Video Transcript
Two objects, A and B, are in
deep space. The distance between the
centers of mass of the two objects is 20 meters. Object A has a mass of 30,000
kilograms and object B has a mass of 55,000 kilograms. What is the magnitude of the
gravitational force between them? Use a value of 6.67 times 10 to
the negative 11th cubic meters per kilogram second squared for the universal
gravitational constant. Give your answer to three
significant figures.
Okay, so, in this scenario, we
have these two objects, called A and B. So, let’s say here we have our
objects A and B. And we’re told that the
distance between the centers of mass of these two objects is 20 meters. If the center of mass of object
A is here and the center of mass of object B is here, that tells us that this
distance here is 20 meters. Along with this, we’re told the
mass of object A and the mass of object B as well as the fact that these two
objects are in deep space.
Being in deep space means that
A and B are the only objects nearby. When we compute the magnitude
of the gravitational force between them, we can ignore or neglect any other
masses or objects. Continuing on then, we can
represent the mass of object A as 𝑚 sub A and that of object B as 𝑚 sub B. Now that we know our object
masses as well as the distance that separates the centers of mass of these two
objects, let’s recall Newton’s law of gravitation.
This law says that the
gravitational force between two objects, we’ll call it 𝐹, is equal to the
universal gravitational constant, big 𝐺, times the mass of each one of these
objects. We’ll call them 𝑚 one and 𝑚
two. Divided by the distance between
the objects’ centers of mass, we’ll call that 𝑟, squared. Looking at this equation, we
can see that for our scenario with objects A and B, we know their masses. And we also know the distance
separating their centers of mass. And along with that, we’re told
in the problem statement a particular value to use for the universal
gravitational constant.
At this point then, we can
begin to calculate the magnitude of the gravitational force between objects A
and B. It’s equal to the value we’re
given to use as capital 𝐺 times the mass of object A, 30,000 kilograms, times
the mass of object B, 55,000 kilograms. All divided by 20 meters
quantity squared. Note that all the units in this
expression are already in SI base unit form. We have meters and kilograms
and seconds. To three significant figures,
this force is 2.75 times 10 to the negative fourth newtons. That’s the magnitude of the
gravitational force between objects A and B.
