How to Find the Angle of a Child on a Swing at Maximum Height

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SUMMARY

The discussion focuses on calculating the angle of a child on a swing at maximum height, with the swing's rope length set at 2.5 meters and the child's velocity at the lowest point recorded at 0.7 m/s. The relevant physics equation used is 1/2Vi^2 = gh, which was applied to determine the maximum height of 0.025 meters. Participants suggest using a free-body diagram to further analyze the forces acting on the child to find the angle between the ropes and the vertical at this height.

PREREQUISITES
  • Understanding of basic physics concepts, particularly energy conservation.
  • Familiarity with kinematic equations and their applications.
  • Ability to draw and interpret free-body diagrams.
  • Knowledge of gravitational potential energy calculations.
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  • Study the principles of energy conservation in mechanical systems.
  • Learn how to construct and analyze free-body diagrams in physics.
  • Explore the relationship between height and angle in pendulum motion.
  • Investigate the effects of varying swing lengths on maximum height and angle.
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This discussion is beneficial for physics students, educators, and anyone interested in understanding the mechanics of pendulum motion and energy conservation principles.

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1. Child on a Swing
This child involves a child swinging on a swing supported by ropes of length 2.5 m. The child's velocity at the bottom of his arc is given as .7 m/s. The goal of the problem is to find the angle between the ropes and the vertical when the child is at his maximum height.


Homework Equations


1/2mVi^2 = mgh
divide through by m ---> 1/2Vi^2 = gh


The Attempt at a Solution


In solving this problem, I was able to find the child's maximum height using the above equation. This I found to be .025 m, however, beyond this point I am at a loss for what to do.

Any help would be greatly appreciated!
 
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try to draw a free-body diagram .. and go on from there ..
 

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