Represent the object as a particle, per our particle model.

The first step is to draw F , which of course points down.

grav, on box, by Earth

**We might as well draw an axis**

perpendicular to the surface of

contact, while we're at it.

perpendicular to the surface of

contact, while we're at it.

**One trick in drawing your incline's angle is to make it small. That way you know which angle in your force diagram will be the same angle.**

**Now you can draw the normal force, which is always "normal," or perpendicular, to the surface of contact.**

**Friction will, of course, act up the hill, if velocity is constant. (Something needs to be balancing gravity's component down the hill.)**

Remember what Newton's First Law tells us: if velocity is constant along an axis (such as parallel to the incline surface), forces must be balanced.

Remember what Newton's First Law tells us: if velocity is constant along an axis (such as parallel to the incline surface), forces must be balanced.

**Which vector(s) are you going to break down into components to show a balance of forces with hash marks?**

**Note that friction acts tangent to the surface and the normal force acts perpendicular to the surface; therefore, they are at right angles.**

**Because of your decision to break up F into components--and not the other vectors--hash marks (equality marks) can be easily drawn to show the balance of forces, i.e., to show that velocity is constant both perpendicular and tangential to the surface of contact.**

grav

Hints and Clues

Don't break up friction or F into components to convey a balance of forces; breaking up one forces you to break up the other (since friction and F are at right angles to each other).

There's probably a decomposition that requires breaking up only one force vector, such as gravity in the case of an incline, or tension in the case of a diagonal rope.

norm

norm

Hints and Clues

Note that the components make a right angle with each other.

Why?

Newton's laws of motion are applied along one axis at a time.

By keeping the forces along two mutually exclusive axes, we can speak with confidence about what happens along one axis without worrying what happens along another.

**Hints and Clues**

Following the rule of separating components with a right angle has the added benefit of keeping you from making a component longer than the original force vector.

Put another way, it ensures you make the original force vector that you are decomposing into the hypotenuse of the right triangle.

Projection Axes

If the idea projecting a vector onto axes is hard to get used to, imagine a flashlight far away, shining perpendicularly on the original, physical vector. The shadow on the axis is the imagine vector, or component.

Now point the flashlight 90 degrees to create the other shadow/component.