00:01
All right, so we have an astronaut in outer space on a space shuttle, standing on a scale, and we're told that the space shuttle is a distance of 200 miles from earth, or from the center, sorry, from the surface of earth.
00:14
So in meters, this is 321 ,800 meters.
00:20
And let's draw a free body diagram of this astronaut.
00:23
I'm sorry that, you know, that initial drawing wasn't really the most compelling illustration of a space shuttle.
00:29
Maybe this makes it better if i draw arrows of their velocity.
00:33
But anyway, so the weight of the astronaut, which is like m .g is going down.
00:39
The centripetal force is also pointing towards the center of earth because they're moving.
00:44
And the normal force in the scale points in the opposite direction.
00:48
So if we write this out, what we've got is the centripetal force is equal to mg minus the normal force.
00:55
And so for the next part, we're told the astronaut is weightless when the normal force is zero when the scale reads zero.
01:03
And so what that means is we have mv squared over r equals m g.
01:08
Now in reality, m g is the weight.
01:11
It's actually the gravitational force the astronaut feels.
01:16
And so to make this a little bit more appropriate, let's use like newton's gravitational force formula to determine the force or the velocity because we want to find v here.
01:27
So if we look at this equation...