Video Transcript
If the acceleration due to gravity
on Mars is three-eighths the acceleration due to gravity on Earth, what is the
weight of an object on Mars if it weighs 184 newtons on Earth?
This question is asking us to
calculate the weight of an object on Mars given its weight on Earth. Recall that the weight of an object
is equal to the mass of the object multiplied by the acceleration due to gravity
experienced by the object. The value of the acceleration due
to gravity is different on different planets because it depends on the planetβs size
and mass. This means an object with a
particular mass will have a different weight on Mars than it does on Earth.
Letβs call the acceleration due to
gravity of Earth π sub Earth. This means that the weight of an
object on Earth, which weβll call π sub Earth, is equal to π times π sub
Earth. Similarly, we can call the
acceleration due to gravity on Mars, π sub Mars. The weight of an object on Mars is
equal to π times π sub Mars. Weβre told that the acceleration
due to gravity on Mars is three-eighths the acceleration due to gravity on
Earth. Mathematically, we can write this
as π sub Mars equals three-eighths times π sub Earth.
Letβs substitute this expression
for π sub Mars into the formula for the weight of an object on Mars. We see that π times π sub Mars is
equal to π times three-eighths times π sub Earth. Rewriting this expression slightly,
we can see that the weight of an object on Mars is equal to three-eighths times π
times π sub Earth.
Now, we notice something very
interesting in this formula. These last two terms here, π times
π sub Earth, actually equal the weight of an object on Earth. We are told that the weight of the
object on Earth is equal to 184 newtons. Substituting this in, we see that
the weight of the object on Mars is equal to three-eighths times 184 newtons. Completing this calculation gives
us a value of 69 newtons.
So the weight of the object on Mars
is equal to 69 newtons if it weighs 184 newtons on Earth.
