Chapter 8: Conservation of Energy

potential energy belongs to a _____not a _____

system, not a single object alone.

h is defined as....

the elevation of the object above zero level, not just y= 0 leel

power is defined as...

the rate at which work is done •P=W/t

if heat is considered as a transfer of energy...

then the total energy is conserved in any process

1/2mv1^2 + mgy1 = 1/2 mv2^2 + mgy2 can be applied...

to any object moving WITHOUT friction under the action of gravity •constant force can't act perpendicular to the direction of motion

if you choose a system on which NO external forces do work then..

you need to apply conservation of energy to that system direclty

Potential energy is associated with a_____and a _____on one object is always exerted by some other object

• a force • a force

alternative definition of a conservative force

• a force is conservative if the NET WORK done by the force on an object moving around a CLOSED PATH is ZERO

the concept of potential energy cannot be defined and is meaningless for...

• a nonconservative force.

energy is a conserved quantity as long as....

• no nonconservative forces do work.

conservative system

• only conservative forces do work •energy transformed from kinetic to potential and vice versa

change in gravitational potential =

•-WG=mg(y2-y1)

nonconservative forces

•any work that they do depends on the path taken •ex. friction and a push or pull exerted by a person

What is physically important in any situation is the _______because that is what is related to the work done and it is ____that can be measured

•change in the potential energy •change in potential energy

force of gravity is what kind of force?

•conservative

the elastic force is....

•conservative

if the kinetic energy K increases, then the potential energy U must...

•decrease by an equivalent amount to compensate because: change in U= - change in K •this way the total K+ U remains constant.

when taking into account nonconservative forces such as friction, the mechanical energy...

•does not remain constant but DECREASES

if the forces are NOT constant, and or the path is not simple (which approach is better)

•energy

perhaps the most common example of potential energy is...

•gravitational potential energy. •ex. heavy brick held above the ground has potential energy because of its position relative to the earth. It has the ability to do work, for if it was released, it will fall to the ground due to the GRAVITATIONAL force.

principle of conservation of mechanical energy for conservative forces:

•if ONLY conservative forces are doing work, the total mechanical energy of a system neither increases nor decreases in any process. •t stays constant

for an object raised to a height y above the Earth's surface, the change in gravitational potential energy is....

•mgy

a conservative force can be a function only of....

•position and cannot depend on other variables like time or velocity

the work done by a conservative force is...

•recoverable - if positive work is done by an object on one part of a closed path, an EQUIVALENT amount of negative work will be done by the object on its RETURN

rocking allowed to fall due to earth's gravity

•rock starts from rest, all of the initial energy is potential energy •as rock falls, the potential energy mgy decreases, but the rock's kinetic energy increases to compensate •total mechanical energy at point 1= total mechanical energy at point 2. •just before the rock hits the ground, all of the initial potential energy will have been transformed into kinetic energy

In general, we define the change in potential energy associated with a particular conservative force as....

•the NEGATIVE WORK done by that force •only applicable for conservative forces for which the integral depends on the end points and not on the path taken. •does not apply to nonconservative forces

conservative force

•the WORK done by the force on an object moving from one point to another depends on the INITIAL and FINAL POSITIONS of the object and is INDEPENDENT of the particular path taken

If the roller-coaster car is subject to frictional forces, then the initial total energy of the car will be equal to...

•the car's kinetic energy plus the potential energy at an subsequent point along its path plus the amount of thermal energy produced in the process.

zero level is...

•the elevation at which the gravitational potential energy (mgh) is 0.

potential energy

•the energy associated with forces that depend on the position or configuration of objects relative to the surroundings. •energy possessed by a body by virtue of its position relative to others

total mechanical energy

•the sum of the kinetic energy plus the potential energy of the system at any moment •E=K+ U

whenever work is done, energy is being...

•transferred from one body to another so the power is the rate at which energy is transformed: P= dE/dt

unit for power

•watts= 1 J/s

if the forces involved are constant (which approach best)

•work and energy or Newton's laws

if you choose as your system a particle or rigid object on which external forces do work, then you can use the....

•work energy principle: the work done by the external forces on your object equals the change in its kinetic energy

potential energy ______exist for an isolated system

*DOES NOT

the potential energy of the system where x is the displacement of the spring from its unstretched length. If neither friction nor any other force is acting, conservation of mechanical energy tell us that

1/2mv1^2 + 1/2kx1^2 = 1/2 mv2^2 + 1/2kx2^2 •K+ U •for elastic PE only

energy conservation with dissipative forces equation

1/2mv1^2 + mgy1 = 1/2mv2^2 + mgy2 + Ffr(l)

the gravitational potential energy at any point a vertical height y above some reference point =

U grav= mgy

the potential energy of a spring compressed or stretched an amount x from equilibrium is...

Uelastic (x) = 1/2kx^2