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The Nature of Energy

The Nature of Energy. The Nature of Energy. Energy The ability to cause change. Scalar quantity. Does NOT depend on direction. Unit: kg*m 2 /s 2 = N*m = Joule (J) All energy can be broadly classified as potential or kinetic . Potential energy – energy in storage.

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The Nature of Energy

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  1. The Nature of Energy

  2. The Nature of Energy • Energy • The ability to cause change. • Scalar quantity. • Does NOT depend on direction. • Unit: kg*m2/s2 • = N*m • = Joule (J) • All energy can be broadly classified as potential or kinetic. • Potential energy – energy in storage. • Kinetic energy – energy in motion.

  3. Forms of Energy • Energy can change from one form to another. • Remember “I SCREAM” • I = Internal • S = Sound • C = Chemical • R = Radiant • E = Electrical • A = Atomic • M = Mechanical

  4. Forms of Energy • Internal Energy • energy assoc. with particles in a substance. • temperature and phase are assoc. w/ internal energy. • Sound Energy • released when an object vibrates. • needs a medium in which to travel.

  5. Forms of Energy • Chemical Energy • Energy stored in chemical bonds. • Batteries, gasoline, and food all store chemical potential energy. • Radiant Energy • Energy carried by light. • Electrical Energy • Energy assoc. w/ the movement of electrons through a substance.

  6. Forms of Energy • Atomic Energy • Energy stored in the nucleus of an atom (nuclear energy). • Mechanical Energy • Kinetic = energy assoc. with a moving object. • Potential = energy assoc. with an object b/c of its position or deformation.

  7. Kinetic Energy (K) • Energy of a moving object. • K = ½ mv2

  8. Kinetic Energy

  9. Kinetic Energy

  10. Kinetic Energy • What is the kinetic energy of a 1500.-kg vehicle moving at 20.0 m/s? • K = ½ mv2 • K = ½ (1500. kg)(20.0 m/s)2 • K = ½ (1500. kg)(400. m2/s2) • K = 3.00x105 J

  11. Kinetic Energy • A .30-06 bullet has a mass of 11.2 grams and a kinetic energy of 3840 J. What is the speed of the bullet? • First convert grams to kilograms: • 11.2 g = 0.0112 kg • K = ½ mv2 • 3840 J = ½ (0.0112 kg)v2 • 686 000 m2/s2 = v2 • v = 828 m/s

  12. Gravitational Potential Energy • Ug – Energy stored by an object because of its position in a gravitational field. • Ug = mgh • m = mass (kg) • g = gravity (m/s2) • h = height (m) • Must always be measured relative to some point.

  13. Gravitational Potential Energy • As an object falls, Ug turns to K. • Ug + K = Mechanical Energy • In a world w/o friction, Mech. Energy is constant. • K + Ug = constant for all falling bodies • In the real world, friction robs moving objects of energy • Mech. Energy of a free-falling body in Earth’s atmosphere constantly diminishes.

  14. Ideal World Real World Ug,o K = 0 Ug,o K = 0 K = Ug,o K < UG,o Mechanical Energy

  15. Mechanical Energy • A 2.00-kg stone is dropped from a height of 50.0 meters. What is its velocity when it reaches the ground? (Ignore air resistance) • In the absence of drag, its K upon reaching the ground = its starting Ug. • Ug = mgh = (2.00 kg)(9.81 m/s2)(50.0 m) • Ug = 981 J • K = 981 J

  16. Mechanical Energy • A 2.00-kg stone is dropped from a height of 50.0 meters. What is its velocity when it reaches the ground? (Ignore air resistance) • K = 981 J • 981 J = ½ (2.00 kg)v2 • 981 J = (1.00 kg)v2 • 981 m2/s2 = v2 • v = 31.3 m/s

  17. Mechanical Energy • The Titan roller coaster at Six Flags Over Texas features a drop of 255 feet (77.7 meters) and has a top speed of 85 mph (38.0 m/s).

  18. Ug = 38.1 million Joules Mechanical Energy • If the mass of a roller coaster train is 5000. kg, what is the GPE of the train at the top of the first hill (relative to the bottom of the hill)? • GPE = mgh = (5000. kg)(9.81 m/s2)(77.7 m) • GPE = 3.81x107 J

  19. Ug = 38.1 million Joules K = 36.1 million Joules Mechanical Energy • The 5000.-kg train is moving at 38.0 m/s at the bottom of the first hill. What is the car’s KE? • KE = ½ mv2 • KE = ½ (5000. kg)(38.0 m/s)2 • KE = 3.61x107 J

  20. Ug = 38.1 million Joules K = 36.1 million Joules Mechanical Energy • How much of the car’s Mech. Energy was converted to other forms in the first drop? • 3.81x107 J – 3.61x107 J = 2.0x106 J • What kinds of energy might the mechanical energy have been converted to?

  21. Mechanical Energy • Imagine a 50.0-kg crate perched on shelf 2.0 meters above the ground. • Now imagine the same crate on the same shelf, except now it’s on the Moon. • Does the crate have more, the same, or less Ug on the Moon than it has on Earth? • It has less because g is smaller on the Moon than it is on Earth.

  22. Elastic Potential Energy • Ue = energy stored by an object when it is deformed. • Most common example: springs • Ue = ½ kx2 • k = spring constant (N/m) • x = stretch (m)

  23. For You Calculus People • Recall that Fspring = kx. • If f(x) = ½ kx2, then f’(x) = kx • In other words, the force needed to stretch a spring to a distance x is the first derivative of the potential energy stored in the spring when it is stretched to x. • Also, the potential energy is the integral of a force-vs-stretch graph.

  24. Elastic Potential Energy F = kx Ue = ½ kx2

  25. Elastic Potential Energy • How much force is required to stretch a 50.0-N/m spring 25.0 cm? How much potential energy is stored in the stretched spring? • Fs = kx • Fs = (50.0 N/m)(0.250 m) = 12.5 N • Ue = ½ kx2 • Ue = ½ (50.0 N/m)(0.250 m)2 = 1.56 J

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