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**Chapter 7 Conservation of Energy**

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**Recap – Work & Energy The total work done on a particle**

is equal to the change in its kinetic energy

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Potential Energy The total work done on an object equals the change in its kinetic energy But the total work done on a system of objects may or may not change its total kinetic energy. The energy may be stored as potential energy.

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**Potential Energy – A Spring**

Both forces do work on the spring. But the kinetic energy of the spring is unchanged. The energy is stored as potential energy

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**Conservative Forces If the ski lift takes you up a displacement h, the**

work done on you, by gravity, is –mgh. But when you ski downhill the work done by gravity is +mgh, independent of the path you take

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**Conservative Forces The work done on a particle by**

a conservative force is independent of the path taken between any two points

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**Potential-Energy Function**

If a force is conservative, then we can define a potential-energy function as the negative of the work done on the particle

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**Potential-Energy Function**

potential-energy function associated with gravity (taking +y to be up) The value of U0 = U(y0) can be set to any convenient value

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**Potential-Energy Function of a Spring**

By convention, one chooses U0 =U(0) = 0

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**Force & Potential-Energy Function**

In 1-D, given the potential energy function associated with a force one can compute the latter using: Example:

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**7-1 Conservation of Energy**

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**Conservation of Energy**

Energy can be neither created nor destroyed Closed System Open System

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**Conservation of Mechanical Energy**

If the forces acting are conservative then the mechanical energy is conserved

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**Example 7-3 (1) How high does the block go? Initial mechanical energy**

of system Final mechanical energy of system

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**Example 7-3 (2) Forces are conservative, therefore,**

mechanical energy is conserved Height reached

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**Example 7-4 (1) How far does the mass drop? Initial mech. energy**

Final mech. energy

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Example 7-4 (2) Final mech. energy = Initial mech. energy

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Example 7-4 (3) Solve for d Since d ≠ 0

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**Example 7-4 (4) Note is equal to loss in gravitational potential**

energy

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**Conservation of Energy & Kinetic Friction**

Non-conservative forces, such as kinetic friction, cause mechanical energy to be transformed into other forms of energy, such as thermal energy.

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**Work-Energy Theorem Work done, on a system, by external**

forces is equal to the change in energy of the system The energy in a system can be distributed in many different ways

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**Example 7-11 (1) Find speed of blocks after spring is**

released. Consider spring & blocks as system. Write down initial energy. Write down final energy. Subtract initial from final

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**Example 7-11 (2) Initial Energy Take potential energy of system**

to be zero initially Kinetic energy of system is zero initially

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**Example 7-11 (3) Final Energy Kinetic and potential energies of**

system have changed

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**Example 7-11 (4) Subtract initial energy from final energy**

But since no external forces act, Wext = 0, so Ef = Ei

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Example (5) And the answer is… Try to derive this.

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**E = mc2 E = mc2 In a brief paper in 1905 Albert Einstein wrote**

down the most famous equation in science E = mc2

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**Sun’s Power Output Power 1 Watt = 1 Joule/second**

100 Watt light bulb = 100 Joules/second Sun’s power output 3.826 x 1026 Watts

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**Sun’s Power Output Mass to Energy**

Kg/s = x 1026 Watts / (3 x 108 m/s)2 The Sun destroys mass at ~ 4 billion kg / s

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Problems To go…

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Ch. 7, Problem 19

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Ch. 7, Problem 29

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Ch. 7, Problem 74

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