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.
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?
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
US Fossil Fuel Use (1949-2001)
90
number of Quads/yr
80
70
60
Coal
50
Natural gas
40
Petroleum
30
Total fossil
20
10
0
1940
1950
1960
1970
1980
year
1990
2000
2010
US Renewable Energy Use (1949-2001)
number of Quads/yr
8
7
6
Conv. Hydro
5
Biomass
4
Geothermal
3
Solar
2
Total renewable
1
0
1940
1960
1980
year
2000
2020
Total US Energy Use (1949-2001)
number of Quads/yr
120
100
total fossil
80
nuclear
60
total renewable
40
total
20
0
1940
1960
1980
year
2000
2020