Physics and Astronomy Outreach Program at the University of British Columbia Physics and Astronomy Outreach Program at the University of British Columbia.

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

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

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

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

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

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

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:

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

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