Finding the Velocity of a Swinging Ball Around a Post

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In summary, the ball will have a velocity of 5.42 m/s when it is at its highest point over the lower post.
  • #1
jjd101
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Homework Statement


A ball on a 6.5 m long string swings down and wraps around a post that is 4.0 m below the post the string is attached to. If the ball is released level with the post to which it is attached, what will be the velocity of the ball when it is at its highest point over the lower post?


Homework Equations


circular momentum? Inertia of a ball on a string

The Attempt at a Solution


I really have no idea where to start on this problem, i was thinking you start with the initial acceleration of 9.8 due to gravity but that doesn't translate to an initial angular velocity.
 
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  • #2
Use conservation of energy! What forms of energy are involved here? Where's the energy coming from to give the ball motion?
 
  • #3
gravitiational potential energy and kinetic energy??
 
  • #4
jjd101 said:
gravitiational potential energy and kinetic energy??

Yes. So determine the change in energies for the various locations.
 
  • #5
? do i split it up into sections like pie to 3pie/2, 3pie/2 to 2pie, 2pie to pie/2?
 
  • #6
jjd101 said:
? do i split it up into sections like pie to 3pie/2, 3pie/2 to 2pie, 2pie to pie/2?

You can split it up any way you like, as long as you get the information you need in order to find the kinetic and potential energies at the various locations. Personally, since gravitational potential energy is involved, I'd be more concerned about the change in heights of the object at the various points, rather than any angle. Why not draw a picture of the situation at each critical point and see if you can label the changes in height.
 
  • #7
the change in height goes from 4m above the post to 2.5m above the post, aka 1.5m lesss than the drop point, but i don't know how to do this energy problem without mass?
 
  • #8
jjd101 said:
the change in height goes from 4m above the post to 2.5m above the post, aka 1.5m lesss than the drop point, but i don't know how to do this energy problem without mass?

Leave it in as a variable if you wish; you'll find that it cancels out anyways.
 
  • #9
i left m in as a variable and ended up with velocity is equal to 5.42m/s. Is this correct?
 
  • #10
jjd101 said:
i left m in as a variable and ended up with velocity is equal to 5.42m/s. Is this correct?

It looks fine.
 
  • #11
thanks
 

1. What factors affect the motion of a ball swinging around a post?

The motion of a ball swinging around a post is affected by several factors, including the initial force given to the ball, the mass of the ball, the length of the string, and the presence of external forces such as air resistance or friction.

2. How does the length of the string impact the motion of a ball swinging around a post?

The length of the string affects the speed and period of the ball's motion. A longer string will result in a slower swing and longer period, while a shorter string will result in a faster swing and shorter period.

3. Can a ball swinging around a post ever reach a state of equilibrium?

No, a ball swinging around a post will never reach a state of equilibrium because there will always be a gravitational force acting on the ball, causing it to continue swinging.

4. How does the mass of the ball impact its motion when swinging around a post?

The mass of the ball affects the force of gravity acting on it and therefore impacts the speed and period of its motion. A heavier ball will swing slower and have a longer period, while a lighter ball will swing faster and have a shorter period.

5. What is the formula for calculating the period of a ball swinging around a post?

The formula for calculating the period of a ball swinging around a post is T = 2π√(L/g), where T is the period, L is the length of the string, and g is the acceleration due to gravity (9.8 m/s²). This formula assumes that there is no air resistance or friction present.

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