Weight, Mass, and Gravitational Field Strength

Key Equation

• Weight (W) = Mass (m) × Gravitational Field Strength (g)
• W = m × g
• Units:
  • Weight: Newtons (N)
  • Mass: Kilograms (kg)
  • Gravitational field strength: Newtons per kilogram (N/kg) or meters per second squared (m/s²)

Example Calculations

On Earth

• Mass: 100 kg
• Gravitational Field Strength (Earth): 9.8 N/kg

Calculation of Weight on Earth:

• W = m × g
• W = 100 kg × 9.8 N/kg
• Weight: 980 N

On Mars

• Mass: 100 kg
• Gravitational Field Strength (Mars): 3.7 N/kg

Calculation of Weight on Mars:

• W = m × g
• W = 100 kg × 3.7 N/kg
• Weight: 370 N

Direct Proportionality

• Weight and Gravitational Field Strength: Directly proportional
  • Increase in gravitational field strength → Increase in weight
  • Decrease in gravitational field strength → Decrease in weight
• Weight and Mass: Directly proportional

Practice Problems

Problem 1: Calculate Mass from Given Weight

• Given: Earth's gravitational field strength, 9.8 N/kg

• Person A: Weight = 680 N

  • Formula: W = m × g
  • Substitute values: 680 N = m × 9.8 N/kg
  • Rearrange for mass: m = 680 N / 9.8 N/kg
  • Mass: 69.4 kg

• Person B: Weight = 470 N

  • Formula: W = m × g
  • Substitute values: 470 N = m × 9.8 N/kg
  • Rearrange for mass: m = 470 N / 9.8 N/kg
  • Mass: 47.9 kg

Review Questions

• Attempt problems to practice the use of the equation W = m × g
• Use given weights and gravitational field strengths to calculate masses
• Rewatch and review for clarity

Resources

• For more practice, visit kscience.com
• Additional videos, worksheets, and quizzes available
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