Archive for Newtonian Mechanics

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.

Dreams, Planes and Automobiles

Posted in Biographical, Covid-19, Education, Maynooth, The Universe and Stuff with tags , , , , , on November 20, 2020 by telescoper

I’ve blogged before about the strange dreams that I’ve been having during this time of Covid-19 lockdowns, but last night I had a doozy. I’ve recently been doing some examples of Newtonian Mechanics problems for my first-year class: blocks sliding up and down planes attached by pulleys to other blocks by inextensible strings; you know the sort of thing.

Anyway, last night I had a dream in which I was giving a lecture about cars going up and down hills taking particular account of the effects of friction and air resistance. The lecture was in front of a camera and using a portable blackboard and chalk, but all that was set up outside in the middle of a main road with traffic whizzing along either side and in the presence of a strong gusty wind. I had to keep stopping to pick up my notes which had blown away, dodging cars as I went.

It would undoubtedly make for much more exciting lectures if I recorded them in such a situation, but I think I’d be contravening traffic regulations by setting up in the middle of the Straffan Road. On the other hand, I could buy myself a green screen and add all that digitally in post-production…