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

AI Thread Summary
Mechanical energy is conserved during the swinging process as long as the friend continues to swing back and forth without stopping. The discussion highlights the relationship between potential and kinetic energy, emphasizing that energy remains constant in the absence of external forces. If the swing were to stop, energy would be lost due to damping effects. The equations provided illustrate the calculations for kinetic and potential energy in the context of swinging. Overall, the conclusion is that mechanical energy is conserved while swinging at the lake hangout.
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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