Applying F=ma to a Particle Subject to a Resistive Force

We can applyto a particle subject to several forces, withbeing 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 forceSuppose also that the particle is subject to a forcewhich may be constant or zero.

Applyinggives(1)

At the moment this equation is not much use. It becomes much more useful in general if we remember thatandSubstitution 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