Inertia and Physics.. Paul Chick

[Don A. Gilmore]

----- Original Message ----- 
From: "Richard Brekne" <Richard.Brekne@grieg.uib.no>
To: "Pianotech" <pianotech@ptg.org>
Sent: Friday, December 26, 2003 4:52 PM
Subject: Re: Inertia and Physics.. Paul Chick
> Instead, let me ask a concrete question. If it takes one newton to
> accelerate an object with a mass of one kilogram at one meter per
> second, and that object bangs into another object... will the first
> object impart a force of exactly one newton upon the second ?

No.  The one newton is a constant force on the first object and it will
accelerate it faster and faster as long as the force remains constant.  So
the speed at impact would depend on how long the object had been
accelerating.  After 6 seconds, it's going 6 m/s; after 75 seconds, it's
going 75 m/s, etc.

The first object would have kinetic energy depending on its velocity at
impact  (KE = 1/2 mv^2).  How much of that energy is imparted to the other
object depends on the mass of the second object, the hardness and nature of
the materials, the shape, whether or not they contact obliquely or head-on
etc.  If they are both made out of steel you will obviously have a different
situation than if they are both made out of putty.

Here is where "momentum" is used.  Total momentum (m * v, in magnitude and
direction, of both objects added together) is conserved in a collision.  And
it's conserved whether the items stick together or not and is independent of
the nature of impact.  Total energy is also conserved, but some kinetic
energy may be lost as heat or vibration energy after impact.

For a typical collision you need to know more than just the velocity and
mass of the two objects before impact.  If you know how fast and in what
direction one of them is going *after* the collision, for example, you can
determine how fast and in what direction the other one will go.

There are some special cases like with a perfectly "elastic" collision (the
objects are hard and don't dissipate energy) then energy and momentum are
both conserved.  If it is a head-on collision their respective velocities
after impact can be calculated using both conservation of momentum and
conservation of energy together.  If they don't hit head-on, though, you're
screwed and need more information like before.

If it is a perfectly "inelastic" collision (the objects stick together at
impact) the resulting velocity of the stuck-together pair can be determined
using conservation of momentum alone, since we know that the velocity of
both objects will be the same magnitude and direction.  Kinetic energy will
*not* be conserved in such a collision, in fact generally a lot of it will
be lost.

These special cases are not necessarily just in a fantasy world either.
They can often closely approximate a real situation.  The inelastic
collision, for example, can be quite accurate if little or no friction is
involved.  Mechanisms in a machine that latch together on contact are a
perfect example.

Now what is the force of impact?  Well, think of it as if there is a spring
on the end of one object.  When the two collide the spring compresses.  One
object starts slowing down and the other speeds up (assuming it was at
rest).  And as the spring compresses the force between the objects
increases.  At some point the compression of the spring will come to a stop
and it will start expanding again.  The force gets smaller as the spring
elongates and finally is zero when the objects separate.  So you see there
is no real constant "force" of impact; it is a changing curve.

Now we have all sorts of new goodies to argue about!

Don A. Gilmore
Mechanical Engineer
Kansas City


>
> Cheers, and thanks for your patience in all this.
>
> RicB