Archive for Potential

The Mechanics of Nursery Rhymes

Posted in Cute Problems, The Universe and Stuff with tags , , , , on December 30, 2020 by telescoper

I’ve always been fascinated by Nursery Rhymes. Some people think these are little more than nonsense but in fact they are full of interesting historical insights and offer important advice for the time in which they were written. One such story, for example, delivers a stern warning against the consequences of placing sleeping babies in the upper branches of trees during windy weather.

Another important role for nursery rhymes arises in physics education. Here are some examples that students of elementary mechanics may find useful in preparation for their forthcoming examinations.

1. The Grand Old Duke of York marched 10,000 men up to the top of a hill and marched them down again. The average mass of his men is 65 kg and the height of the hill is 500m.

(a) Estimate the total work done in marching the Duke of York’s men up to the top of the hill.

(b) If, instead of marching down again, the men take turns sliding down a frictionless slide back to where they started, estimate the average speed of a man when he reaches the bottom of the hill.

(You may assume without proof that when they were up they were up, and when they were down they were down and, moreover, when they were only half way up they were neither up nor down.)

2. By calculating the combined rest-mass energy of half a pound of tuppenny rice and half a pound of treacle, and assuming a conversion efficiency of 10%, estimate the energy released when the weasel goes pop. (Give your answer in SI units.)

3. The Moon’s orbit around the Earth can be assumed to be a circle of radius r. A cow of mass m is standing on the Earth (which has mass M, and radius R). Derive a formula in terms of r, R, M, m and Newton’s Gravitational Constant G for the energy the cow needs in order to jump over the Moon.

(The Earth, Moon and cow may be assumed spherical. You may neglect air resistance and udder frictional effects. )

Feel free to contribute similar problems through the Comments Box.

Britain’s Potential Explained

Posted in Politics, The Universe and Stuff with tags , , , on December 14, 2019 by telescoper

As a physicist I was intrigued by the recent use by Tory election campaigners of the slogan “Unleash Britain’s Potential”, so I decided to study the matter in more detail. I am pleased to say I am now ready to report on my conclusions.

First here is a sketch of Britain’s potential, which I denote V(r):

How do we interpret this potential?

Recall that the force F(r) derived from V(r) is given by

F(r) = - \frac{dV(r)}{dr}.

The gradient of this potential being negative the force is directed towards increasing values of r. By Newton’s Second Law this means accelerated motion to the right (i.e. in the direction of increasing isolation), accompanied by steady and irreversible decline.

Note also that the form of this potential implies that there is something completely repulsive at its origin.

I hope this clarifies the situation.

The Higher Education Green Paper – Expert Commentary

Posted in Education with tags , , , , on November 6, 2015 by telescoper

Hot news in Higher Education today is that the long-awaited Higher Education Green Paper is now published. A summary of this discussion document which is called Fulfilling our Potential: Teaching Excellence, Social Mobility and Student Choice can be found here. I haven’t got time to provide a detailed response this morning, so I will defer to an acknowledged expert on the subject of “fulfilling potential”, Dylan Moran: