Sir Isaac Newton first presented his three laws of motion
in the "Principia Mathematica Philosophiae Naturalis" in 1686. His second law
defines a force to be equal to the differential change in momentum
per unit time as described by the calculus of mathematics, which Newton also
developed. The momentum is defined to be the mass of an object m times its velocity
v. So the differential equation for force F is:
F = d(m * v) / dt
If we take very small time increments, we can write a difference equation from the
differential equation:
F = (m1 * v1 - m0 * v0) / (t1 - t0)
If the mass is a constant, using the definition of acceleration a as the
change in velocity with time, the second law reduces to the more familiar product
of a mass and an acceleration:
F = m * a
The force, acceleration, velocity, and
momentum have both a magnitude and a direction associated with them.
Scientists and mathematicians call this a
vector quantity.
The equations shown here are actually vector equations and
can be applied in each of the
component directions.
The external
force
F for a rocket is a combination of the
weight,
thrust,
drag and lift
of the vehicle.
If we know the external force F, the equations can be solved
to describe the
motion
of a rocket in flight. For some simple cases, we can write equations which
describe the location and velocity of the rocket at any time in the flight.
For the more general case, we can use a
computer program
to solve the equations.
The assumption of constant mass works well for
stomp rockets
and fairly well for
solid model rockets,
but not very well for
bottle rockets
or
full scale rockets
because of the large decrease in the mass of these rockets during flight as the
propellants are expelled.
Guided Tours
-
Newton's Laws of Motion:
-
Rocket Translation:
-
Forces, Torques and Motion:
-
Flight Equations:
Activities:
Fundamental Terminology: Grade 10-12
Newton Car: Grade 10-12
Related Sites:
Rocket Index
Rocket Home
Beginner's Guide Home
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