and no pushes

This is why I always say that intro physics is SO filled with right triangles.

Still, do not memorize this.

Slightly smaller than without friction. Good, that makes sense

Yup, previous annotation is verified.

The force parallel to the slope will exist if there is some tilt angle θ. It equals \(\vec{w}\) if \(\theta=90\) but equals zip zap if \(\theta=0\). So it has to be proportional to the \(\sin\left(\theta\right)\).

NICE. These components are important when analyzing forces and putting together a free body diagram and a net force calculation, but \(\vec{w}_{\perp}\) and \(\vec{w}_{\parallel}\) are also tricky to sketch in and keep track of.

GMTA

The molecules and atoms of the material act like a tiny trampoline, flexing downward (like the table in Fig. 1(b)) microscopically but exerting plenty of Newtons \(\perp\) to the surface.

So this section 4.5 is also a vocabulary section in which to learn the nomenclature.

This kind of problem and questions could be used to torture a physics graduate student. That is, it is a very difficult problem because of the concepts through which one must matriculate to the calculations, which are quite simple in themselves.

key finding.

Whereas if YOU, an external agent wanted to accelerate her to the left, your push would have to be leftward.

Because this is in the structure of the physical universe, the mundane skateboarders demonstration on first day of lecture is a good demonstration for understanding all forces

HUGE

This is not unreasonable. The normal force, perpendicular to the surface, i.e., to the rails, rises from the intermolecular and interatomic forces in the steel alloy of the rails. They act like little trampolines, dipping just enough to support whatever weight is on it... up until the weight passes the rail's breaking point.

Same as the relationship between the propulsion force Fp from the road surface on the chopper and the friction force f, in the homework

Why we concentrated on that part of Ch. 3

As in HW 3.

an extrapolation that Galileo first made.

This was Aristotle's view. An arrow flies through the air because it presses into the air, air rushes bacwards behind the arrow and then pushes the arrow forward.

Note: the net force can be absent from the free body diagram, for clarity, but the net force could also be drawn in over to the side or overlaid on the f.b.d. if labeled clearly and not too cluttered up.

e.g., the forces of cohesion that hold the skateboard together, which is why you cannot make a skateboard of jello.

i.e., graphical or analytical methods

or the skateboarders' demonstration

I.e., non-quantum

Non-relativistic, v << c.

A short paragraph to describe a very complex controversy! The paragraph is acceptable, but does not do it justice. Well worth reading about, e.g., Galileo's Daughter, by Dava Sobel (UCF Main Library General Collection - 4th Floor QB36.G2 S65 1999 Available)

This is the ordinary assumption in elementary physics. Air flow properties are very difficult to model, so we ignore them. This is the same as saying to our speeds are not large enough to draw appreciable drag from the air, so they can be ignored... until you need high precision!

Sneak preview on syllabus is related to this analysis. Study both.

ooops should be Ry^2

Lovely diagram

The angles here are not that helpful. Main thing is to build resultant from four components Ax, Ay, Bx, By, then get the trig on the resultant R

Huge. Fig. 2 is one to keep in mind all of the semester.

Very important

Excellent sentence about analysis of a ballistic trajectory

This is known as "adding in quadrature" -- i.e., add the squares of each perpendicular side.

Oh, no! Nothing could be further from the truth! But we can provisionally accept this statement for the moment.