How Do Gravitational Potential and Kinetic Energy Relate in Energy Conservation?

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SUMMARY

The discussion centers on the relationship between gravitational potential energy (PE) and kinetic energy (KE) in the context of energy conservation. The key equations referenced are Wgravity = mgh for gravitational potential energy and KE = 1/2mv² for kinetic energy. A critical insight is that when analyzing energy conservation, mass cancels out, leading to the conclusion that PE equals KE at the bottom of a fall, expressed as mgh = 1/2mv², which simplifies to v² = 2gh. This demonstrates that the speed of an object at the bottom of a fall is independent of its mass.

PREREQUISITES
  • Understanding of gravitational potential energy (PE) and kinetic energy (KE)
  • Familiarity with the equations Wgravity = mgh and KE = 1/2mv²
  • Basic knowledge of algebra for manipulating equations
  • Concept of energy conservation in physics
NEXT STEPS
  • Study the derivation of the equations for gravitational potential energy and kinetic energy
  • Explore the concept of energy conservation in different physical systems
  • Learn about the implications of mass cancellation in energy equations
  • Investigate real-world applications of energy conservation principles in mechanics
USEFUL FOR

Students studying physics, educators teaching energy concepts, and anyone interested in understanding the principles of energy conservation and its mathematical foundations.

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Homework Statement

box.jpg

Homework Equations


Wgravity = mgh
KE=1/2mv2

The Attempt at a Solution



I know the gravitational potential energy is different because mgh accounts for mass.
But the book says that B is correct. I don't know why because isn't the less mass you have the faster you go? 2KE/m=v2
 
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okgo said:

Homework Equations


Wgravity = mgh
KE=1/2mv2

The Attempt at a Solution



I know the gravitational potential energy is different because mgh accounts for mass.
But the book says that B is correct. I don't know why because isn't the less mass you have the faster you go? 2KE/m=v2

Step back a bit and look at the equations.

PE = KE at the bottom.

m*g*h = 1/2*m*v2

v2 = 2*g*h

The mass has canceled out.
 

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