Making a Nine Square A Nine Square is a matching game that requires matches on the edges of 9 tiles that fit into a 3 by 3 grid. The information on adjacent edges should match up. To prepare for your Nine Square , being by listing the matches below. Create 18 distinct matches. There may be twoor more entries in the Match Column for each Term/idea/equation/image. Term/idea/equation/image Matches Potential Energy Gravitational *Ep Elastic. * EEL. *EG Kinetic Energy Gravitational Potential Energy Elastic Potential Energy Law of Conservation of Energy Zero Maximum Mechanical Energy Term/idea/equation/image Matches Joule Unit for Energy * Newton-meter ‘k’ Factor in EEL formula Spring coefficient quadruples EKMAX

Energy 60 ME = KE + PE Potential energy (PE) is the energy Energy is an important topic with scientific, political and social implications. The energy needs of modern society are growing. In science, Energy can be studied from many perspectives: Our study of Energy begins with the basics: Potential energy (PE) is the energy stored by an object due its position. Gravitational potential energy (Egrav) is the stored energy due to the vertical position of an object within Earth's gravitational field. Elastic potential energy (EEL) is the stored energy due to the position of an object effected by an object that deforms (like a spring or a rubber band). Energy definition: the ability (or capacity) to do work. Energy unit: JOULES Energy is a scalar quantity. Mechanical energy is in two forms: Kinetic Energy Potential Energy the energy of motion the energy of position ME = KE + PE Mechanical Energy of a system is the sum of the kinetic and potential energy. Kinetic energy (KE) is defined as the energy possessed by an object due to its motion. An object must be moving to possess kinetic energy. The amount of kinetic energy (KE) possessed by a moving object is dependent upon mass and speed. 60

Mechanical energy: Potential Energy Potential energy (PE) is the energy stored by an object due position. There are several forms of potential energy. Nuclear potential energy is the potential energy of the particles positioned inside an atomic nucleus. These particles are bound together by the strong nuclear force. Magnetic and electrical potential energies also store energy based on the position of electric charges and magnetic fields. Gravitational potential energy (Egrav) is the stored energy due to the vertical position of an object within Earth's gravitational field. Formula: EGRAV = mgh Where “m” is the object’s mass, “h” is the height and “g” is the strength of the gravitational field. A familiar story exists about Isaac Newton being struck on the head by an apple. If the apple was 2 meters above the ground and its mass was 0.5 kg, what was the apple’s Gravitational potential energy? G: m = 0.5 kg, h = 2 m, g = 9.8 m/s/s U: EGRAV E: EGRAV = mgh S: EGRAV = (o.5kg) (2 m) (9.8 m/s/s) S: The apple’s gravitational potential energy was 9.8 joules. The food stores Chemical potential energy (ECHEM). The position of atoms in molecules stores energy in molecular bonds. When those bonds are broken, energy is released. Batteries also store energy as Chemical potential energy (ECHEM). Elastic potential energy (EEL). Is due to the position of a spring or elastic band. When it is deformed (stretched or compressed), energy is stored. Formula: EEL = ½ k x2 Where “k” is the stiffness of the spring and “x” is the change in the spring or elastic band’s length. When mass changes by a factor, EGRAV changes by the same factor. See page 11 to review using formulas for predictions When height changes by a factor, EGRAV changes by the same factor. 61

Mechanical energy: Kinetic Energy Kinetic energy (KE) is defined as the energy possessed by an object due to its motion. Temperature is due to the kinetic energy of the molecules in a substance. When temperature increases, the molecules move faster. Similarly, a decrease in temperature will mean the molecules move more slowly relative to each other. So, temperature is one measure of kinetic energy. An object must be moving to possess kinetic energy. The amount of kinetic energy (KE) possessed by a moving object is dependent upon mass and speed. Formula: EK= ½ m v2 Where “m” is the mass of the object and “v” is the object’s velocity. Examples: Determine the Kinetic energy of a 60. kg man moving at 3.0 m/s. G: m =60. kg, v = 3.0 m/s U: EK E: EK= ½ m v2 S: EK = ½ (60. kg) (3.0 m/s)2 S: The man’s kinetic energy is 270 joules. a 0.0003032 kg bullet moving at 1256.8 m/s. G: m =0.0003032kg, v = 1256.8 m/s S: EK = ½ (0.0003032kg) (1256.8 m/s)2 S: The bullet’s kinetic energy is 239.6 joules. When mass changes by a factor, EK changes by the same factor. See page 11 to review using formulas for predictions When velocity changes by a factor, EK changes by the factor squared. 62

