The numeric approximation is nice, but you could have solved it analytically (using derivative wrt theta and solving when its 0) - that way you demonstrate that this gives you the correct solution and why you use numeric methods, to solve "complicated" equations easily
Yes, absolutely. You could take the derivative to solve this also. However, I made this for an algebra-based class so they could do this without calculus. Actually, I think this way also helps students understand the fundamental idea of the derivative and the max-min problem.
This is great. A mention of how the result could’ve been found using calculus would’ve been a nice teaching bonus.
True.
Maximize the denominator, which will minimize the Tension, and doing that gives a value of ~1.07965 at x ~ 0.386526 radians (22.1463° )
Something like solving dT/d(theta)=0?
@@fizixxInteresting. I'm getting that the best angle is tan-1(mu) or 22.195.
Loved this, I should start learning how to code in Python
The numeric approximation is nice, but you could have solved it analytically (using derivative wrt theta and solving when its 0) - that way you demonstrate that this gives you the correct solution and why you use numeric methods, to solve "complicated" equations easily
Yes, absolutely. You could take the derivative to solve this also. However, I made this for an algebra-based class so they could do this without calculus.
Actually, I think this way also helps students understand the fundamental idea of the derivative and the max-min problem.
I calculated the derivative of T and it turned out that theta = arctan(mus)