Archive for cute problems

A Cube of Resistance

Posted in Cute Problems with tags , , , on September 14, 2017 by telescoper

It has been brought to my attention that I haven’t posted any cute physics problems recently, so here’s one (which involves applying Kirchoff’s laws) that’s a bit harder than A-level standard which might be of interest to students about to begin a degree in physics this month!


The above image, produced using the advanced computer graphics facilities available at Cardiff University’s Data Innovation Research Institute, represents a cube formed of 12 wires each of which has resistance 1Ω.

What is the electrical resistance between: (i) A and G; (ii) A and H; and (iii) A and D?

As usual, answers through the comments box please!

A Question of Equilibrium

Posted in Cute Problems with tags , on March 30, 2017 by telescoper

It’s been quite a while since I’ve been able to find time to post any items in the cute problems folder, and I don’t have much time today either, but here’s a quickie. You may well find this a lot harder than it looks at first sight. At least I did!

An isolated system consists of two identical components, each of constant heat capacity C, initially held at temperatures T1 and T2 respectively. What is the maximum amount of work that can be extracted from the system by allowing the  two components to reach equilibrium with each other?

As usual, answers through the comments box please. There is no prize, even if you’re right.

 

 

A Problem of Wires on the Rails

Posted in Cute Problems with tags , , , on October 5, 2014 by telescoper

It’s been a long time since I posted a cute physics problem so here’s one about magnetism for your edification and/or amusement.

Two long wires are laid flat on a pair of parallel rails perpendicular to the wires. The spacing d between the rails is large compared with x, the distance between the wires. Both wires and rails are made of material which has a resistance ρ per unit length. A magnetic flux density B is applied perpendicular to the rectangle formed by the rails and the wires. One wire is moved along the rails with uniform speed v while the other is held stationary. Derive a formula to show how the force on the stationary wire varies with x and use it to show that the force vanishes for a value of x approximately equal to μ0v/4πρ.

Give a physical interpretation of this result.

HINT: Think about the current induced in the wires…

 

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.

Driving Test

Posted in Cute Problems with tags on May 16, 2012 by telescoper

I’m currently stuck in the office while my third year students are tackling an exam I set. I have to wait by the telephone in case there’s a problem with the paper that I have to sort out.

As a quick diversion I thought I’d give my blog readers a little test of their own. Try this little poser: