*Notes to a video lecture on http://www.unizor.com*

__Weight__

*Weight*of an object, by definition, is the force of gravity a

planet attracts this object with. Usually, the word "weight" implies the

magnitude of this force; its direction is, obviously, always towards a

center of a planet.

So,

*weight*is not a characteristic of an object itself, it's a

characteristic of an object relative to a planet. In most cases, this

planet is our Earth, though we sometimes say, for example, that a

particular object weighs on the Earth 6 times more than on the Moon.

This only means that the force of gravity on the surface of the Moon is 6

times weaker than on the surface of the Earth.

Do we feel weight as the force of gravity?

Not quite. What we can feel is pressure (

*reaction force*) from the surface we stand on, that equalizes gravitational force to hold us at fixed position on a floor or on a ground.

If there is no support (like for a person jumping with a parachute from

an airplane before a parachute is open, if we ignore the air

resistance), we don't feel weight, we are weightless. We have different

senses, but not a sense of gravity.

So, feeling weightless is not really an absence of gravity, it's absence

of a reaction force that balances the gravity (equal in magnitude and

opposite in direction) and holds us fixed relatively to a planet.

This reaction force is not just against our feet, when we stand on the

floor, it's everywhere inside our body as well, since the body maintains

its shape. We feel this pressure of a reaction force everywhere inside.

That's why it's very difficult to emulate the gravity with some special

equipment on a spaceship.

People on a spaceship with non-working engines flying around the Earth

on an orbit feel weightless, because they are constantly falling towards

the Earth together with a spaceship (no support!) from the straight

line trajectory tangential to an orbit; planet attracts them with

gravitational force, and only because of the speed, they maintain

constant distance from the planet.

Since weight is a force, it is measured in units of force, like

*newtons*in SI.

The

*weight*of an object of mass

**on a surface of a planet of mass**

*m***and radius**

*M***is, as we know,**

*R*

*W = G·M·m /R²*where

**is a universal gravitational constant,**

*G*

*G = 6.674·10*^{−11}N·m²/kg²Since we are talking about weight as a force, which is a subject to the

Newton's Second Law, we can determine the acceleration this force causes

to an object of mass

**, if acts alone:**

*m*

*a = W/m = G·M /R²*Notice that on the surface of Earth this acceleration is constant since

all components of this expression (gravitational constant

**,**

*G*mass of Earth

**and its radius**

*M***) are constants.**

*R*So, we can calculate this constant once and for all and, knowing the mass of an object

**,**

*m*we can determine its weight by multiplying it by this constant, which

is, as we determined in the previous lecture, an acceleration of free

fall, which on the surface of Earth is traditionally symbolized by

letter

**:**

*g*

*g = G·M /R²*The value of this constant is, approximately,

**.**

*9.8 m/sec²*But, to be precise, it's not the same at different points on the Earth

because the shape of the Earth is not exactly a sphere and its mass is

not uniformly distributed within its volume.

Moreover, it obviously changes with height (getting smaller) since the higher elevation is equivalent to a greater radius

**(distance to a center of the Earth) of an object.**

*R*Now we can say that for an object of mass

**the weight on the surface of the Earth is**

*m***. If mass**

*W=m·g=9.8·m***is measured in**

*m**kilograms*, this weight is measured in

*newtons*.

Analogous calculation for other planets, based on their mass and radius, show the following values of free falling acceleration:

on Sun - 274.1 m/sec²

(objects are 28 times heavier on Sun than on Earth),

on Jupiter - 25.93 m/sec²

(objects are about 2.6 times heavier on Jupiter than on Earth),

on Moon - 1.625 m/sec²

(objects are about 6 times lighter on Moon than on Earth).

Historically, the weight is rarely measured in

*newtons*. More customary units are:

1 pound (abbreviated

*lb*) equals to 4.44822

*newtons*- the weight of an object of mass 0.454 kg on Earth;

1 kilogram-force (usually, simply called 1 kilogram, skipping "-force", and abbreviated

*kgf*, but plain

*kg*can also be used, when implication to weight is obvious) equals to weight of an object of mass of 1 kg on Earth, that is 9.8

*newtons*;

and others.

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