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The Nature of Energy The Nature of Energy Energy The ability to cause change. Scalar quantity. Does Unit: NOT depend on direction. 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. 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 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. 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. 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. Kinetic Energy (K) Energy of a moving object. K = ½ mv2 Kinetic Energy Velocity = 5 m/s Kinetic Energy (J) 1400 1200 1000 800 600 400 200 0 0 20 40 60 Mass (kg) 80 100 Kinetic Energy Kinetic Energy (J) Mass = 10 kg 16000 14000 12000 10000 8000 6000 4000 2000 0 0 10 20 30 40 Velocity (m/s) 50 60 Kinetic Energy What is the kinetic energy of a 1500.-kg vehicle moving at 20.0 m/s? K = K = K = K = ½ mv2 ½ (1500. kg)(20.0 m/s)2 ½ (1500. kg)(400. m2/s2) 3.00x105 J 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 K g = 0.0112 kg = ½ mv2 3840 J = ½ (0.0112 kg)v2 686 000 m2/s2 = v2 v = 828 m/s 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. Gravitational Potential Energy As an object falls, Ug turns to K. Ug In a world w/o friction, Mech. Energy is constant. K + K = Mechanical Energy + 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. Mechanical Energy Ideal World Ug,o K=0 K = Ug,o Real World Ug,o K=0 K < UG,o 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 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 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). 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 Ug = 38.1 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 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? Ug = 38.1 million Joules K = 36.1 million Joules 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? has less because g is smaller on the Moon than it is on Earth. It 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) 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. Elastic Potential Energy k = 50 N/m Spring Force (N) 12 10 8 6 4 2 Ue = ½ kx2 0 0 5 10 Stretch (cm) 15 20 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