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EXTRACT
B.
For the table of contents of the
EXTRACT of the compendium.
Return to EXTRACT A
Part A: Static and dynamic mechanics.
Chapter A.2 The mechanics of an impact.
1. The impulse and the moving mass.
In an impact the items involved will change their
velocities dependent of their masses, their velocities when the
impact starts, their ability to absorb energy and the direction
of the forces acting on the items.
When a body m1 with a velocity
V01 strikes another body m2 with a velocity lower
than V01. Both bodies will be affected by the same impulse.
Both the force and the time the force acts towards the bodies
are equal, giving the bodies a change in their velocities as:
dV = F/m * t.
m = mass of the body
2. The laws of constancy of energy
and moving mass during an impact.
The Law of conservation of Energy:
An important law of physics to have in mind is:
| THE SUM OF ENERGY IS CONSTANT AND CAN ONLY BE TRANSFORMED INTO ANOTHER STATE OF ENERGY, EITHER KINETIC OR THROUGH DEFORMATION TO END AS AN INCREASE OF TEMPERATURE OF THE BODY ITSELF AND/OR IT'S SURROUNDINGS.
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The law of the conservation of the moving masses
during an impact:
| THE TOTAL QUANTITY OF THE MOMENTUM (Sum of product (m * v) ) IS THE SAME BEFORE AND AFTER THE IMPACT.
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3. The two phases of the impact
Phase A:
This phase lasts from the impact starts until
the bodies have reached their maximum deformation. At this moment
the bodies have obtained an equal velocity Vu. I will call this
moment Tu.
The energy absorbed by deformation at Tu is equal
to the change in the quantity of the kinetic energy.
Phase B:
In this phase the impact might be ended or it
proceeds until the bodies are apart, depending on the mechanical
properties of the objects as the force between the bodies are reduced.
4. The elastic and non elastic impacts.
We are talking about two theoretical outer limits
of elasticity: Absolute elastic
and Absolute non elastic
or Plastic.
(The elastic abilities of a body means it's ability to regain
it's structure when the pressure is released.)
In an absolute non elastic impact
or plastic impact the body will remain laying quite still
on the ground after falling down.
In an absolute elastic impact
it should jump up again with the same speed and up to the same level.
In the plastic case all the energy
used for deformation when the velocity of the two bodies are equal,
will remain as deformation and further to be transformed into
an increase of temperature. In the elastic case all the
energy absorbed by deformation will be transformed back into kinetic
energy, giving the body the same velocity but in the opposite direction.
In fact all impacts between real bodies will have
an elasticity between those theoretic limits. The changes in velocity
and the deformation during Phase A is independent of the bodies
elasticity. If the bodies are absolutely non elastic (plastic)
the impact are ended at Tu. Now the two bodies are moving with
the same velocity in the same direction.
If the bodies have any degree of elasticity, and
every real body has, the impact will continue into Phase B depending
on the elasticity of the bodies involved. If all deformation at
Tu are transformed back into kinetic energy as an absolute elastic
impact, the bodies would obtain a change of velocity twice as
high as during Phase A .The time the impacts lasts will be twice
as well as the distance the bodies run from the moment of striking
until they are released.
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The contents of, or any part of
this compendium, are not allowed to be made public or copied without
my permission.
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