171–180 of 231 posts
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That's a good question, and I suppose the mgh formula isn't a suitable answer, so my answer would be something like: if you lift an object to some height, and then you repeat that action (lifting it from there to twice the height), you've done twice the work, and doing twice the work requires twice the caloric intake.
> if you lift an object to some height, and then you repeat that action (lifting it from there to twice the height), you've done twice the work, and doing twice the work requires twice the caloric intake. You’re introducing two new intuitions, and it’s not intuitively obvious how they are related to each other. Why would work correlate 100% with caloric intake, and caloric intake 100% with kinetic energy? Certainly,…
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While it is true that some cars can brake harder due to downforce etc, the point from GP was that both cars brake/ decelerate at the same rate. Regardless of how exactly that deceleration is achieved.
> the point from GP was that both cars brake/ decelerate at the same rate Point is that’s not always true. If they are the same type of car, and the car happens to be the kind with downforce, then their rate of deceleration greatly depends on air speed. A downforce car decelerates faster at higher speeds. This is why you often see race cars lock their wheels towards the end of the braking zone, never at the beginning…
That’s not the only reason, and I’m not even sure it’s the majority reason.
Braking in a straight line offers more braking traction than braking while turning. What happens towards the end of a braking zone? The turn in. (Which also shifts weight to the outside tire and away from the inside tire.)
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> We know intuitively that a ball atop a 20ft ladder has twice the potential energy of a ball atop a 10ft ladder. What makes this intuitive? The foundation of the asker’s question is that it seems intuitive that kinetic energy would increase linearly with speed, but that turns out to be wrong.
The effort to move a piece of furniture from 1st to 2nd floor is the same as the effort to move it from the 2nd to the 3rd. We have good intuition for this by our experience, which derives a linear relationship. The effort to move a piece of furniture up two floors is double the effort of moving it up one floor (ie you have to put the same effort twice, assuming enough rest). I would not say we have the same intuitio…
For me, the most intuitive explanation is that: Force = change in momentum with time Energy = Force x distance Now consider how much energy can be dissipated by a tiny change in momentum over a small distance dx, when we are at a given velocity v: dE = F dx = (dp/dt)dx = m (dv/dt) dx = m dv (dx/dt) = m v*dv The intuition is that in order to apply a force through some distance, I have to change the velocity of an obje…
After reading a few answers I still feel like I haven't seen an intuitive answer to the question: why does it take so much more energy to go from 1 to 2 than from 0 to 1? I have been thinking about it and only been able to come up with something that feels intuitive but not at all precise and I don't know how correct. When you stand still you may use your surroundings to gain some speed, like by pushing against a wal…
Sounds intuitive but what about rocket propulsion?
Back-of-napkin calculation says that if you managed to perfectly match exhaust speed with current speed, leaving all the expelled propellant stationary, it would only take quadratic amounts of fuels to reach higher speeds. Like the kinetic energy equation predicts.
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> if you lift an object to some height, and then you repeat that action (lifting it from there to twice the height), you've done twice the work, and doing twice the work requires twice the caloric intake. You’re introducing two new intuitions, and it’s not intuitively obvious how they are related to each other. Why would work correlate 100% with caloric intake, and caloric intake 100% with kinetic energy? Certainly,…
Friction. Work isn't just about height.
Earlier quoted context omitted.
The effort to move a piece of furniture from 1st to 2nd floor is the same as the effort to move it from the 2nd to the 3rd. We have good intuition for this by our experience, which derives a linear relationship. The effort to move a piece of furniture up two floors is double the effort of moving it up one floor (ie you have to put the same effort twice, assuming enough rest). I would not say we have the same intuitio…
Scale up the numbers in you example: The effort to move a piece of furniture from 10,000th to 20,000th floor is NOT the same as the effort to move it from the 20,000th to the 3rd. The reduced gravity will help you.
But more to the point the kinetic energy here is being turned into gravitational potential energy. If you move to a place with a weaker gradient in gravitational potential of course the same amount of kinetic energy moves you farther up.
It's easiest to visualize in terms of conversion from potential energy. We know intuitively that a ball atop a 20ft ladder has twice the potential energy of a ball atop a 10ft ladder. And we also know when they fall, by the time they reach the ground and all the potential energy has been converted to kinetic energy, the previously higher ball will have twice the kinetic energy too. But a twice higher ball won't have…
> We know intuitively that a ball atop a 20ft ladder has twice the potential energy of a ball atop a 10ft ladder. ...no ? dropping something 10 times from 1ft is nowhere near energetic/damaging as once from 10tf