GPE (3)

Gravitational Potential Energy (GPE)

• Definition: Work done to move mass in a gravitational field.

Work and Gravitational Force

• Requires work to move mass from initial position (Ri) to final position (Rf).

• Work is done against a varying gravitational force.

Calculating Work

• Graphical approach: Area under the curve in a force vs. distance graph

• As mass m is lifted from Ri to Rf, this is the work done against gravity.

Reference Points

• Reference level for GPE can be arbitrary (e.g., surface of the Earth, infinity).

• GPE can be positive, negative, or zero depending on the reference level, such as for a watermelon at varying heights.

Types of Gravitational Potential Energy Problems

1. Object moved away from planet surface.

2. Object placed in orbit from the surface.

3. Object falls toward the planet under gravity without air resistance considerations.

Example Calculations

• Work required to lift objects:

  • If 4.00 x 10^3 kg is lifted to 3.2 x 10^5 m.

  • Initial position = surface, Final position = 3.2 x 10^5 m above surface.

  • Coordinates: Ri = 6.38 x 10^6 m, Rf = 6.70 x 10^6 m.

• For a vehicle lifted to a circular orbit:

  • Mass = 1.60 x 10^3 kg, Height = 2.0 x 10^6 m above the Moon.

Escape Velocity Predictions

• General escape velocity formula involves mass and radius of the planet.

• Example question on escape velocities between Earth and Saturn, showcasing the mass and radius relationship.

Satellite Energy in Orbit

• Total Energy of a satellite = Gravitational Potential Energy (GPE) + Kinetic Energy (KE).

• GPE can be expressed with respect to satellite characteristics and orbital mechanics.

• Velocity requirements vary by location:

  • Escape velocities differ across celestial bodies (e.g., Earth, Mercury, Venus).

• Tables of relative velocities emphasize variation in gravitational pulls.