Archive for problems

A Sticky Physics Problem

Posted in Cute Problems with tags , , on May 1, 2014 by telescoper

As I often do when I’m too busy to write anything strenuous I thought I’d post something from my back catalogue of physics problems. I don’t remember where this one comes from but I think you’ll find it interesting…

Oil of viscosity η and density ρ flows downhill in a flat shallow channel of width w which is sloped at an angle θ. The oil is everywhere of the same depth, d, where d<<w. The effect of viscosity on the side walls can be assumed to be negligible.

If x is a coordinate that represents the vertical position within the flow (i.e. x=0 at the bottom and x=d at the top), write down a differential equation for the velocity within the flow  v(x) as a function of x. Use physical arguments to derive appropriate boundary conditions at x=0 and x=d and use these to solve the equation, thereby determining an explicit form for v(x). Hence determine the volume flow rate in terms of η, ρ, θ, d and w as well as the acceleration due to gravity, g.

As usual, answers through the comments box please!

 

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The Problem of the Dangling Magnet

Posted in Cute Problems with tags , , , , on February 20, 2013 by telescoper

Here’s a variation on a physics problem we discussed in my first-ever Skills in Physics Tutorial at the University of Sussex. I hadn’t realized that solutions were provided for Tutors so had to exercise my enfeebled brain in finding a solution. You’ll probably find it a lot easier…

A rectangular bar magnet hangs vertically from a pivot at one of its ends. When gently displaced the magnet undergoes small oscillations either side of the vertical with a period of one second.  A horizontal magnetic field is then applied so that the equilibrium orientation of the magnet is  45° to the vertical. If the magnet is gently displaced from this new position, what is the new period of oscillation?

Comment: you do not need any further information about the size, shape or mass of the magnet in order to solve this problem.