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This calculator (by Stephen R. Schmitt) computes the final velocities for an elastic collision of two masses in one dimension. The program is operated by entering
the masses and initial velocities of two objects, selecting the rounding
option desired, and then pressing the Calculate button. All
entries are cleared by pressing the Clear button. It is assumed
that m2 is to the right of m1
and that positive velocities are to the right. If the program returns
the error message:
cannot solve then the two masses would not
collide -- check the initial velocities you specified
Notes
The
total momentum of the system is a conserved quantity. Equating
the total momentum before and after the collision:
m1·vi1 + m2·vi2 = m1·vf1 + m2·vf2
This
equation is valid for any 1-dimensional collision. Note that,
assuming we know the masses of the colliding objects, the
above equation only fully describes the collision given the
initial velocities of both objects, and the final velocity
of at least one of the objects.
An
elastic collision is one in which the total kinetic energy
of the two colliding objects is the same before and after
the collision. For an elastic collision, kinetic energy is
conserved. That is:
0.5·m1·vi12 + 0.5·m2·vi22 = 0.5·m1·vf12 + 0.5·m2·vf22
The
collision is fully specied given the two initial velocities
and masses of the colliding objects. Combining the above equations
gives a solution to the final velocities for an elastic collision
of two objects:
vf1 = [(m1 - m2)·vi1 + 2 m2·vi2]/(m1 + m2)
vf2 = [2 m1·vi1 - (m1 - m2)·vi2]/(m1 + m2)
Copyright
© 2004, Stephen R. Schmitt |
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