You don't feel the force of gravity...
In this video were going to take a look at two things… First we'll walk you through how to calculate the reading on the scale as this elevator moves around… and in doing that, we're going to wind up talking about something called apparent weight, which is the fact that you don’t actually feel the force of gravity… What you feel is something holding you up.
See, the first thing we need to do here is look at the Free Body Diagram of our person in this elevator…
A FBD being a picture showing all the individual forces acting on an object.
So First there's gravity
Now in the absence of other forces this person would just freefall downward, (hand to the right) like an apple from a tree.
Meaning something has to be holding up our person and in this problem that force is actually coming from the scale.
Now where most people get stuck on this problem is in just what a scale actually reads.
See when you stand on a scale, the scale doesn't read how hard gravity’s pulling down on you, instead the scale reads how hard it’s having to push upward.
Just try jumping up and down on a scale, you’ll see the scale reading go up then down, not because you suddenly weigh more or less, but because the scale isn’t pushing consistently on you.
Now the whole point of a FBD like this, is that it helps us apply Newton's
See the 2nd Law is an equation that says the net force or sum of all forces acting on an object is equal to that object's mass times acceleration.
And a FBD is really just a picture of the left half of Newton’s 2nd Law, or what we call the net force.
So if we say up is the positive direction; this upward force by the scale is positive and the downward force by gravity is negative.
And this leaves us with an equation that relates the reading on the scale to the acceleration of the person and the elevator.
So, let’s start with a simple scenario where this elevator is at rest and our person, let's give them a mass of 50kg, is just standing there.
In this case the acceleration of the elevator is zero. We find the scale is going to read a value equal to the weight of the person 490N.
There's no big surprises here, you might expect a scale to read the weight of whatever you put on it.
But next, let's say the elevator is moving steadily upward at 2m/s. Now you may be inclined to think that there now has to be more force upward on the person, because they’re moving up; but remember going back to our equation, the force on the person is dependent on their acceleration, not their speed.
So lets change the motion of this elevator again, and this time let’s make this elevator accelerate upward at 3m/s2; Now this is where things start to get a little weird.
See in order to make the person accelerate upward, there has to be more force up on the person than down…
Going back to our equation, if you plug in a is positive 3 (it's positive because it's upward) the force by the scale will be 640N.
and it’s not that the person weighs more. Remember weight’s always mg, for this person that’s 490 Newtons.
But our scale reads more, and what's critical, is the person will actually feel heavier. and that ‘feeling of weight’ is what we call their apparent weight.
So if we change this and have the elevator accelerate downward at 3m/s2.
The reading on the scale or the apparent weight of the person, is 340N. The person feels lighter; even though gravity is unchanged; its still mg (or 490N)
Lets cut the cable of this elevator, so that the elevator freefalls downward.
Any object in freefall on the surface of Earth accelerates downward at roughly 9.8m/s2,
So plugging -9.8 into our equation for ‘a’, we find that the force by the scale on the person must equal zero… Meaning nothing is holding the person up, they’re in freefall just like the elevator.
Now they aren't actually weightless, gravity is still pulling on them, but their apparent weight, what they feel; is zero.
And this is actually true for astronauts in space too.
An astronaut in Orbit feels weightless, not because there's no gravity in space but because nothing is holding them up.
The acceleration due to gravity at the ISS is about 9m/s2…. Meaning the ISS, and everyone in it, are perpetually freefalling toward the Earth,
Let's take this elevator and accelerate it downward at 19.6m/s2, or two times the acceleration due to gravity, the person would stand upside down on the scale; feeling completely normal; the force between the person and the scale would be 490N… And this is the sort of thing pilots have to worry about when its dark or stormy; a pilot may feel in their seat as though they are flying along straight and level, when in fact they are upside down and about to crash.
Next time you step into an elevator I want you to think about your apparent weight and how heavy you feel, compared to how hard gravity is actually pulling on you.…