A Level Maths Notes: M4 – Applying F=ma to a Particle Subject to a Resistive Force
We can apply
to
a particle subject to several forces, with
being
the resultant of all the forces, or the vector sum of the forces.
Often the resistive force depends on the velocity – at low speeds,
the resistive force is proportional to the velocity. Suppose we write
that the resistive force
Suppose
also that the particle is subject to a force
which
may be constant or zero.
Applying
gives
(1)
At the moment this equation is not much use. It becomes much more
useful in general if we remember that
and
Substitution
of these into (1) gives
After some rearrangement we have
(2)
If
the particle is attached to a string as shown below it will
experience an additional force of tension:
The equation (2) becomes
