--------- #1301 - Can Bird Poop Break a Car Windshield?
- A lady had a cracked windshield and claimed a bird had done it. The car was parked. The bird poop over the cracked windshield was 4 inches in diameter. To break a car windshield you need in excess of 50 million Pascal of pressure. One Pascal of pressure is one Newton of force per square meter of area. Wait a minute I will do the math:
- Attachment - Likely Bird
- If the 4 inch circle of bird poop was 2 millimeters thick it would be a cylinder 4 inch diameter circle and 2 millimeters high.
- A 4 inch diameter is a 0.05 meter radius. (1 foot = .3048 meters. 0.33 feet = 0.1016 meter diameter, or, 0.051 meter radius, R = 0.051 m)
- The volume of a cylinder is = pi * h * R^2
-------------------- Volume = 3.14 * 2*10^-3 * ( 0.05)^2 meters^3
------------------- Volume = 1.62 * 10^-5 meters^3
- If the density of the bird poop is about the same as the density of water it would be about 1,000 kilograms / meter^3.
------------------- Density = mass / volume
------------------ Mass = Density * Volume
----------------- Mass = 1,000 kg/m^3 * 1.62 *10^-5 m^3
------------------ Mass = 0.0162 kilograms of bird poop hit the windshield.
- To determine how hard the mass of poop hit the windshield we need to know the velocity of the poop in flight. We do not know how high the bird was when it released the poop. But, if we assume the velocity became constant (terminal velocity) then the force of gravity was balanced with the opposing force of the air resistance, and, we can calculate the velocity.
- The force of the air resistance is a function of the density of the air, the cross sectional area of the poop, the drag coefficient of the shape of the poop and the velocity squared.
------------- The Force of the Air Resistance = ½ d * A * C * v^2
--------------- “d” = density of the air = 1.2 kilogram / meter^3
--------------- “A” = the cross sectional area of the sphere shaped poop.
--------------- “C” = the drag coefficient of a sphere which is 0.47.
- The poop was spherical in flight before it hit the windshield. This is important because the air resistance is a function of the cross-sectional area of the sphere. We calculated the volume of the poop and we know the formula for the volume of a sphere.
----------------------- Volume = 1.62 * 10^-5 meters^3
----------------------- Volume of a sphere = 4/3 * pi * r^3
----------------------- r^3 = 1.62*10^-5 * 3 /4 /pi
----------------------- r^3 = 0.387 * 10^-5 m^3
------------------------ r = 1.56*10^-3 m
----------------------- radius of the sphere of the poop = 0.00156 meters.
---------------------- Cross Sectional Area = A = pi*r^2
--------------------- A = 3.14 * 2.46*10^-4 m^2
--------------------- A = 7.74 * 10^-4 meters^2
--------------------- Force of Air Resistance = ½ d * A * C * v^2
---------------------- F air = ½ (1.2 kg / m^3) * (7.74*10^-4 m^2) * (0.47) * v^2
----------------------- F air = (2.18*10^-4) * (v^2) kg / m
- The other balancing force to achieve a constant velocity is the force of gravity:
-------------- The Force of gravity = mass * acceleration
------------------ F = m * a, or in this case m * g
----------------- Where “g” is the acceleration of gravity near the surface of the Earth, 32 feet per second per second, or 9.8 meters per second^2.
------------------ F g = 0.0162 kg * 9.8 m/sec^2
------------------ F g = 0.16 kg * m/sec^2
- OK, now we are ready to set the 2 forces equal to each other to determine the velocity of the poop when it hit the windshield.
------------------------- F air = F g = (2.15*10^-4) * v^2 kg / m = 0.16 kg * m/sec^2
-------------------- v^2 = 7.4 *10^4 m^2/sec^2
------------------- v = 27.2 m /sec
------------------ 1 m / sec = 2.237 miles / hour
------------------- v = 60.6 miles per hour
- Now we know how fast the poop hit the windshield. The energy with which it hit the windshield was the Kinetic Energy which = ½ * mass * velocity^2:
---------------------- KE = ½ * m * v^2
--------------------- KE = ½ * .0162 kg * (26.8 m/sec)^2
----------------------- KE = 5.8 kg * m^2 / sec^2
- Action = reaction. The energy is always “conserved” so the work done on the windshield must equal this Kinetic Energy. Energy is the ability to do work and Work is the force moving over a distance. Here we assume the distance the force works over is the radius of the poop as it is smashed against the windshield.
------------------------ Force * distance = KE
------------------------ Force * 0.0156 m = 5.8 kg * m^2 / sec^2
----------------------- Force = 372 kg * m / sec^2
--------------------- Force = 372 newtons
- The pressure the force exerts on the windshield is a function of the area of the collision. The amount of force changes over the duration of the collision. What we have calculated is the average force. The contact area also changes over the course of the collision. The radius of the poop expands from 0.00156 meters to 0.051 meters. We will assume the contact area at maximum force was at a radius of 0.01 meters.
-------------------------- Pressure = Force / Area
---------------------- Pressure = 372 newtons / pi *r^2
--------------------- Pressure = 372 newtons / 3.14 * (0.01m)^2
---------------------- Pressure = 1.18 million Pascal
- This pressure is way to low to smash the car windshield. If we assume the peak force was 3 times larger than the average force this only gets us up to:
-------------------- Pressure = 3.55 million Pascal.
- What if there was a small rock that was imbedded in the bird poop? The contact area could have been more concentrated to a radius of 0.001 meters.
--------------------- Pressure = 1116 newtons / pi * (0.001 m)^2
-------------------- Pressure = 355 million Pascal.
- That pressure would surely break the windshield that can normally withstand only 50 million Pascal. Of course, another explanation could be that there was a flaw in the windshield that would shatter under less pressure.
- If you got through this an remained conscious that is a good thing. Consciousness is that annoying time between naps. The best way to learn something you did not know is to teach someone who did not know it.
_______________________________________
Other physics reviews:
(1) #1183 - Mysteries for science students
(2) # 1074 Physics the way I learned it.
(3) # 738 The science of physics
(4) # 762 The trouble with physics
(5) #531 Joseph Henry - an American teacher
(6) #532 Robert Millican - a physics teacher
(7) #524 Physics keeps getting simpler.
(8) #534 The physics of a CD
(9) #559 The laws of motion
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707-536-3272, Thursday, September 22, 2011
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