Centripetal Motion: Tetherball

In summary, the tetherball has a mass of 1kg, is sent around a vertical pole in a horizontal circular path, and has a tension in the rope that keeps it in motion. The ball has a velocity of 4.53m/s and a period of 2.91s.
  • #1
tigerwoods99
99
0

Homework Statement



Tetherball is seen on playgrounds across the globe. It consists of a vertical pole with a ball attached to the top with a rope. The ball has a mass of 1kg and is sent around the pole in a horizontal circular path. If the rope has a length of 2.25 meters and makes an angle of 20.9 degrees with the pole, (not theta).

Radius of path = .802m i got that part.
The velocity of the tetherball =
The period of the tetherball's motion=
The tension in the rope = I got that also.


Homework Equations





The Attempt at a Solution

 
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  • #2
What are the forces acting on the ball?
Which force keeps the ball in the circular motion?
 
  • #3
I think i figured it out. I used the square root of radius * 9.8 to find the minimum velocity it can stay in a circular path.
 
  • #4
During the circular motion of the ball, three forces act on the ball.
If T is the tension in the rope, T*cosθ balances the weight of the ball and T*sinθ provides the centripetal force which keeps the ball in the circular motion.
 
  • #5
thats correct! So if the velocity is not given, nor the time, using the square root of .802 *9.8 to give me 2.8m/s correct?
 
  • #6
No.
T*sinθ/Τ*cosθ = (m*v^2/R)/mg.
Simplify and substitute the values to find v.
 
  • #7
ok doing it that way i got 4.53 m/s is that correct?
Thanks a lot btw
 
  • #8
Check the calculation again.
After simplification you get
tanθ = v^2/Rg.
Now solve for v.
 
  • #9
tan (69.1) = v^2 / .802*9.8
2.618 = v^2 / 7.8596
2.057 = v^2
4.5361 = v

Are you sure?
 
  • #10
Here θ is the angle made by the rope to the pole. According to your problem that is equal to 20.9 degrees.
 
  • #11
Oh ok, in the past I have been taught to use the theta to the x axis.
 
  • #12
okay
 
Last edited:
  • #13
Would the tension force be: 18.92 N

FT = mv^2/r +mgsin69.1


and are you positive tanθ = v^2/Rg. is correct?

That would give me 1.732m/s
 
Last edited:
  • #14
Your answer is correct.
 
  • #15
Both the FN and V?
 
  • #16
Your calculation of v is correct. In the problem you have to find the period.
t = 2*π*R/v.
 
  • #17
Yes I have figured that one out, because it is in a circular orbit circumference can be used.

t = 2.91s
 
  • #18
You said the calculation of v is correct, is the calculation of FN correct as well?!?
 
  • #19
tigerwoods99 said:
You said the calculation of v is correct, is the calculation of FN correct as well?!?
What is FN?
 
  • #20
Never mind I figured out everything is right! Thanks for all your help
 

1. What is centripetal motion?

Centripetal motion is the motion of an object in a circular path due to the force acting towards the center of the circle.

2. How does centripetal motion relate to tetherball?

Tetherball is a game that involves a ball attached to a pole by a rope. The motion of the ball around the pole is an example of centripetal motion.

3. What is the force that causes centripetal motion in tetherball?

The force that causes centripetal motion in tetherball is the tension in the rope. As the ball moves around the pole, the tension in the rope constantly pulls it towards the center of the circle.

4. How does the speed of the ball affect its centripetal motion in tetherball?

The speed of the ball affects the centripetal force required to keep it in motion. The faster the ball moves, the greater the centripetal force needed to keep it in a circular path.

5. What happens if the tetherball is hit at an angle instead of directly towards the pole?

If the tetherball is hit at an angle, it will still move in a circular path, but the direction of the force acting on it will change. This will cause the ball to move in a different direction and possibly wrap around the pole in a spiral pattern.

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