## Total Contact Force

\[R\]

for a body resting on a smooth surface is perpendicular to the surface. For a surface that is not smooth we can consider the reaction force to consist of two components: a normal component \[R\]

, perpendicular to the surface, as for a smooth surface, and a friction component, \[Fr\]

tangential to the surface.The total contact force is then, according to Pythagoras Theorem

\[\sqrt{R^2 +Fr^2}\]

.If the body is on the point of slipping, the friction force is equal to

\[\mu R\]

where \[\mu\]

is the coefficient of friction. Th magnitude of the contact force is then \[\sqrt{R^2+(\mu R)^2} = R \sqrt{1_ \mu^2}\]

.(1)For a body at rest in limiting equilibrium or moving with a constant velocity, there is no net force and the magnitude of the total reaction force is (1) above.

If the particle is at rest on a slope, the total con-act force must be in opposition to the force of gravity i.e. it must be vertically up.