Weight on Earth vs Weight on Moon Video Lecture - Class 9

hello class professor Anderson here
let's attack this question of how much
you weigh on the earth versus how much
you weigh on the moon what we just saw
was gravity due to the earth pulling us
down has a force F sub G which is
negative G mass of the earth mass of us
divided by the radius of the earth
squared and we plug in those numbers and
what we saw was that is negative M times
little G which we know right little G is
9.8 meters per second squared
so let's say that the mass of you is a
hundred kilograms let's see what this
number is then we get 100 kilograms
times 9.8 meters per second squared all
in SI units we get 980 Newtons
what about your weight well remember
when we talked about weight what we said
was your weight is really how hard is
the floor pushing up on you
or if you're standing on a scale what's
the normal force of that scale pushing
back up on it and this is why when you
are in freefall you feel weightless for
the scale underneath you everything's
falling at the same rate you don't feel
any weight at all there's nothing
pushing back up on you but when you're
standing on the earth and you're not
accelerating up or down then that normal
force is exactly equal to mg because
you're not accelerating
and so your weight your perceived weight
is just mg and now we know what that is
it's 980 Newtons and the negative sign
we took into account right there already
so this is your perceived weight all
right that's when you're on the earth
let's now compare that number to the
moon yeah you're gonna go up to the moon
and you're gonna do the same experiment
you're gonna stand on a scale let's see
what the normal force is pushing back up
on you so let's change everything to the
moon we now have the mass of the moon
the radius of the moon the force we will
call F sub M your mass of course stays
exactly the same if you have a mass of a
hundred kilograms on the earth you go to
the moon you're still a mass of a
hundred kilograms what changes is the
force on you and let's calculate what F
sub M is in this case it's still
negative G m1 m2 over R squared but now
of course we have the mass of the moon
the mass of you and the radius of the
moon quantity squared and let's punch in
some of those numbers and see what we
get I have them right here for you this
is still six point six seven times ten
to the minus eleven the mass of the moon
is seven point three six times ten to
the twenty two kilograms we're gonna
stay in SI units here the radius of the
moon is one point seven four times ten
to the six meters okay and if you punch
in all those numbers into your
calculator you should get something
around negative one hundred and
sixty-two Newton's all right and so you
say my weight on the moon
is the size of this normal force but the
normal force is just equal to M G on the
moon we'll call it and that is 162
Newtons
so this is your weight on the moon so
you knew the answer before we started
you of course weigh less on the moon
because the mass of the moon is much
smaller even though the radius of the
moon is smaller that's not enough to
compensate for that smaller amount of
mass and so you weigh six to seven times
less on the moon
and you're familiar with this already
because when those astronauts went to
the moon you know when they went to the
moon right and you saw them jumping
around even though they have like giant
backpacks full of you know equipment and
air containers and things like that
right they're able to jump pretty high
bounce around on the moon and that's
because there's not as much gravity
pulling on them they don't weigh as much
and so their muscles which have
developed on the earth are strong big
quadricep muscles and when you flex
those muscles and you jump on another
planet that doesn't pull you down as
hard you can jump higher fact if we did
like Olympics on the moon be able to
jump really really high right be able to
jump really really far be able to break
all sorts of records so really that's
what we should do it we should just
develop humans on the earth put them up
on the moon let them compete Thank You
fun