Two 0.64 kg basketballs, each with a radius of 13 cm, are just touching. Ignore any other gravitational interactions.
(a) How much energy is required to change the separation between the centers of the basketballs to 1.0 m?
in J
(b) How much energy is required to change the separation between the centers of the basketballs to 10 m?
in J
To solve this problem, we need to use the formula for the gravitational potential energy between two objects:
U = -G * (m1 * m2) / r
where U is the gravitational 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 two objects, and r is the separation between their centers.
Let's calculate the gravitational potential energy for each scenario:
(a) For a separation of 1.0 m:
First, we need to calculate the masses of the basketballs.
The mass of each basketball is given as 0.64 kg.
Now, let's calculate the gravitational potential energy:
U = -G * (m1 * m2) / r
U = -6.674 × 10^-11 * (0.64 * 0.64) / 1.0
Calculating this expression will give us the answer for part (a) in joules.
(b) For a separation of 10 m:
We will use the same formula:
U = -G * (m1 * m2) / r
U = -6.674 × 10^-11 * (0.64 * 0.64) / 10.0
Calculating this expression will give us the answer for part (b) in joules.
Remember to substitute the values correctly to get the accurate answers.