PM [10] Energy in Motion

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ENERGY OF LINEAR MOTION


Newton’s First Law of Motion

Newton’s First Law of Motion states that:

“A particle in rest will remain forever at rest, and a particle in uniform rectilinear motion will continue to move on forever at constant speed in the same direction.

It will change its state of motion only and only when it is compelled to do so by forces impressed on it.”

I


First Law of Motion

According to Newton’s First Law of Motion, a material body of mass 𝑚𝑚𝑝𝑝 staying at rest will remain at rest indefinitely.

Its velocity 𝑣𝑣 is zero:

𝑣𝑣 = 0

Subsequently, its momentum 𝑝𝑝𝑝𝑝is zero:

𝑝𝑝𝑝𝑝 = 𝑚𝑚𝑝𝑝𝑣𝑣 = 0 The statue is on a skateboardto eliminate resistance from the ground


Body in Motion

Also according to Newton’s First Law of Motion, the particle or material body in motion will remain in motion indefinitely.

Its velocity 𝑣𝑣 is:

𝑉𝑉𝑉𝑉𝑉𝑉𝑉𝑉𝑉𝑉𝑉𝑉𝑉𝑉𝑉𝑉 = 𝑣𝑣

Subsequently, its momentum 𝑝𝑝𝑝𝑝becomes:

𝑝𝑝𝑝𝑝 = 𝑚𝑚𝑝𝑝𝑣𝑣Assuming that there is no air resistance to the

movement which will cause loss in momentum & energy


Change in Dynamical States

𝑣𝑣𝑝𝑝 = 0

𝑝𝑝𝑝𝑝 = 0

𝑣𝑣𝑝𝑝

𝑝𝑝𝑝𝑝 = 𝑚𝑚𝑝𝑝𝑣𝑣

There is an obvious change in the dynamic states of the system Change


Force Effects the ChangeAccording to the First Law, there must be an external force responsible for such a change. In this case, it the push or pull exerted by an external agent – the mover.

𝑣𝑣𝑝𝑝 = 0 → 𝑣𝑣𝑝𝑝

𝑝𝑝𝑝𝑝 = 0 → 𝑚𝑚𝑝𝑝𝑣𝑣

The mover exerts a force 𝑭𝑭 on the statue

The statue moves after the push

𝐹𝐹


The distance 𝑑𝑑 in which force is applied:

𝑑𝑑 = 1/2 0 + 𝑣𝑣 𝑉𝑉

=12 𝑣𝑣𝑉𝑉

The applied force 𝐹𝐹:

𝐹𝐹 =𝑑𝑑𝑝𝑝𝑑𝑑𝑉𝑉 =

𝑚𝑚𝑣𝑣𝑉𝑉

Acceleration from 0 to 𝑣𝑣

Velocity

Distance

𝑣𝑣

𝑑𝑑

Force

Distance

𝐹𝐹

𝑑𝑑

Force up to release point


The Energy graph

If we draw a graph with distance as the horizontal x-axis and force as the vertical y-axis, then we can see the quantity represented by the area of the two quantities relevant to the motion:

𝑾𝑾𝑾𝑾𝑾𝑾𝑾𝑾 𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸

= 𝐹𝐹𝐹𝐹𝐸𝐸𝐹𝐹𝐸𝐸 × 𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐸𝐸𝐹𝐹𝐸𝐸

𝑊𝑊𝑉𝑉𝑊𝑊𝑊𝑊 =12 𝑣𝑣𝑉𝑉 ×

𝑚𝑚𝑣𝑣𝑉𝑉 =

12𝑚𝑚𝑣𝑣

2FO

RCE

DISTANCE

𝑾𝑾𝑾𝑾𝑾𝑾𝑾𝑾 (𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸)= 𝐹𝐹𝐹𝐹𝐸𝐸𝐹𝐹𝐸𝐸

× 𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐸𝐸𝐹𝐹𝐸𝐸

Starting to push Point of release

𝑊𝑊𝑉𝑉𝑊𝑊𝑊𝑊 = 𝐸𝐸𝐸𝐸𝑉𝑉𝑊𝑊𝐸𝐸𝑉𝑉 =12𝑚𝑚𝑣𝑣2


Energy in terms of Work

So energy may have many forms. But whatever form it may be, the basic definition of energy is expressed in terms of work:

Work

In physics, the definition is even more precise. Work is done when a force 𝐹𝐹 moves a body through a distance 𝑑𝑑:

𝑊𝑊𝑉𝑉𝑊𝑊𝑊𝑊 = 𝐹𝐹 × 𝑑𝑑 d

F

Work = F x d


Unit of energy

in SI units, energy is measured in joules.One joule is the energy transferred to an object by moving it a distance of 1 metre against a force of 1 newton.

1 𝐽𝐽 = 1 𝐸𝐸 ∙ 𝑚𝑚

= 1 𝑊𝑊𝐸𝐸 ∙ 𝑚𝑚 ∙ 𝑠𝑠−2 ∙ 𝑚𝑚

= 1 𝑊𝑊𝐸𝐸 ∙ 𝑚𝑚2 ∙ 𝑠𝑠−2

This joule is the unit of both work and kinetic energy, and, of all kinds of energy.

1 m

Force = 1 newton


Transfer of energy = transfer of phonon

As we have established in our previous discussions, the application of force is equivalent to the injection of phonons from one object to another. Since phonons are the carriers of energy, they will be transferred from one body to another whenever a force is applied. If the force is continuous over a distance, the quantity of phonon will build up until the force stops. Then the energy of the body is equal to the total amount of phonons injected and retained by the body..

Force MotionPhononstransferred


Energy-Phonon Equivalence

The interpretation of energy by phonons is therefore even simpler.Since energy is conserved:

12𝑚𝑚𝛾𝛾𝑉𝑉2 =

12𝑚𝑚𝑝𝑝𝑣𝑣2

Or:

𝑚𝑚𝛾𝛾𝑉𝑉2 = 𝑚𝑚𝑝𝑝𝑣𝑣2

We can see that the work done is actually the transfer of phonons from the mover to the moved.

The movedThe phononsThe mover


TRANSFER TO OTHER ENERGY FORMSTo be continued on:

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PM [10] Energy in Motion