Questions: A bowling ball (mass = 5.6 kg, radius = 0.11 m) and a billiard ball (mass = 0.36 kg, radius = 0.028 m) may each be treated as uniform spheres. What is the magnitude of the maximum gravitational force that each can exert on the other? Number i Units

Solution Steps

We need to calculate the maximum gravitational force that a bowling ball and a billiard ball can exert on each other. This force is given by Newton's law of universal gravitation.

The gravitational force \( F \) between two masses \( m_1 \) and \( m_2 \) separated by a distance \( r \) is given by:

\[ F = \frac{G \cdot m_1 \cdot m_2}{r^2} \]

where \( G \) is the gravitational constant, approximately \( 6.674 \times 10^{-11} \, \text{N} \cdot \text{m}^2/\text{kg}^2 \).

The minimum distance between the centers of the two spheres is the sum of their radii:

\[ r = r_1 + r_2 = 0.11 \, \text{m} + 0.028 \, \text{m} = 0.138 \, \text{m} \]

Substitute the known values into the gravitational force formula:

• \( m_1 = 5.6 \, \text{kg} \) (mass of the bowling ball)
• \( m_2 = 0.36 \, \text{kg} \) (mass of the billiard ball)
• \( r = 0.138 \, \text{m} \)

\[ F = \frac{6.674 \times 10^{-11} \, \text{N} \cdot \text{m}^2/\text{kg}^2 \cdot 5.6 \, \text{kg} \cdot 0.36 \, \text{kg}}{(0.138 \, \text{m})^2} \]

Calculate the force:

\[ F = \frac{6.674 \times 10^{-11} \cdot 5.6 \cdot 0.36}{0.019044} \approx 7.086 \times 10^{-9} \, \text{N} \]

Final Answer