3. Worked Example 1: Gravitational Force Between Two Objects

Question:

• Find the force of attraction between:
• Ball A 0.01 kg
• Ball B 520g = 0.52 kg
• Distance between centres: 1 m

Solution:

Using Newton's Law of Universal Gravitation:

$F = G \frac{m_1 m_2}{r^2}$

$F = \left( 6.67 \times 10^{-11} \right) \frac{(0.01)(0.52)}{(1)^2}$

$F = :success[3.57 × 10⁻¹⁴ N]$

4. Worked Example 2: Weight in Orbit

Question:

• An object weighs 720 N on Earth.
• It orbits at a height equal to Earth's diameter.
• What is its weight in orbit? Step-by-Step Solution:

1. Determine the number of Earth radii:

• On Earth's surface → 1 radius from the centre.
• In orbit → 2 more radii above, so 3 radii from the centre.

2. Square this value:

• (3)² = 9.

3. Use the inverse square law:

• Weight is reduced by a factor of 9.

4. Calculate new weight: $\frac{720}{9} = :success[80 N]$

3. Worked Example: Weight on Mars

Question:

• The Mars Rover has a mass of 174 kg.
• The acceleration due to gravity on Mars is g=3.7 m/s².
• Calculate its weight on Mars. Solution:

$F_g = mg$

$F_g = (174)(3.7)$

$F_g = :success[643.8 N] (towards the centre of Mars)$