The work-energy theorem
Investigation 10B: Work and energy for launching a paper plane
Have you ever folded a paper airplane and
thrown it? Have you launched it with an
elastic band? A paper airplane and elastic
band form a system that provides insight
into the relationship between work and
energy. When the elastic band is pulled
back, it stores elastic potential energy.
When it is released, the elastic band does
work on the airplane to launch it. You will
compare the energy stored in the elastic
band to the kinetic energy of the launched
airplane.
Part 1: Measure work done to extend an
elastic band
1. Hold the elastic band between two
fingers while pulling on the band with
one end of a spring scale. Measure the
distance the band is stretched.
2. Measure the force required to stretch the elastic band four different distances. Tabulate your
results.
#1
#2
#3
#4
Force (N)
distance (m)
3. Make a line graph of force versus distance (on the next page). Calculate the work required to
stretch the elastic band using the area under the curve of your graph.
Questions
a. Why does the area under the curve of a force versus distance graph represent the work done to
stretch the band?
b. What is the total work done to stretch the elastic band for each distance you measured?
#1
#2
Force (N)
distance (m)
Work (J)
1
#3
#4
Delete this picture below and cut and paste your graph from Excel in the same space
c. What is the theoretical maximum velocity for the airplane if it is launched by stretching the
band the largest distance you measured?
v=
2Wnet
m
Part 2: Estimate the velocity of the launched airplane
The work done by the elastic band on the paper airplane is W = ΔEk = ½ mv2. To calculate the change
in kinetic energy of the paper airplane, its velocity must be measured or estimated.
1. Design a procedure to measure the airplane's initial velocity when it is launched.
What variables will you measure? What equipment and/or technology is appropriate?
2. Using your procedure, make the measurements and calculations needed to estimate the
airplane's velocity. Ask yourself if this answer is reasonable.
3. Calculate the efficiency of the rubber band system in launching the paper airplane. Do this by
comparing the stored elastic potential energy of the rubber band you derived in part 1 with the
initial kinetic energy of the airplane.
Questions
a. Describe your procedure to measure the plane's launch velocity.
b. In the investigative procedure you designed, what are the independent, dependent, and
controlled variables?
2
c. Calculate the airplane's experimental launch velocity by launching the plane horizontally from
a height of 1 meter. Measure the distance the plane traveled. The experimental launch
velocity will be the distance the plane traveled multiplied by 0.452 (s). Also calculate the
kinetic energy using the airplane's experimental launch velocity. Show your work.
𝐸𝑥𝑝𝑒𝑟𝑖𝑚𝑒𝑛𝑡𝑎𝑙 𝐿𝑎𝑢𝑛𝑐ℎ 𝑉𝑒𝑙𝑜𝑐𝑖𝑡𝑦 = 𝑑𝑖𝑠𝑡𝑎𝑛𝑐𝑒 𝑎𝑖𝑟𝑝𝑙𝑎𝑛𝑒 𝑡𝑟𝑎𝑣𝑒𝑙𝑒𝑑 ∗ 0.452
d. How efficient is the elastic band system? Explain the significance of the value you obtain.
Efficiency =
Ek
´100 0 0
W done
Applying new knowledge
𝑊𝑜𝑟𝑘 = ∆ 𝐾𝑖𝑛𝑒𝑡𝑖𝑐 𝐸𝑛𝑒𝑟𝑔𝑦
𝑊𝑜𝑟𝑘 = 𝐹𝑜𝑟𝑐𝑒 ∙ 𝑑𝑖𝑠𝑡𝑎𝑛𝑐𝑒
𝑊 = ∆𝐾𝐸
1
𝐾𝐸 = 2 𝑚𝑎𝑠𝑠 ∙ 𝑣𝑒𝑙𝑜𝑐𝑖𝑡𝑦 2
1
𝐹𝑑 = 2 𝑚𝑣 2
1. A 1500 kg car accelerates from rest to a speed of 25 m/s over a distance of 45 meters.
a. What is the change in kinetic energy of the car?
b. What is the net work done on the car?
c. What is the net force applied to the car?
2. A 1500 kg car traveling at 20 m/s skids to a stop. The force of friction between the tires and the
road is 12,000 N.
a. What is the change in kinetic energy of the car?
b. How far does the car skid?
3
Rubric
Part 1
Questions a
Part 1
Questions b
Graph
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Part 1
Questions c
Part 2
Questions c
Part 2
Questions d
Applying New
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Knowledge
1a
Applying New
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1b
Applying New
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1c
Applying New
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2a
Applying New
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2b