Answer 1:
If the force of the egg striking the floor or
ground is greater than the force that the egg
shell can exert on itself to keep its shape, the
egg will break. Some eggs are stronger than
others, depending on how thick the shell is.
Certain chemicals, such as the pesticide DDT, are
known to cause egg shells to be thinner and easier
to break. I don't know what is "normal" for
different species of birds.

Answer 3:
An egg, and anything else for that matter, will
break ("fail") when the force applied is greater
than that required to cause a loss of
loadbearing capacity. Often this
corresponds to the formation and growth of cracks.
(Hopefully this is intuitive  once the material
separates into two pieces (cracks), load cannot be
transferred from one to the other.) Eggshells fail
in a brittle manner (more or less), so the force
to cause the formation of the crack is larger than
the force to keep it growing: once a crack
starts, it won't stop even if the load is
removed. (There is
much more happening at the
atomic level, but I think it is beyond the scope
of this question.) For objects of the same
material, size matters  a small object can't hold
up the same force as a large one. So to compare
loads across size scales, force F is
normalized by
the area it acts on A to give a quantity called
stress, σ=F/A. In these terms, a material
(such as
eggshell) will break when the stress exceeds the
failure stress (sometimes called strength) of the
material. Note  it is still force that causes
failure; rewriting it as stress is a way to
compare the relevant forces at different sizes.
The force required to break the egg can be
estimated using a bit of physics.
If an egg breaks by dropping it from a height
of 4 ft, the force applied to the egg must be
greater than what the eggshell can withstand. In
this case, the force is from the collision of the
egg with the ground. For collisions, forces are
governed by conservation of a quantity called
momentum p. The momentum of an object with
mass m is given by mass*velocity, m*v. In a
collision, the force F on an object of mass m can
be calculated by manipulating Newton's 2nd
Law, F=m*a, into a slightly different form.
Acceleration a is defined as the change in
velocity dv that occurs over some time
t. So, Newton's 2nd Law can be rewritten as
F=m*(dv/t), or F*t=m*dv.
This second form is called the
ImpulseMomentum Change equation, because
F*t is a quantity called impulse, and m*dv
is the change in momentum (as follows from m*v
being momentum). To reach a specific number for F,
values for each of these terms need to be given.
The mass of an egg m is around 50 g (assuming a
mediumlarge egg in the USA), and the time of the
collision t must be estimated, which I'll take as
0.01 seconds. The change in velocity dv is the
difference between the velocities before and after
impact. After is easy  0 m/s. The velocity must
be estimated, which can be done with more physics.
The energy of the falling egg just before it
hits the ground is all kinetic energy (
simple,
more
detail ), given by
W = K E = 0.5*m*v^{2}
(m = mass of egg, v =
velocity). But, assuming the egg was dropped from
a standstill (i.e., had no velocity at 4 ft above
the ground), all of this this kinetic energy used
to be entirely potential energy (
simple, more
details ). The (gravitational) potential
energy of
the egg at 4 ft from the ground is given by
P E = m*g*h (g = acceleration due to gravity, h =
distance above ground). Putting it all together
and rearranging a bit produces
v = (2*g*h)^{0.5}. Now, using known values
of g = 9.81 m/s^{2} and h = 4 ft = 1.22 m, v
= 4.89 m/s.
Putting all of it together into the equation
F=m*(dv/t), the force to break the egg is 24.5 N,
or around 5.5 lbs.

Answer 4:
When you drop the egg, it accelerates due to
gravity. This means that the force of
gravity pulling on the egg will cause the egg to
go faster. This means that the egg
will gain momentum (which is a fancy word
for speed) as it falls. When the egg
hits the ground after falling the 4 feet, the
momentum very suddenly goes to zero
since the egg stops moving. This causes the egg to
experience a very large force
from the ground. This large force causes the
delicate egg shell to break. Why
does the sudden change in momentum cause a large
force? Well momentum and
force are related by a quantity that physicists
call impulse!
Basically if something
experiences a very sudden change in momentum, that
corresponds to a large
force. If something experiences a gradual change
in momentum, the force is
smaller. Think of how if you are in a car and it
stops quickly you might feel like
there is a big force pulling on your seat belt. On
the other hand, if the car stops
slowly you might not feel too much. It is the same
idea!
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