"Pat" <[Only registered users see links. ]> wrote in message
If you were to slam these two objects head on into each other,
and they stuck together, they would come to a dead stop. As Tom
pointed out, the momentum of each object is m * v, so their
momenta (which are each a vector quantity... direction is really
important) net to zero.
Now for such slow speeds, the energy of each one... the amount of
"force times time" it took to get them up to speed, is much
greater for the lighter but faster one (in this case)
Energy = 1/2 * mass * (velocity)^2
In your example, it took twice the force or twice the time to get
the smaller mass to the higher speed.
Unfortunately, this is where common language usage of terms like speed,
impact, force, momentum, energy, inertia gets pretty muddy. In the
newspapers, words like this describing a football player's motion are
all used pretty much interchangably.
When you start wanting to do things quantitatively, like you're doing,
then the *precise* definitions used in physics become crucial.
What's true in the statement above is that the *momentum* of both
objects is the same, which means that in an impact with a stationary
object, the result will be comparable in terms of the *momentum* of the
struck object after the collision.
However, the *force* applied depends on the interval of time of the
contact. This is why, even though your change of momentum is the same
in both cases, stopping your head with an airbag is preferred over
stopping your head with the steering wheel in a collision.
Moreover, the *energy* delivered depends on the details of the
collision and whether some of that energy is devoted to breaking up the
structure of the struck object. Consider the damage of bullet, which
has less momentum than a swung 2x4.
On 10 Mar 2006 17:00:15 -0800, "Pat" <[Only registered users see links. ]> wrote:
No, the correct formula is : Force = Acceleration x Mass
(in a socalled inertial reference system)
Acceleration is "change of velocity"
In your examples the objects travel at a constant velocity (i.e
accelaration = zero) and therefore the force is zero in both cases.
On Fri, 10 Mar 2006 17:00:15 -0800, "Pat" <[Only registered users see links. ]> wrote
in <email@example.com .com>:
No, mass*velocity is actually momentum. Force is defined in
physics as the rate of change of momentum. In classical physics
this turns out to be mass*(change in velocity)=mass*acceleration.
To approach the problem you posed, it's better to find the force
from energy. The analysis would go as follows:
Kinetic energy is 1/2*mass*velocity^2=1/2*mass*velocity*velocity.
So the first object has 1/2*50*100*100 KE units of kinetic energy
= 250'000 KE units
The second object has 1/2*100*50*50 KE units
= 125'000 KE units
Now, in a collision, the kinetic energy will be converted to
potential energy over equal distances. So the 50 lb object
will have twice the force than the 100 lb object even though
both have the same momentum.
This is bourne out by observations that faster-moving smaller
cars often inflict as much damage to an SUV as another SUV at a
Hope this helps.
// The TimeLord says:
// Pogo 2.0 = We have met the aliens, and they are us!