= Chapter 5

== Apparent Weight

Actual weight is $F_w = m g$

Your *apparent weight*, $w_"app"$, is the weight you feel

$w_"app" = F_upright(N)$ (only normal force goes up rather than down)

$F_upright(N) = m g + m a$ where $a$ is, say, the acceleration of the elevator you're standing in
- Feel heavier when elevator starts going up or when it stops going down (upward acceleration)
- Feel lighter when elevator starts going down or when it stops going up (downward acceleration)

== Inclines

Normal force is always perpendicular to surface of contact (common mistake)

== Friction

There are three kinds of friction:

- Static friction: $arrow(f)_s lt.eq mu_s n$. Applies when object is not moving. It adjusts itself so that the net force is 0, but it can only increase to $mu_s n$ at most.
  - Maximum static friction: $arrow(f)_s_"max" = mu_s F_N$
- Kinetic friction: $arrow(f)_k = mu_k n$. Applies when object is moving.
- Rolling friction: $arrow(f)_r = mu_r n$. Applies when object is rolling.

Coefficient of friction in range $[0, 1)$

=== Interacting Objects

According to Newton's Third Law:

- Every force occurs as one member of an action/reaction pair of forces.
- The two forces act on *different* objects.
- The two forces point in opposite directions and have the same magnitude.

== Ropes and Pulleys

=== Ropes

*Massless string approximation:* Mass of rope is 0.

Generally, *the tension in a massless string/rope equals the magnitude
of the force pulling on the end of the string/rope*. As a result:
- A massless string/rope "transmits" a force undiminished from one end
          to the other, i.e., if you pull on one end of a rope with force $F$,
          the other end pulls on whatever it's attached to with the same force.
- The tension in a massless string/rope is the same from one end to the
          other.

=== Pulleys

The tension in a massless string is unchanged by passing over a massless,
frictionless pulley (assume such a pulley for problems in Chapter 5).
