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So far in these lectures we've talked about mass, about acceleration and about forces, but we never used the word "weight," and weight is a very nonintuitive and a very tricky thing which is the entire subject of today's lecture.

What is weight? Here you stand on a bathroom scale.

Gravity is acting upon you, the force is mg, your mass is m.

The bathroom scale is pushing on you with a force F scale and that F scale —

which in this case if the system is not being accelerated is the same as mg —

that force from the bathroom scale on you we define as weight.

When I stand on the bathroom scale I could see my weight is about 165 pounds.

Now, it may be calibrated in newtons but that's, of course, very unusual.

If I weigh myself on the moon where the gravitational acceleration is six times less then I would weigh six times less —

so far, so good.

Now I'm going to put you in an elevator and I'm going to accelerate you upwards and you're standing on your bathroom scale.

Acceleration is in this direction and I will call this "plus" and I will call this "minus." Gravity is acting upon you, mg and the bathroom scale is pushing on you with a force F.

That force, by definition, is weight.

Before I write down some equations, I want you to realize that whenever, whenever you see in any of my equations "g" g is always plus 9.8.

And my signs, my minus signs take care of the directions but g is always plus 9.8 or plus 10, if you prefer that.

Okay, it's clear that if this is accelerated upwards that F of s must be larger than mg; otherwise I cannot be accelerated.

And so we get Newton's Second Law: F of s is in plus direction...

minus mg —

it's in this direction —

equals m times a and so the bathroom scale indicates m times a plus g.

And I have gained weight.

If this acceleration is five meters per second squared in this direction I am one and a half times my normal weight.

If I look on the bathroom scale, that's what I see.

Seeing is believing —

that is my weight.

If I accelerate upwards, with 30 meters per second squared 30 plus 10 is 40 —

I am four times my normal weight.

Instead of my 165 pounds, I would weigh close to 700 pounds.

I see that —

seeing is believing.

That is my weight.

Now I am going to put you in the elevator —

here you are —

and I'm going to accelerate you down.

This is now a.

And just for my convenience I call this now the plus direction just for my convenience —

it doesn't really matter.

So now we have here mg —

that is gravity acting upon you.

And now you have the force from the bathroom scale.

Clearly, mg must be larger than F of s;

otherwise you couldn't go being accelerated downwards.

So if now we write down Newton's Second Law then we get mg minus F of s must be m times a.

This holds for acceleration down and so I get F of s equals m times g minus a.

This is one way of doing it and you put in positive values for a.

If a is five meters per second squared you get ten minus five is five —

your weight is half.

You've lost weight.

Being accelerated down, you've lost weight.

You could also have used this equation and not go through this trouble of setting up Newton's Law again.

You could simply have said "Okay, this a is minus in this coordinate system" and so you put in a minus five and a plus ten —

you get the same answer.

So you have lost weight when you accelerate downwards.

What is weight? Here you stand on a bathroom scale.

Gravity is acting upon you, the force is mg, your mass is m.

The bathroom scale is pushing on you with a force F scale and that F scale —

which in this case if the system is not being accelerated is the same as mg —

that force from the bathroom scale on you we define as weight.

When I stand on the bathroom scale I could see my weight is about 165 pounds.

Now, it may be calibrated in newtons but that's, of course, very unusual.

If I weigh myself on the moon where the gravitational acceleration is six times less then I would weigh six times less —

so far, so good.

Now I'm going to put you in an elevator and I'm going to accelerate you upwards and you're standing on your bathroom scale.

Acceleration is in this direction and I will call this "plus" and I will call this "minus." Gravity is acting upon you, mg and the bathroom scale is pushing on you with a force F.

That force, by definition, is weight.

Before I write down some equations, I want you to realize that whenever, whenever you see in any of my equations "g" g is always plus 9.8.

And my signs, my minus signs take care of the directions but g is always plus 9.8 or plus 10, if you prefer that.

Okay, it's clear that if this is accelerated upwards that F of s must be larger than mg; otherwise I cannot be accelerated.

And so we get Newton's Second Law: F of s is in plus direction...

minus mg —

it's in this direction —

equals m times a and so the bathroom scale indicates m times a plus g.

And I have gained weight.

If this acceleration is five meters per second squared in this direction I am one and a half times my normal weight.

If I look on the bathroom scale, that's what I see.

Seeing is believing —

that is my weight.

If I accelerate upwards, with 30 meters per second squared 30 plus 10 is 40 —

I am four times my normal weight.

Instead of my 165 pounds, I would weigh close to 700 pounds.

I see that —

seeing is believing.

That is my weight.

Now I am going to put you in the elevator —

here you are —

and I'm going to accelerate you down.

This is now a.

And just for my convenience I call this now the plus direction just for my convenience —

it doesn't really matter.

So now we have here mg —

that is gravity acting upon you.

And now you have the force from the bathroom scale.

Clearly, mg must be larger than F of s;

otherwise you couldn't go being accelerated downwards.

So if now we write down Newton's Second Law then we get mg minus F of s must be m times a.

This holds for acceleration down and so I get F of s equals m times g minus a.

This is one way of doing it and you put in positive values for a.

If a is five meters per second squared you get ten minus five is five —

your weight is half.

You've lost weight.

Being accelerated down, you've lost weight.

You could also have used this equation and not go through this trouble of setting up Newton's Law again.

You could simply have said "Okay, this a is minus in this coordinate system" and so you put in a minus five and a plus ten —

you get the same answer.

So you have lost weight when you accelerate downwards.

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