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Potential Energy And Conservative Forces

# Potential Energy And Conservative Forces. Two General Forces Conservative Non Conservative

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Potential EnergyAnd Conservative Forces

Two General ForcesConservative

Non Conservative

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.

What is Potential EnergyPotential energy is the energy

stored in an object.

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 EnergyThe gravitational potential

energy isPE = m g h

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.

Work and PEWork equals the change in

Potential Energy

W = mghf - mghi

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?

To Be Turned In Before You LeaveA student has six textbooks, each

with a thickness of 4.0 cm and a weight of 30 N. What is the minimum work the student would have to do to place all the books in a single vertical stack, starting with all the books on the surface of the table.