gerak dlm satu dimensi

7/29/2019 Gerak Dlm Satu Dimensi

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Gerak dlm Satu Dimensi

Mekanika: Adalah ilmu yang mempelajari mengenai gerak bendakinematika = gerak

dinamika = gaya yang berkaitan dengan gerak dan dengan sifat-sifat benda yang bergerak

Kinematika partikel: Yang dibahas adalah gerak benda ideal partikel.

Secara matematis, partikel diperlakukan sebagai sebuah titik, yaitu benda tanpa ukuran,sehingga rotasi dan vibrasi (getaran) tidak perlu diperhitungkan terlebih dahulu.

Dalam kenyataannya, tidak ada benda tanpa ukuran di alam ini.Kecepatan rata-rata: Kecepatan partikel adalah laju (rate) perubahan posisi terhadap waktu.

Kecepatan sesaat (laju = speed)= Adalah kecepatan partikel pada suatu saat sembarang

Percepatan= Percepatan sebuah partikel adalah laju (rate) perubahan kecepatan terhadap waktu.

GLB ( Gerak Lurus Beraturan )= Gerak lurus beraturan adalah gerak sebuah benda lintasannyaberupa garis lurus dengan kecepatan tetap

GLBB(Gerak Lurus Berubah Beraturan)= Gerak lurus berubah beraturan adalah gerak sebuah benda

yang lintasannya berupa garis lurus dengan percepatan tetap.

GLBB dibagi menjadi 2 macam :

a. GLBB dipercepatadalah GLBB yang kecepatannya makin lama makin cepat.Contoh GLBB dipercepat adalah gerak buah jatuh dari pohonnya.

Ada 2 macam grafik yang dapat dibentuk dari GLBB dipercepat ini:

Grafik hubungan antara v terhadap t

Grafik hubungan antara s terhadap t


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GLBB diperlambat

adalah GLBB yang kecepatannya makin lama makin kecil (lambat).

Contoh GLBB diperlambat adalah gerak benda dilempar ke atas.

Prinsip GLB upaya untuk mempertahankan kecepatan (konstan).

Prinsip GLBB upaya untuk mendapatkan perubahan kecepatan.

vt = v0 + at s = s0 + (v0 + vt) t s = s0 + v0 t + at2 vt2 = v02 + 2 a (s-s0)

Newtons Laws

Newtons First Law {Law of Inertia}Newtons Second Law {F = m.a}Newtons Third Law {Action Reaction} Law of Universal Gravitation

1.INERTIA: the tendency of an object to resist any change in its motion

Inertia is a property of matter and does not depend on the position or location of the object.

2. MASS : a quantitative measure of inertia.

3. FORCE : a push or pull

Mass

is measured in kilograms. is the measure of the inertia of an object. Inertia is the natural tendency of a body resist changes in motion.

What is force?

1) Force is a push or pull

2) Force is the capacity to do work or cause physical change

Grafik hubungan antara v terhadap tGrafik hubungan antara s terhadap t

2

'

r

GmmF


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3) Force = Mass times acceleration (F = ma)

4) A force is that which changes or tends to change the state of rest or motion of a body.

Force : the agency of change, changes the velocity

Newtons First Law

is a vector quantity., measureNewtons.Law of Inertia

A body remains at rest or moves in a straight line at a constant speed unless acted upon by a force.

No mention of chemical composition

No mention of terrestrial or celestial realms

Force required when object changes motion

Acceleration is the observable consequence of forces acting

Everyday Applications of Newton's First Law: Coffee in car, Seat belt, To dislodge ketchup from the bottom

of a ketchup bottle.

What does this mean?

Basically, an object will keep doing what it was doing unless acted on by an unbalanced force.

If the object was sitting still, it will remain stationary. If it was moving at a constant velocity, it will keep

moving.

It takesforce to change the motion of an object.

What is meant by unbalanced force?

Some Examples from Real Life:

1. A soccer ball is sitting at rest. It takes an unbalanced force of a kick to change its motion.2. Two teams are playing tug of war. They are both exerting equal force on the rope in opposite

directions. This balanced force results in no change of motion.

forces on an object are equal and opposite, they are said

to be balanced, and the object experiences no change in

motion. If they are not equal and opposite, then the

forces are unbalanced and the motion of the object

changes.


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Newtons First Law is also called the Law of I nertia

Inertia: the tendency of an object to resist changes in its state of motion

The First Law states that all objects have inertia. The more mass an object has, the more inertia it has (and

the harder it is to change its motion).

Example:

A powerful locomotive begins to pull a long line of boxcars that were sitting at rest. Since the boxcarsare so massive, they have a great deal of inertia and it takes a large force to change their motion. Once they

are moving, it takes a large force to stop them.

On your way to campus, a bug flies into your windshield. Since the bug is so small, it has very little inertia

and exerts a very small force on your car (so small that you dont even feel it).

If objects in motion tend to stay in motion, why dont moving objects keep moving forever?

Things dont keep moving forever because theres almost always an unbalanced force acting upon it.

A book sliding across a table slows down and stops because of the force offriction.

