# Chapter 8 - Potential Energy and Conservation of Energy Conservative vs. Non-conservative Forces Definition of Potential Energy Conservation Of Mechanical

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• Chapter 8 - Potential Energy and Conservation of EnergyConservative vs. Non-conservative ForcesDefinition of Potential EnergyConservation Of Mechanical Energy Determining Potential EnergyGravitational near the surface of the earthGravitational anywhere - escape velocityElasticDetermining the Force From Potential Energy FunctionsWork Done by Non-conservative ForcesPower

• PowerRate at which work is done.

Average Power

Instantaneous Power

• UnitsPower[M-L2/T3]Watt (W)J/s N-m/sHP =550 ft-lb/s

Physical Quantity

Dimension Symbol

SI MKS

SI CGS

US Customary

Length

[L]

m

cm

ft

Mass

[M]

kg

g

slug

Time

[T]

sec

sec

sec

Acceleration

[L/T2]

m/s2

cm/s2

ft/s2

Force

[M-L/T2]

newton (N)

kg-m/s2

Dyne

g-cm/s2

pound (lb)

slug- ft/s2

• Conservative vs. Non-conservativeConservative - A force is said to be conservative if the work done by the force acting on a object moving between two points is independent of the path the particle takes between the points.Non-conservative - depends on the path

• Example: Gravity near the surface of the earth

• Alternative definitionA force is conservative if the net work done by the force on an object moving around any closed path is zero.Gravity is a conservative force!

• A nonconservative forceFriction is a nonconservative force!

• Potential EnergyEnergy associated with the position or configuration of a system.The change in potential energy associated with a particular conservative force is the negative of the work done by that force.

• Examples:Gravity

Springs

• Differential formOne dimension:Three dimensions:

• Potential Energy SummaryPotential energy is only associated with conservative forces. It is the negative of the work done by the conservative force.The zero point of potential energy is arbitrary and should be chosen where it is most convienient.Potential energy is not something a body has by itself, but rather is associated with the interaction of two or more objects.

• Conservation of Mechanical EnergyWork-Energy PrincipleDefinition of Potential Energy

• Problem solving strategy

• Who is going faster at the bottom?Assume no frictionAssume both have the same speed pushing off at the top

• Problem 1A Block of mass m is released from rest and slides down a frictionless track of height h above a table. At the bottom of the track, where the surface is horizontal, the block strikes and sticks to a light spring.Find the maximum distance the spring is compressed.m = 2 kg, h = 1 m, k = 490 N/m

• Problem 2A ball (mass m) on a string (length L) is released from rest with the string horizontal. What is the speed when it reaches its lowest point?What if the string was not horizontal, instead being released from some angle q?

• Energy conservation with dissipative forcesTotal energy is neither increased or decreased in any process. Energy can be transformed from one form to another, and transferred from one body to another, but the total amount remains constant.

• Example 3A roller coaster with mass of 1000 kg starts at a height of 40 m and is found to reach a height of only 25 m before coming to a stop. It traveled a distance of 400 m. Estimate the average friction force.Is the friction force constant?

• Problem 7A 2 kg block is attached to a light spring of force constant 500 N/m. The block is pulled 5 cm to the right and of equilibrium. How much work is required to move the block?If released from rest, find the speed of the block as it passes back through the equilibrium position ifthe horizontal surface is frictionless.the coefficient of friction is 0.35.

• ExampleA ball of mass 4.64 kg is taken to a position 3 moon radii above the surface of the moon where it is dropped from rest. What is the speed of the ball as it just starts to make contact with the surface of the moon? Mm = 7.35 x 1022 kgRm = 1.74 x 106 m

• Gravitational potential energy again

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