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In this case, the total mechanical energy is not conserved . Therefore, external forces are often referred to as non-conservative forces.

A quick review of internal forces

On the other hand, you also learned that if work is done on an object only by internal forces, the total mechanical energy possessed by the object cannot change. However, it can be transformed from potential energy to kineticenergy and vice versa.

In this case, the total mechanical energy is conserved . Therefore, internal forces are often referred to as conservative forces.

A quantitative relationship

The quantitative relationship between work and mechanical energy can be stated as follows:

MEf = MEi + We

where

  • MEf and MEi represent the final and initial total mechanical energy possessed by the object respectively.
  • We represents the work done on the object by external forces.

This equation states that the final amount of mechanical energy possessed by an object is equal to the initial mechanical energy plus the work done on theobject by external forces.

Potential energy plus kinetic energy

The total mechanical energy at any point in time can be the sum of potential energy (gravitational or elastic potential energy) and kinetic energy due to motion.

Given that, we can rewrite the earlier equation as:

KEf + PEf = KEi + PEi + We

where

  • KEf and PEf represent the final kinetic and potential energy respectively.
  • KEi and PEi represent the initial kinetic and potential energy respectively.
  • We represents the work done on the object by external forces.

As mentioned, the work done by external forces can be either positive or negative work. Whether the work is positive or negative depends on the cosine ofthe angle between the direction of the force and the direction of the displacement of the object.

An ideal rocket example

Consider the following scenario. The owners of an experimental rocket lift the rocket onto a platform above ground level and set it up for firing.

Later, when they fire the rocket, it goes straight up while the rocket engine is burning. When the rocketengine runs out of fuel and stops burning, the rocket coasts to its apex and stops climbing.Then it falls back to the surface of the earth in an unglamorous free fall.

Simplifying assumptions

We will make some simplifying assumptions:

  • The mass of the fuel is insignificant relative to the combined mass of the rocket and its payload. Therefore, expenditure of fuel doesn't affectthe mass of the rocket in a significant way.
  • Air resistance is negligible. The rocket acts as if in a vacuum.

Initial conditions

Here are the initial conditions for the rocket experiment:

  • Platform height = 15 meters.
  • Mass of rocket and payload = 10kg.
  • Thrust of rocket is constant at 150 newtons during burn.
  • Burn time for the rocket = 10 seconds.

Legs of the trip

We will analyze the rocket's round trip from the ground, into the air, and back to the ground in several legs as described below:

  • Leg A: Manually lifting the rocket from the ground to the platform.
  • Leg B: Displacement of the rocket under rocket-engine power straight up.
  • Leg C: Displacement of the rocket without power while coasting to the apex.
  • Leg D: Displacement of the rocket in free fall from the apex back to the ground.