If you throw a ball upwards it will eventually slow down and fall because of the force ofgravity.

In outer space, away from gravity and any sources of friction, a rocket ship launched with a certain speed

and direction would keep going in that same direction and at that same speed forever.

Newtons Second Law

The Sum of the Forces acting on a body is proportional to the acceleration that the body experiences

F = aS F = (mass) a

What does F = ma mean?

Force is directly proportionalto mass and acceleration. Imagine a ball of a certain mass moving at a certain

acceleration. This ball has a certain force.

Now imagine we make the ball twice as big (double the mass) but keep the acceleration constant. F = ma

says that this new ball has twice the force of the old ball.

Now imagine the original ball moving at twice the original acceleration. F = ma says that the ball will again

have twice the force of the ball at the original acceleration.

If you double the mass, you double the force. If you double the acceleration, you double the force.

What if you double the mass andthe acceleration?

(2m)(2a) = 4F

Doubling the mass andthe acceleration quadruples the force.

So . . . what if you decrease the mass by half? How much force would the object have now?

F = ma basically means that the force of an object comes from its mass and its acceleration.

Something very massive (high mass) thats changing speed very slowly (low acceleration), like a glacier,can still have great force.

Something very small (low mass) thats changing speed very quickly (high acceleration), like a bullet, canstill have a great force. Something very small changing speed very slowly will have a very weak force.


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Newtons Third Law

Action-Reaction For every action force there is an equal and opposite reaction force

The Law of Gravity = Every mass exerts a force of attraction on every other mass.

Weight

Weight is the magnitude of the force of gravity acting on an object. Weight = Fgrav Fgrav = mass x gravity

Normal Force

The normal force on an object that is being supported by a surface is thecomponent of the supporting force that is perpendicular to the surface.

FNNormal Force is a force exerted by one object on another in a direction

perpendicular to the surface of contact.

The normal force is always perpendicular to the surface but is not alwaysopposite the force of gravity.

On an angle, the normal force is calculated using Fn = mgcos. The is the angle of the ramp.

G = 6.67 10-11 Nm2/kg2


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Elevator

Apparent Weight


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Apparent Weight

FRICTION

Friction opposes the applied force. The force of friction is proportional to the normal force. It is easier to push a chair across the floor at a constant speed than to push a heavy desk across the

floor at the same speed.

Because the desk is heavier than the chair, the desk experiences a greater normal force and thereforegreater friction.

Two types of friction: Static and KineticSTATIC FRICTION

The resistive force that keeps objects from moving is called the force of static friction.

Static Friction = Fs

As long as the object doesnt move, the static friction is always equal to the opposite in direction to theapplied force.

Fs = -Fapplied

When the applied force is as great as it can be without moving the object, the force of static friction reaches

its maximum value, called Fsmax

KINETIC FRICTION

Once an object exceeds Fsmax, it begins to move.

The resistive force that opposes the relative motion of two contacting surfaces that are moving is called the

force of kinetic friction (Fk)

Normal Force Is Not Always Equal to the Weight


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Coefficients of Friction

Friction depends on the surfaces in contact. The quantity that expresses the dependence on frictional forces on the particular surfaces in contact

is called the coefficient of friction.

Coefficient of friction is represented by the symbol and pronounces mu. k= Fk/Fn Divide the Force of kinetic friction by the normal force s = Fsmax / Fn Divide the maximum value of static friction by the normal force

Finding Friction

If the value of is known and the normal force is known, then the magnitude of the force of friction can becalculated.

Ff= Fn

The kinetic friction is always less than or equal to the maximum static friction.

Think about pushing a car that is sitting still or pushing a car that is already moving.

The coefficient of kinetic friction is always less than or equal to the coefficient of static friction.

Coefficient of Friction = Kinetic Friction {Ff= mkFN }

Static Friction {Ff ms FN} In most cases, mk < ms.

For example, if you throw a 500 g book on floor where k = 0.1, the force of friction would

be.............................

s kmaterials


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Air Resistance=

Whenever an object moves through a fluid medium, like air or water, the fluid provides a resistance to the

motion.

When an object falls through the air, its velocity increases until the air resistance balances the downward

force of gravity.

The object falls with a constant speed, called terminal speed.

Tension (Tensile Force)

Tension is the force in a string, chain or tendon that is applied tending to stretch it. FT


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MOMENTUM IMPULS

Konsep Impuls-Momentum :

Dalam proses yang sebenarnya sering kali didapatkan keadaan Gaya bekerja dalam waktu yang sangat singkat, seperti dalam proses tumbukanatau peluruhan

Melibatkan banyak massa sekaligus

Konsep Impuls-Momentum memudahkan kita untuk menyelesaikan persoalan seperti ini.Momentum

Momentum(SIunitkgm/s, atauNs)adalah hasil kali massa dan kecepatan benda (p = mv).

Momentum linear partikel : Apabila suatu objek bergerak pada bidang acu tertentu, maka objektersebut memiliki momentum terhadap bidang acu tersebut. Momentum sangat tergantung dengan

bidang acu. Maksudnya adalah suatu objek dapat memiliki momentum yang berbeda apabila bidang

acunya berbeda.

