HSC Physics Does ∆U always equal mg∆h?

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A tutorial sheet of gravitational potential energy questions is below.

  1. What do the symbols in the equation ∆U=mg∆h mean?
  2. When is it correct to use the equation ∆U=mg∆h?
  3. What is the meaning of the equation U=-GMm/r?
  4. When should we use the equation U=-GMm/r?
  5. An object of mass m is lifted through a vertical height ∆h from the surface of the Earth. If the radius of the Earth is R shew that ∆U=mg∆hR/(R+h), where g is the acceleration due to gravity at the surface of the Earth.
  6. An apple of mass 85 g falls from a height of 2.5 m to the ground. What is the change in gravitational potential energy of the apple? [0.99999961mg∆h ≅ mg∆h, -2.08 J]
  7. Mt Everest is 8848 m sbove sea level. If the radius of the Earth is 6400 km show that the increase in gravitational potential energy of a climber of mass m in going from sea level to the top of Mt Everest is 0.9986mg∆h.
  8. The International Space Station (ISS) orbits the Earth at an average altitude of 408 km. If its mass is 419,700 kg determine the gain in gravitational potential energy in lifting this mass from the surface of the Earth to its final height.[0.9401mg∆h, 1.58x1012 J]