If it takes 10 energy units to move a 10kg weight 10 meters, does the energy expended go up as the time used decreases?
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Energy is Force * Distance. In this case the distance stays the same, so we must ask ourselves if the Force changes.
Well, since we know the time decreases, then we know the object moved faster. If it moved faster then it must have had more force applied to it. And since distance is the same, we know that more force means more energy used.
That said, this assumes a constant force being applied. It gets more complicated if that isn’t the case.
Energy is Force * Distance. In this case the distance stays the same, so we must ask ourselves if the Force changes.
Well, since we know the time decreases, then we know the object moved faster. If it moved faster then it must have had more force applied to it. And since distance is the same, we know that more force means more energy used.
That said, this assumes a constant force being applied. It gets more complicated if that isn’t the case.
Movement, in and of itself, does not take energy.
Movement *against a force*, like friction or gravity, takes energy, at least from the perspective of just you and the moving object (energy is still conserved overall, but you + the moving object might gain or lose it when taken in isolation).
If you’re pushing an object along the ground, the main force resisting movement is friction. And for everyday objects at everyday speeds, friction (with a surface) is independent of how fast the object moves: it’s just the weight of the object (or more properly, the normal force, but the two are equal for an object lying on a surface) times a number called the coefficient of (kinetic) friction that describes how “slippery” the object is. In other words, regardless of your speed, for any fixed object, the frictional force is ~the same.
The energy required to move an object against a force (or the energy gained by letting it move with a force) is called *work*. And the formula for work is W = F * d, where F is the force you’re moving with or against and d is the distance you move. Since in this case both the force from friction, and the distance moved, are the same, the amount of work required is the same, too.
Note that we’re making a lot of simplifying assumptions here, though. Like most engineering/mechanics questions, there are details that can matter, like the exact surface structure of the object we’re moving.
Movement, in and of itself, does not take energy.
Movement *against a force*, like friction or gravity, takes energy, at least from the perspective of just you and the moving object (energy is still conserved overall, but you + the moving object might gain or lose it when taken in isolation).
If you’re pushing an object along the ground, the main force resisting movement is friction. And for everyday objects at everyday speeds, friction (with a surface) is independent of how fast the object moves: it’s just the weight of the object (or more properly, the normal force, but the two are equal for an object lying on a surface) times a number called the coefficient of (kinetic) friction that describes how “slippery” the object is. In other words, regardless of your speed, for any fixed object, the frictional force is ~the same.
The energy required to move an object against a force (or the energy gained by letting it move with a force) is called *work*. And the formula for work is W = F * d, where F is the force you’re moving with or against and d is the distance you move. Since in this case both the force from friction, and the distance moved, are the same, the amount of work required is the same, too.
Note that we’re making a lot of simplifying assumptions here, though. Like most engineering/mechanics questions, there are details that can matter, like the exact surface structure of the object we’re moving.
I’ve been thinking more about this, and I think I may have guess wrongly about what you meant. Here is a simple scenario where it would work like you think (energy is the same, even if one is faster):
Two space ships travel 100km. The first space ship accelerates to 100 m/s over the first km then travels the rest of the 99km at that speed with no more acceleration.
The second ship accelerates to 100 m/s over the entire 100km, not reaching it’s top speed until the very end of the journey.
In both cases the energy used is the same (the amount of kinetic energy the space ship has at 100 m/s), but the first ship would get to it’s destination much faster.
The key point that makes this work is that the top speed of each ship is the same – it’s only the acceleration that’s different.
So I guess the most correct answer to your original question is: it depends. A higher speed requires more energy, but it doesn’t matter how fast you reach that speed (ignoring real-life mechanical limitations).
I’ve been thinking more about this, and I think I may have guess wrongly about what you meant. Here is a simple scenario where it would work like you think (energy is the same, even if one is faster):
Two space ships travel 100km. The first space ship accelerates to 100 m/s over the first km then travels the rest of the 99km at that speed with no more acceleration.
The second ship accelerates to 100 m/s over the entire 100km, not reaching it’s top speed until the very end of the journey.
In both cases the energy used is the same (the amount of kinetic energy the space ship has at 100 m/s), but the first ship would get to it’s destination much faster.
The key point that makes this work is that the top speed of each ship is the same – it’s only the acceleration that’s different.
So I guess the most correct answer to your original question is: it depends. A higher speed requires more energy, but it doesn’t matter how fast you reach that speed (ignoring real-life mechanical limitations).
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