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 cross sectional 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
D
1 2
C D Av
2 = density of air = 1.29 kg/m 3
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.
D
1 4
Av
2
F g
mg F net
mg
1 4
Av
2 Physics and Astronomy Outreach Program at the University of British Columbia
Terminal Velocity
Falling Cats • Terminal velocity is reached when
F net
0
mg
mg
4 1 1 4
Av
2
term
Av
2
term F net
0
D
1 4
Av
2
v term
4
mg
A F g
mg
Physics and Astronomy Outreach Program at the University of British Columbia
Calculation
Falling Cats • For a cat falling flat:
m
4 .
1 kg
A
( 0 .
2 )( 0 .
1 ) m 2 0 .
1 m 2
v cat term
4
mg
A
( 4 )( 4 .
1 )( 9 .
8 ) 35 m/s ( 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 ) m 2 0 .
64 m 2
v human term
4
mg
A
( 4 )( 65 )( 9 .
8 ) ( 1 .
29 )( 0 .
64 ) 56 m/s Physics and Astronomy Outreach Program at the University of British Columbia
•
Comparison
F impact
ma
m
v
t
Falling Cats Cats hit the ground at a lower velocity,
v cat term
35 m/s <
v human term
56 m/s • The anatomy of a cat having four legs allows them to lengthen the deceleration time during impact compared to a human
F cat impact
<
F human impact
Physics and Astronomy Outreach Program at the University of British Columbia