Ferry's wheel

Classical Mechanics Level 2

A particle slides down from the topmost point of a circular ring (like a Ferris wheel standing perpendicular to the ground) along a smooth chord making an angle of θ \theta with the vertical.

For which value of θ \theta will the particle take the longest time to descend?

θ = 0 ∘ \theta=0^\circ θ = 4 5 ∘ \theta=45^\circ θ = 8 9 ∘ \theta=89^\circ the same for all the above

View wiki
Rajdeep Ghosh by Rajdeep Ghosh , 17, India

This section requires Javascript.
You are seeing this because something didn't load right. We suggest you, (a) try refreshing the page, (b) enabling javascript if it is disabled on your browser and, finally, (c) loading the non-javascript version of this page . We're sorry about the hassle.

1 solution

Rajdeep Ghosh
Jun 25, 2017

Now, By Thales' Theorem, angle ABC=90.

So, AB=2rcos θ \theta

Now, component of g along AB is gcos θ \theta .

So,

2rcos θ \theta = 1 2 \frac{1}{2} gcos θ \theta t 2 t^{2}

or,t= 2 r g \sqrt{\frac{r}{g}}

So, the time is independent of θ \theta

This, infact is a very interesting result. This means that when you slide a number of balls at different angles with same initial velocity then all balls will reach the other side of the circle at the same time!

4 Helpful 0 Interesting 0 Brilliant 0 Confused

0 pending reports

×

Problem Loading...

Note Loading...

Set Loading...