Two 0.53-g basketballs, each with a radius of 17 cm, are just touching.

How much energy is required to change the separation between the centers of the basketballs to 1.1 m? (Ignore any other gravitational interactions.)

How much energy is required to change the separation between the centers of the basketballs to 11 m? (Ignore any other gravitational interactions.)

dfs

To calculate the required energy to change the separation between the centers of the basketballs, we need to calculate the gravitational potential energy.

The formula for gravitational potential energy is:
PE = -G * (m1 * m2) / r

Where:
PE is the potential energy
G is the gravitational constant (approximately 6.674 × 10^-11 N*m^2/kg^2)
m1 and m2 are the masses of the basketballs
r is the separation between the centers of the basketballs

First, let's calculate the mass of each basketball:
mass = density * volume

Given:
density = 0.53 g/cm^3
radius = 17 cm

We can calculate the volume of a basketball using the formula:
volume = (4/3) * pi * r^3

Now, we can calculate the mass of each basketball:
mass = density * volume

Next, let's calculate the separation between the centers of the basketballs in meters.

For the first part of the question, the separation is given as 1.1 m.

Now, let's calculate the energy required using the formula for gravitational potential energy.

Finally, we can substitute the values we have into the formula and calculate the potential energy.