In each hand you hold a 0.15 kg apple.

What is the gravitational force exerted by each apple on the other when their separation is 0.25 m?

What is the gravitational force exerted by each apple on the other when their separation is 0.50 m?

To calculate the gravitational force exerted by each apple on the other, you can use Newton's Law of Universal Gravitation.

The formula for gravitational force is:

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

where:
F is the gravitational force
G is the gravitational constant (6.67430 x 10^-11 Nm^2/kg^2)
m1 and m2 are the masses of the objects
r is the distance between the centers of the objects

In this case, both apples have the same mass of 0.15 kg.

For the first question, when the separation is 0.25 m:

F = (G * m1 * m2) / r^2
F = (6.67430 x 10^-11 Nm^2/kg^2 * 0.15 kg * 0.15 kg) / (0.25 m)^2

Calculating this, the gravitational force exerted by each apple on the other is approximately 2.6744 x 10^-10 N.

For the second question, when the separation is 0.50 m:

F = (G * m1 * m2) / r^2
F = (6.67430 x 10^-11 Nm^2/kg^2 * 0.15 kg * 0.15 kg) / (0.50 m)^2

Calculating this, the gravitational force exerted by each apple on the other is approximately 6.686 x 10^-11 N.

To calculate the gravitational force exerted by each apple on the other, we can use Newton's law of universal gravitation:

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

Where:
F is the gravitational force
G is the gravitational constant (approximately 6.67430 × 10^-11 N m^2/kg^2)
m1 and m2 are the masses of the two apples
r is the separation between the centers of the two apples

For the first scenario, where the separation is 0.25 m:
m1 = m2 = 0.15 kg
r = 0.25 m

Substituting these values into the formula, we get:

F = (6.67430 × 10^-11 N m^2/kg^2 * 0.15 kg * 0.15 kg) / (0.25 m)^2

Simplifying the equation, we have:

F = (6.67430 × 10^-11 N m^2/kg^2 * 0.0225 kg^2) / 0.0625 m^2

F = (1.5017175 × 10^-12 N m^2/kg^2) / 0.0625 m^2

F ≈ 2.4 × 10^-11 N

Therefore, the gravitational force exerted by each apple on the other when their separation is 0.25 m is approximately 2.4 × 10^-11 N.

For the second scenario, where the separation is 0.50 m:
m1 = m2 = 0.15 kg
r = 0.50 m

Using the same calculation method as above, we find:

F = (6.67430 × 10^-11 N m^2/kg^2 * 0.0225 kg^2) / 0.25 m^2

F = (1.5017175 × 10^-12 N m^2/kg^2) / 0.25 m^2

F ≈ 6.01 × 10^-12 N

Therefore, the gravitational force exerted by each apple on the other when their separation is 0.50 m is approximately 6.01 × 10^-12 N.

Force=GM1M2/distance^2

Notice if you figure one, the next distance is twice, so force is 1/4 of the original.