application math in physics (kinetic and potential energy)

8/3/2019 Application math in physics (Kinetic and Potential Energy)

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KINETIC ANDPOTENTIAL ENERGY

BY :

NOR ATIKAH ABDULRAZAK

NORKAMALIAH OSMAN @ MOHD

NORDIN


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INTRODUCTION Kinetic energy and potential energy are

the one area in Science where Calculus isapplied.

The concept that we use is differential

calculus and integral calculus.


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OBJECTIVES You will be able to define and identify

Kinetic and Potential energy.

You will be able to give examples of thetwo forms of energy.

You will be able to explain what is thepotential and kinetic energy.


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DEFINITION OF KINETIC ENERGY

The energy of motion.

Measured by:KE= (Mass) (Velocity)

2

Kinetic energy is calculated by one half of the objects mass,multiplied by the objects speed- squared.


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EXAMPLES OF KINETIC ENERGY

Shooting a rubberband.

Water falling overthe fall.

Releasing the arrowfrom the bow.


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DERIVATION: The work done by accelerating an object at the time

interval dt is given by the vector product of force anddisplacement.

Applying the product rule we see that:

dx

dtV=


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Therefore (assuming constant mass), the following can

be seen:

Since this is a total differential (that is, it only depends onthe final state, not how the particle got there), we can

integrate it and call the result kinetic energy:


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POTENTIAL ENERGY

Energy due to position or stored

energy.

Measure by:PE= (weight) (gravity) (Height)

Potential energy is calculated by:The objects weight, multiplied by the earths gravitational pull (9.8 m/sec

sq), multiplied by the distance the object can fall.


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EXAMPLES OF POTENTIAL ENERGY:

Stretching a rubber band..-Stores energy bcoz it has the ability of doingwork

Water at the top of a waterfall..-Stores energy bcoz has the ability of falling

YoYo in held in your hand..-Stores energy bcoz of alter it

position

Drawing a Bow-Stores energy bcoz of its position haschanged n has capability of shooting the arrow.


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ELASTIC POTENTIAL ENERGY

The elastic potential energy stored in a stretchedspring can be calculated by finding the worknecessary to stretch the spring a distance x fromits un-stretched length:

an ideal spring will follow Hooke's Law:


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The work done (and therefore the storedpotential energy) will then be:


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POTENTIAL ENERGYCONVERTED TO KINETIC

ENERGY

When stored energy begins to move,

the object now transfers frompotential energy into kinetic energy.

Standing still Running


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Example 1 A ball of mass 20 g placed at height of 5 m. Find

the value of the potential energy stored in thebody. (g = 10 m/s2).

Solution Here,

m = 20 g = 0.02 kg, h = 5 m ,

g = 10 m/s2, P.E. = ?

As we know that the potential energy(P.E.) = mgh

= 0.02 10 5 = 1 Joule


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Example 2

A heavy metal ball of mass 8 kg has the kineticenergy 16 Joule. Find the velocity of the heavyball.

Solution Here, K.E. = 16 Joule, m = 8 kg, v = ?

The formula for the kinetic energy = m v2

v2 = 2 K.E. / m

= 2 16 / 8= 4

v = 2 m/s


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SUMMARY OF WHAT YOUVE LEARNED..

Example using a coin:

Holding a coin in you hand, alters the coinsoriginal position.

The coin has potential energy, because it has

ability to do work. Dropping the coin in the bank, changes the

stored energy into motion.

This transfers the coins energy frompotential to kinetic energy.


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THE END...

application math in physics (kinetic and potential energy)

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