# 5.4 Mass and weight

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By the end of the section, you will be able to:
• Explain the difference between mass and weight
• Explain why falling objects on Earth are never truly in free fall
• Describe the concept of weightlessness

Mass and weight are often used interchangeably in everyday conversation. For example, our medical records often show our weight in kilograms but never in the correct units of newtons. In physics, however, there is an important distinction. Weight is the pull of Earth on an object. It depends on the distance from the center of Earth. Unlike weight, mass does not vary with location. The mass of an object is the same on Earth, in orbit, or on the surface of the Moon.

## Units of force

The equation ${F}_{\text{net}}=ma$ is used to define net force in terms of mass, length, and time. As explained earlier, the SI unit of force is the newton. Since ${F}_{\text{net}}=ma,$

$1\phantom{\rule{0.2em}{0ex}}\text{N}=1\phantom{\rule{0.2em}{0ex}}\text{kg}·{\text{m/s}}^{2}.$

Although almost the entire world uses the newton for the unit of force, in the United States, the most familiar unit of force is the pound (lb), where 1 N = 0.225 lb. Thus, a 225-lb person weighs 1000 N.

## Weight and gravitational force

When an object is dropped, it accelerates toward the center of Earth. Newton’s second law says that a net force on an object is responsible for its acceleration. If air resistance is negligible, the net force on a falling object is the gravitational force, commonly called its weight     $\stackrel{\to }{w}$ , or its force due to gravity acting on an object of mass m . Weight can be denoted as a vector because it has a direction; down is, by definition, the direction of gravity, and hence, weight is a downward force. The magnitude of weight is denoted as w . Galileo was instrumental in showing that, in the absence of air resistance, all objects fall with the same acceleration g . Using Galileo’s result and Newton’s second law, we can derive an equation for weight.

Consider an object with mass m falling toward Earth. It experiences only the downward force of gravity, which is the weight $\stackrel{\to }{w}$ . Newton’s second law says that the magnitude of the net external force on an object is ${\stackrel{\to }{F}}_{\text{net}}=m\stackrel{\to }{a}.$ We know that the acceleration of an object due to gravity is $\stackrel{\to }{g},$ or $\stackrel{\to }{a}=\stackrel{\to }{g}$ . Substituting these into Newton’s second law gives us the following equations.

## Weight

The gravitational force on a mass is its weight. We can write this in vector form, where $\stackrel{\to }{w}$ is weight and m is mass, as

$\stackrel{\to }{w}=m\stackrel{\to }{g}.$

In scalar form, we can write

$w=mg.$

Since $g=9.80\phantom{\rule{0.2em}{0ex}}{\text{m/s}}^{2}$ on Earth, the weight of a 1.00-kg object on Earth is 9.80 N:

$w=mg=\left(1.00\phantom{\rule{0.2em}{0ex}}\text{kg}\right)\left({9.80\phantom{\rule{0.2em}{0ex}}\text{m/s}}^{2}\right)=9.80\phantom{\rule{0.2em}{0ex}}\text{N}.$

When the net external force on an object is its weight, we say that it is in free fall    , that is, the only force acting on the object is gravity. However, when objects on Earth fall downward, they are never truly in free fall because there is always some upward resistance force from the air acting on the object.

Acceleration due to gravity g varies slightly over the surface of Earth, so the weight of an object depends on its location and is not an intrinsic property of the object. Weight varies dramatically if we leave Earth’s surface. On the Moon, for example, acceleration due to gravity is only ${1.67\phantom{\rule{0.2em}{0ex}}\text{m/s}}^{2}$ . A 1.0-kg mass thus has a weight of 9.8 N on Earth and only about 1.7 N on the Moon.

