Work and Energy

INDIVIDUAL DUE

Work and energy

Arranged By:

MUH. HUSNUL KHULUQ

081104175

MATHEMATICS ICP

DEPARTMENT OF MATHEMATICS

FACULTY OF MATHEMATICS AND SCIENCE

UNIVERSITAS NEGERI MAKASSAR

2008 / 2009

WORK AND ENERGY

As we have all known, we utilized Newton's laws to analyze the motion of objects. Force and mass information were used to determine the acceleration of an object. Acceleration information was subsequently used to determine information about the velocity or displacement of an object after a given period of time. In this manner, Newton's laws serve as a useful model for analyzing motion and making predictions about the final state of an object's motion. In this unit, an entirely different model will be used to analyze the motion of objects. Motion will be approached from the perspective of work and energy. The affect that work has upon the energy of an object (or system of objects) will be investigated; the resulting velocity and/or height of the object can then be predicted from energy information. In order to understand this work-energy approach to the analysis of motion, it is important to first have a solid understanding of a few basic terms.

When a force acts upon an object to cause a displacement of the object, it is said that work was done upon the object. There are three key ingredients to work - force, displacement, and cause. In order for a force to qualify as having done work on an object, there must be a displacement and the force must cause the displacement.

A. Work

1. Definition of Work

In our daily live, work is always meant as the all of the activities done to get the certain purpose. It is different with it definition based on the physics science which is stated that “Work is the amount of the force multiplying with the displacement”. It also means that the work depends on the work and the displacement. When the force works in a thing until it does the displacement, it means that there exists working.

There are several good examples of work which can be observed in everyday life-a horse pulling a plow through the field, a father pushing a grocery cart down the aisle of a grocery store, a freshman lifting a backpack full of books upon her shoulder, a weightlifter lifting a barbell above his head, an Olympian launching the shot-put, etc. In each case described here there is a force exerted upon an object to cause that object to be displaced.

As the mathematics formulation of this mulberry defined that work is the product of force and the movement:

W = Fs cos

where W = Work (J), F = Force (N), and s = movement (m), and is the angle between the work and the direction of the movement or displacement. So the unit of this mulberry is Nm or Joule. One joule means the work which is done by 1N of the force and the thing do displacement one meter.

Force and the movement are both vector mulberry. As the dot multiplication between two vector’s mulberries will produce scalar mulberry. That is why this mulberry is known as scalar.

2. Kinds of the Work

There are many kinds of the work which are necessary studying about, such as:

a. The Positive Value Working

The work may have a positive value when the direction of the movement is also in the same direction to the force done. For example; when there a force F works in a thing so it does displacement. When all the forces has a similar direction to the displacement.

F₁ F₁ F₂

S

The work is positive

b. The Negative Value Working

On occasion, a force acts upon a moving object to hinder a displacement. Examples might include a car skidding to a stop on a roadway surface or a baseball runner sliding to a stop on the infield dirt. In such instances, the force acts in the direction opposite the objects motion in order to slow it down. The force doesn't cause the displacement but rather hinders it. These situations involve what is commonly called negative work. The negative of negative work refers to the numerical value which results when values of F, s and theta are substituted into the work equation. Since the force vector is directly opposite the displacement vector, theta is 180 degrees. The cosine (180 degrees) is -1 and so negative value results for the amount of work done upon the object. Negative work will become important (and more meaningful) in discussion about the relationship between work and energy.

F₁ f_s F₁

S

The work done by f_s is negative working

c. The Noël Value Working

The third case of the work is when the thing in which the force works doesn’t do the movement or the displacement. For example; when a man pushes the wall and the wall doesn’t move. It means that the man doesn’t do any working. In other word, the work is noel or nothing.

The work is zero

3. Graph of the Work

When we make the graph which is related between the force and the movement of the thing which is caused by the force itself, then the work is the area which is formed between the line and the Cartesian axis.

F(N)

W

S(m)

Relation between the Force (F) and the movement (s)

B. Energy

1. Definition of Energy

In our daily live, we have all known that the energy could be raised in many forms, such as; wind energy, light energy, chemical energy, nuclear energy, and so many other forms. Based on the explanation about many kinds of energy, we may understand that the energy is able to be exchanged into other forms. So, we may draw a simple conclusion that the energy is the ability to do work.

2. Kinds of Energy

a. Kinetics Energy

Kinetics energy is the energy which has by a thing because of its motion. For example: when the man run, the car run, and so many others which do the motion will has each of kinetics energy. It means that this kind of energy depends on the mass (m) and the velocity (v) of the thing which does the motion.

When there exists a beam with the mass m is silent in the initial condition. Then the work done is defined as:

(1)

While the distance (s) which is reached by the beam is:

(2)

We substitute the equation (1) to equation (2)

By using the derivation of Irregular Straight Movement equation and the second Law of Newton, we got that:

From that we know that

b. Potential Energy

The potential energy that is going to discuss is gravitation potential energy where the gravitation potential energy is the energy which has by a thing because of its position (high). It means that everything in the certain position has each gravitation potential energy. The amount of the potential energy of the thing depends on the mass and gravitation which influences the thing, and also the highness.

In order to lift a thing with the weight known as mg to the place in the high h to the floor, it is needed a minimum force as F=mg. So, we get the potential energy can be defined as

c. Mechanical Energy

Mechanical energy in this case is the amount of energy which also influenced by the gravitation. We mean here mechanical energy is the addition of potential energy and the kinetics energy. Based on the law of the eternity of mechanical energy, we get that:

Em₁ = Em₂

Ep₁ + Ek₁ = Ep₂ + Ek₂

C. The Relation Between Work and Energy

Based on the explanation about the two kind mulberries, that are work and energy, we may get a simple relation based on it definition. We have all known that energy is the ability or capability to do work. There may be we may draw the conclusion such as the change of energy will cause the work.

In related with the potential energy and so with the kinetics energy it may be drawn as:

□ The relation between potential energy and the work

□ The relation between kinetics energy and the work