# 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.

y oxygen is shift to first place
What is coriolis firce
Angular accelaration force,as the result of the rotatation of earth
Arzoodan
Due to the rotation of the earth the winds at the equator get deflected in opposite direction and therefore cause some currents in the Northern and Southern hemisphere which are opposite in there spin.
Varsha
Thats correct.
Arzoodan
if cos = x/y then sec = y/x if sin = y/x then cosec = x/y
if cosβ=x/y then what is cosecβ
. if cosβ=x/y what is cosecβ
Abubakar
if cosΦ=x/y what is cosecΦ
Abubakar
What are the unknown symbols?
Jan
Î²
Jan
Î¦
Jan
It is defined that cosec = 1/sin and sec = 1/cos
Jan
Do you understand this?
Jan
of cours
Arzoodan
∇(f/g) = (g∇f − f∇g)/g^2 , at points x where g(x) 6= 0 please help me to solve the problem ....
In a pulley system 2 boxes r hanging in both sides of pulley. An other box was joined to the left box through a rope & get accelerated downward. If all the boxes have same mass ,then what will be the acceleration of that system ?
it may be mg
Amalesh
∇(f/g) = (g∇f − f∇g)/g2 , at points x where g(x) 6= 0 plus solve it
11
What is momentum
is the product of mass to it's velocity (mv)
Ahmed
momentum
quatity of motion present in a body or product of mass and velocity
Shakeel
what is hydration energy
the energy................................................
Rika
what is momentum
dont know want to know the answer
Rika
it's the product of mass multiplied by velocity
harsha
the quantity of motion possessed by a body is called its momentum.by virtue of which a body can exert a force in the agency which tend to stop it .it is a common experience that stronger force is required to stop more massive body.also faster the body moves harder it is to stop it .this is why
Manoj
momentum is product of mass and velocity and it is denoted by "P".
Manoj
show that the cross product of vector axb=-bxa
Nature of the physical low
1/2 mv2 =mgh prove that
Rashika
study work energy theorem properly
Rohan
v2=u2+2gh...u=0...so 1/2 mv2=1/2m(2gh)=mgh
Talha
how can I become confident in physics
practice more and more question ,,,,if u get trouble in any one question infact do that again and again.
jyotirmayee
is theory important or numericals
arshdeep
both ,,,,because without understanding theory ,,,,u can't able to solve problemsss or numericals
jyotirmayee
which books I can follow for IIT jee prep for mcq and which for mcq
arshdeep
what can make me good in physics
lovet
how can I solve qsns in physics cuz I understand most of the theories but facing problem during solving the qsns.
Rohan
what can make me good in physics
Rika
Can someone please tell what really happened to planet Pluto
Pluto was consider as a dwarf planet and not a planet a planet should satisfy the three criteria viz.it should have a orbit around the sun,it should be spherical in shap,and it should clear its orbit . since,Pluto satisfy the first two criteria so it was not considered as a planet .
Manoj
but it was seen that earth also not cleared its orbit but earth is a planet so another criteria was made that a planet should have grater gravitational force other than its orbit and earth follow this but Pluto wasn't satisfied this criteria .so Pluto wasn't consider as a planet.since it follow the
Manoj
first two criteria so it gets a another name called dwarf planet
Manoj
what are the first 20 elements in periodic table.
what happened to the rest now, or have you forgotten?
Ejiba
Hydrozen helium lithium berrilium boron carbon nitrogen oxygen flourine neon sodium magnesium aluminium silicon phosphorous sulphur chlorine argon potassium calcium
Rika
you said 20 elements and thats here
Rika
correct
osobase
yes i know
Rika
excuse me any one here
Rika
yes
harsha
what is momentum
Rika
it is the product of mass and velocity
harsha
thanks
Rika
momentum p = mass X velocity
harsha
Hydration energy?
osobase
p= m*v
harsha
Hydration enery?
Rika
Hydration energy?
Rika
The heat energy released when new bonds are made between the ions and water molecules is known as the hydration enthalpy of the ion
harsha
hydration energy is also called as hydration enthalpy.
harsha
yes what is hydration Energy?
osobase
correct
osobase
Tripple point of water?
osobase
yes it is.
harsha
where water exists in all the three states
harsha
at that point it exists as water (liquid) , ice (solid) and vapours (gas)
harsha
yeap
Rika
What is d tripple point pressure of water?
osobase
it's 6 milli bar
harsha
in mmhg?
osobase
mmHg?
osobase
I can't remember the exact number
harsha
76 cm of Hg = 1 bar
harsha
calculate it for 6millibar
harsha
wrong
osobase
okay.
harsha
4.6mmHg
osobase
what is hydrodynamics
Manoj
the branch of physics that deal with the motion of fluids and the force acting on a solid body immersed in it . fluids means a substance that has no fixed shape and yields easily to external pressure viz.gas or liquid in other words a substance that able to flow easily.
Manoj