Teaching About Energy

1. Teaching About Energy Transparencies

2. 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.

3. Activity 1 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?

4. Activity 1 “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

5. Activity 2 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.

6. Activity 2 “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 mv2/2. • mv2/2 is called Kinetic Energy (Energy of Motion). • Decrease of gravitational potential energy = increase of kinetic energy.

7. Activity 3 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.

8. Activity 3 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 ky2/2, where y = displacement from equilibrium.

9. Activity 3 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)ky2 = (1/2)k(y′+ mg/k)2 = (1/2)ky′2 + mgy′+ (1/2)m2g2/k. • Thus, the quadratic dependence on displacement about equilibrium point (y = 0 or y′= -mg/k) includes both elastic and gravitational potential energy.

10. Activity 4 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.

11. Activity 4 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.

12. Activity 5 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.

13. Activity 6 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.

14. Activity 6 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.

15. Activity 7 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 30oC. • 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?

16. Activity 8 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/m2)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.

17. Activity 8 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