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Teaching About Energy. Transparencies. 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.

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### Teaching About Energy

Transparencies

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.

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

“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 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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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?

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.

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

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