Gravitational Potential Energy of a Sphere

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SUMMARY

The discussion focuses on calculating the gravitational potential energy (ΔPE) of a sphere using the equation ΔPE = G × M₁ × M₂ (1/Ri - 1/Rf). The participants confirm the validity of the derived velocity equation v = 2√(GM/d) and the relationship between potential energy and kinetic energy, expressed as ΔPE = -ΔKE. The calculations provided demonstrate the total potential energy change when considering two masses, resulting in ΔPE total = -2GMm/d.

PREREQUISITES
  • Understanding of gravitational potential energy concepts
  • Familiarity with the gravitational constant (G)
  • Knowledge of mass (M₁, M₂) and distance (Ri, Rf) variables
  • Basic algebra for manipulating equations
NEXT STEPS
  • Study gravitational potential energy calculations in different contexts
  • Explore the implications of ΔPE = -ΔKE in various physical systems
  • Learn about the gravitational constant (G) and its significance in physics
  • Investigate the relationship between potential energy and kinetic energy in dynamic systems
USEFUL FOR

Students studying physics, educators teaching gravitational concepts, and anyone interested in the mathematical relationships between potential and kinetic energy in mechanics.

reminiscent
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Homework Statement


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Homework Equations


ΔPE = G × M₁ × M₂ (1/Ri - 1/Rf)
where
G = gravitational constant
M₁ = mass of one object
M₂ = mass of the other object
Ri = initial distance
Rf = final distance
ΔPE = -ΔKE

The Attempt at a Solution


My solution is v = 2√(GM/d). I am making sure it is correct.
 
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I believe your answer is correct. But we can't tell if your steps are correct unless you show your work.
 
TSny said:
I believe your answer is correct. But we can't tell if your steps are correct unless you show your work.
ΔPE = G × M₁ × M₂ (1/Ri - 1/Rf)
ΔPE 5M= G × 5M × m (1/2d - 1/d) = -5GMm/2d
ΔPE M= G × M × m (1/d - 1/2d) = GMm/2d
ΔPE total = ΔPE 5M + ΔPE M = -2GMm/d

ΔPE = -ΔKE = 2GMm/d
(1/2)mv2 = 2GMm/d
v = 2√(GM/d)
 
reminiscent said:
ΔPE = G × M₁ × M₂ (1/Ri - 1/Rf)
ΔPE 5M= G × 5M × m (1/2d - 1/d) = -5GMm/2d
ΔPE M= G × M × m (1/d - 1/2d) = GMm/2d
ΔPE total = ΔPE 5M + ΔPE M = -2GMm/d

ΔPE = -ΔKE = 2GMm/d
(1/2)mv2 = 2GMm/d
v = 2√(GM/d)
Looks good.
 

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