11–20 of 231 posts
F=ma (Force equals mass times acceleration)
W=Fd (work equals force multiplied by distance)
V^2=2ad (velocity squared equals two times acceleration times distance)
So W = Fd = ma(v^2/2a)
Finally: W=1/2mv^2 (work equals 1/2 mass times velocity squared)
So this explains why car crashes can be so dramatic, as a doubling of speed results in 4x the kinetic energy.
Fun little anecdote: A blue care is travelling along at 70 units, and a red car (exact same make and model) is catching up to it going 100. When they're both right beside each other a bend in the road reveals an obstacle blocking both lanes, so both cars brake at the same intensity and deceleration. The blue care stops right before the obstacle. Since the red car was going at a faster speed, and braked at the same ra…
But if the cars produce downforce this is no longer true because you brake harder (more friction available) at higher speeds!
This is how F1 cars pull 4G when breaking. Some custom cars (like one of Ken Block’s last monsters or the Valkyre) use active aero braking to even greater effect.
Physics is an endless source of frustration to me. It feels like a mix of random tricks, most of which I don’t understand. I find math and compsci reasonably understandable, can read research papers in both fields ( and have published papers) etc. There’s something specific about physics I don’t get but I’ve never been able to figure out what. The main symptom is that most cause -> consequence in such demonstrations…
More than twenty years ago, I quit a program that taught math/cs/physics (the notorious French "classes préparatoires") ~almost precisely over this: I felt like I was being taught physics like it was an axiomatic system where the tricks should not be questioned, they just work so "shut up and calculate" (and you don't even need to be doing quantum mechanics for that). I just felt like we never got to the heart of the…
Maths (and especially compsci!) are constructions by and for humans.
Is it any wonder it is as you describe? It would be odd if it was any other way.
Physics is an endless source of frustration to me. It feels like a mix of random tricks, most of which I don’t understand. I find math and compsci reasonably understandable, can read research papers in both fields ( and have published papers) etc. There’s something specific about physics I don’t get but I’ve never been able to figure out what. The main symptom is that most cause -> consequence in such demonstrations…
It seems that we're exact opposites! But if mathematics is your thing, it might be interesting for you to explore trying to learn things from a lagrangian perspective first? Not sure if it'll help you with gaining an intuitive understanding, but at least it'll be interesting! https://en.wikipedia.org/wiki/Lagrangian_mechanics
Earlier quoted context omitted.
More than twenty years ago, I quit a program that taught math/cs/physics (the notorious French "classes préparatoires") ~almost precisely over this: I felt like I was being taught physics like it was an axiomatic system where the tricks should not be questioned, they just work so "shut up and calculate" (and you don't even need to be doing quantum mechanics for that). I just felt like we never got to the heart of the…
The world just is, regardless of what we think about it. Physics is our best attempt so far to understand and predict it at a low level, but it will always be incomplete. Maths (and especially compsci!) are constructions by and for humans. Is it any wonder it is as you describe? It would be odd if it was any other way.
Because it's not momentum. ;p F=ma (Force equals mass times acceleration) W=Fd (work equals force multiplied by distance) V^2=2ad (velocity squared equals two times acceleration times distance) So W = Fd = ma(v^2/2a) Finally: W=1/2mv^2 (work equals 1/2 mass times velocity squared) So this explains why car crashes can be so dramatic, as a doubling of speed results in 4x the kinetic energy.
So in some sense energy is momentum in the time direction (though it's not a Euclidean 4D space, so beware of assumptions). For an object at rest, this becomes its E=mc² equivalence. Kinetic energy is just a straightforward "rotation" of the frame.
Earlier quoted context omitted.
More than twenty years ago, I quit a program that taught math/cs/physics (the notorious French "classes préparatoires") ~almost precisely over this: I felt like I was being taught physics like it was an axiomatic system where the tricks should not be questioned, they just work so "shut up and calculate" (and you don't even need to be doing quantum mechanics for that). I just felt like we never got to the heart of the…
The world just is, regardless of what we think about it. Physics is our best attempt so far to understand and predict it at a low level, but it will always be incomplete. Maths (and especially compsci!) are constructions by and for humans. Is it any wonder it is as you describe? It would be odd if it was any other way.
Fun little anecdote: A blue care is travelling along at 70 units, and a red car (exact same make and model) is catching up to it going 100. When they're both right beside each other a bend in the road reveals an obstacle blocking both lanes, so both cars brake at the same intensity and deceleration. The blue care stops right before the obstacle. Since the red car was going at a faster speed, and braked at the same ra…
> The blue car, using ½mv², shed (~70²=) 4900 units of energy (we'll hand wave away the constants). So the red car, which had (100²=) 10000 units of kinetic energy to start, also shed 4900 units, which means it had 5100 units of energy when it collided, and so was going (√5100~) 71 But if the cars produce downforce this is no longer true because you brake harder (more friction available) at higher speeds! This is how…
Because it's not momentum. ;p F=ma (Force equals mass times acceleration) W=Fd (work equals force multiplied by distance) V^2=2ad (velocity squared equals two times acceleration times distance) So W = Fd = ma(v^2/2a) Finally: W=1/2mv^2 (work equals 1/2 mass times velocity squared) So this explains why car crashes can be so dramatic, as a doubling of speed results in 4x the kinetic energy.
Actually, it is momentum, sorta. Galilean 3D momentum isn't conserved under special relativity. The energy-momentum four-vector, however, is, under all lorentz-transformed frames. So in some sense energy is momentum in the time direction (though it's not a Euclidean 4D space, so beware of assumptions). For an object at rest, this becomes its E=mc² equivalence. Kinetic energy is just a straightforward "rotation" of th…
This is linear.
One small nuance... saying "kinetic energy is just a straightforward rotation of the frame" is close, but it's the total energy that is the time component of the four-momentum and mixes with the spatial momentum under Lorentz transformations. Kinetic energy is the difference between that transformed total energy and the invariant rest energy. So kinetic energy isn't itself a four-vector component, but it arises from how the time component changes when viewed from a different inertial frame.
Earlier quoted context omitted.
> The blue car, using ½mv², shed (~70²=) 4900 units of energy (we'll hand wave away the constants). So the red car, which had (100²=) 10000 units of kinetic energy to start, also shed 4900 units, which means it had 5100 units of energy when it collided, and so was going (√5100~) 71 But if the cars produce downforce this is no longer true because you brake harder (more friction available) at higher speeds! This is how…
But what if the cars are spherical cows?