Conservation of Energy in Gravity

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SUMMARY

The discussion focuses on calculating the final speed of a boy falling from a roller coaster using the conservation of energy principles. The key equations utilized are the gravitational potential energy (GPE) and kinetic energy (KE) formulas, specifically mgh = 1/2mv² and v = √2gh. For an initial speed of 0 m/s, the final speed is calculated to be 19.8 m/s, while with an initial speed of 5 m/s, the final speed is 20.4 m/s. The participant expresses confusion regarding the calculations and seeks clarification on the application of the equations.

PREREQUISITES
  • Understanding of gravitational potential energy (GPE)
  • Knowledge of kinetic energy (KE) equations
  • Familiarity with basic algebra and square root calculations
  • Concept of conservation of energy in physics
NEXT STEPS
  • Review the derivation of the equations for conservation of energy in gravitational systems
  • Practice problems involving different initial velocities and heights using the formula v² = u² + 2gh
  • Explore the implications of energy conservation in non-vertical motion scenarios
  • Investigate real-world applications of energy conservation in roller coasters and other amusement park rides
USEFUL FOR

This discussion is beneficial for physics students, educators, and anyone interested in understanding the principles of energy conservation in gravitational contexts.

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Homework Statement


A boy at the top of a roller coaster falls through a vertical distance of 20m. What is the final speed of the boy if:
a) His initial speed was 0
b) His initial speed was 5 ms-1


Homework Equations


GPE at top = KE at bottom
mgh = 1/2mv^2
gh = 1/2v^2
v = √2gh

if the initial velocity (u) was not equal to zero, the maths becomes slightly different

initial total energy = final total energy
1/2mu^2 + mgh = 1/2mv^2

therefore...

v^2 = u^2 + 2gh


The Attempt at a Solution



a) 2x9.8x20 = 392

b) 5^2 + 2x9.8x20 = 417


The answers are:
a) 19.8 ms-1
b) 20.4 ms-1
What on Earth am I doing wrong... what can I do... or what? D: I just don't understand!
 
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If v2=392 m2/s2, what is v?
 
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