The Nature of Energy

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

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

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

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

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

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

Kinetic Energy

What is the kinetic energy of a kg vehicle moving at 20.0 m/s? What is the kinetic energy of a kg vehicle moving at 20.0 m/s? K = ½ mv 2 K = ½ mv 2 K = ½ (1500. kg)(20.0 m/s) 2 K = ½ (1500. kg)(20.0 m/s) 2 K = ½ (1500. kg)(400. m 2 /s 2 ) K = ½ (1500. kg)(400. m 2 /s 2 ) K = 3.00x10 5 J K = 3.00x10 5 J

Kinetic Energy A bullet has a mass of 11.2 grams and a kinetic energy of 3840 J. What is the speed of the bullet? A 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: First convert grams to kilograms: 11.2 g = kg 11.2 g = kg K = ½ mv 2 K = ½ mv J = ½ ( kg)v J = ½ ( kg)v m 2 /s 2 = v m 2 /s 2 = v 2 v = 828 m/s v = 828 m/s

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

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

Mechanical Energy Ideal World U g,o K = 0 K = U g,o Real World U g,o K = 0 K < U G,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) 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 U g. In the absence of drag, its K upon reaching the ground = its starting U g. U g = mgh = (2.00 kg)(9.81 m/s 2 )(50.0 m) U g = mgh = (2.00 kg)(9.81 m/s 2 )(50.0 m) U g = 981 J U g = 981 J K = 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) 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 K = 981 J 981 J = ½ (2.00 kg)v J = ½ (2.00 kg)v J = (1.00 kg)v J = (1.00 kg)v m 2 /s 2 = v m 2 /s 2 = v 2 v = 31.3 m/s 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). 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 kg, what is the GPE of the train at the top of the first hill (relative to the bottom of the hill)? If the mass of a roller coaster train is 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) GPE = mgh = (5000. kg)(9.81 m/s 2 )(77.7 m) GPE = 3.81x10 7 J GPE = 3.81x10 7 J U g = 38.1 million Joules

Mechanical Energy The kg train is moving at 38.0 m/s at the bottom of the first hill. What is the car’s KE? The 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 KE = ½ mv 2 KE = ½ (5000. kg)(38.0 m/s) 2 KE = ½ (5000. kg)(38.0 m/s) 2 KE = 3.61x10 7 J KE = 3.61x10 7 J U g = 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? How much of the car’s Mech. Energy was converted to other forms in the first drop? 3.81x10 7 J – 3.61x10 7 J = 2.0x10 6 J 3.81x10 7 J – 3.61x10 7 J = 2.0x10 6 J What kinds of energy might the mechanical energy have been converted to? What kinds of energy might the mechanical energy have been converted to? U g = 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. 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. 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 U g on the Moon than it has on Earth? Does the crate have more, the same, or less U g on the Moon than it has on Earth? It has less because g is smaller on the Moon than it is on Earth. It has less because g is smaller on the Moon than it is on Earth.

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

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

Elastic Potential Energy F = kx U e = ½ kx 2

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? 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? F s = kx F s = kx F s = (50.0 N/m)(0.250 m) = 12.5 N F s = (50.0 N/m)(0.250 m) = 12.5 N U e = ½ kx 2 U e = ½ kx 2 U e = ½ (50.0 N/m)(0.250 m) 2 = 1.56 J U e = ½ (50.0 N/m)(0.250 m) 2 = 1.56 J