The Nature of Energy The Nature of Energy

The Nature of Energy

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

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

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

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

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

Kinetic Energy (K) l Energy l. K of a moving object. = ½ mv 2

Kinetic Energy

Kinetic Energy

Kinetic Energy l What is the kinetic energy of a 1500. -kg vehicle moving at 20. 0 m/s? l. K = ½ mv 2 l K = ½ (1500. kg)(20. 0 m/s)2 l K = ½ (1500. kg)(400. m 2/s 2) l K = 3. 00 x 105 J

Kinetic Energy l. 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? l First convert grams l 11. 2 g = 0. 0112 kg l. K to kilograms: = ½ mv 2 l 3840 J = ½ (0. 0112 kg)v 2 l 686 000 m 2/s 2 = v 2 l v = 828 m/s

Gravitational Potential Energy l Ug – Energy stored by an object because of its position in a gravitational field. l Ug = mgh lm = mass (kg) l g = gravity (m/s 2) l h = height (m) l Must always be measured relative to some point.

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

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

Mechanical Energy l. 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) l In the absence of drag, its K upon reaching the ground = its starting Ug. l Ug = mgh = (2. 00 kg)(9. 81 m/s 2)(50. 0 m) l Ug = 981 J l K = 981 J

Mechanical Energy l. 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) l. K = 981 J l 981 J = ½ (2. 00 kg)v 2 l 981 J = (1. 00 kg)v 2 l 981 m 2/s 2 = v 2 l v = 31. 3 m/s

Mechanical Energy l 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).

Mechanical Energy l 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/s 2)(77. 7 m) l GPE = 3. 81 x 107 J l Ug = 38. 1 million Joules

Mechanical Energy l 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 mv 2 l KE = ½ (5000. kg)(38. 0 m/s)2 l KE = 3. 61 x 107 J l Ug = 38. 1 million Joules K = 36. 1 million Joules

Mechanical Energy l How much of the car’s Mech. Energy was converted to other forms in the first drop? l l 3. 81 x 107 J – 3. 61 x 107 J = 2. 0 x 106 J What kinds of energy might the mechanical energy have been converted to? Ug = 38. 1 million Joules K = 36. 1 million Joules

Mechanical Energy l Imagine a 50. 0 -kg crate perched on shelf 2. 0 meters above the ground. l Now imagine the same crate on the same shelf, except now it’s on the Moon. l Does the crate have more, the same, or less Ug on the Moon than it has on Earth? has less because g is smaller on the Moon than it is on Earth. l It

Elastic Potential Energy l Ue = energy stored by an object when it is deformed. l Most l Ue common example: springs = ½ kx 2 lk = spring constant (N/m) l x = stretch (m)

For You Calculus People l Recall that Fspring = kx. l If f(x) = ½ kx 2, then f’(x) = kx l 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. l Also, the potential energy is the integral of a force-vs-stretch graph.

Elastic Potential Energy F x k = Ue = ½ kx 2

Elastic Potential Energy l 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? l Fs = kx l Fs = (50. 0 N/m)(0. 250 m) = 12. 5 N l Ue = ½ kx 2 l Ue = ½ (50. 0 N/m)(0. 250 m)2 = 1. 56 J