Bola yang bergerak memiliki momentum apabila bidang acu adalah lubang di tanah.Tetapi apabila bidang

acu adalah titk pusat massa bola, maka momentumnya = 0.

Apel yang bergerak bersama lift, memiliki momentum

apabila pengamat berada di luar lift.

Tetapi apabila pengamat berada di dalam lift maka

momentum apel = 0 karena kecepatan gerak apel terhadap

pengamat = 0.

Tumbukan

Dalam proses tumbukan antara dua benda ketika kedua benda

dilihat sebagai satu kesatuan, gaya yang terlibat hanyalah gaya internal. Sehingga pada semua proses

tumbukan, selama tidak ada gaya eksternal, total momentum sistem konstan.

Ketika tumbukan terjadi, partikel 1 memberi gaya ke partikel 2 sebesar F21, dan partikel 2 memberigaya ke partikel 1 sebesar F12.

Dari hukum Newton kedua, F12 = dp/dt , sehingga p1= F12 dt

Besaran integral di ruas kiri persamaan di atas juga disebut sebagai impuls yang diberikan oleh gaya

F12.Untuk partikel kedua berlaku:
http://en.wikipedia.org/wiki/SIhttp://en.wikipedia.org/wiki/SIhttp://en.wikipedia.org/wiki/SIhttp://en.wikipedia.org/wiki/Kilogramhttp://en.wikipedia.org/wiki/Kilogramhttp://en.wikipedia.org/wiki/Meters_per_secondhttp://en.wikipedia.org/wiki/Meters_per_secondhttp://en.wikipedia.org/wiki/Meters_per_secondhttp://en.wikipedia.org/wiki/Newtonhttp://en.wikipedia.org/wiki/Newtonhttp://en.wikipedia.org/wiki/Secondhttp://en.wikipedia.org/wiki/Secondhttp://en.wikipedia.org/wiki/Secondhttp://en.wikipedia.org/wiki/Secondhttp://en.wikipedia.org/wiki/Newtonhttp://en.wikipedia.org/wiki/Meters_per_secondhttp://en.wikipedia.org/wiki/Kilogramhttp://en.wikipedia.org/wiki/SI


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Tumbukan elastic: Dalam tumbukan elastik, energi sistem sebelum dan sesudah tumbukan tetap sama.

Koefisien e disebut koefisien resistusi, dan untuk kasus tumbukan elastik nilai e = 1.

Tumbukan tak elastik

Tumbukan tak elastik adalah tumbukan yang mana setelah tumbukan kedua benda menyatu danbergerak dengan kecepatan sama, sehingga v1

= v2.

Ini berarti pada tumbukan total tak elastik, nilai e = 0. Untuk sembarang tumbukan tak elastik, nilai eadalah antara kedua kasus tadi, yaitu 0 e < 1.

Work, Energy, & Power

What is work?

Work is defined simply as a force which is applied through a displacement, or distance.

Work is done against some agent, such as gravity, the stiffness of a spring, inertia, or friction. It is

independent of time, meaning that there are no restrictions on how fast or slow the work is done.

We learned about work, which is the force times distance (times the cosine of the angle in between the two).

The longer the distance you apply the force over, the more work you do.


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What is energy?

Energy is a property that enables something to do work , Energy has various forms (kinetic, potential, rest

energy)

Mechanical energy : Kinetic energy, and Potential energy

Rest Energy

Mass and Energy are related to each other and can be converted into each other.

The rest energy of a body is the energy equivalent of its mass.

E0 = m0c2

E0 (m=1 kg) = 1 kg x (3 108)2 (cm/s)2 ~ 1017 J

PE (m=1 kg, h=9 km) = mgh = 1 kg x 9.8 m/s2 x 9000 m ~ 105 J

1 watt = 1 joule per second {1 W = 1 J/s}also electrical term,

1 watt = 1 volt x 1 ampere

1 kilowatt = 1000 watts

1 kilowatt hour = 1000 watts for one hour

1000 J/s x 3600 s = 3,600,000 J

Conservation of Energy

Energy cannot be created or destroyed.

It can only be changed from one form to another.

The above statement is called the law of conservation of energy

The potential energy of the weight can be changed to kinetic energy is the weight is allowed to freefall.

AS IT LOSES POTENTIAL ENERGY (gets closer to the ground) IT GAINS KINETIC ENERGY (gains

speed in freefall).

THE LOSS OF POTENTIAL ENERGY IS EXACTLY EQUAL TO THE GAIN OF KINETIC

ENERGY.(frictionless case)

mgh = 1/2 mv2

work/energy theorem

Conservative systemsidealized system, no work is done, total energy change is zero

Nonconservative systems

real systems mechanical energy does not remain constant energy is added from outside the system or escapes from the system there is friction, which creates forces


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Kerja pegas Rumus:F = k x

Power

The difference between work and power is one of time. The rate at which work

is done is power. The faster a weight is lifted overhead the more power is

consumed.

graph with low friction graph with high friction

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