Find Velocity of Centripetal Ball Before Swing Out

  • Thread starter PrudensOptimus
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    Centripetal
In summary, the conversation discusses how to find the velocity of a ball attached to a vein that is being swung by Hercules. The max tension of the vein is 300N and the length from the vein to the ball is .8 meters. The ball has a mass of 1.2kg. The conversation also mentions using force and acceleration to calculate velocity and using a free body diagram to determine the position and final speed of the ball. The problem assumes that the ball is traveling in a horizontal circle and ignores gravity.
  • #1
PrudensOptimus
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How do you find the place when the ball is about to "swing" out?

A ball is attached to a vein, which has max tension of 300N; and Hercules is swinging the vein above his head. The length from vein to ball is .8meters. The ball has mass of 1.2kg..

How do you find the velocity of the ball just before it swings out?


Please advise... Thanks you!
 
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  • #2
What's a vein? Do you mean chain?

In any case, here's a hint: The max tension is also the max centripetal force that can be supplied.
 
  • #3
The ball will escape when it's 'centripetal force' is greater than the max tension of the vein.

Hopefully, you know that Force = Mass * Acceleration.

If you know your max 'centripetal force', then you can calculate your max centripetal acceleration.

Knowing your max centripetal acceleration and your radius, you can calculate your max velocity.
 
  • #4
Centrepidal force is = mv^2/r,

but i don't know my velocity... What is another way to find Centrepedal force?

The only force in the x direction is the Tension force in the x component...

But i don't know that.
 
  • #5
Is this right? :


Fc = 300
mv^2/r = 300
v = sqrt (300R/m)
 
  • #6
You got it.
 
  • #7
aha! Thanks! That was sooo much simpler than I thought...

But... how can we do this based on FreeBody Diagram?

There's 2 forces: Tension and Gravity right?

And Tension has 2 components: x and y.

...

Any advise on how I should draw the free body diagram?
 
  • #8
and at what position is the ball when it is about to fall out?

Do i use V^2 = V0^2 + 2ax? What is its final speed? 0?
 
  • #9
I've been assuming that the ball travels in a horizontal circle. To give you a better answer, I'd need to see what this apparatus looks like. Do you have a picture?
 
  • #10
your assumption is right. it is just a plain circle.
 
  • #11
If the ball is traveling in a horizontal circle, and the tension in the "vein" (what's a vein?) is also horizontal, then the problem ignores gravity. You've already solved the problem.
 

1. What is centripetal force?

Centripetal force is the force that keeps an object moving in a circular path. It is directed towards the center of the circle and is necessary for the object to maintain its circular motion.

2. How is centripetal force related to velocity?

The magnitude of the centripetal force is directly proportional to the velocity of the object in circular motion. This means that as the velocity increases, the centripetal force required to keep the object in its circular path also increases.

3. How do you calculate centripetal force?

The formula for calculating centripetal force is Fc = mv^2/r, where Fc is the centripetal force, m is the mass of the object, v is the velocity, and r is the radius of the circular path. This formula can be rearranged to find any of the variables if the others are known.

4. How does the velocity of a ball before swing out affect its centripetal force?

The velocity of the ball before it swings out affects the magnitude of the centripetal force required to keep it in its circular path. A higher velocity means a larger centripetal force is needed, while a lower velocity requires a smaller centripetal force.

5. Can the velocity of a ball before swing out be calculated using the formula for centripetal force?

Yes, the formula for centripetal force can be rearranged to solve for velocity. The formula becomes v = √(Fc*r/m), where v is the velocity, Fc is the centripetal force, r is the radius, and m is the mass of the object. However, this formula assumes a perfect circular path and does not take into account other factors such as friction or air resistance.

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