The Law of Conservation of Energy The Law of Conservation of Energy states that energy cannot be created or destroyed; it simply changes form. The Law of Conservation of Energy is helpful in analyzing the flow of energy in many systems. In the food chain, energy is dissipated as each organism provides nourishment for the next one on the chain. The energy is not lost. It is converted to tissue, heat or waste. In mechanical systems, energy is transformed to accomplish a task. When mechanical systems ‘waste’ energy, the energy that is ‘lost’ is not really lost at all. The ‘wasted’ energy which may be due to friction, vibration or sound is considered EDISS since it is energy that does not contribute to the task the mechanical system is intended to perform. Consider the closed system at the left. In a closed system, energy does not flow in or out. If the clay had 40 J of EGRAV before it was dropped, there would be 40 J of energy later but not all of it would be EGRAV. It could be EK (when it is moving), EEL (when it compresses the spring) or a combination. BIOLOGY Consider the closed system at the right. Remember  In a closed system, energy does not flow in or out. If the clay had 40 J of EGRAV before it was dropped, there would be 40 J of energy after it hit the ground. However, the kinds of energy in the system at the end are kinds that cannot be easily recovered: sound and heat. When energy changes to a type of energy that we cannot recover or use, this is called Dissipated energy (EDISS). Dissipated Energy is not ‘gone’; it has changed to a form we cannot recover and use. 63

Energy Transformations & The Law of Conservation of Energy The Law of Conservation of Energy states that energy cannot be created or destroyed; it simply changes form. For the example below, the coaster is frictionless so no energy will be dissipated due to friction. The roller coaster below shows how the gravitational potential energy of the car at A is converted to kinetic energy as the car reaches B. When the car rolls downhill from A to B (EGRAV decreases), it speeds up (EK increases). As the coaster rolls uphill from B to C, the coaster slows down (EK decreases) as it moves upward (EGRAV increases). At A: Car stopped at the highest point EGRAV = 25,000 Joules EK = 0 Joules hA = 50. m Car stopped at the highest point EGRAV = 2500 Joules EK = 0 Joules At C: Car slowing down as it moves up hill EGRAV = 20,000 Joules EK = 5,000 Joules A C Finding the velocity at B: G: EK at B = EGRAV at A EK at B = 25,000 Joules mcoaster = 50 kg U: VB (velocity at B) E: EK = ½ m v2 S: 25,000 J = ½ (50kg) v2 25,000 J = (25kg) v2 1,000 J/kg = v2 v = 32 m/s S: The coaster is moving at 32 m/s at point B. At B: Car moving at the lowest point EGRAV = 0 Joules EK = 25,000 Joules hC= 40. m mcoaster = 50. kg g = 10 m/s/s hB = 0.0 m B h = 0 m h = 0 m 64 h = 0 m

How WORK affects Energy When work changes EK By doing work stop a moving object, the kinetic energy of the object is reduced. The brakes do work on the car to slow it down. The force from the brakes that slows the car is called a non-conservative force since the energy is transferred to a form that cannot be recovered. The energy is not ‘lost’. The original kinetic energy is transformed to dissipated energy(EDISS) Energy: the ability (or capacity) to do work. Work: the transfer of energy Net Force Based on the definitions, it is clear that Work and Energy are closely related. The best way to understand this relationship is through examples. When work changes EGRAV By doing work against gravity to lift an object, more energy is stored in it. The weight lifter does work against gravity on the dumbbell that she has raised to shoulder height. She has stored energy in the dumbbell by increasing its height. Since the force to raise the dumbbell transferred to become energy stored due to its higher position, the lifting force is called a conservative force. Work Energy Principle: WNC = (ΔKE)+(ΔPE) so WNC = EDISS If an object falls, it’s EGRAV is transformed to EK as it falls. If the air resistance is negligible, then as EGRAV decreases EK will increase by the same amount. In this case, the object’s weight (Fg) is the force that makes the object fall. In this case, Fg is a conservative force since all energy is converted to EK. Putting it together: BUT. If there is air resistance, not all of the EGRAV will change to EK. In that case, the force from air resistance will be a non-conservative force that will convert some energy to EDISS. 65