The coolest number!
[youtube]AuA2EAgAegE[/youtube]

I prefer φ, because... it's simple and cool!

#TeamPhi

Now I want a st-[tex]\rho[/tex]-berry [tex]\pi[/tex].

4 years passed since the destraction of the world....feel like it was just yesterday

I was bored one day, so I decided to make an analogy. If I had a grain of rice for every time I went around the earth, to travel the distance equivalent to the distance to Proxima Centauri, I could fill about 8 buses with rice.

How are analogies involving buses and similar containers calculated? What kind of buses are used? Is the space occupied by seats accounted for? What about the poles that adorn the interior of some public vehicles? If I ever tried to make an analogy similar to this I would probably spend a few days just trying to answer all the questions I have!

Oops, somehow that got posted twice. I can't remove it, perhaps an moderator can. 

I just looked up the average volume of a bus and it gave me 27 m³.

I would but deleting posts doesn't work on mobile.

Today's APOD:

"Once Upon a Solstice Eve"

Taken by Petr Horálek

Marvelous photo.  I love those kinds of projections.

I just had a car accident! 
Luckily no-one got involved, just me and my foolishness...

That's actually a fairly common experience and I've nearly had an accident that way, myself.  It's pretty scary!  And it all comes down to physics.

All objects will move in a straight line with constant speed unless acted on by some force.  Your car is no different.  If you're driving through a curve, a force is necessary to make it follow that curve.

We can consider the curve to be a part of a circle with a radius [tex]R[/tex].  To follow that curve, there needs to be a centripetal force [tex]F_c = \frac{mv^2}{R}[/tex].  This centripetal force is supplied by friction between the tires and the road surface, and this friction force has a maximum strength of [tex]F_{max}=\mu mg[/tex], where [tex]\mu[/tex] is the coefficient of friction between the tire and road.  m is the mass of your vehicle and g is the gravitational acceleration on Earth.

Equate these to solve for the maximum speed you can have through the curve:
[tex]F=ma=\mu mg = \frac{mv^2}{R} \Rightarrow v_{max} = \sqrt{\mu gR}[/tex]

This tells us the fastest speed we can have for a curve with a given radius of curvature and a coefficient of friction.  If we try to drive faster than that, then the tires will not be able to provide enough force to keep us along the curve, and we'll begin to slide.  Notice the max speed is slower for a smaller coefficient of friction, a smaller radius of curvature (sharper turn), or if gravity is weaker (harder to drive in low gravity, as anybody who plays with rovers in KSP will know from experience).

Let's apply some numbers:

The coefficient of friction between tires and dry road surface is typically around 0.7.  Suppose the curve forms part of a circle with a radius of 25 meters.  Then the maximum speed we can safely drive is about 13m/s, or 47km/hr.  What if the road is wet?  This decreases the coefficient of friction to about 0.4.  In that case our max speed for that curve is only 35km/hr!  So the road conditions are very important.  

It's also very important to note that even at speeds below this theoretical maximum, it is easier to lose control than if you were driving straight, especially if you're also trying to correct your steering or applying the brakes.  So we have to be cautious with curves.  Apply the brakes before you enter the curve so that you're already at a safe speed, and give yourself an extra margin for safety if the roads are wet.

That's actually a fairly common experience and I've nearly had an accident that way, myself.  It's pretty scary!  And it all comes down to physics.

All objects will move in a straight line with constant speed unless acted on by some force.  Your car is no different.  If you're driving through a curve, a force is necessary to make it follow that curve.

We can consider the curve to be a part of a circle with a radius [tex]R[/tex].  To follow that curve, there needs to be a centripetal force [tex]F_c = \frac{mv^2}{R}[/tex].  This centripetal force is supplied by friction between the tires and the road surface, and this friction force has a maximum strength of [tex]F_{max}=\mu mg[/tex], where [tex]\mu[/tex] is the coefficient of friction between the tire and road.  m is the mass of your vehicle and g is the gravitational acceleration on Earth.

Equate these to solve for the maximum speed you can have through the curve:
[tex]F=ma=\mu mg = \frac{mv^2}{R} \Rightarrow v_{max} = \sqrt{\mu gR}[/tex]

This tells us the fastest speed we can have for a curve with a given radius of curvature and a coefficient of friction.  If we try to drive faster than that, then the tires will not be able to provide enough force to keep us along the curve, and we'll begin to slide.  Notice the max speed is slower for a smaller coefficient of friction, a smaller radius of curvature (sharper turn), or if gravity is weaker (harder to drive in low gravity, as anybody who plays with rovers in KSP will know from experience).

Let's apply some numbers:

The coefficient of friction between tires and dry road surface is typically around 0.7.  Suppose the curve forms part of a circle with a radius of 25 meters.  Then the maximum speed we can safely drive is about 13m/s, or 47km/hr.  What if the road is wet?  This decreases the coefficient of friction to about 0.4.  In that case our max speed for that curve is only 35km/hr!  So the road conditions are very important.  

It's also very important to note that even at speeds below this theoretical maximum, it is easier to lose control than if you were driving straight, especially if you're also trying to correct your steering or applying the brakes.  So we have to be cautious with curves.  Apply the brakes before you enter the curve so that you're already at a safe speed, and give yourself an extra margin for safety if the roads are wet.

Amazing explanation... The radius of the curve is 33m so the max safe speed was approximately 54km/h, the cases are three:

• I was going too much fast.
• I've found an area of the road in which the coefficient of friction was below 0.7 (maybe because of ice).
• Brakes influenced stability a lot and I've lost control because of that!

I forgot to mention that the road was uphill, in that case was the coefficient of friction higher because the slope exercised an "additional force"?

I forgot to mention that the road was uphill, in that case was the coefficient of friction higher because the slope exercised an "additional force"?

Oh yes, the slope will be another factor. This is not because it provides an additional force, but because it decreases the strength of the normal force (that of the ground pushing up on the car, to balance the force due to gravity), which decreases the maximum strength of friction that we can have.  The normal force follows the cosine of the slope: [tex]F_{normal} = \mu mgcos\theta[/tex].  So with the road angle the max safe speed is [tex]v_{max}=\sqrt{\mu gRcos\theta}[/tex]

Road slopes are kept to fairly shallow angles and so this isn't a very big correction.  At 10 degrees the max speed is reduced by only 0.8%, and even for some of the steepest roads at ~20 degrees, it's only 3% less.  But it is another factor which acts against us for safely taking the curve.

So I think the best answer for what happened is a combination of effects.  Being too close to the maximum safe speed for the curve with a slight uphill made it easier to lose control and harder to regain it, and control was probably lost due to braking.

There is a lot that can be said on braking itself.  It's a bit counter-intuitive since you'd think it just slows you down and therefore makes you safer.  But the problem is that by braking on a turn, you're trying to get an additional acceleration out of your tires, at the same time that they are already providing an acceleration in order to follow the curve.  Any acceleration with the car requires friction, and as we just saw there is only so much that can be applied before you lose traction and start to slide.  This is why we don't want to have to brake during the turn, but rather before we go into it, so that we can just coast through the turn.  If you do need to brake, then it's best to apply them gently, and try to feel for that limit where traction is being lost and not push beyond that.