FSFSSFW ∠≡⇒== θθcos.

F

AB

X

W

Dari ke dua gambar di atas, jelaskan Dari ke dua gambar di atas, jelaskan transformasi dan transfer energi yang transformasi dan transfer energi yang terjadi !!!!!!!!!!!!terjadi !!!!!!!!!!!!

F

AB

X

W

θθ cos cos. FxxFxFW ===

Dot Product :

Berapa besar kerja yang dilakukan ???????

Kerja oleh gaya yang berubah

Work done by a variable force

Conservative Force

A conservative force may be defined as one for which the work done in moving between two points A and B is independent of the path taken between the two points.

For a constant force F which moves an object in a straight line from x1 to x2 , the work done by the force can be visualized as the area enclosed under the force line below

For the more general case of a variable force F(x) which is a function of x, the work is still the area under the force curve, and the work expression becomes an integral.

Dalam bentuk integral garis, kerja dinyatakan sebagai berikut :

DAYA (P watt)

Daya adalah kerja yang dilakukan setiap satuan waktu.

Daya rata-rata :

Daya sesaat :

t

WP =

VFdt

dSF

dt

dWP .. ===

Kinetic Energy(Ek Joule)

Kinetic energy is energy of motion. The kinetic energy of an object is the energy it possesses because of its motion. The kinetic energy* of a point mass m is given by

Kinetic Energy Concept

More Detail on Kinetic Energy Concept

For any function of x, the work may be calculated as the area under the curve by performing the integral

Potential Energy

Potential energy is energy which results from position or configuration. An object may have the capacity for doing work as a result of its position in a gravitational field (gravitational potential energy), an electric field (electric potential energy), or a magnetic field (magnetic potential energy). It may have elastic potential energy as a result of a stretched spring or other elastic deformation.

Potential Energy Function

If a force acting on an object is a function of position only, it is said to be a conservative force, and it can be represented by a potential energy function which for a one-dimensional case satisfies the derivative condition

The integral form of this relationship is

Potential Energy Concept

The potential energy U is equal to the work you must do to move an object from the U=0 reference point to the position r. The reference point at which you assign the value U=0 is arbitrary, so may be chosen for convenience, like choosing the origin of a coordinate system.

The force on an object is the negative of the derivative of the potential function U. This means it is the negative of the slope of the potential energy curve. Plots of potential functions are valuable aids to visualizing the change of the force in a given region of space.

Spring Potential EnergySince the change in Potential energy of an object between two positions is equal to the work that must be done to move the object from one point to the other, the calculation of potential energy is equivalent to calculating the work. Since the force required to stretch a spring changes with distance, the calculation of the work involves an integral.

The work can also be visualized as the area under the force curve:

The general expression for gravitational potential energy arises from the law of gravity and is equal to the work done against gravity to bring a mass to a given point in space. Because of the inverse square nature of the gravity force, the force approaches zero for large distances, and it makes sense to choose the zero of gravitational potential energy at an infinite distance away.

The gravitational potential energy near a planet is then negative, since gravity does positive work as the mass approaches. This negative potential is indicative of a "bound state"; once a mass is near a large body, it is trapped until something can provide enough energy to allow it to escape. The general form of the gravitational potential energy of mass m is:

Gravitational Potential Energy

However, for objects near the earth the acceleration of gravity g can be considered to be approximately constant and the expression for potential energy relative to the Earth's surface becomes

where h is the height above the surface and g is the surface value of the acceleration of gravity.

Gravitational Potential

Gravitational Potential Integral

Energy of a Truck

Potential Energy

Potential Energy DerivativeIf the potential energy function U is known, the force at any point can be obtained by taking the derivative of the potential.

Potential Energy Integral

If the force is known, and is a conservative force, then the potential energy can be obtained by integrating the

force.

Energy can be defined as the capacity for doing work. It may exist in a variety of forms and may be transformed from one type of energy to another. However, these energy transformations are constrained by a fundamental principle, the Conservation of Energy principle. One way to state this principle is "Energy can neither be created nor destroyed". Another approach is to say that the total energy of an isolated

system remains constant.

Conservation of Energy

Energy in Mass on Spring

Contoh lain dari aplikasi kekekalan energi adalah gerak jatuh bebas /vertikal.