Final answer:
To calculate the gravitational force between two objects, use Newton's Law of Universal Gravitation, which takes into account the masses of the objects and the distance between their centers. For part a, calculate the gravitational force using the formula F = G * (m1 * m2) / r^2. For part b, calculate the ratio of the gravitational force to the weight of the 90 g ball using the formula Ratio = F / (m * g).
Step-by-step explanation:
In order to calculate the gravitational force between two objects, we can use Newton's Law of Universal Gravitation, which states that the force of gravity is directly proportional to the product of the masses of the objects and inversely proportional to the square of the distance between their centers.
Part a - For the 8.0 kg lead ball and the 90 g lead ball, the gravitational force they exert on each other can be found using the equation:
F = G * (m1 * m2) / r^2
Where F is the gravitational force, G is the gravitational constant (approximately 6.67 x 10^-11 N.m^2/kg^2), m1 and m2 are the masses of the two objects, and r is the distance between their centers. Plugging the values into the equation, we have:
F1 = 6.67 x 10^-11 * (8.0 kg * 0.09 kg) / (0.15 m)^2
Part b - The ratio of this gravitational force to the weight of the 90 g ball can be calculated by dividing the gravitational force by the weight of the ball. The weight of an object can be calculated using the equation:
Weight = mass * gravitational acceleration (g)
Substituting the values into the equation, we have:
Ratio = F / (m * g)