Gravitational Potential Energy Calculation

Key Concepts

• Gravitational Potential Energy (GPE):
  • Energy stored in an object due to its position above the Earth's surface.
  • Caused by the force of gravity acting on the object.

Energy Conversion

• Lifting an object (e.g., a ball) transfers chemical energy from muscles to gravitational potential energy in the object.
• When the object falls, gravitational potential energy is converted to thermal energy and kinetic energy.

Equation for Gravitational Potential Energy

• Formula: [ \text{Gravitational Potential Energy (J)} = \text{mass (kg)} \times \text{gravitational field strength (N/kg)} \times \text{height (m)} ]
• Gravitational field strength is usually provided in questions; standard value on Earth is 9.8 N/kg.

Example Problem

• Problem: A crane lifts a 75 kg mass to a height of 8 m. Calculate the GPE gained.
  • Solution:
    • Mass = 75 kg
    • Gravitational field strength = 9.8 N/kg
    • Height = 8 m
    • [ \text{GPE} = 75 \times 9.8 \times 8 = 5880 \text{ J} ]

Practice Question

• Problem: A ball with a mass of 500 g is lifted 1.5 m above the ground. Calculate the GPE gained.
  • Solution Steps:
    • Convert mass from grams to kilograms: 500 g = 0.5 kg
    • Gravitational field strength = 9.8 N/kg
    • Height = 1.5 m
    • [ \text{GPE} = 0.5 \times 9.8 \times 1.5 = 7.35 \text{ J} ]

Additional Resources

• Additional questions and practice can be found in the Vision Workbook available through the provided link.