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Teaching About Energy Transparencies

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Activity 1 Roller coaster brainstorming: Factors to consider Go up slowly and up a gentle incline to enhance anticipation. Go up fast to provide thrills from the start. Make first incline steep to reduce land area needed. Make first incline gentle to reduce force required to pull cars up the hill. Make first hill high enough for the roller coaster to reach the end. Keep safety in mind at all times.

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Designing a roller coaster: How to reach the top of the first hill? Measure the force needed to pull a cart up each slope. Measure the distance the cart travels each slope. How are the forces and distances related? Activity 1

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“Up the Hill” Results: How are the forces and distances related? Force times distance for each slope is the same. We call the product of force and distance “work”: Work = Force x distance Work done to lift an object directly upward through distance H is said to increase gravitational potential energy: mgH = increase in gravitational potential energy Activity 1

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What happens when the coaster rolls down the hill? How does the decrease in gravitational potential energy depend on speed? Measure the speed of the cart at different heights above the table. Calculate the decrease in gravitational potential energy at each point. Make a graph of decrease in gravitational potential energy vs. speed. Activity 2

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“Down the Hill” Results: How does the decrease in gravitational potential energy depend on speed? Decrease in gravitational potential energy varies as the square of the speed. The graph of decrease in gravitational potential energy vs. square of speed is a straight line through the origin with a slope of half the mass. Decrease of gravitational potential energy = increase in mv 2 /2. mv 2 /2 is called Kinetic Energy (Energy of Motion). Decrease of gravitational potential energy = increase of kinetic energy. Activity 2

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Elastic Potential Energy: How does the potential energy of a spring depend on how much it is stretched? Use Hooke’s Law to measure the spring constant (k). Allow the spring (with mass m) to oscillate above a motion detector. Calculate the KE of the mass at each time. Consider the maximum KE to be the total energy of the oscillating mass (PE = 0 at this point). Subtract the KE from E (total energy) at each point to determine PE. Consider the position of the mass to represent zero displacement when KE = maximum. Subtract this value from positions at other times to determine the spring’s displacement. Make a graph of PE vs. spring displacement. Activity 3

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Elastic Potential Energy Results: How does the potential energy of a spring depend on how much it is stretched? Potential energy varies as the square of the displacement of the spring. The graph of potential energy vs. square of displacement is a straight line through the origin with a slope of half the spring constant (k). (Even if the straight line doesn’t pass through the origin, the y-intercept represents a constant, which is arbitrary for defining PE.) The expression for elastic potential energy is ky 2 /2, where y = displacement from equilibrium. Activity 3

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Elastic Potential Energy Results: (continued) Since the equilibrium point for a mass m on the spring is mg/k lower than that of the bottom of the spring in a zero gravity environment, the expression for PE relative to the equilibrium point in zero gravity (y′ = y – mg/k) is (1/2)ky 2 = (1/2)k(y′ + mg/k) 2 = (1/2)ky′ 2 + mgy′ + (1/2)m 2 g 2 /k. Thus, the quadratic dependence on displacement about equilibrium point (y = 0 or y′ = -mg/k) includes both elastic and gravitational potential energy. Activity 3

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GPE to Thermal Energy: How is temperature increase related to decrease of gravitational potential energy? Insert temperature probe into container of metal shot. Record initial temperature. Invert container 100 times and remeasure temperature. Repeat this four more times (at intervals of 100 inversions for a total of 500). Make a graph of temperature vs. number of inversions. What relationship does this indicate between the temperature increase and the number of inversions? Determine the temperature increase for one inversion. Activity 4

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GPE to Thermal Energy: (continued) Calculate the gravitational potential energy decrease for one inversion. Divide this by the mass of the metal shot to calculate the gravitational potential energy decrease per unit mass for a single inversion. If the decrease in gravitational potential energy is considered to equal the increase in thermal energy, what is the thermal energy increase per unit mass for each inversion? Divide the thermal energy increase per unit mass for one inversion by the temperature increase for one inversion. This is known as the specific heat. Activity 4

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Power of a Student: At what rate can you do work while climbing stairs? Walk or run up the stairs and measure the time for each trial. Determine the work done by calculating the change in gravitational potential energy. Find the power, or rate of doing work, by dividing the work done by the time. Convert to kJ/min and Cal/min. Activity 5

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Electrical to Thermal Energy: What variables determine the temperature increase of water? First, heat 200 g water for different amounts of time (< 3 minutes). Make a graph of temperature change vs. energy input. Heat different amounts of water (< 225 g) for the same amount of time (2 minutes). Make a graph of temperature change vs. mass of water. Activity 6

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Electrical to Thermal Energy: How does temperature change depend on energy input and mass? The graph of temperature increase vs. energy input is linear. The graph of temperature increase vs. mass shows an inverse relationship. Therefore ΔT = constant x energy input/m, or energy input = (new) constant x m x ΔT The (new) constant is known as the specific heat. Activity 6

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Energy from Chemical Fuels: How do you measure the energy released by burning a given amount of a chemical fuel? Measure the mass of a candle both before and after using it to heat 100 g water so that its temperature increases by about 30 o C. Calculate the increased thermal energy of the water. Calculate the amount of thermal energy input to the water, and divide this by the mass of the candle that burned. This will give the number of kJ per gram. Compare this with the accepted value of 47 kJ/g. How can you explain differences between your result and the accepted value? Activity 7

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Efficiency of Energy Conversion: What percentage of the electrical energy input to a light bulb is converted into light energy? Measure the intensity of light (in W/m 2 )at different distances from a 40-W light bulb. Multiply the intensity of light by the area of a sphere equal to the distance from the light bulb to find the rate at which light is emitted from the bulb (“light power”). Calculate the ratio Light Power/Electrical Power (40 W) to find the efficiency with which the light bulb converts electrical energy to light. Activity 8

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Energy is neither produced nor used: it is transformed! Energy “sources”: “more useful” forms of energy, to be transformed to meet our needs Energy “production”: transformation of “more useful” forms of energy into a form that meets our needs Energy “use”: transformation of energy in a form that met our needs into “less useful” forms Energy “conservation”: “using” the least amount of a “more useful” form of energy to accomplish a given task Activity 8

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