Particles on Slopes (2)

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 toWe want to find the the coefficient of friction in in terms ofandif the block is on the point of moving up the slope.

Resolving perpendicular the the slope gives

Resolving parallel to the slope gives

Dividing (2) by (1) gives

We can divide each term in the numerator and denominator by(3)

Suppose instead that we were asked to findjust sufficient to start the block moving up the slope. We can rearrange (3):