Is Mechanical Energy Conserved During Swinging at a Lake Hangout?"

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Homework Help Overview

The discussion revolves around the conservation of mechanical energy in the context of a swinging motion from a tree over a lake. The original poster describes a scenario where a friend swings back and forth without letting go, prompting questions about energy conservation during this motion.

Discussion Character

  • Exploratory, Conceptual clarification, Assumption checking

Approaches and Questions Raised

  • Participants discuss the relationship between potential and kinetic energy in the swinging motion. Some suggest that mechanical energy is conserved as long as the swinging continues without stopping, while others introduce the idea of damping if the swing ceases.

Discussion Status

The discussion is ongoing, with various interpretations of mechanical energy conservation being explored. Some participants have provided equations related to energy but have not reached a consensus on the conditions under which energy is conserved.

Contextual Notes

There is an implicit assumption about the absence of external forces such as air resistance or friction, which may affect the conservation of mechanical energy. The scenario is set in a casual environment, which may influence the participants' perspectives on the problem.

geauxKTM
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Homework Statement

at a lake hangout there is a tree to swing from over the lake.. Friend is scared and doesn't let go and swings back and forth severall times without stopping. Is his mechanical energy conserved during the swinging process?



Homework Equations





The Attempt at a Solution

 
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I know its potential and kinetic energy
 
If he doesn't stop swinging back and forth then his mechanical energy is conserved but if he stops then his swing is being dampened, but in this case i would say that his mechanical energy is conserved.
 
E(mech) = E(pot) + E(kin)

E(kin) = 1/2mv^2 = 1/2m(A^2-x^2)w^2 = 1/2k(A^2-x^2)

E(tot) = 1/2kx^2 + 1/2k(A^2-x^2)

therefore the equation simplifies to give you one formula
 

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