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Conservative ForcesA force is conservative if the
work it does on an object moving between two points is the same no matter the path the object takes between the points.
Conservative ForcesVisual Example:
◦Think of a diver climbing to the top of a 10 meter diving platform.
◦The diver must do work against gravity in order to climb to the top of the platform.
◦Once at the top, however, he can recover the work – as kinetic energy – by taking the dive.
Conservative ForcesVisual Example Cont:
◦His speed just before hitting the water will give him a kinetic energy equal to the work that he did against gravity when he climbed to the top of the platform.
Non-Conservative ForcesA non-conservative force is
generally dissipative. This release usually becomes heat or sound.
Work done against a non-conservative force cannot easily be recovered.
FrictionFriction is a non-conservative
force.
Energy is lost to friction in the form of heat and sound.
GravityGravity is a conservative force.
Think of a swimmer diving off a diving board and another sliding down a frictionless slide of the same height.
The work done by gravity on both swimmers is the same.
Conservative Force & Potential Energy
Conservative forces have another useful property: The work they do can be recast as potential energy.
Potential energy is a quantity that depends only on the beginning and end point of a path. Not the path taken.
Gravitational Potential Energy
A hammer driving a nail into a wall does work and has kinetic energy.
Gravitational Potential Energy
If I were holding a hammer in my hand, it would have potential energy. Because it has the “Potential” to fall from my hand and hit a nail, driving it into the floor.
Gravitational Potential Energy
PE = m g h
PE – Potential Energym – Massg – Acceleration due to gravityh – the height of the object
Gravitational Potential EnergyPotential energy has units of
Joules.
PE = m g h kg (m/s2) m kg m2/s2
Which is a Joule
Gravitational Potential EnergyWhen dealing with problems
involving gravitational potential energy, it is important to choose a position at which to set energy equal to zero.
Gravitational Potential EnergyThis choice is completely
arbitrary because the important quantity is the difference in potential energy, and this difference will be the same regardless of the choice of zero level.
However, once this position is chosen, it must be fixed for the entire problem.
ExampleRichard wants to know how much
potential energy his cat has when it climbs to the top of the tree near his house. The tree is 15 meters high and the cat has a mass of 5 kilograms. How much potential energy does the cat have?
ExampleA baby carriage is sitting at the
top of a hill that is 41 m high. The carriage with the baby weighs 9 N. How much Potential Energy does the carriage have?
You Try:How much more potential energy
does a 1.0 kg hammer have when it is on a shelf 1.2 m high than when it is on a shelf 0.90 m high?
Six identical books, 4.0 cm thick and each with a mass of 0.80 kg, lie individually on a flat table. How much work would be needed to stack the books one on top of the other?