physics and astronomy outreach program at the university of british columbia physics and astronomy...
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Physics and Astronomy Outreach Program at the University of British ColumbiaPhysics and Astronomy Outreach Program at the University of British Columbia
Lecture Notes
Animals
Falling Cats
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Physics and Astronomy Outreach Program at the University of British ColumbiaPhysics and Astronomy Outreach Program at the University of British Columbia
• Physics: Develop concept of air drag and investigate how it affects free fall and results in a terminal velocity.
• Biology: To understand how air drag partially explains why cats sustain less damages after a free fall than a human.
Falling CatsGoals
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Physics and Astronomy Outreach Program at the University of British ColumbiaPhysics and Astronomy Outreach Program at the University of British Columbia
• Physics: Air resistance determines a terminal velocity which depends on cross-sectional area and mass.
• Biology: Cats have a different cross-sectional area and mass than humans.
Falling CatsBig Ideas
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Physics and Astronomy Outreach Program at the University of British ColumbiaPhysics and Astronomy Outreach Program at the University of British Columbia
• A drag force exists opposite to the motion due to air resistance
Falling CatsDrag
2
2
1AvCD D
A
v
= cross-sectional area
= density of air = 1.29 kg/m3
= speed
DC = drag coefficient 0.5
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Physics and Astronomy Outreach Program at the University of British ColumbiaPhysics and Astronomy Outreach Program at the University of British Columbia
• A falling object experiences the force of gravity and drag.
Falling CatsDrag
2
4
1AvD
mgFg
2
4
1AvmgFnet
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Physics and Astronomy Outreach Program at the University of British ColumbiaPhysics and Astronomy Outreach Program at the University of British Columbia
• Terminal velocity is reached when
Falling CatsTerminal Velocity
2
4
1AvD
mgFg
Fnet mg1
4Av term
2
0 mg 14
Av term2
A
mgvterm
4
0netF
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Physics and Astronomy Outreach Program at the University of British ColumbiaPhysics and Astronomy Outreach Program at the University of British Columbia
Falling CatsCalculation
m/s35)1.0)(29.1(
)8.9)(1.4)(4(4
A
mgvcatterm
kg1.4m22 m1.0m)1.0)(2.0( A
• For a cat falling flat:
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Physics and Astronomy Outreach Program at the University of British ColumbiaPhysics and Astronomy Outreach Program at the University of British Columbia
• For a human falling flat:
Falling CatsCalculation
m/s56)64.0)(29.1(
)8.9)(65)(4(4
A
mgvhumanterm
kg65m22 m64.0m)6.1)(4.0( A
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Physics and Astronomy Outreach Program at the University of British ColumbiaPhysics and Astronomy Outreach Program at the University of British Columbia
Falling CatsComparison
m/s56humantermv<m/s35cat
termv
• Cats hit the ground at a lower velocity,
• The anatomy of a cat having four legs allows them to lengthen the deceleration time during impact compared to a human
t
vmmaFimpact
catimpactF < human
impactF