Powers analisys for ball stuck in a Chimney

[sronen20]

Hi,

If we'll build a chimney from 2 walls with a decreasing width (meaning, the length between the walls gets smaller as we go down the chimney, since the walls both have a small slope), and then throw a ball down that chimney, it would get stuck.
I am having hard time computing the forces that cause this affect. in order to resist the gravity, it seams I need very strong normal force (going to infinity as the slope goes to 0).
but when I try to express mg by perpendicular and Tangent vectors, I receive values smaller then mg (and obviously not going to infinity).

can someone help?
thanks :-)

 

[Antiphon]

Hi,

If we'll build a chimney from 2 walls with a decreasing width (meaning, the length between the walls gets smaller as we go down the chimney, since the walls both have a small slope), and then throw a ball down that chimney, it would get stuck.
I am having hard time computing the forces that cause this affect. in order to resist the gravity, it seams I need very strong normal force (going to infinity as the slope goes to 0).
but when I try to express mg by perpendicular and Tangent vectors, I receive values smaller then mg (and obviously not going to infinity).

can someone help?
thanks :-)

You are solving the problem without friction. In a real chimney, it would be friction acting tangentially to the wall, not a balanced force acting normal to the wall. Your answer is correct- a frictionless ball in a nearly parallel chimney would get stuck at a place with nearly infinite compressive forces on it.