Potential Energy and Conservation of Energy
coasterAni.gif (170430 bytes)


Previously Asked Questions

Q:     Explain the conservation of energy during free fall.

A:    The object is assumed to fall from a position of rest (v=0) at a high elevation h to a lower elevation.  At the highest elevation point (starting point) the object has a potential energy equal to mgh and a kinetic energy equal to 0.  As it falls, its potential energy decreases because the elevation h decreases, and its kinetic energy increases because its velocity increases (kinetic energy is given by KE = 1/2 mv2.)  The amount of potential energy lost during the fall is converted exactly into the kinetic energy acquired as the velocity increases.

Q:    What is the difference between a conservative and a nonconservative force?

A:    By definition, a conservative force is a force for which the work done on a closed path is equal to zero.   Examples of conservative forces are the gravitational, electrical, and magnetic forces.  Climbing a mountain from the bottom of the valley to the top and back means that no total work has been produced. The energy expended by the climber on the way up is regained, free of charge, from the work done by the force of gravity on the way back to the bottom of the valley. (Sorry all of you who get tired both ways :-<). 

An example of a nonconservative force is the force of friction.  It produces non-zero work even if the path is closed.  (Driving from home to work and back home means continuous work produced by the force of friction between the car and the road; this amount of work is performed at the expense of energy consumed by burning gasoline from the fuel tank.)

Q:    Consider a mountain with two positions in which a rock can rest, situated one at the top of the mountain and the second at a lower elevation.  a) How is the potential energy for a rock sitting at the top of the mountain determined?  b) How can the difference in potential energy be calculated for the object situated in the two mentioned positions?

mountain.jpg (5785 bytes)A:     a) The potential energy of an object is, by definition, the energy of position with respect to a given reference.  Without specifying the reference point the potential energy is meaningless.  So, if the reference level is chosen at the bottom of the valley, then the potential energy at the top of the mountain is mghA.   If the reference level is chosen at the intermediary mountain peak, then the potential energy at the top of the mountain is mghB.

 

 

b)    The difference in potential energy between points A and B is determined by the difference in altitudes between the two points:

UA - UB = mghA - mghB  = mg (hA - hB) = mg (delta.gif (839 bytes)h)

   In this case the elevation of either of the two mountain peaks with respect to the bottom of the valley (taken as reference) does not need to be known.  Only the difference (delta.gif (839 bytes)h) in altitudes between A and B is needed.

Q:    How is sea level determined?

A:     Although measuring the level of the sea sound like an easy thing to do it is very difficult because so many variables affect sea-levels.  Most measurements are made by tide gauges placed on piers.  They measure the height of the sea with respect to a nearby geodetic benchmark (a precisely know point on the globe) sometimes global positioning satellites (GPS), which remain at a known height above the earth, are used to determine the height of tides.  The tide gauges take into account various local conditions like weather and time of year.  They do not, however, take into account the compression of the sea floor caused by the weight of the water and they do not take into account the expanding/bulging of the earth.  These must be corrected for later.  There are many other variables which go into determining the precise height of the sea.

Visit Determining global sea level rise to learn more about sea-levels.

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References

Equations

Potential Energy
delta.gif (839 bytes)U = -delta.gif (839 bytes)W 8-6.gif (279 bytes)
Gravitational Potential Energy
delta.gif (839 bytes)U = mg ( yf - yi ) = mg delta.gif (839 bytes)y U = mgy
Elastic Potential Energy U(x) = onehalf.gif (67 bytes) k x2
Mechanical Energy
K2 + U2 = K1 + U1 delta.gif (839 bytes)E = delta.gif (839 bytes)K + delta.gif (839 bytes)U = 0
Potential Energy Curves
8-19.gif (240 bytes) K(x) = E - U(x)
Work by Nonconservative Forces
Wapp = delta.gif (839 bytes)K + delta.gif (839 bytes)U = delta.gif (839 bytes)E delta.gif (839 bytes)E = - fk d
Principle of Conservation of Energy 8-34.gif (753 bytes)

W = delta.gif (839 bytes)E total = delta.gif (839 bytes)K + delta.gif (839 bytes)U + delta.gif (839 bytes)Eint

Power 8-36.gif (166 bytes)
Instantaneous Power 8-37.gif (157 bytes)

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Mechanics List of Topics

Measurements Newton's Laws Potential Energy and Conservation of Energy Rotation of
Rigid Bodies
Elasticity
Vectors Forces and Fields Linear Momentum Angular Momentum Mechanical
Oscillations
Motion of Point-Mass Objects in One Dimension The Gravitational Field Collisions Torque Mechanical Waves
Motion of Point-Mass Objects in Two and Three Dimensions Kinetic Energy
and Work
Circular Motion of Point-Mass Objects Equilibrium Sound

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