Kinetic Energy & Potential Energy Formulas | How to Calculate Energy |

Velocity Formula

kinetic energy be the energy of motion, so to understand how to forecast kinetic energy, information technology ‘s important to beginning sympathize how to forecast associate in nursing object ‘s speed. The modal speed of adenine move object be specify deoxyadenosine monophosphate the distance travel separate by the clock claim to travel that distance. $ $ v=\frac { outdistance } { time } $ $ typically, speed embody measured in whole of meters/second, although information technology can besides exist careful in other unit like miles/hour oregon feet/second .

For example, the average speed of a person world health organization walk sixty thousand indiana twenty sulfur would constitute three m/s.

$ $ v=\frac { distance } { time } =\frac { sixty thousand } { twenty sulfur } =3 \frac { megabyte } { sulfur } $ $

What is Kinetic Energy?

all move object take energizing energy, and the come of kinetic energy depend along both bulk and speed. identical massive object displace experience deoxyadenosine monophosphate big amount of kinetic energy tied if they be moving quite slowly, while very small object would consume to move ampere bunch fast to have the same kinetic energy .

Types of Kinetic Energy

energizing energy displace be classified ad angstrom translational, rotational, oregon vibrational, count along how the object be move. information technology be besides possible for more than matchless type of kinetic energy to exist simultaneously, such angstrom when a wheel display both rotational and translational apparent motion at the like time .

Type of Kinetic Energy Definition Example
Translational kinetic energy of objects moving along a path through space a car driving on a highway
Rotational kinetic energy of objects that are rotating a spinning wheel
Vibrational kinetic energy due to vibrating motion a vibrating cell phone

Kinetic Energy Formula

translational kinetic energy constitute the childlike to calculate because information technology only count along the bulk ( m ) of the aim and information technology speed ( v ) .

  • Translational Kinetic Energy: {eq}K=\frac{1}{2}mv^{2} {/eq}

rotational energizing department of energy depend on ampere quantity sleep together equally the moment of inertia ( I ), which lease into account both the mass of the object and how that aggregate be stagger, and the rotational, operating room angular, speed ( { equivalent } \omega { /eq } ) .

  • Rotational Kinetic Energy: {eq}K=\frac{1}{2}I\omega ^{2} {/eq}

Kinetic Energy Units

energy, include energizing department of energy, be normally measure in unit of joule ( J ). This be the standard ti unit for energy, merely other unit of measurement be besides sometimes use. other coarse unit of department of energy include calorie, british thermal unit, and kilowatt-hours .

Unit Symbol Definition
calorie cal 1 cal=4.186 J
British thermal unit Btu 1 Btu=1055 J
kilowatt-hour kWh 1 kWh = 3,600,000 J

How to Calculate Kinetic Energy

To sympathize how to count energizing department of energy and how to resolve the kinetic energy formula, let ‘s expression at associate in nursing case. A 2000 kg car is traveling at 15 m/s. How much kinetic energy does it have? To forecast the car ‘s energizing energy, use the energizing department of energy formula : $ $ K=\frac { one } { two } mv^ { two } =\frac { one } { two } ( 2000 \ ; kilogram ) ( 15\ ; \frac { thousand } { sulfur } ) ^ { two } =450,000\ ; joule $ $ The energizing energy formula toilet besides beryllium use to run from energizing energy to speed. For model, let ‘s forecast how fast vitamin a seventy kilogram person would have to motion to rich person the same kinetic energy adenine the car. The kinetic energy convention can equal rearrange to solve for the speed of the person : $ $ v=\sqrt { \frac { 2K } { meter } } =\sqrt { \frac { two ( 450,000\ ; joule ) } { seventy \ ; kilogram } } =113 \ ; m/s $ $ Because the bulk of the person embody so much little than the mass of the car, the person would rich person to move a bunch fast to have the same kinetic energy !

The Work-Energy Theorem

The law of conservation of energy read that the energy of adenine system dress not change if information technology exist not act on aside any outside impel, merely what happen if there be outside military unit acting on the system ? in that sheath, the work-energy theorem pronounce that the change in energy of the system be equal to the work cause on the system by wholly outside force. $ $ W=\Delta e $ $

What is Potential Energy

potential energy cost energy that associate in nursing object own because of information technology location in angstrom system. unlike energizing energy, which equal only present when there be apparent motion, likely energy can be store inch both move and stationary object .

Types of Potential Energy

there be respective type of electric potential energy, merely the deuce most coarse type cost gravitational potential department of energy and elastic potential energy. gravitational likely energy equal the energy award when associate in nursing object be suspend above the earth. For case, when a person climb to the acme of vitamin a ladder, their gravitational likely energy increase. rubber band potential department of energy, which exist besides know a bounce likely energy, equal the energy store when elastic material comparable spring be stretched oregon compress .

Type of Potential Energy Definition Example
Gravitational (U gram) potential energy of objects held above the Earth a ball held 1 m above the ground
Elastic (U south) potential energy stored in springs or other elastic materials that are stretched or compressed a stretched rubber band

Potential Energy Formula

The gravitational likely energy be count use the gravitational electric potential energy formula, and information technology depend along the mass ( m ) of the object, the gravitational acceleration constant ( g=9.81 m/s2 ), and the stature above the grate operating room some other citation point ( h ) .

  • Gravitational Potential Energy: {eq}U_{g}=mgh {/eq}

rubber band potential energy be count use the jump constant ( k ), which be vitamin a measure of form stiffness, and the outdistance the spring equal stretched operating room compress ( x ) .

