A 6.5- bowling ball and a 7.1- bowling ball rest on a rack 0.80 apart.
Part A- What is the force of gravity exerted on each of the balls by the other ball?
Part B- At what separation is the force of gravity between the balls equal to 2.2×10−9 ?
To solve Part A, we need to calculate the force of gravity exerted on each of the balls by the other ball. The force of gravity can be determined using Newton's law of universal gravitation, which states that the force F between two objects is given by the equation:
F = G * (m1 * m2) / d^2
Where:
- F is the force of gravity between the objects
- G is the gravitational constant (approximately 6.674 × 10^-11 N⋅m^2/kg^2)
- m1 and m2 are the masses of the objects
- d is the separation between the objects
In this case, we have two bowling balls with masses of 6.5 kg and 7.1 kg, respectively, and they are separated by a distance of 0.80 m.
Using the equation above, we can calculate the force of gravity exerted by one ball on the other:
F = (6.674 × 10^-11 N⋅m^2/kg^2) * ((6.5 kg) * (7.1 kg)) / (0.80 m)^2
Calculating the numbers, we find:
F ≈ 3.7218 × 10^-9 N
Therefore, the force of gravity exerted on each of the balls by the other ball is approximately 3.7218 × 10^-9 N.
To solve Part B, we need to find the separation distance at which the force of gravity between the balls is equal to 2.2 × 10^-9 N. We can rearrange the equation from Part A to solve for the separation distance:
d = sqrt((G * (m1 * m2)) / F)
Plugging in the known values:
d = sqrt((6.674 × 10^-11 N⋅m^2/kg^2 * (6.5 kg) * (7.1 kg)) / (2.2 × 10^-9 N))
Calculating the numbers, we find:
d ≈ 0.7222 m
Therefore, the separation distance at which the force of gravity between the balls is equal to 2.2 × 10^-9 N is approximately 0.7222 meters.