Gravitational Potential Energy of a Sphere

  • #1
131
2

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.
 

Answers and Replies

  • #2
TSny
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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.
 
  • #3
131
2
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)
 
  • #4
haruspex
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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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