# Resolving Vectors down a Slope (plus a little bit about friction)

Sometimes, it’s just convenient to represent a single vector by TWO vectors at right angles to each other. Take a look at this diagram. It isn’t a free-body diagram, since I have included resolved components. A FBD would only show W and R

This isn’t labelled very well, I ought to have said that W means ‘weight’ which is equal to ‘mass x g’, but it muddles the diagram. If I now resolve W into two mutually perpendicular components, in red, Wsinθ acts down the slope and Wcosθ acts perpendicular to it. It is Wsinθ which causes the body to accelerate down the slope.When there is no sliding occurring, the frictional  force can have any value from zero up to a maximum value of FR as given in the below equation. If the slope become so steep that the object is moving then the coefficient of static friction is replaced by the smaller coefficient of dynamic friction. (We know how much easier it is to keep a car moving when we’re pushing it than to get it moving in the first place.)

If  this is large enough, the body starts to slide down the slope  The green vector, R is the NORMAL REACTION. This is numerically equal to Wcosθ but always acts AWAY FROM A SURFACE. It is an electrostatic force since if two bodies are touching, their electron clouds overlap a little bit and charges in both bodies are pushed apart. The charges tend to resist being separated hence exert a force to prevent this happening. Weight is of course, gravitational, so these two forces are NOT Newtonian pairs.

A Newtonian Pair of forces is one in which the forces are:

* equal and opposite

* act on different bodies

* are of the same KIND ( 4 available – gravitational, electromagnetic, strong nuclear, weak nuclear)

The pull of the Earth on the Moon (and vice-versa) is an example of a Newtonian pair.

Here’s a link to this idea used in practice-finding the acceleration of a body down an inclined plane.