3.6.5 Gravitational Potential Energy

• Gravitational potential energy (E_p) is energy stored in a mass due to its position in a gravitational field
  • If a mass is lifted up, it will gain E_p (converted from other forms of energy)
  • If a mass falls, it will lose E_p (and be converted to other forms of energy)

• The equation for gravitational potential energy for energy changes in a uniform gravitational field is:

Gravitational potential energy (GPE): The energy an object has when lifted up

• The potential energy on the Earth’s surface at ground level is taken to be equal to 0
• This equation is only relevant for energy changes in a uniform gravitational field (such as near the Earth’s surface)

Derivation of GPE Equation

• When a heavy object is lifted, work is done since the object is provided with an upward force against the downward force of gravity
  • Therefore energy is transferred to the object

• This equation can therefore be derived from the work done

• There are many scenarios that involve the transfer of kinetic energy into gravitational potential, or vice versa
• Some examples are:
  • A swinging pendulum
  • Objects in freefall
  • Sports which involve falling, such as skiing and skydiving

• Using the principle of conservation of energy, and taking any drag forces as negligible:

Loss in potential energy = Gain in kinetic energy

Step 1: Write down the known quantities

• • Vertical height, h = 750 sin 25°
  • E_k = 0.85 E_p

Step 2: Equate the equations for E_k and E_p

E_k = 0.85 E_p

½ mv² = 0.85 × mgh

Step 3: Rearrange for final speed, v

Step 4: Calculate the final speed, v