AP Physics 1 Exam Question - Gravitational Force and Fields

A small object with a mass of 2 kg is located at a distance of 4 meters from another object with a mass of 5 kg. The gravitational constant is 6.674 × 10^-11 N m^2/kg^2.

a) Determine the magnitude of the gravitational force between the two objects. b) If the small object is moved to a distance of 8 meters from the larger object, what would be the new magnitude of the gravitational force?

Answer:

a) To determine the magnitude of the gravitational force between the two objects, we can use the formula for gravitational force:

F = (G * m1 * m2) / r^2

where F is the force, G is the gravitational constant, m1 and m2 are the masses of the two objects, and r is the distance between them.

Let's substitute the given values into the formula:

G = 6.674 × 10^-11 N m^2/kg^2 (gravitational constant)
m1 = 2 kg (mass of the small object)
m2 = 5 kg (mass of the larger object)
r = 4 m (distance between the two objects)

Plugging into the formula:

F = (6.674 × 10^-11 N m^2/kg^2 * 2 kg * 5 kg) / (4 m)^2
F = (6.674 × 10^-11 N m^2/kg^2 * 10 kg^2) / 16 m^2
F = (6.674 × 10^-10 N m^2) / 16
F ≈ 4.17125 × 10^-11 N

Therefore, the magnitude of the gravitational force between the two objects is approximately 4.17125 × 10^-11 N.

b) To find the new magnitude of the gravitational force when the distance is doubled to 8 meters, we can use the same formula:

F = (G * m1 * m2) / r^2

Substituting the known values:

G = 6.674 × 10^-11 N m^2/kg^2 (gravitational constant)
m1 = 2 kg (mass of the small object)
m2 = 5 kg (mass of the larger object)
r = 8 m (new distance between the two objects)

Plugging into the formula:

F = (6.674 × 10^-11 N m^2/kg^2 * 2 kg * 5 kg) / (8 m)^2
F = (6.674 × 10^-11 N m^2/kg^2 * 10 kg^2) / 64 m^2
F = (6.674 × 10^-10 N m^2) / 64
F ≈ 1.041015625 × 10^-11 N

Therefore, the new magnitude of the gravitational force between the two objects, when the distance is doubled to 8 meters, is approximately 1.041015625 × 10^-11 N.