Tricky(?) Centripetal Motion Problem

In summary, the problem involves whirling a tennis ball on a string with a period of 0.75 seconds and a mass of 150 g in circular motion with a radius of 0.95 m. The goal is to find the downward angle of the string from the horizontal, the tension in the string, and the string length. The approach is to analyze the forces acting on the ball, including tension, gravity, and the centripetal force. Using Newton's second law and vector addition, the correct answer can be obtained by finding the angle and decomposing the tension into its vertical and horizontal components.
  • #1
realslow
27
0

Homework Statement


I whirl a 'tennis ball on a string' above my head (horizontally) with a period of 0.75 seconds. The ball has a mass of 150 g and the circular motion has a radius of 0.95 m. What is the downward angle of the string from the horizontal, the tension in the string, and the string length?


Homework Equations


Fc = 4π2mRf2


The Attempt at a Solution


Okay, I tried for very long to get to the answers .. with no success.
I think I am having trouble getting the situation set up.
I tried using like a banked curve situation to split into vertical and horizontal..
I think I can get Fc, but I am stuck after that :(
Please help!
 
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  • #2
First make a drawing. Show the forces. The resultant is equal to the centripetal force.

ehild
 
  • #3
What forces act on the ball? Draw a free body diagram. What's the ball's acceleration?

Analyze horizontal and vertical force components using Newton's 2nd law.
 
  • #4
Okay, thank you, I will try the question again!
 
  • #5
Would the net force of the vertical component be 0?
 
  • #6
Yes. But you need a long arm to whirl that ball above your head :)

ehild
 

Attachments

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  • #7
Okay, I will consider that, thanks!
I'm really having trouble with this question..
For the horizontal component, does FC = FT - Fapp in this case?
 
  • #8
What is Fapp? Draw those forces. What forces act on the ball?

ehild
 
  • #9
Fapp would be Fgsinθ
The forces I drew were FT, Fapp, Fg and FN
Maybe I'm not drawing the diagram right :( should I have two separate diagrams for horizontal and vertical? Because I'm only drawing one...
 
  • #10
You have too many forces. Look at the ball. What forces act on it?

ehild
 

Attachments

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  • #11
I know tension force is for sure, but isn't gravity working on it as well?
 
  • #12
Oh I guess so, I just noticed your diagram hehe sorry :)
 
  • #13
The resultant has to be equal to the centripetal force, and it is horizontal. Calculate the centripetal force. You need the angle of the thread with the horizontal. But it is the same as the direction of T. You have right triangles composed of the forces, find the angle. I go to sleep...

ehild
 
  • #14
Alright, I will try once again! Thanks for the help :) Good night!
 
  • #15
realslow said:
Alright, I will try once again! Thanks for the help :) Good night!

How are you getting on?

ehild
 
  • #16
It's not going so well :( this question is really making me depressed *sighs*
I tried getting the angle, but I can't. I've tried getting two equations for the unknown angle, but I only ended up with one, so.. I'm at a dead end.
 
  • #17
You see the forces in the picture: red for the tension, green for the force of gravity. Their resultant is the centripetal force, and it is horizontal. These three forces make a right angle. You can calculate the magnitude both of the centripetal force and gravity. How is related alpha to Fcp and G?

The other approach is decomposing the tension into vertical and horizontal components. The vertical component is of equal magnitude and opposite to G. The horizontal component is equal to the centripetal force.

You can calculate the centripetal force from the given data: period, radius, mass.

ehild
 
  • #18
Ahh thank you so much! Many many thanks :D I finally got the correct answer!
However, I would really appreciate it if you could explain why the three forces made a triangle :) I'm thinking along the lines of vectors, but I'm not too sure..
 
  • #19
Do you know how to add vectors?

ehild
 
  • #20
Yes, I do :)
So I guess my vectors reasoning was pretty accurate then!
Thank you soooo much for your help!
 

1. What is centripetal motion?

Centripetal motion is a type of circular motion in which an object moves around a central point while constantly changing direction. This change in direction is caused by a force called centripetal force, which is always directed towards the center of the circular path.

2. How is centripetal force related to centripetal motion?

Centripetal force is the force that causes an object to follow a circular path. In other words, it is the force that keeps an object moving in a circular motion. Without centripetal force, an object would move in a straight line instead of a circular path.

3. What is the difference between centripetal force and centrifugal force?

Centrifugal force is often confused with centripetal force, but they are actually two different forces. Centripetal force is the force that keeps an object moving in a circular path, while centrifugal force is the apparent outward force that is felt by an object moving in a circular path. It is not an actual force, but rather the result of inertia.

4. How do you calculate centripetal force?

The formula for centripetal force is F = mv^2/r, where F is the force, m is the mass of the object, v is the velocity, and r is the radius of the circular path. This formula shows that centripetal force is directly proportional to the mass and the square of the velocity, and inversely proportional to the radius.

5. What are some real-life examples of centripetal motion?

Some common examples of centripetal motion include the Earth's orbit around the Sun, a car moving around a circular track, and a satellite orbiting the Earth. Other examples include a washing machine spinning clothes, a rollercoaster moving around a loop, and a ball attached to a string and swinging in a circular motion.

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