← Friction and forces in two dimensions

Draw the free-body diagram: object on an incline

For a parked car on a level road, the free-body diagram almost draws itself. A skier at rest on a snowy slope is harder.

Three forces hold her there: her weight, the slope's normal force, and friction. One of the three arrows is the one students most often draw wrongly.

Build the diagram one arrow at a time, and the right directions follow.

Here is the skier as a box, with the slope's surface drawn as a tilted reference line.

First arrow: the weight. Weight is Earth's pull, so it points straight down, whatever the slope's angle. It never tilts with the ramp.

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Arrow 1: the weight points straight down, whatever the slope.

A barrel rests on a ramp. On its free-body diagram, in which direction does the weight point?

Second arrow: the normal force. A surface's normal force is perpendicular to the surface itself, so on an incline it points perpendicular to the ramp face, not straight up.

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Arrow 2: the normal force is perpendicular to the ramp face, not straight up.

The classic error is drawing the normal force straight up. Straight up is the level-floor special case, where the surface happens to be horizontal. The rule is perpendicular to the surface.

A crate rests on a ramp. On its free-body diagram, in which direction does the normal force point?

Third arrow: friction. Friction acts parallel to the surface. The skier at rest tends to slide down the slope, so static friction points up the slope.

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Arrow 3: the skier tends to slide down, so static friction points up the slope. The three arrows balance, because she stays at rest.

For a moving object the same parallel line holds, read from the slide itself. A toboggan sliding down the slope gets kinetic friction up the slope. A sled still sliding up the slope after a shove gets kinetic friction down the slope.

Every arrow's tail sits at the center of the box.

A skier stands at rest on a slope. On her free-body diagram, in which direction does the static friction point?

On an incline, the weight points straight down, the normal force points perpendicular to the ramp face, and friction points parallel to the ramp face, against the slide or the attempted slide.

A crate rests on a 20° loading ramp. State the direction of each force on the crate's free-body diagram.

List the forces on the crate: weight, normal force, friction.

The weight points straight down, whatever the ramp's angle.

The normal force points perpendicular to the ramp face.

The crate tends to slide down the slope, so static friction points up the slope, parallel to the ramp face.

Three arrows, every tail at the crate's center.

Weight straight down; normal force perpendicular to the ramp face; static friction up the slope, parallel to the ramp face.

A toboggan slides DOWN an icy 25° slope. State the direction of the kinetic friction on its free-body diagram.

Friction acts parallel to the surface, opposing the sliding.

The toboggan slides down the slope.

So the kinetic friction points up the slope, parallel to the ramp face.

The kinetic friction points up the slope, parallel to the ramp face.

Your turn

The free-body diagram shows a box at rest on a 25° ramp. Which statement describes the diagram?

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A sled is given a shove and slides UP a ramp, still moving upward. In which direction does the kinetic friction on the sled act?

A box rests on a ramp whose angle can be changed. Which force on the box's free-body diagram points straight down at EVERY ramp angle?