2007-11-14 - Friction
Today's nonsense
- We need to pay for a few tickets to send Spiller up to Florida over Thanksgiving.
- Homework due tomorrow.
- "I have pretty bad aim. I can't guarantee I'll miss." - Katie ... kind of like "my battery is out of cameras"
Friction
When you apply a horizontal force to an object resting on the floor. It either moves or does not move. What if it doesn't move? Then the friction is greater. There are two types of friction: static and kinetic (friction of movement). The object may not move because the force of static friction, Vector f_(s), exerted by the floor on the object, opposes the applied force. Until you apply enough force to overcome the statitic friction, there will be no movement. Once you get the object moving, so if you have no net acceleration and no force, the ....
f_(s,max) = μ_(s) * F_(n).
f_(s) < = μ_(s) * F_(n).
Where Mu is called the coefficient of static friction.
Say it takes 80 Newtons to move a box from a floor, if you apply 60 Newtons, then the static friction is one value, then 40 Newtons, well, the static friction will be that value.
If you push the object hard enough, it will slide across the floor. To keep up the object sliding with constant velocity, you must exert a force on the object that is equal in magnitude and opposite in direction to the force of kinetic friction, Vector f_(K) (also called sliding friction), exerted by the floor
f_(k) = μ_(k) * F_(n)
where μ_(k) is called the coefficient of kinetic friction.
ex 1) A bartender slides a mug of mass 0.45 kg horizontally along the bar with initial speed 3.5 m/s The mug comes to rest near the customer fter sliding 2.8 m. Find the coefficient of kinetic friction.
HWDWSTP? FBD.
Calculate a_(x)
V^(2) = V_(0)^(2) + 2a_(x)(delta x)
0 = (3.5)^(2) + 2a_(x) * (2.8)
a_(x) = -2.1875 m/sec^2.
μ_(k) = (-a_(x)) / g = 2.1875/9.81 and it's unitless, it's just a coefficient.
2) A block rests on an iclined plane surface. The angle of inclination is increased until it reaches a critical angle, θ_(c), after which the block begins to slide. Find the coefficient of static friction, μ_(s). We are going to put this on a tilted frame of reference, because we want our normal force of friction to be straight up.
Sum of F_y = F_n - mgcos(theta) = ma_y = 0
Sum of F_x = mgsin(theta) - f_s = ma_x = 0 (because the static friction is keeping it in place).
What's the largest that theta can be such that the acceleration is zero, and it's not moving, so do you know how to start that problem? You start with the soon to be infamous f_s, soon to be infamous because we haven't used it enough to, .... then we did just like we did on the last example. The static friction is equivalent to what, based on what this says? mgsin(theta) = Normal force * coefficient of static friction.
Coefficient of static friction = tan(theta)
μμμμμμμμμμμμμμμμμμμμ = Mu