Why do mountain roads rarely go straight up the slope but wind up gradually?
The roads follow natural inclines that are not so steep. You will do this same thing naturally when walking up a steep incline, you go up at an angle because the walking is easier in the short term.
Because cars can't go "straight up" and roads that go straight up would tend to crumble to say nothing of how extraordinarily difficult (and expensive) it would be to construct such a road.
Picture an inclined plane wound around the mountain.
A smaller force is required to climb to the top, although one must travel a longer distance.
About the steepest stretch of road I've ever been on was a 15% incline, and that was truly pushing the cars to maintain speed (a lot of other cars couldn't maintain speed; any steeper and I'd have probably hit maximum RPMs I could hit without blowing the engine). One also has to consider that mountains are also more prone to freezing conditions, and a very steep incline will become completely impassable in inclement weather. The engineers could probably answer this better.
I think you did a fine job of answering the question!
I once made the mistake of stopping on a steep mountain road. I couldn't get the car moving forward: it just couldn't get up the initial acceleration! I wound up backing down to the bottom to get a running start.
I once took a shortcut in a camper van. It went up a very steep incline of loose gravel road. I reached a point where all I was doing was spinning the wheels. I couldn't turn around; any movement at all, including reversing caused me to start slipping. It was all I could do to stay in one spot.
So I rappelled down the slope.
I would let off the brake just enough to start moving, then put the brake on and let it slide a few more yards until I stopped, then do it again until I reached bottom.
It was a while before my father lent me his camper van again...
It was a while longer before my wife would go camping with me again...
Thanks for the explanation everyone!
Don't forget flash floods and avalanches.
Can this be explained by,
where [tex]\theta[/tex] is the angle of inclination, v is the velocity of the body and g is the acceleration due to gravity, r is the radius of curvature.
Hmm... Is it rappelled or grappelled? Grappelled is going up, and rappelled down? Hmm, turns out rappelled is going down, but what is grappelled? Maybe grappelled is both ways.
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