*9.8 = 5.48

 

[Astronuc]

Assuming conservation of energy holds, then PE₁ + KE₁ = PE₂ + KE₂, or $\Delta$KE = $\Delta$PE.

The gravitational potential energy increases with height, so minimum velocity and kinetic energy occur at the top of the arc, and max. velocity (speed) and KE occur at the bottom.

The total energy seems right and the speed at the bottom.

Tension at top seems correct, but tension at bottom needs to use the velocity (tangential speed) at the bottom.