Questions & Answers

what us maxima and minima
MiXUP Reply
Maxima s below equilibrium. Whilst minima s above. Equilibrium
Afran
Wht is demand
Afran
is the willingness and the ability of a consumer to purchase goods at a given price and at a particular point in time.
Assan
Ohhk different question? Ask
Afran
why is the demand curve downwards sloppy?
Assan
3 Reasons.. 1... diminishing marginal utility 2... substitution effect 3...income effect
Harshita
thanks
Assan
Because of the negative or inverse relationship between price and quantity demanded
Afran
what is the law of diminishing returns states?
Assan
ohk
Assan
The law states that all other things being equall as much of variable factor(labour) is employed on fixed factor(land) the marginal product rises..attain a maximum and begins to fall.
Afran
What is income elasticity of demand
Afran
what is monetary policy
Edward
Monetary policy is an attempt to influence the economy by opera ting in such monetary variables
Afran
thanks
Edward
Wlcm
Afran
Wht is disutility?
Afran
is disutility? is rightly writing?
Yhlas
is it i wanna say
Yhlas
Yes please Disutility
Afran
what is macro economics?
Oyas
the branch of economics concerned with large-scale or general economic factors, such as interest rates and national productivity.
idk
in other words it is the study of the economic as a whole
idk
What is an Economic growth
Ayumo Reply
Economic growth is the process whereby the real per capita income of an economy increases over a long period of time.
Nureni
what is the generally accepted defination of economics and by who
IDY Reply
Economics is defined by Lionel Robbins as a social science which studies human behaviour as a relationship between ends and scarce means which have alternative uses
Tba
Importance of economic
Achike Reply
Helps in decision making
MP
I need like 5 importance
Achike
hi
Physcal
Hey
Muhammad
hellow dear.
juwel
hello
Al-ameen
Hello
MP
it helps an individual in rational decision making process
Assan
Fine and u
Buzabaryaho
how does it make individual in rational dicision making decisions
Annor
if an individual is faced with unlimited wants.
Assan
it also helps an individual in arranging their wants in order of their importance.
Assan
ohk
Annor
ok
Al-ameen
Hello guys
Radah
My name is Radah
Radah
Please what is a scale of preference used for?
Radah
it's use for arranging wants in order of their importance.
Assan
in other words when an individual is faced with unlimited wants,scale of preference would help the individual to select the most important wants.
Assan
Thanks
Radah
welcome
Assan
what is tourism
forgive Reply
Tourism is travel for pleasure or business
Yusuf
It is the commercial organization and operation of holidays and visits to places of interest.
Nureni
who is a price taker?
sam Reply
A price taker is a person or a company who have no control to dictate a prices of a goods or services
Unique
Someone who sets price
Nureni
In the trading world, a price taker is a trader who does not affect the price of the stock if he or she buys or sells shares.
Nureni
A price taker refers to a firm or an individual who sets the price of his good and services based on an external factor. In other words he cannot choose and set a price by himself. An example is a firm operating in perfect competition where prices are set through the price mechanism.
Tba
in a common and suitable sense state the law of diminishing returns
Unique Reply
The higher the satisfaction derived from a particular commodity,the lower the demand for it but that law doesn't match in some instances.
Nureni
state the features of an imperfect competitive market
Naomi
@NURENI instance like wat
Unique
imperfect competitive market involves large number of sellers and buyers price makers selling cost product differentiation free entry and exit of a firms
Unique
is economics a science
Alex Reply
yes. a social science.
Carlos
Yes of cause It uses scientific principles in its research. That is to say, analyzing data, making experiment as well as making deductions and drawing conclusions
Aziz
U can understand the scientific nature of economics by learning about the methods used by Abhijit Banerjee(indian) ,the nobel prize laureate 2019.
Harshita
it is considered as a social science
idk
Hence, economics is a science, a social science many can call it, or more appropriately, a young science
Taha
it can be called social science because of behaviour ,which is unpredictable.There r many theroies in economics which make economics a social science But some economic theories makes it science
Harshita
human behaviour*
Harshita
remember science derives from the root words "to know". With that being said most fields of study can be considered as a science or soft science, for they possess key knowledge to attaining understanding of our world.
Alexander
economics is a science cos it deals with human wants, desire or neads in order to satisfy them
Unique
according comparision of political science economic is science.
Hassan
what's the question?
Nureni Reply
Discuss economics system
Henry Reply
discuss institutional system
Henry
Give 3 at most advantages and disadvantages of economics system and institutional syatem
Henry
Give the features characteristics of market or free enterprise
Henry
The structure of an economy is largely determined by the economic system which is a function of the economic ideology of the nation
Nureni
The economic system is grouped into 5 groups: 1: Pure market 2: Developed market 3: Centrally planned or Socialist 4: Mixed market and 5: Market Socialist Economic systems
Nureni
what is inflation
Prince Reply
Inflation is a sustained and general rise in the price of all goods and services of an economy
Tba
hello everyone , I'm New here, third degree price discrimination?
Saeed Reply
2nd degree price discrimination?
Saeed
hi
Kini
hi
Mitchel
Hi
MP
price paid by consumers after the sales tax is called?
Pinias Reply
why government impose price floor on certain products?
Pinias
how can black market be occurred when price ceiling is introduced?
Pinias
How can inflation affect goods and services?
Ph
When prices rise for energy, food, commodities, and other goods and services, the entire economy is affected
Joan
If inflation becomes too high the economy can suffer conversely, if inflation is controlled and at reasonable levels, the economy may prosper. With controlled, lower inflation, employment increases.
Joan
Is it necessary to make decision when it fails you
Evelin Reply
Pls when what fails u
MP
I think so
Kini
well i might naught know what you on about but i gotta tell you, it is necessary
Troy
yep
Ibe
Kk
MP
yep
Ibe
how can the demand side approach solve unemployment
Tshepiso Reply
demand solves unemployment when it is addressed with supply you can't just expect demand to work alone without supply the two are interconnected
Nureni
You have to apply the concept of aggregate demand
Tba
That is apply demand side policies to boost aggregate demand hence increasing need for labour and decreasing unemployment(more people get jobs)
Tba
Difference between extinct and extici spicies
Amanpreet Reply
Researchers demonstrated that the hippocampus functions in memory processing by creating lesions in the hippocampi of rats, which resulted in ________.
Mapo Reply
The formulation of new memories is sometimes called ________, and the process of bringing up old memories is called ________.
Mapo Reply
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Source:  OpenStax, Accessible physics concepts for blind students. OpenStax CNX. Oct 02, 2015 Download for free at https://legacy.cnx.org/content/col11294/1.36
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