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Originally Posted by blue2000s
momentum is actually 1/2 x mass x velocity squared.
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My head hurts!
I have found conflicting anwers to the formula for momentum. It seems physics is not that precise after all.
Deborah,
First, energy and momentum are very different properties.
An object takes time to stop moving. The momentum of an object can be
describes as the amount of force required to stop the object in one second.
When a constant force is applied to an object, it is the force multiplied by
the time over which it is applied that yields the change of momentum of the
particle. Also, momentum is a vector: it has a direction to it. Momentum
points in the direction of an object's velocity.
An object continues to travel while its velocity drops to zero.
The kinetic
energy of an object can be described as the amount of force required to stop
the object over a distance of one meter. When a constant force is applied
to an object, it is the force multiplied by distance traveled along the SAME
AXIS as the force that determines the change of kinetic energy. Kinetic
energy is a scalar: it has no direction.
An object changing direction but neither speeding up nor slowing down is an
example of changing momentum but not changing kinetic energy. If the object
does speed up or slow down, both momentum and kinetic energy will change.
For example, consider throwing a rock upward at a certain speed. If you
double the rock's initial speed, the rock will require twice the time and
four times the distance to reach zero speed. Thus, the rock with the
doubled speed has twice the momentum and four times the kinetic energy.
Dr. Ken Mellendorf
Physics Instructor
Illinois Central College
Momentum is m*v, and kinetic energy is m*v*v/2, so if momenta and energies
are the same, we have:
1) m1*v1 = m2*v2
2) m1*v1*v1 = m2*v2*v2
using (1) in (2) yields
m1*v1*v1 = (m1*v1)*v2 -> v1 = v2
using this in (1) shows that m1 = m2
So, yes, if a particle has the same momentum and the same kinetic energy
as another particle, their masses and velocities must be equal
But having the same momentum does not by itself imply having the same
energy. A heavy particle moving slowly can have the same momentum as
a light particle moving swiftly.
--
Tim Mooney
Advanced Photon Source, Argonne National Lab.