Predicting Motion of a Swing on a Non-Horizontal Branch

In summary, the conversation discusses the motion of a swing suspended from a non-horizontal tree branch with fixed points C and D. After an initial kick, the only external force acting on the system is gravity. To predict the motion of the swing, it is necessary to have complete information about the four points and the initial kick, as well as the distribution of mass on the swing. The conversation also mentions using conservation of energy to derive equations for the motion.
  • #1
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TL;DR Summary
Do you understand swings?
swing.png


A swing is suspended from a non-horizontal tree branch. Points C and D are fixed in space. All 4 line segments in the diagram have constant distance. After some initial "kick" imparts energy to the system the only force acting externally on the system is gravity.

Is it possible to predict the motion of the swing?
 
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  • #2
Yes, if we have enough information to completely specify the problem. What are the four points and what is attached between them? Where is the “initial kick” applied and what force is it, applied for how long? How is the mass of the swing distributed?
 
  • #3
AB is the seat. AC and BD are the ropes. CD is the branch. I assume the system remains under tension. The initial kick could be positioning the swing away from the minimum energy position then releasing. Mass is centered on the swing seat with some non zero moment of inertia.
 
  • #4
I define ##\theta## to be the angle a rope makes relative to z and ##\phi## is the angle relative to x. The branch is in the xz plane. From conservation of energy I got
$$ \frac{r_A^2}{2} \left[\left(\frac{\partial\theta_A}{\partial t}\right)^2 + \left(\frac{\partial\phi_A}{\partial t}\right)^2\right]+ \frac{r_B^2}{2}\left[\left(\frac{\partial\theta_B}{\partial t}\right)^2 + \left(\frac{\partial\phi_B}{\partial t}\right)^2\right] - r_A\cos \theta_A - r_B\cos\theta_B = 0$$
Am I on the right track?
 

FAQ: Predicting Motion of a Swing on a Non-Horizontal Branch

How does the angle of the swing affect its motion on a non-horizontal branch?

The angle of the swing will affect its motion on a non-horizontal branch because it determines the direction and magnitude of the force acting on the swing. A steeper angle will result in a greater force pulling the swing downwards, causing it to swing faster and with a larger amplitude.

What factors influence the period of the swing on a non-horizontal branch?

The period of the swing on a non-horizontal branch is influenced by several factors, including the length of the swing, the mass of the swing, the angle of the swing, and the strength of the gravitational force. These factors all contribute to the overall force acting on the swing and therefore affect its period.

How does the surface of the branch affect the motion of the swing?

The surface of the branch can affect the motion of the swing in several ways. A rough surface may cause more friction, slowing down the swing's motion. A smooth surface may result in less friction, allowing the swing to move more freely. Additionally, the shape and curvature of the branch can also impact the direction and speed of the swing.

Can we accurately predict the motion of a swing on a non-horizontal branch?

Yes, it is possible to accurately predict the motion of a swing on a non-horizontal branch using mathematical equations and principles of physics. However, there may be some variables that are difficult to account for, such as wind or the elasticity of the branch, which may affect the swing's motion.

How does the length of the branch affect the motion of the swing?

The length of the branch can have a significant impact on the motion of the swing. A longer branch will result in a longer period and slower motion of the swing, while a shorter branch will lead to a shorter period and faster motion. This is because the length of the branch affects the distance the swing must travel and the force of gravity acting on it.

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