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Physics I 95.141 LECTURE 14 10/25/10

This lecture covers problems related to the conservation of energy, including determining the spring constant and calculating energy values for various scenarios. It also discusses the concepts of friction, work-energy, gravitational potential energy, escape velocity, and power.

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Physics I 95.141 LECTURE 14 10/25/10

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  1. Physics I95.141LECTURE 1410/25/10

  2. Conservation of Energy Problem

  3. Conservation of Energy Problem (a) What is the spring constant of Martin’s tighty-whiteys? Δy=5m M=40kg

  4. Conservation of Energy Problem (b) What is Martin’s energy before the cougar lets go? Δy=5m θ=37° y=0 M=40kg

  5. Conservation of Energy Problem (c) What is Martin’s speed when he is launched? Δy=5m θ=37° y=0 M=40kg

  6. Conservation of Energy Problem (d) How far does he travel? vo=5.88m/s θ=37° Δy=5m y=0

  7. Administrative Notes • Exam II Monday, November 1, 9:00-9:50 am, OH150 • Exam Review Session • Thursday, OH218, 6:30-9:30 pm • Exam will cover • Ch. 5: Using Newton’s Laws, Friction, Uniform Circular motion • Ch. 6: Universal Law of Gravitation, Kepler’s Laws • Ch. 7: Work & Energy • Ch. 8: Conservation of Energy

  8. Conservation of Energy • In our previous lecture, we talked about the conservation of mechanical energy. • For a system acted on by conservative forces, the mechanical energy of the system (E=U+K) is constant, it is a conserved quantity. • In this case, all of our Forces are conservative, and our Energy consists of potential and kinetic energy.

  9. Examples • Mass sliding in valley • Mass tied to spring

  10. Example (Perfect World) • Mass, starting from rest, sliding in valley 1 3 2 h=20m

  11. Example (Real World) • Mass, starting from rest, sliding in valley 1 3 2 h=20m h=10m

  12. Where does the Energy go? • Clearly, in the previous example, mechanical energy is not conserved • Does this mean Energy is not conserved? • If friction acts on the object, then conservation of mechanical energy no longer holds…. • But does the energy just disappear? • No, it is converted into heat! Thermal Energy

  13. Law of Energy Conservation (New and Improved!!) • The total energy is neither increased nor decreased in any process. Energy can be transformed from one form to another, and transferred from one object to another, but the total amount remains the same.

  14. Friction • Let’s take our previous example: 1 3 2 h=20m h=10m

  15. Example • Say we slide a block down the plane shown below (θ=30º). The block starts with vo=6m/s. • A) If there is no Friction, what should the speed of the block be at point 2? 1 h=10m 2

  16. Example • Say we slide a block down the plane shown below (θ=30º). The block starts with vo=6m/s. • B) The block reaches point 2 with v2=10m/s. What is the change in thermal energy? 1 h=10m 2

  17. Example • -(change in thermal energy)=Wfr • C) What is μk? 1 h=10m 2

  18. Using Work-Energy • Can approach this problem from Work-Energy perspective • Net work done on mass = change in kinetic energy

  19. Work-Energy vs Energy Conservation • When do we use W-E, E-C? • Consider spring-mass on frictionless surface • If mass is our system W-E • External forces are acting • If spring-mass is system E-C • Energy conservation (all forces are internal)

  20. Gravitational Potential Energy • We have so far written the change in gravitational potential energy as ΔU = mgΔy. • Near the surface of the Earth, this is a good approximation. • However, remember, the exact definition for the change in gravitational potential energy is: • We know that Fg changes as a function of distance!

  21. Exact Gravitational Potential

  22. Exact Gravitational Potential

  23. Conservation of Energy (new and improved) • We can now write the expression for conservation of mechanical energy with our new, more precise, gravitational potential energy

  24. Escape Velocity • We are used to thinking that an object shot up from the Earth’s surface will return to Earth. • Is this always the case? • Say I shoot a rocket with

  25. Escape Velocity • What is the lowest speed you can launch a rocket and have it never come back? • This is called the “escape velocity”

  26. Power • Power • The rate at which work is done • The work done divided by the time it takes to do the work. • When an object performs work on another, Energy is transferred (think spring-mass system). Because of this, we can also think of Power as the rate at which energy is transformed.

  27. Example • How much power does it take a 50kg runner to run up a 5m high hill in 20s? • What about in 10s?

  28. Video Example

  29. Video Example • How much Thermal Energy is generated in reentry? • What is the average power generated in reentry?

  30. Solve for Energies • Initial Mech. Energy • Final Mech. Energy • Power

  31. Example • Hydropower: power from water • Size of a hydropower facility determined by power generated • US gets 80,000 MW of power from hydroelectric facilities • 7% of US power supply • 19% of Global Power http://ga.water.usgs.gov/edu/wuhy.html http://www1.eere.energy.gov

  32. Hoover Dam • Maximum Capacity: ~2GW • Height: 221.4m • What is the water flow required to generate the max capacity for Hoover Dam, if turbines are 60% efficient and no dissipative forces? • Solve for flow of 1kg/s

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