Time for a ball on string to travel around a pole.

In summary, the conversation discusses a tetherball with a string length of 1.5m completing a circle around a pole with a string at 30 degrees from the pole. The homework equations used include c=2pir for the circumference of the circle, xsinθ for the distance from the pole to the ball in the x direction, and ycosθ for the distance from the ball to the top of the pole in the y direction. The person is trying to calculate the time period for a circuit around the pole for the ball, taking into account the acceleration caused by the string and the counteracting gravity. They mention using Newton's 2nd law and considering the forces acting on the ball.
  • #1
Nny
2
0

Homework Statement



A tetherball with a string length of 1.5m is hit in such a way that it completes a circle around the pole with the string at 30 degrees from the pole. Assuming it doesn’t lose a significant length during the trip around the pole and hence takes a perfectly circular orbit, what is the time period for a circuit around the pole for the ball? (Remember the acceleration caused by the string has to have a y component such that it completely counteracts the gravity).



Homework Equations



c=2pir //for the circumferences of the sircle it travels.
xsinθ // distance from the pole to the ball, x direction only
ycosθ // distance from the ball to the top of the pole, y direction only

The Attempt at a Solution



I really only got what I have listed above.
x=0.75m , y≈1.299m , c≈4.7124m
I assume I'd need to figure out the force of the hit to keep it that far out from the pole, then calculate time from that, but I'm drawing a blank right now.
 
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  • #2
Apply Newton's 2nd law. What forces act on the ball? What do you know about acceleration and circular motion?
 

1. How does the length of the string affect the time it takes for the ball to travel around the pole?

The length of the string does not affect the time it takes for the ball to travel around the pole. This is because the time it takes for the ball to complete one revolution around the pole is solely dependent on the speed of the ball and the circumference of the circle it travels along.

2. Does the weight of the ball impact the time it takes for it to travel around the pole?

No, the weight of the ball does not impact the time it takes for it to travel around the pole. As long as the speed of the ball remains constant, the weight will not affect the time it takes for the ball to complete one revolution around the pole.

3. How does the height of the pole affect the time it takes for the ball to travel around it?

The height of the pole does not affect the time it takes for the ball to travel around it. This is because the ball is only traveling in a circular motion around the pole, and the height does not impact the circumference of the circle.

4. Is there a mathematical formula to calculate the time it takes for the ball to travel around the pole?

Yes, there is a mathematical formula to calculate the time it takes for the ball to travel around the pole. It is T = (2πr)/v, where T is the time, r is the radius of the circle, and v is the speed of the ball.

5. Can other factors, such as air resistance, affect the time it takes for the ball to travel around the pole?

Yes, other factors such as air resistance can affect the time it takes for the ball to travel around the pole. However, in a controlled environment with minimal air resistance, the impact on the time will be negligible.

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