1. Identify the known values:
- Mass of the space shuttle, m₁ = 1.0 × 10⁵ kg
- Mass of the Earth, m₂ = 5.972 × 10²⁴ kg
- Altitude of the shuttle above Earth's surface = 200.0 km = 200,000 m
- Universal gravitational constant, G = 6.67 × 10⁻¹¹ N·m²/kg²
- Radius of the Earth ≈ 6.371 × 10⁶ m (standard value not given but required)
2. Calculate the distance r between the centers of the two masses:
- r = Earth’s radius + altitude = 6.371 × 10⁶ m + 2.000 × 10⁵ m = 6.571 × 10⁶ m
3. Apply Newton’s Universal Law of Gravitation:
- F = G * (m₁ * m₂) / r²
4. Substitute the values into the formula:
- F = (6.67 × 10⁻¹¹) * (1.0 × 10⁵ * 5.972 × 10²⁴) / (6.571 × 10⁶)²
5. Compute step-by-step:
- Numerator: (6.67 × 10⁻¹¹) * (5.972 × 10²⁹) = 3.983 × 10¹⁹
- Denominator: (6.571 × 10⁶)² = 4.317 × 10¹³
- F = 3.983 × 10¹⁹ / 4.317 × 10¹³ ≈ 9.226 × 10⁵ N
6. Final Answer:
- The force of gravity experienced by the space shuttle is approximately 9.23 × 10⁵ N.
Parent Tip: Review the logic above to help your child master the concept of law of universal gravitation worksheet.
