Max Height of Swing in Circular Motion

In summary, the problem involves a child's playground swing supported by chains that are 4.0m long. The swing is 0.50m above the ground and moving at 6.0 m/s when the chains are vertical. To find the maximum height of the swing, conservation of energy can be used. The change in potential energy is equal to the initial kinetic energy, so the maximum height can be calculated by adding the initial height (0.50m) and the calculated change in height (1.84m). The length of the swing chain (4.0m) may be included to test understanding or for use in another part of the problem.
  • #1
ally1h
61
0

Homework Statement


A child's playground swing is supported by chains that are 4.0m long. If the swing is 0.50m above the ground and moving at 6.0 m/s when the chains are vertical, what is the maximum height of the swing?



Homework Equations





The Attempt at a Solution


Back again.. this time I am LOST. I feel like this should be a circular motion type of problem, but that doesn't entirely make sense since I'm working on energy conservation, linear momentum, torque, and angular momentum. This is what I DO understand:

radius = 4.0m
vi = 6.0 m/s
vf = 0 m/s
The total height is whatever it is plus 0.50m.

I'm lost because I have no clue how to do the problem without a time component or a mass component or an angle. I understand that gravity plays a vertical role, slowing down the speed of the swing.
 
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  • #2
ally1h said:

Homework Statement


A child's playground swing is supported by chains that are 4.0m long. If the swing is 0.50m above the ground and moving at 6.0 m/s when the chains are vertical, what is the maximum height of the swing?

Homework Equations


The Attempt at a Solution


Back again.. this time I am LOST. I feel like this should be a circular motion type of problem, but that doesn't entirely make sense since I'm working on energy conservation, linear momentum, torque, and angular momentum. This is what I DO understand:

radius = 4.0m
vi = 6.0 m/s
vf = 0 m/s
The total height is whatever it is plus 0.50m.

I'm lost because I have no clue how to do the problem without a time component or a mass component or an angle. I understand that gravity plays a vertical role, slowing down the speed of the swing.
It may be easier in this case to consider conservation of energy rather than focusing on circular motion.
 
  • #3
The conservation of energy should be sufficient to answer this problem.

You don't need mass or time. I am pretty sure it is assumed that the ground is flat, otherwise the problem wouldn't be solvable. In the case the ground is flat then you are given an angle which is 90 degrees when the swing as at the bottom of its swing.

The swing is at is maximum velocity when it is at the bottom of its swing (when its not moving upwards). Like you said the swing has no velocity at vf of this problem. This means that at this time it has transferred all of its kinetic energy into ...
 
  • #4
Sorry, I had a dr. appointment...The kinetic energy was transferred into potential energy. This helps a bit, but I feel like I'm still missing something.

I know the change in potential energy is U = mgΔy; I don't know m, but I can figure Δy from the equation: Δy = vi^2 / 2g = (6.0 m/s)^2 / (2)(9.8 m/s) = 1.84 m. So am I just adding 1.84m + 0.50m = 2.34m ??

I feel like I'm missing something, otherwise why would the length of the swing chain (4.0m) be included?
 
  • #5
ally1h said:
I know the change in potential energy is U = mgΔy; I don't know m, but I can figure Δy from the equation: Δy = vi^2 / 2g = (6.0 m/s)^2 / (2)(9.8 m/s) = 1.84 m. So am I just adding 1.84m + 0.50m = 2.34m ??
That's all there is to it. Realize that the equation you used is just an application of energy conservation.
I feel like I'm missing something, otherwise why would the length of the swing chain (4.0m) be included?
I can think of several reasons: (1) Just to see if you know what matters and what doesn't, or (2) The problem might have another part that will require the length of the swing. :smile:
 

What is the "Max Height of Swing in Circular Motion"?

The "Max Height of Swing in Circular Motion" refers to the maximum vertical height that an object reaches during circular motion. It is the highest point that the object reaches before it starts to descend back down.

How is the "Max Height of Swing in Circular Motion" calculated?

The "Max Height of Swing in Circular Motion" can be calculated using the equation h = r(1-cosθ), where h is the max height, r is the radius of the circular motion, and θ is the angle of the swing at the max height.

What factors affect the "Max Height of Swing in Circular Motion"?

The "Max Height of Swing in Circular Motion" is affected by the radius of the circular motion, the initial velocity of the object, and the angle at which the object is released. The height will increase with a larger radius, higher initial velocity, and smaller angle of release.

What is the relationship between the "Max Height of Swing in Circular Motion" and the period of the swing?

The "Max Height of Swing in Circular Motion" is directly proportional to the period of the swing. This means that as the period increases, the max height also increases. This relationship can be seen in the equation h = r(1-cosθ), where the period is represented by θ.

How does gravity affect the "Max Height of Swing in Circular Motion"?

Gravity plays a crucial role in determining the "Max Height of Swing in Circular Motion". It provides the centripetal force that keeps the object in circular motion and affects the speed and acceleration of the object, which in turn affects the max height. In general, a higher gravitational force will result in a lower max height.

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