Transcript Slide 1

Animals
Falling Cats
Lecture Notes
Physics and Astronomy Outreach Program at the University of British Columbia
Goals
Falling Cats
• 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.
Physics and Astronomy Outreach Program at the University of British Columbia
Big Ideas
Falling Cats
• Physics: Air resistance determines a
terminal velocity which depends on
cross-sectional area and mass.
• Biology: Cats have a different crosssectional area and mass than
humans.
Physics and Astronomy Outreach Program at the University of British Columbia
Drag
Falling Cats
• A drag force exists opposite to the
motion due to air resistance
 1
2
D   C D Av
2
 = density of air = 1.29 kg/m3
C D = drag coefficient  0.5
A = cross-sectional area
v = speed
Physics and Astronomy Outreach Program at the University of British Columbia
Drag
Falling Cats
• A falling object experiences the force
of gravity and drag.
1
D  Av 2
4
Fg  mg
1
Fnet   mg  Av 2
4
Physics and Astronomy Outreach Program at the University of British Columbia
Terminal Velocity
Falling Cats
• Terminal velocity is reached when
1
2
Fnet  m g Avterm
4
1
2
0  m g Avterm
4

4mg
vterm 
A
Fnet  0
1
D  Av 2
4
Fg  mg
Physics and Astronomy Outreach Program at the University of British Columbia
Calculation
Falling Cats
• For a cat falling flat:
m  4.1 kg
2
A  (0.2)(0.1) m  0.1 m
cat
vterm

2
4mg
(4)(4.1)(9.8)

 35 m/s
A
(1.29)(0.1)
Physics and Astronomy Outreach Program at the University of British Columbia
Calculation
Falling Cats
• For a human falling flat:
m  65 kg
A  (0.4)(1.6) m2  0.64 m2
human
vterm

4mg
(4)(65)(9.8)

 56 m/s
A
(1.29)(0.64)
Physics and Astronomy Outreach Program at the University of British Columbia
Comparison
Falling Cats
v
Fimpact  ma  m
t
• Cats hit the ground at a lower velocity,
cat
vterm
 35 m/s
human
< vterm
 56 m/s
• The anatomy of a cat having four legs allows
them to lengthen the deceleration time
during impact compared to a human
cat
Fimpact
<
human
Fimpact
Physics and Astronomy Outreach Program at the University of British Columbia