On earth, two parts of a space probe weigh 19200 N and 4130 N. These parts are separated by a center-to-center distance of 6.38 m and may be treated as uniform spherical objects. Find the magnitude of the gravitational force that each part exerts on the other out in space, far from any other objects.
To find the magnitude of the gravitational force that each part exerts 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/kg)^2
m1 and m2 are the masses of the two objects
r is the distance between the centers of the two objects
We are given the weights of the two parts of the space probe, but we need to find their masses. To do this, we can use the equation:
Weight = mass * acceleration due to gravity
We know the weight of each part, and the acceleration due to gravity on Earth is approximately 9.8 m/s^2. Let's calculate the masses of the two parts:
For the first part:
19200 N = mass1 * 9.8 m/s^2
mass1 = 19200 N / 9.8 m/s^2
For the second part:
4130 N = mass2 * 9.8 m/s^2
mass2 = 4130 N / 9.8 m/s^2
Now that we have the masses, we can calculate the gravitational force between the two parts using the formula mentioned earlier:
F = (G * m1 * m2) / r^2
Substituting the values:
F = (6.67430 × 10^-11 N(m/kg)^2) * (mass1) * (mass2) / (r^2)
Finally, we can calculate the gravitational force between the two parts.