- Good morning. Do you feel your weight?
Flipping Physics
- Billy: Of course I feel my weight. Are you daft or something? - Bobby: Yes? - Bo: Duh, it’s the force of gravity. It's my weight.
- Uh. No. Actually, you do not feel the force of gravity acting on you. You do not feel your weight.
Billy: That makes no sense. Bobby: Uh? Bo: Wrong.
- Okay, I will prove it to you.
When you stand on a scale, people often think the scale is measuring the force of gravity acting on you or
what we call your weight.
When you are standing on the surface of the Earth, the force of gravity caused on you by the Earth is constant.
It does not change.
If the scale measures my weight, why does the reading on the scale change when I dance?
"Dancing Macarena"
Hey! Macarena.
- Okay, I get it. Your weight is constant, even when you dance,
however, the measurement on the scale changes as you dance, so the scale does not measure your weight.
- But if the scale does not measure your weight, what does it measure?
- Good question.
- The scale measure the downward force you apply to it, which, according to Newton's Third Law, is equal and
opposite to the force normal acting on you.
In effect, the scale measures the force normal acting on you, which we also call your apparent weight.
Okay, Bo, let’s analyze you standing on a scale. The forces acting on you are your weight,
or the force of gravity, which is down and the force normal, which is up.
Newton’s second law says the net force in the y-direction
equals Force Normal minus Force of Gravity and the net force in the y-direction also equals mass times
acceleration in the y-direction.
In a typical situation where you are just standing there at rest
your acceleration in the y-direction is zero so your force normal equals your weight.
Bo, in that situation your apparent weight and your weight are the same.
Bo, now let’s put you in an elevator which is about to move upward.
Okay it just started to move upward and now is moving at a constant velocity.
And now it has stopped.
Bo, please describe what your weight felt like while that was happening.
- Okay, how did my weight feel?
Uh. For a brief moment when the elevator started up, I felt heavier than normal.
Then I felt normal for a bit. And then when the elevator stopped I felt lighter for just a second.
Okay, at the beginning,
let's call it part 1, when you had an upward or positive acceleration,
your apparent weight was more than your weight. And then, as the elevator and you were moving at a constant
velocity, let's call it part two your apparent weight was the same as your weight.
And at the end, when you had a downward or negative acceleration,
let’s call it part 3, your apparent weight was less than your weight.
Billy, could you please explain this?
- Okay. Going back to the free body diagram and Newton’s second law.
Add force of gravity to both sides of the equation and we get Force Normal equals Force of Gravity plus mass
times acceleration in the y-direction.
In other words, in this specific situation, apparent weight equals
weight plus mass times acceleration in the y-direction.
So during part 1, Bo when you are just starting to move upward, you have an upward or
positive acceleration and therefore mass times acceleration in the y-direction is a positive number
and your apparent weight is greater than your weight.
Which is why you feel heavier as the elevator starts moving upward.
During part 2, when you are moving at a constant velocity,
your acceleration in the y-direction is zero and your apparent weight and your weight are equal.
During part 3, when the elevator is stopping, you have a downward or
negative acceleration and therefore mass times acceleration in the y-direction is a negative number
and your apparent weight is less than your weight.
Which is why you feel lighter as the elevator stops moving upward.
- And then there is the fun example of what happens if we take the whole elevator and drop
it from a very, very tall building.
- Bo: Wait. What?
- It’s a thought experiment. Bo,
we are not going to actually drop you in an elevator from a very, very tall building.
- I think I am going to come back to class now.
- Bobby, what would Bo feel for his apparent weight if he were in a freely falling elevator?
- Bo would be an object in free fall.
His acceleration in the y-direction would be equal to the negative of the
acceleration due to gravity.
Going back to newton’s second law. We can substitute mass times acceleration due to gravity in for weight and
and the negative of the acceleration due to gravity for acceleration in the y-direction.
And, everything cancels out on the right hand side and the force normal equals zero.
If we drop Bo off a very, very tall building, he will feel weightless.
That’s pretty cool. - That is cool.
- Till I hit the ground.
- Notice in this situation that Bo and the elevator would be falling at the same
rate and therefore Bo would appear to float
inside the elevator and he would feel as if he were weightless.
This is called “apparent weightlessness” and is the same thing which happens to
astronauts in the international space station.
Astronauts in the international space station are not actually weightless,
however, they have no force normal acting on them, so they feel as if they are weightless.
Again this is called apparent weightlessness.
Thank you very much for learning with me today.
I enjoyed learning with you.