Video Transcript
The mass of a particle is 15.0
kilograms. What is its weight on Earth? On the Moon, the acceleration
produced by gravity is 1.36 meters per second squared. What is the weight of the particle
on the Moon? What is its mass on the Moon? What is its weight in outer space
far from any celestial body? What is its mass at this point?
In the first part of this exercise,
after having been told that we’re working with a particle of mass 15.0 kilograms, we
want to solve for its weight on Earth. We can recall that weight 𝑤 is
equal to an object’s mass multiplied by the acceleration it experiences due to
gravity. So the weight of the particle on
Earth is equal to 15.0 kilograms times 𝑔, where 𝑔 we know to be 9.8 metres per
second squared. When we calculate this product, if
we assume that 𝑔 is exactly 9.8 metres per second squared, our answer is 147
newtons. That’s the weight of the object on
Earth.
Next, we want to calculate the
weight of the particles not on Earth, but on the Moon. Here, the acceleration due to
gravity is no longer 9.8 metres per second squared, but it’s 1.63 metres per second
squared. This means that the weight of the
particle on the Moon we can call it 𝑤 sub 𝑀 is equal to its mass 15.0 kilograms
multiplied by 1.63 meters per second squared. This is 24.5 newtons. Notice how much less this particle
weighs on the Moon than the Earth. It’s about six times less.
Next, we want to solve for the
particle’s mass on the Moon. This will be simple because mass
doesn’t change regardless of our location. It’s always the same. The mass of the particle on the
Moon or anywhere else is 15.0 kilograms.
Next, we want to solve for weight
in the case of being in outer space far from any celestial body. As we think about the particle
being far away from any large mass, we consider that it’s those large masses that
the source of acceleration due to gravity 𝑔. If we’re far from any celestial
body, that means that the acceleration due to gravity is effectively zero. This means that the object’s weight
which will be equal to its mass times 𝑔 which is zero is itself zero. Far away from any mass, the
particle can truly be said to be weightless.
And, finally, far away from any
celestial body, we want to know the particle’s mass. Well, this is the same as it has
been before. Since mass is a measure of the
amount of material in an object, it doesn’t depend on the environment of the
object. This means that the mass of the
particle as before is 15.0 kilograms.