what is three dimensional coordinate system?
considering the change of vectors in all three dimensions of space
vedanth
direction co-sign of vector questions
opposite
Sonu
opposite mean
Vipin
what is the different between action and reaction?
action is external force. Reaction exists because of the external action. Reaction is mostly an internal force
Yoblaze
The difference is said in the word itself. There is no existance of reaction without an application of action. So action occur first then reaction. Reaction may produce in body itself or to other body i.e., it may be internal or external.
Amalesh
what is total energy
kenetic energy + potential energy + rotational energy
Tony
any body or object can have it ..even in the molecular level
Tony
As you eat your way through a bag of chocolate chip cookies, you observe that each cookie is a circular disk of diameter 8.50 ± 0.02 cm and thickness 0.050 ± 0.005 cm. Find the average volume of a cookie and the uncertainty in the volume.
how can proportionality sign can be replaced by = and propotionality constant aznd why?🙄🙄
because proportionality means linear relationship between the variables involved
Ranjan
When we say to quantities are proportional to each other, what we mean is that the variables maintain a constant ratio to each other.
Ranjan
let us consider an equation y= mx here y and x are variables and m is constant so whenever we divide y by x it maintains constant ratio called m , if m = 1 y=x if m doesn't equal 1 it may be other but for a closed function it is always same I.e the ratio remains constant
krishna
this applying for closed function proportionality sign can be replaced by = followed by a constant multiplier ratio
krishna
considering the propagation of a wave along the x direction on a vibrating string,how can one derive the one dimensional wave equation for the vibrating sting and the speed expression
show whether or not the expression v^2= u^2 sin^2 d- 2gs is dimensionally constant
the period T of a pendulum depends on its mass m, length l and acceleration due to gravity g. using dimensional analysis, derive for T.
Oyetayo
what is physics
Physics is the tool humans use to understand the properties characteristics and interactions of where they live - the universe. Thus making laws and theories about the universe in a mathematical way derived from empirical results yielded in tons of experiments.
Jomari
This tool, the physics, also enhances their way of thinking. Evolving integrating and enhancing their critical logical rational and philosophical thinking since the greeks fired the first neurons of physics.
Jomari
nice
Satyabrata
Physics is also under the category of Physical Science which deals with the behavior and properties of physical quantities around us.
Angelo
Physical Science is under the category of Physics*... I prefer the most is Theoretical Physics where it deals with the philosophical view of our world.
Jomari
what is unit
Metric unit
Arzoodan
A unit is what comes after a number that gives a precise detail on what the number means. For example, 10 kilograms, 10 is the number while "kilogram" is the unit.
Angelo
there are also different types of units, but metric is the most widely used. It is called the SI system. Please research this on google.
Angelo
Unit? Bahay yon
Jomari
How did you get the value as Dcd=0.2Dab
Why as Dcd=0.2Dab? where are you got this formula?...
Arzoodan
since the distance Dcd=1.2 and the distance Dab=6.0 the ratio 1.2/6.0 gives the equation Dcd=0.2Dab
sunday
Well done.
Arzoodan
how do we add or deduct zero errors from result gotten using vernier calliper?
how can i understand if the function are odd or even or neither odd or even
hamzaani
I don't get... do you mean positive or negative@hamzaani
Aina
Verner calliper is an old calculator
Antonio
Function is even if f(-x) =f(x)
Antonio
Function is odd if f(-x) = - f(x)
Antonio
what physical phenomena is resonance?
is there any resonance in weight?
amrit
Resonance is due to vibrations and waves
Antonio
wait there is a chat here
dare
what is the difference between average velocity and magnitude of displacement
ibrahim
how velocity change with time
ibrahim
average velocity can be zero positive negative but magnitude of displacement is positive
amrit
if there is different displacement in same interval of time
amrit
Displacement can be zero, if you came back
Antonio
Displacement its a [L]
Antonio
Velocity its a vector
Antonio
Speed its the magnitude of velocity
Antonio
[Vt2-Vt1]/[t2-t1] = average velocity,another vector
Antonio
Distance, that and only that can't be negative, and is not a vector
Antonio
Distance its a metrical characteristic of the euclidean space
Antonio
Velocity change in time due a force acting (an acceleration)
Antonio
the change in velocity can be found using conservation of energy if the displacement is known
Jose
BEFORE = AFTER
Jose
kinetic energy + potential energy is equal to the kinetic energy after
Jose
the potential energy can be described as made times displacement times acceleration. I.e the work done on the object
Jose
mass*
Jose
from there make the final velocity the subject and solve
Jose
If its a conservative field
Antonio
So, no frictions in this case
Antonio
right
Jose
and if still conservative but force is in play then simply include work done by friction
Jose
Is not simple, is a very unknown force
Antonio
the vibration of a particle due to vibration of a similar particle close to it.
Aina
No, not so simple
Antonio
Frequency is involved
Antonio
mechanical wave?
Aina
All kind of waves, even in the sea
Antonio
will the LCR circut pure inductive if applied frequency becomes more than the natural frequency of AC circut? if yes , why?
LCR pure inductive? Is an nonsense
Antonio
what is photon
Photon is the effect of the Maxwell equations, it's the graviton of the electromagnetic field
Antonio
a particle representing a quantum of light or other electromagnetic radiation. A photon carries energy proportional to the radiation frequency but has zero rest mass.
Areej
Quantum it's not exact, its the elementary particle of electromagnetic field. Its not well clear if quantum theory its so, or if it's classical mechanics improved
Antonio
A photon is first and foremost a particle. And hence obeys Newtonian Mechanics. It is what visible light and other electromagnetic waves is made up of.
eli
No a photon has speed of light, and no mass, so is not Newtonian Mechanics
Antonio
photon is both a particle and a wave (It is the property called particle-wave duality). It is nearly massless, and travels at speed c. It interacts with and carries electromagnetic force.
Angelo