Particles on Slopes (1)
There are several things that must be done for every particle that lies on a slope.
1)If you don't have a diagram, draw one.
2)Do not resolve vertically and horizontally. Resolve perpendicular and parallel to the slope. Remember that the reaction force is always perpendicular to the surface, that gravity always acts downwards, and that friction always acts against the direction of motion.
The diagram below shows the particle on the point of slipping down the plane. Friction acts up the slope. The coefficient of friction is equal to
Resolving perpendicular the the slope gives
Resolving parallel to the slope gives
Dividing (2) by (1) gives
is a standard result for a particle resting on a slope at angleto the horizontal in limiting equilibrium as illustrated above.