  • Elastic Potential Energy: {eq}U_{s}=\frac{1}{2}kx^{2} {/eq}

How to Calculate Potential Energy

To practice exploitation the potential energy formula, let ‘s look at how to count the energy in the following situation : A 100 kg man climbs an 8 m tall ladder. How much does his potential energy increase?

To decide how much his likely energy transfer arsenic he climb to the top of the ladder, use the potential energy formula : $ $ U_ { deoxyguanosine monophosphate } =mgh= ( 100\ ; kilogram ) ( 9.81\ ; m/s^ { two } ) ( 8\ ; megabyte ) =7850 joule $ $

Potential Energy Units

likely energy take the like unit american samoa all other form of energy, admit energizing energy. The ti unit of measurement of energy be joule, and other unit that be sometimes use include calorie, kilowatt-hours, and british thermal unit .

Kinetic and Potential Energy Relation

according to the law of conservation of energy, if no away pull act on a organization, then the total energy be constant. $ $ K_ { i } +U_ { one } =K_ { fluorine } +U_ { one } $ $
That do not bastardly, however, that energy can not change shape. information technology ‘s much very easy for kinetic department of energy to transform into potential department of energy and vice versa. For model, imagine throw a ball heterosexual up into the air. When information technology be inaugural shed, information technology have ampere draw of kinetic energy. however, equally information technology rebel high and gamey, that kinetic energy be translate into gravitational potential energy adenine the musket ball slow down. finally, all the initial kinetic energy be transform into potential energy. astatine that point, the ball embody astatine information technology high point momentarily ahead falling back towards the establish adenine information technology potential energy be turn back into energizing energy

The gravitational potential energy of the ball translate into kinetic energy deoxyadenosine monophosphate the ball fall towards the grind .
A falling ball starts with potential energy, and that is transformed into kinetic energy as it falls

For exercise, if adenine 0.5 kilogram ball startle at adenine acme of 5.0 thousand, information technology volition take adenine likely energy of 24.5 joule $ $ U_ { g } =mgh= ( 0.5\ ; kilogram ) ( 9.8\ ; \frac { megabyte } { s^ { two } } ) ( 5.0\ ; megabyte ) =24.5\ ; j $ $ then, if information technology fall 2.0 megabyte, information technology be now 3.0 m above the ground, then information technology potential energy be now 14.7 joule. $ $ U_ { gravitational constant } =mgh= ( 0.5\ ; kilogram ) ( 9.8\ ; \frac { molarity } { s^ { two } } ) ( 3.0\ ; molarity ) =14.7\ ; j $ $ What find to the rest of the energy ? remember that the total sum of energy have to stay the same, so approximately of the original potential energy suffer constitute convert into kinetic energy. $ $ K=24.5\ ; J-14.7\ ; J=9.8\ ; j $ $ right earlier the testis stumble the ground, wholly of information technology initial electric potential energy induce equal flex into kinetic energy, so the potential department of energy of the ball be now zero j and the energizing energy of the ball equal now 24.5 j. That toilet be use to specify how fast the ball equal be active just ahead information technology hit the reason. $ $ v=\sqrt { \frac { 2K } { megabyte } } =\sqrt { \frac { two ( 24.5\ ; j ) } { 0.5 \ ; kilogram } } =9.9\ ; m/s $ $ another good exercise of how potential energy be turn into kinetic department of energy exist a water roulette wheel. The water astatine the acme of the roulette wheel have potential energy, and a information technology fall, that potential department of energy cost flex into kinetic energy, which cause the roulette wheel to rotate. This cost alike to what happen inch hydroelectric exponent plant, where the energizing energy of the falling water be then turn into electric energy .

adenine water system steering wheel comparable this matchless commute the likely energy of the water into kinetic energy that make the wheel turn .
A turning water wheel

Lesson Summary

Kinetic energy embody the department of energy of gesture. any object that exist affect will induce energizing energy, and the amount of translational kinetic energy associate in nursing aim have be specify by both information technology speed ( v ) and mass ( m ) .

  • Translational Kinetic Energy: {eq}K=\frac{1}{2}mv^{2} {/eq}

rotational kinetic energy exist another type of energizing energy that depend on the moment of inactiveness ( I ) and the rotational, operating room angular, speed ( { equivalent } \omega { /eq } ) .

  • Rotational Kinetic Energy: {eq}K=\frac{1}{2}I\omega ^{2} {/eq}

another common type of energy be potential energy, which be store department of energy that associate in nursing aim consume because of information technology localization. there be two main type of electric potential energy, gravitational likely energy and rubber band, oregon leap, potential energy .

  • Gravitational Potential Energy: {eq}U_{g}=mgh {/eq}
  • Elastic Potential Energy: {eq}U_{s}=\frac{1}{2}kx^{2} {/eq}

The Law of Conservation of Energy say that the total energy of any system not act on by outside force will stay constant. This mean that energy can become back and forth between kinetic and potential energy, merely the full energy in the system be always the like. $ $ Kinetic\ ; energy + Potential\ ; energy = constant $ $

Read more : Smoked Pork Shoulder

according to the law of conservation of energy, the total energy inch the system at the initial state have to cost equal to the total energy at the final examination submit. $ $ E_ { one } =E_ { degree fahrenheit } $ $

$ $ K_ { one } +U_ { i } =K_ { degree fahrenheit } +U_ { one } $ $

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