Distance – Again!
This is a futile task. No-one who needs to know reads this. Still and all …
This evening’s Toronto Star carries yet-another-story of high-speed driving. The article focuses, as always, on the legal laws of the city/province/country, with total disregard for the laws of physics and mathematics.
Humans make human laws and humans can sometimes get away with breaking human laws.
But humans DISCOVER laws of physics, and humans can NEVER get away with breaking laws of physics.
To his credit, Toronto police Sgt. Tim Burrows does wave his hands about and circle the issue; it is as if he knows it is there, but can’t quite pull the trigger.
Here it is.
You can look all this up in a book; you can do the calculations with elementary school mathematics, using pencil and paper.
The distance a body moves is given by the formula:
S = ½ ut * at^2
You can read that out aloud as “ess equals you tee times a half ay tee squared”
The time taken to brake under steady deceleration is given by the formula:
t = v/a
“Tee equals vee divided by ay”
Since the final velocity is zero, we can set u=0 and disregard the ut term.
Substituting v/a for t in the first equation, we find:
S = (v^2)/2a
In short, the distance traveled while braking is proportional to the SQUARE of the velocity.
And here’s the beauty of it all:
IT MATTERS NOT ONE WHIT whether you are using kilometers per hour, feet per second, or lupin pods per cats meow!
IT MATTERS NOT ONE WHIT whether you are driving a farm tractor or a lamborghwossit. Maserati. Hyundai Excel. Whatever.
Whatever vehicle is in use (car, ship, train etc) for whatever its braking acceleration is, the distance it will travel under braking is directly proportional to the square of the velocity.
Period.
The star article discusses three speeds:
200 km/h – the speed at which the cars were clocked.
70 KM/h – Toronto police Sgt. Tim Burrows quote
50 KM/h – the recommended MAXIMUM speed for the stretch of road.
Those three speeds squared yield 40,000; 4,900; 2,500.
Go on, work it out for yourself on paper, with pencil.
The ratio of those three “velocity squared’s” to the lowest one comes out to 16.00; 1.96; 1.00.
Go on, work it out for yourself on paper, with pencil.
At the speed limit, you are at par with anyone else driving at the speed limit.
At 20 Km/h over the speed limit (and my guess is that Toronto police Sgt. Tim Burrows has seen plenty of that!), it will take you almost twice the distance to stop.
Another way of saying that is that you have only half as much available space around you as have I traveling at 50 km/h.
But at 200 km/h, you have a miserly 1/16 the space available to you.
At times I wonder if idiots would still be idiotic enough to drive a car 16 times as wide as they do now.
The answer is YES! “.
Neither man owned the car they were driving.”. In other words, they really and truly just don’t care.
So why should we?
May Nearly Might!
This is not about Green Cars; you can order your car in whatever color you choose. It is a favorite pastime of mine to admire a car’s paint job and say to myself “I’d like a car that color!”.
The Toronto Star has another ‘fear’ article, sliding people towards a stampede to get-the-deal while it is still on.
“The premier did not have a clear answer on how much the incentive program will cost, but noted it will not last forever”; this is what we in the trade call a ”no-brainer”. Nothing lasts forever (except the laws of physics), no program, no person, no artifact, no mountain.
Two paragraphs down we hit our stride with “ … These vehicles …, are nearly guaranteed to last 15 to 20 years …”.
In my books, “nearly guaranteed” can be replaced by “not guaranteed”. After all, if something is guaranteed, it is guaranteed. If it is not “guaranteed”, then it is “not guaranteed”.
And if something is “nearly guaranteed to last 15 to 20 years” then it is “NOT guaranteed to last 15 to 20 years”.
You may think this a bit harsh, but note how the phrase “15 to 20 years” sticks in your mind; penultimately “guaranteed”; and fading out of sight “nearly”, which tries to convince you that it is, oh, say 99.99999%.
The truth is probably closer to “We don’t have enough experience to determine the true life value that can be guaranteed”. But the consumer is led to believe that these artifacts will last 15 to 20 years, for sure.
The article is littered with would-be promises: “”It may be through the course of a day when you are plugged in at work to a smart grid, you can draw down electricity from the battery and contribute that to the system of electricity,” he said. “You end up being a purchaser and seller of electricity through your electric car.””
Again, the “may be” is at the head of the paragraph, the promise is at the end. Readers are left with the idea of receiving money from Ontario Hydro, just for parking their car during the day and night.
I have doubts about perpetual energy, and I have doubts about monetary gains being made off an artifact that was purchased for non-monetary gains.
I would like to see “may be” quantified, with verified figures of tests showing (a) how much parking is required (b) how frequently and (c) how much electricity is fed back from the car (sorry, I meant to write ‘battery’) and hence (d) how much money is generated.
Come to think of it, if the electricity-generating scam^H^H^H^H scheme is such a good one, why don’t we eliminate the car and just stack a mountain of car batteries in our basement?
I’m off to buy some more shares in lead, and plastic!
Babies Bodies
This is still about Energy. Please don’t email me and say that I’m heartless. I’m not. I avoid treading on ants, and can be seen lifting a waterlogged worm from the concrete footpath and placing it back on the grass.
I’m so clucky that I stand in line to hold and cuddle the latest addition to the human race, when it is presented in my client’s office.
Today’s Toronto star (http://www.thestar.com/news/gta/article/662664) runs a story about a toddler who survived a two-storey plunge down a shopping mall elevator shaft yesterday.
We should not be surprised.
We are, of course, delighted that no apparent harm was done. I’ll bet that any lasting damage is more likely to be found in the parent than in the child.
Why should we not be surprised?
Well, in “River Out Of Eden”, Richard Dawkins begins the with a startling, yet true claim on behalf of all organisms that have ever lived: not a single one of our ancestors died before they reached adulthood and begot at least one child.
Babies (of all mammals and most animals anywhere) are built to survive.
Bones are soft, eyes are protected in sockets recessed into bony skulls, baby fat is still available to absorb some of the energy that is implicit when a body falls, converting potential energy into kinetic energy. (see also “Energy – again!”).
Babies are born prematurely; they have to be born before their head grows too big to exit the womb, but brain development proceeds for at least another three years (have you any specific memories prior to your third birthday). The bones and the body in general is still incapable of survival, is still being formed.
Think of a baby as a machine that has evolved to survive falling out of trees, off rocks, rolling down hillsides, getting knocked to the ground by boisterous siblings and so on, and you’ll start to see a baby as an energy-absorbing machine.
And relax; I still like cuddling them.
