Statics

Honestly, there is not much thing to say here except: “Go and solve some problems”, but anyway I’ll leave some interesting facts/ideas.

Moments to note

• Every piece of rope feels Tension in both directions (Newton’s laws). Sometimes it’s the same along it (massless rope) and sometimes it’s not.
• There are two frictions: kinetic and static. $f_k={\mu }_{k}N$, while static $f_s\le {\mu }_{s}N$. The way to remember it is just a thought experiment. If an object stands on the ground and you slightly push it, then it stays there (lol). But if $f_s={\mu }_{s}N$ (note equality), then it means that standing object slides to the left, when you just barely push it to the right. So, the equality is true at the limiting case!
• If the system is motionless, then torques also cancel. There is a good problem on torques (2.11) that requires proof by induction
• Recall the ‘rope wrapped around the pole’ proof

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Problems to solve

• 2.1: Hanging rope
• 2.3: Motionless chain - cool problem where you have to use calculus knowledge, like cutting a chain into million small pieces. My mistake: wrong length (dl) calculation.
• 2.4: Keeping a book up: default problem on frictions. My mistake: to find minimum or maximum take derivatives!
• 2.6: Supporting a disk: almost can solve fully. My mistake 1 : massless rope has the same tension! My mistake 2: rope with a friction wrapped around a pole!
• 2.8: Hanging chain (4-star): My mistake: wrong choice of coordinates; sometimes keep everything in terms of components, e.g. just $T_y(x)$ not $T(x)\cdot \sin (\alpha )$
• 2.9: Hanging gently: Overthought the problem, much simpler. (Still need to resolve)
• 2.10: Mountain climber (4-star): Need to solve
• 2.11: Proof related to torques: Cool
• 2.14: Leaning sticks: Simple torque equalities
• 2.16: Balancing the stick: Had a correct idea, but some math went wrong
• 2.17: The katushka: correct.
• 2.18: Stick on a circle: correct
• 2.19: Many sticks and circles: Very interesting problem that needs some logic! You also learn how to find the converging sum
• 2.35: Wisely choose a pivot point!
• 2.38: Stacks: they way you solve these types of problems is by considering N=1,2,3 … n