Energy And Work

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Energy

Energy is a hard thing to grasp. Right now, the best we can do is to use a definition developed in the 18th century. Energy was thought of as a substance like quantity that could be transferred from one object to another. This "substance" was named caloric and cannot be created nor destroyed. Energy is responsible for all change. For example, when you kick a soccer ball, energy is transferred from your body to the ball. Another example is when a log burns in a woodstove, it releases its energy and transfers it to the stove and to the surrounding room.

Energy can be transferred from one object to another. The way energy is stored can be compared to the way money is "stored" in a bank. In a bank, you can keep money in a savings account, checking account or certificate of deposit. Likewise, objects can store energy in various "accounts" such as the kinetic account or the potential account. How does energy manifest itself when it is stored in these accounts?

Kinetic account (Ek):

  • Microscopic Kinetic Account: We usually think of this as heat. A hot object has more energy stored than a cool object.
  • Macroscopic Kinetic Account: Any object that moves, has energy in the macroscopic kinetic account. A car moving at 30 mph has more energy than the same car moving at 10 mph.

Potential account:

  • Gravitational Potential Energy (Epg): This is a measure of the energy required to move particles of matter from the surface of the earth (or any baseline) to a specified height..
  • Elastic Potential Energy (Epe): This is a measure of the energy stored in a spring or any elastic object that is stretched or compressed.
  • Chemical Potential Energy (Ecp): This is a measure of the energy stored in "high energy foods or fuels" like carbohydrates, fats or gasoline. 
    •


We can define a system as being either open or closed. For example, the classroom is an open system where people and energy can move in and out of. A thermos is a fairly good representation of a closes system where energy can not either leave or enter. We can represent whether energy moves into or out of a system with an energy flow diagram. Energy can move in or out of a system by essentially three ways. It can be lost or gained by heating (Q), working (W) or radiating (R).
Now we can put together energy bar graphs and energy flow diagrams. Lets take the example a stationary soccer ball being kicked horizontally. If we define the system as the soccer, we can see that energy enters the system by work..

Work

Work is one way to transfer of energy. We can calculate the work done on an object by multiplying the applied force by the distance over which the force is applied.

W = F * d

F = force (Newtons)       

d = distance (meters)       

W = work (Newton*meters)       

1 Joule = 1 Newton*meter

We should note that:

  • work is a scalar quantity and therefore has only magnitude. There is no direction associated with work or energy.
  • the force acting on the object needs to be in the same direction as the object moves
    • . Forces applied at an angle need to be resolved into perpendicular components, one of which acts along the direction that the object moves.
  • work is only done if there is a force exerted and there is movement of the object.
  • the force responsible for the work can act in the same or opposite direction as the motion of the object
    • . The motor exerts a force on the car and does work. The brakes on the car exert a force in the opposite direction of the car's movement and also do work.

Representing Energy

If we temporarily throw away the equation for work, we have the opportunity to understand what work actually is. When you apply a force and move an object you are actually transferring energy stored in your muscle to the object. Depending on how the force is applied, you may be giving energy to or taking energy from either the potential "account" or the kinetic "account". The chemical potential energy in your muscle tissue is transferred to the object. At the end of the task, your muscle has slightly less energy than before whereas the object has slightly more energy. Work is simply a transfer of energy from one body to another.
We can calculate work graphically. A graph of Force vs. distance can be integrated to find the work done or the energy transferred. Integrating a graph means simply taking the area under the graph.

Calculating Energy

Potential Energy

  • Gravitational Potential Energy
    •  - the energy due to gravity of an object at some height above a baseline. A ball at the top of an incline has gravitational potential energy as does water at the top of a waterfalls. The equation for gravitational potential energy is:

Epg = mgh

m = mass (kg)                            

 g = gravitational field intensity (9.8 N/kg)
h = height above a baseline (m)                     

Epg = gravitational potential energy (J)

 

  • Elastic Potential Energy
    • - the energy in a compressed or stretched elastic object like a rubber band. For a spring or rubber band the formula for elastic potential energy is

Epel = kx2
        2

k = spring constant (N/m)       

x = displacement from equilibrium position (m)       

Epel = elastic potential energy (J)


Kinetic Energy

Kinetic energy can be pictured at both a microscopic and macroscopic level. Large objects like planets, people, bowling balls and mosquitos that are moving have "macroscopic" kinetic energy. Movement at the molecular level such as vibration of molecules is considered "microscopic" kinetic energy. While we can "see" large objects moving, we cannot see motion at the molecular level. We can however feel the kinetic energy of molecules moving. Molecules with a higher kinetic have a higher temperature than the same molecules with lower kinetic energy. The formula for calculating kinetic energy at any level is:

Ek = mv2
          2

m = mass (kg)                               

v = speed (m/s)                               

Ek = kinetic energy (J)


Conservation of Energy

In any system, the total amount of energy remains the same. This is the law of conservation of energy. Although no energy can be created or destroyed, energy can be transformed from one kind to another. Some examples:

A bow with an arrow has work done on it so that the bow has elastic potential energy. When the string of the bow is released and the elastic potential energy decreases to zero. As this happens, the arrow accelerates, which results in an increase in kinetic energy. If we start from when the bow has energy in the elastic account, we see that the energy is moved to the kinetic account and then to the gravitational potential account.


A closer look at the situation reveals that:

            DEk + DEpel = 0           or               |DEk| = |DEpel|
 

  • A ball is thrown straight up into the air. As the ball goes up it slows down, decreasing its kinetic energy. As the ball's elevation increases, its potential energy increases. On the way down the exact opposite thing is happening.

Examining the potential and kinetic energies reveals that:

            DEk + DEpg = 0           or               |DEk| = |DEpg|


Collisions

In any interaction between two objects, energy is conserved. However there are two distinct types of collisions. They are:

Elastic - the kinetic energy is conserved. The sum of the kinetic energies after the collision is equal to the initial kinetic energy of the system. Elastic collisions take place between objects that don't "give" when they collide. An example might be the collision between two billiard balls, or the two marbles from our second conservation of momentum experiment.

Inelastic - although the total energy is conserved, the sum of the kinetic energies after the collision is less than the initial kinetic energy of the system. Inelastic collisions take place between objects that "give", like balls of clay, cars or the car and dart from our first conservation of momentum experiment.


Power

Power is the rate at which work is done, energy is consumed or energy is generated.

P = W / t  = E / t

W = work (J)        E = energy (J)        t = time (s)        P = power (Joules / s)        1 Watt = 1 Joule / s

As we saw in the lab on Human Power Output, one can do the same amount of work but have quite different power outputs, depending on the time over which the task is completed. Electric companies supply us with energy, not power. The rate at which you use the energy is power. The electric company bills you per kilowatt * hour, which is a unit of energy (power * time).

Some Interesting Links About:

Work and Conservation Of Energy: http://library.thinkquest.org/16600/intermediate/energy.shtml

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