Notes

Some Cautions	Kinetic Energy	Potential Energy	Conservation of Mechanical Energy	Conservation of Energy Law
Work by a Constant Force	Work Energy Principle	Forces	Forms of Energy

Some Cautions

Throughout this chapter, you will encounter terms that have meanings in English that are different from their meanings in physics.

The words work, energy, and power have specific definitions in physics that are somewhat related to but definitely not the same as their meanings in everyday conversations.

For example, when you say you have worked really hard on your homework, you are speaking English and not physics.

It may seem confusing at first to say that no work is done in trying to push a stalled car that won't move or in holding a heavy box up in the air.

On the microscopic level, the cells in your muscles are contracting and expanding and therefore doing work, however, no net work is done on the car or the box.

A person holding a bag of groceries is another good example. How much work does he do holding the bag of groceries? None.

 

Work: By a Constant Force

 

†  When a force F is applied to an object, the work done on it, W, is given by

 

     W = Fdcosq      and is expressed in Nm or joules,

 

     where q is the angle between F and d, the displacement vector. This means that the work is defined as the product of the component of the force parallel to the displacement vector.

 

†  Note that the perpendicular component does no work

†  Friction

    ]  Opposes motion, so work done on the object by frictional forces will be negative.

    ]  This can be thought of as work done by the object rather than work done on the object – it

          results in a loss of energy for the object

 

 

Kinetic Energy

 

†  Kinetic energy

     ð Translational Kinetic Energy this chapter: KE = (1/2)mv²   Units are also joules 

     ð Rotational Kinetic Energy in chapter 8

†  Energy is a scalar; it represents the capacity to do work.

†  Kinetic energy refers to the energy associated with motion, an action (see above) which has the capacity to do work.

†  Translational kinetic energy of an object is given by KE = (1/2)mv²

†  Work-Energy Principle

    The net work on an object, W_net, is given by the objects change in kinetic energy

 

     W_net = DKE                       NOTE: If the body is deformed, then this does not apply - some energy goes into the deformation process...

 

†  The increase or decrease of a body’s KE depends on the sign of the work done on that body

     (see friction comments above)

 

Potential Energy

 

†  PE describes the forces on a body that are a function of its position with regard to other bodies.

†  Gravitational PE_G refers to the capacity of an object to do work based on the force of gravity acting

     on it and is given by

 

   PE_G = mgy where y is the height relative to some height where PE_G = 0

 

Springs

 

†  The change in a body’s potential energy is defined as the negative of the work done by gravity to move the body between the two points

†  A spring not at its normal length has potential energy when the force is removed.

†  The work of a spring is given by Hooke’s law or the spring equation

 

     Fs = - ks  

 

     where k is a constant depending on the spring and x is the displacement from its normal

     length

 

†  The elastic potential energy of a spring is given by

     (1/2)kx²

     

†  Robert Hooke: Contemporary of (in the shadows of...) Newton, Boyle, Huygens

     ð Biography: http://www.ucmp.berkeley.edu/history/hooke.html

     ð Hooke's Law: http://en.wikipedia.org/wiki/Hooke's_law

     ð Robert Hooke Bio and Picture

 

Forces: Conservative and Nonconservative

 

†  Conservative forces are forces for which the work done is independent of the path taken. It

     depends only upon the starting and finishing positions.

†  Nonconservative forces are forces for which the work done depends on the path taken.

†  http://www.ac.wwu.edu/~vawter/PhysicsNet/Topics/Energy/PEandForces.html

†  http://www.batesville.k12.in.us/physics/PhyNet/Mechanics/Energy/stored_energy.htm

 

Principle of Conservation of Mechanical Energy

 

†  Ideal Mechanical Process 

†  The mechanical energy is the sum of the kinetic and potential energies

†  When only conservative forces are acting on a system, the total mechanical energy is conserved.

 

    KE₁ + PE₁ = KE₂ + PE₂

 

†  When gravity (a conservative force) is the only force acting on a system

 

    (1/2)mv₁² + mgy₁ = (1/2)mv₂² + mgy²

 

†  When the only force involved comes from a massless spring (a conservative force)

 

     (1/2)mv₁² + (1/2)kx₁² = (1/2)mv₂² + (1/2)kx₂²

 

Forms of Energy

 

†  Three of the many different types of energy are listed below

     ]  Thermal (portions of chapters 13 through 15)

     ]  Electrical (portions of chapters 16 through 22)

     ]  Nuclear (portions of chapters 26 through 32)

†  All forms of energy are essentially kinetic or potential energy at microscopic or atomic level.

†  All forms of energy can be converted to others.

 

Conservation of Energy Law

 

The total energy remains constant during the transfer or transformation of energy involving both conservative and nonconservative forces.