Video Transcript
Two objects, object I and object
II, are both 120 meters above the surface of the Moon, where the only force that
acts on either of them is the gravitational force of the Moon. Neither object has any motion other
than that due to its gravitational acceleration. Object I and object II each have
masses of 1.5 kilograms. What is the ratio of the mass of
object I to the mass of object II? What is the ratio of the
gravitational force on object I to the gravitational force on object II? What is the ratio of the
acceleration toward the lunar surface of object I to the acceleration toward the
lunar surface of object II?
Looking at our first question, we
are asked to find the ratio of the mass of object I to object II. This is the same thing as saying
we’re gonna take mass one and divide it by mass two to come up with our ratio. In the problem, we’re told that
both of our objects, object I and object II, each have masses of 1.5 kilograms. Therefore, we can plug in 1.5
kilograms for mass one and 1.5 kilograms for mass two. When we divide 1.5 kilograms by 1.5
kilograms, we get 1.0. The ratio of mass of object I to
the mass of object II is 1.0.
For our second question, we’re
asked to find the ratio of the gravitational force on object I to the gravitational
force on object II. To set up the ratio, we divide the
gravitational force on object I by the gravitational force on object II. We need to recall that the
gravitational force on an object is equal to the mass of the object times the
acceleration due to gravity of the object at that position. Plugging in our values, 𝑚 one and
𝑚 two both have values of 1.5 kilograms. And the acceleration due to gravity
in both is the acceleration due to gravity from the Moon. Since there’s an acceleration due
to gravity of the Moon in the numerator and the denominator, they cancel each other
out. When we divide 1.5 kilograms by 1.5
kilograms, we get 1.0 again. The ratio of the gravitational
force on object I to the gravitational force on object II is 1.0.
In our third question, we are asked
to find the ratio of the acceleration toward the lunar surface of object I to the
acceleration toward the lunar surface of object II. We can find the ratio by dividing
the acceleration of object I by the acceleration of object II. From the problem, we are told that
the only force that acts on either of them is the gravitational force of the Moon
and that neither object has any motion other than that due to its gravitational
acceleration. This means that both object I and
object II have acceleration due to gravity that are the same, 𝑔 of the Moon. When we divide 𝑔 of Moon by 𝑔 of
Moon, we get 1.0. The ratio of the acceleration
toward the lunar surface of object I to the acceleration toward the lunar surface of
object II is 1.0.
