Loop the Loop with Frictional Work

[10Exahertz]

Question: If the Radius of the loop-the-loop is 10meters, from how high above the ground should the object be dropped in order to successfully complete the loop, with friction?

I attempted to solve it, but get the integral of cos(theta)dx, or more properly ds, and i do not know how to finish the equation and resolve this.
Thanks, Steven

 

[mfb]

Friction just on the initial slope?
cos(theta) is constant, the integral should be easy to evaluate. What is the integral of a constant?

 

[haruspex]

Friction just on the initial slope?

It sounds like the coefficient of friction applies all the way. I believe it is solvable, but a bit messy.
10Exahertx, please clarify.

 

[AlephNumbers]

Solvable by hand, but I would recommend using visual python to really get a grasp of what's going on there.

 

[mfb]

It sounds like the coefficient of friction applies all the way. I believe it is solvable, but a bit messy.
10Exahertx, please clarify.

I think we had a similar thread a while ago, without a proper answer (and this and this thread also did not find one). The integral looks messy. Certainly not the type of homework you get in High School.

 

[10Exahertz]

The question is indeed considering friction throughout the entire loop the loop, and I agree, the Integral gets very messy. This isn't for high school though, college.

 

[AlephNumbers]

Alright, show us your work.

 

[AlephNumbers]

Oh my gosh I am such an idiot. What I mean is have you made any progress?

 

[10Exahertz]

No, it gets very weird, I tried to define cos(theta) in terms of x and s(the arclenght of the ramp) to make it solvable (I suppose like a gradient), but then I am left with a Theta somewhere in the equation because I cannot find a way to define x without using hsin(theta) or something like it.
I could find the gradient more easily if I knew the equation of the ramp, and knowing the equation of the ramp would make more sense in this case because friction is a path dependent, non consrvative force, so a different ramp yields different answers, right?

 

[AlephNumbers]

Consider the normal force at the bottom of the loop, halfway to the top of the loop, and at the top of the loop. What is the normal force at each of these points? Can you define the normal force as a function?

 

[AlephNumbers]

Upon further inspection of the problem, I realize that my solution is probably incorrect. I'll try to work it out, but I'm sure someone else will be along to help you.

 

[mfb]

Before we continue: @10Exahertz, please post the full and exact problem statement. This is part of the forum rules exactly to avoid confusion like you see it here.

If friction is considered for the whole loop, you probably want to set up a differential equation.