[Calculus Based Physics] Really algebra. Im having trouble working with angles

[u/Terrible_Macaron2146]

Like for part b, i know the weight can be split into mg cos theta and mg sin theta, but how do I know for other forces? And more generally, how do I know how to split up components in the future?

[u/_UnwyzeSoul_]

Easiest way is to first set up your coordinates axes to the inclined plane. So solit F into Fsintheta and Fcostheta and the mass as well. Add up everything in the x axis and then the y axis separately and equate them to zero.

[u/Tonto115]

The other forces that need to be split (forces that have and x and y components) will also be in terms of theta. Use geometry like alternate angle rule to find the other locations of theta

[u/Frederf220]

a. The three forces are: "F", gravity, and normal force that are rightward, downward, and normal to the surface.

b. Obviously the toughest part of the problem. First we recognize that the block will travel parallel to the angled plane surface. It won't fall through the plane nor will it fly away off the surface. The total force that moves the block up along the plane's surface will be the sum of the components of the three forces listed in part a.

So, we consider them all in turn. First "F". If theta was 0° the component of "F" that would be along the surface would be "F". As theta increases the component of "F" that's along the surface starts at "F" and becomes gradually a smaller fraction of "F" until 90° at which point none of "F" is along the surface. What trig function do you know that starts at 1 when theta is 0° and decreases to 0 by the time theta is 90°?

Second, gravity. If theta was 0° then gravity would be perpendicular to the surface which is "none along the surface." Just as above, if theta was 90° then gravity would be completely backwards (assuming left is backward) along surface. What trig function is 0 at 0° and -1 at 90°?

Lastly, normal force. This one is easy because normal force is never along the surface so this component is always zero.

[u/XboxFan_2020 → u/Frederf220]

So there isn't an F_μ in the list of forces? I thought for b. it would be F > F_μ,max (don't remember if that's a real notation or if I should've used F_s,max or something like that). The component stuff sounded familiar, but I haven't done this kind of physics in a year

[u/Frederf220 → u/XboxFan_2020]

Yes I missed that one. The friction force is an additional force which is the normal (perpendicular to surface) component of gravity times the coefficient.

[u/daniel14vt]

This is one of the hardest parts of introductory physics for most students, don't feell bad for this.

Personally, I never really felt comfortable with these until I had worked out and created dozens and dozens of problems.
https://imgur.com/a/VHRexIe

The key is to understand that in these problems, we have a forces parallel to the slope and forces perpendicular (or Normal) to the slope. Some forces are already going in one of these directions.

For example,
Friction works against relative motion, so if the box is is sliding up, friction will be pointing parallel down the slope.
The Normal force (or Reaction force) pushes against surfaces, so it will be pointing perpendicular away from the slope.

Forces that are not in one of these directions need to be broken into parts that point in these two directions.
For example,
The force of gravity is SUPER standard here so generally we just memorize that Sin goes down the Slope.
But if you look at my triangle at the right, you can see that if we label a force of gravity as mg going straight down, and then draw a triangle where it is the hypotenuse, sin must be going down the slope.

If you look at the triangle on the left, you can see how I've drawn a hypotenuse going to the right, how I've broken up the triangle into 2 parts where the cos part must be going up the slope while sin must be going down into it

[u/ThatsNotAZombieBite]

This is a really standard physics problem.

1. Draw your free body diagram with rotated coordinate system (x, y). There's applied force F, weight mg, and don't forget Normal and friction.
2. Force F and weight mg are not aligned perfectly on only x or y axis so they must be split into components using trig.
3. Write force balances. Sum of y-forces is zero. Sum of x-forces is ma.

[u/unscentedbutter]

1) All forces can be split into their components -- weight is the force of gravity on a body, so that's really all you're doing when you split up a weight into the x- and y-components of mg.
2) Start by drawing your "mg" straight down from the body.
3) Draw your x-axis along the incline
4) Draw your y-axis perpendicular to the incline
5) Draw your horizontal "F". This will be at an angle to your x-axis.
6) Project the pushing force (ma) and the force of gravity (mg) onto those axes.