Hey, I have this question here, the hardest one on this sheet, and I've been stuck on it all day now. I'd really appreciate maybe just a hint, as I want to do it myself but I just need a kickstart.

I drew three free body diagrams for each position of the pendulum, then marked off tension and the force of gravity. I ended up with three equations but it never went anywhere and I truly am stuck on this. Any hints would be appreciated. Thanks.

Yea you are right about the FBD's in my head, I was just stuck and decided to draw a picture

For question 1, I set the length to one just to play around with the question. By doing that, I found that the heigh at point at (40degrees) was 0.234m, and at point B it was 0.06m. By solving the equation
PEa = PEb + KEb, I got v = 1.85 m/s.

Then I got the idea I could use Fnet = mv^2/r - maybe I will try solving for the mass now or something. Anyways I will keep trying with this.

I have no idea if that is what you were suggesting? I'm just playing around with it trying to see if something can be done.

I also converted the 60 degree trip in total to rads, and got 1.05 rads. Am I getting warmer or colder? lol

For question 2, I'm not done with the first question, but I willget back to you.

My thinking when I did the 0.234 and 0.06 was this: (I could be wrong)

When we've done these questions in class before (it's a grade 12 physics class), when the pendulum is on y axis going straight down, it is assumed it's height is zero. So if there is a 40 degree line that is going off of the vertical, then you do the cosine thing and get the number 0.766.This is the height from the end of the 40 degree line to the x axis above. So for me, I subtracted this number from 1 and got 0.234.

Same procedure for the other one too. Does this make sense to you or have I made an error?

Alright, so you've assumed that the bottom of the pendulum is h=0. That's perfectly fine.

Now that you've justified the velocity at this point. You need to be a bit more careful with the FBD at 20 degrees. What direction is Fnet? What direction is T, the tension? What direction is gravity?