“Drivers’ Ed.” Physics Interesting examples from the Alabama Driver Manual Albert A. Gapud...

“Drivers’ Ed.” Physics

Interesting examples from the Alabama Driver Manual

Albert A. GapudUniversity of South Alabama

gapud@southalabama.edu

AAPT-Alabama Meeting

Apr 5 2014

Issues:

1. Using a seat belt

2. Reducing speed when turning

3. Blind spots

4. Stopping distance

5. Following distance

Seat belt• Page 31: Alabama safety belt and child restraint laws

Newton’s Law of Inertia!

Can hurt you…– Consider: If your car hits a wall at 40 mph, you will go

through your windshield at 40 mph.– You keep moving even if the car does not

… unless you make yourself a part of the car.– Also explains why:

• We don’t put things on the dashboard

Seat belt• Page 31: Alabama safety belt and child restraint laws

Newton’s Law of Inertia!

Can help you…!– How seat belt locks up!– Clutch lever snaps when belt is jerked– Weighted pendulum tilts when accelerated

Reducing speed when turning• Page 22: Reduce speed before making turns.• Centripetal force is required!

– Fc = mv2/R. Reducing v : Required Fc reduced more rapidly.– Usually provided by: static friction.

• Static friction: required for rolling• Coefficient, μs :

– rubber on dry concrete : about 0.8– rubber on wet concrete : about 0.3, less than half!

• Maximum friction = μs N = μs x weight = μs x (1600x 10 N)

• = mv2/R. So max

Example: 90 degree intersection turn: curb radius:

local streets: R = 15 ft = 4.6 m : max v : dry = 6.1 m/s = 14 mph, wet = 3.7 m/s = 8

mph

arterial streets: R = 35 ft = 10.7 m: max v : dry = 9.3 m/s = 21 mph , wet = 5.7 m/s =

13 mph

sm

Rv 16000

Mirrors and blind spots• Page 65: Check “blind spot” before changing lanes.• Geometric optics: law of reflection, ray trace

Mirrors and blind spots• Page 65: Check “blind spot” before changing lanes.• Geometric optics: law of reflection, ray trace

Blind area on either side due to:

Limited field of view of mirrors

(m.1 and m.2 angled inward)

Mirrors and blind spots• Page 65: Check “blind spot” before changing lanes.• Geometric optics: law of reflection, ray trace

Blind area on either side due to:

Limited view of mirrors

(m.1 and m.2 angled outward)

Stopping / following distance• Page 38: eye to brain to foot to wheel to road.• Stopping distance: static target (e.g., debris)

– Student exercise? Find reaction time that was used.• tr = 0.74 s

– Student exercise? Find the acceleration (assume constant).• a = -19.4 ft/s2

– Issue with significant digits??

Stopping / following distance• Page 37: avoiding rear end collisions

• Comparison: One c.l. per 10 mph vs. 2-sec rules:One c.l. per 10 mph equivalent to: “1.36-sec rule”

2-sec rule equivalent to: “1.47 c.l. per 10 mph”

Stopping / following distance• Page 37: avoiding rear end collisions

• How well do these help avoid rear end collisions?Graphed x(t). x1 = x2 means collision.

Other assumptions: same acceleration (deceleration) for the two cars, one shifted by the reaction time.

Stopping / following distance• Rules for following distance: comparison

– How do these help, in a typical situation?

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.00

2

4

6

8

10

12

14

16

18

20

22black = your carred = car in front

tr = 0.74 s

1cl/10mph = 1.36 sec

d

ista

nce

, in

ca

r le

ng

ths

time (s)

initial = 55 mphreaction time = 0.74 s

acceleration = 19.6 ft/s2

1 car length = 20 ft

2sec = 1.47 cl/10mph

Stopping / following distance• Rules for following distance: comparison

– How do these help, in a typical situation?

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.00

2

4

6

8

10

12

14

16

18

20

22black = your carred = car in front

tr = 0.74 s

+ 2.5 cl

1cl/10mph = 1.36 sec

d

ista

nce

, in

ca

r le

ng

ths

time (s)

initial = 55 mphreaction time = 0.74 s

acceleration = 19.6 ft/s2

1 car length = 20 ft

2sec = 1.47 cl/10mph

+ 5 cl

Separation at stop = d – votr (ft)

or D – (vo/20)tr (cl)

Stopping / following distance• Rules for following distance: comparison

– How do these help, in a typical situation?

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.00

2

4

6

8

10

12

14

16

18

20

22black = your carred = car in front

0.54 cl/10mph

tr = 0.74 s

+ 0 cl+ 1 cl+ 2.5 cl

1cl/10mph = 1.36 sec

1sec

d

ista

nce

, in

ca

r le

ng

ths

time (s)

initial = 55 mphreaction time = 0.74 s

acceleration = 19.6 ft/s2

1 car length = 20 ft

2sec = 1.47 cl/10mph

+ 5 cl

Separation at stop = d – votr (ft)

or D – (vo/20)tr (cl)

Further Reading: “Car physics”The Isaac Newton School of Driving:

Physics & Your Carby Barry Parker: Professor Emeritus of Physics,

Idaho State University and son of a car mechanic

Mainly a good source of conceptual examples from all fields of physics– Driving, Engines, Electrical system, Brakes,

Suspension & Transmission, Aerodynamics, Collisions

– Racing

– Traffic and Chaos

– Future technologies

(hybrid, fuel cell)

Further Reading: “Car physics”Fast Car Physicsby Chuck Edmondson: Professor of Physics, US

Naval Academy, racing enthusiast

More quantitative, detailed treatment, with ultimate goal of fast-car racing: Possible source of student projects?– Finding shift points, shifting properly

– Drag force, gear ratios

– Rounding curves efficiently

– Tires and load transfer

– Steering and suspension

– Future/green technologies

Final notes• Many other possible topics• Goal: Show physics in our daily life• Driver’s ed still fresh w/ HS students• “Car physics”: entry point for HS students?

gapud@southalabama.edu

Spare slides

Stopping / following distance• Rules for following distance: comparison

– How do these help, in a typical situation?

Separation at stop = d – votr (ft)

or D – (vo/20)tr (cl)

Following rule up to t = 0

0 2 4 6 8 10 12 14 16 180

10

20

30

40

50

60

70

80

900.54 cl/10mph 1cl/10mph = 1.36 sec

2sec = 1.47 cl/10mph

black = your carred = car in front

spe

ed

, in

ft/s

distance, in car lengths

initial = 55 mphreaction time = 0.74 s

acceleration = 19.4 ft/s2

1 car length = 20 ft

Here, condition is:

x2 (v=0) > x1 (v=0)