Energy

1. Energy Gravitational & Elastic Potential Energy

2. Assessment Statements • Outline what is meant by change in gravitational potential energy. • List the different forms of potential energy and describe examples of work’s relation to potential energy.

3. Work = Energy • Energy is the capacity to do work • Potential Energy: Stored capacity to do work • Gravitational potential energy (perched on cliff) • Elastic potential energy (like in compressed spring) • Chemical potential energy (stored in bonds) • Nuclear potential energy (in nuclear bonds) Energy can be converted between types

4. Gravitational Potential Energy • Potential energy that is dependent on height is called gravitational potential energy.

5. Elastic Potential Energy • Energy that is stored due to being stretched or compressed is called elastic potential energy.

6. Gravitational Potential Energy • A waterfall, a suspension bridge, and a falling snowflake all have gravitational potential energy.

7. Gravitational Potential Energy • If you stand on a 3 meter diving board, you have 3 times the EP, than you had on a 1 meter diving board.

8. Gravitational Potential Energy • “The bigger they are the harder they fall” is not just a saying. It’s true. • Objects with more mass have greater Gravitational PE.

9. Gravitational Potential Energy The energy that a mass has due to its position relative to the surface of the Earth. The height is measured relative to an arbitrary zero point. Unit: kg(m/s2)m = Nm = J (Joule)

10. Gravitational Potential Energy • Notes • An object's gravitational potential energy is not a "fixed" quantity but rather a "relative" quantity. The gravitational potential energy of a body is always measured "relative" to some convenient baseline, such as the Earth's surface; however, all convenient reference levels are equally valid. For example, if you are standing with a 1 kilogram object one meter above the carpet on the ninth story of a tall building, and calculate its gravitational potential energy with respect to the floor and also calculate its gravitational potential energy with respect to the basement floor, you will get two very different values, both are equally valid. • The expression mgh, for the gravitational potential energy of an object, is nothing more than an expression of the work required to raise an object of mass m kilograms to a height of h meters.

11. Example: Ramp • Ramp 10 m long and 1 m high • Push 100 kg all the way up ramp • Would require mg = 980 N (220 lb) of force to lift directly (brute strength) • Work done is (980 N)(1 m) = 980 N·m in direct lift • Extend over 10 m, and only 98 N (22 lb) is needed • Something we can actually provide • Excludes frictional forces/losses 1 m

12. Force from ramp Net Force Component into ramp h Weight = mg W= Fd =mgh W=Fd W=Fd W Work on piano = change in energy of piano = same!

13. Use of Ramp Straight Lift W = 2000N • Superman is lifting a piano (weight 2000N) straight up onto a 1 m high platform. How much work is he doing? • You are pushing the same piano along a 10 m long (frictionless) ramp onto the 1 m platform. How much work are you doing? • How much force do you apply to the piano? • How much energy did the piano gain by being lifted • Where did that energy come from?

14. Elastic Potential Energy • The energy that an object has due to its amount of stretch or compression. • The amount of stretch or compression is from its natural equilibrium position. • Unit: N/mm2 = Nm = J (Joule)

15. Springs - Restoring Force • When you pull on (stretch) a spring, it pulls back (top picture) • When you push on (compress) a spring, it pushes back (bottom) • Thus springs present a restoring force: • x is the displacement (in meters) • k is the “spring constant” in Newtons per meter (N/m) • the negative sign means opposite to the direction of displacement

16. Stored energy in a Spring Do work on a spring to compress it or expand it from equilibrium. Hooke’s law Work = Potential Energy – therefore the spring now has stored potential energy due to how much the spring has changed in length (Δx).

17. Elastic Potential Energy Person does work = FsΔx in pulling the box and stretching the spring.

18. Elastic Potential Energy The amount of work or potential energy can be determined from a graph of Force vs. stretch of a spring by taking the area under the graph. Since F = kx for a spring it shows that Ep = ½ kx2. DPE=-FDx F Dx

19. Gravitational Potential Energy • You are 1.80 m tall. • A 0.1 kg apple, which is hanging 1 m above your head, drops on you. • How much potential energy does it loose? • 0 J • 0.49 J • 0.98 J • 4.9 J 1 m

20. In a hydroelectric power plant one ton of water is passing through the turbines per second. The water is falling 100 meters before hitting the turbines. • Assuming 100% efficiency, how much electrical power can the turbines generate?

21. What is net work? mgh. What is net work? mgh. Example (cont): Problem does not change if we introduce a horizontal component of velocity.

22. Energy Gravitational & Elastic Potential Energy

24. Potential Energy

25. Conservation of Energy • PE + KE = constant

26. Potential Energy = F x distance = (Mass x g) x height Potential Energy

27. Energy Storage in Spring • Applied force is kx (reaction from spring is kx) • starts at zero when x = 0 • slowly ramps up as you push • Work is force times distance • Let’s say we want to move spring a total distance of x • would naively think W = kx2 • but force starts out small (not full kx right away) • works out that W = ½kx2 • A compressed (or stretched) spring and mass combination will oscillate • exchanges kinetic energy for potential energy of spring