These units are typically given as J/s and W-s, or W/s. If this energy expenditure happens in one second, then it is defined as one joule/second or one watt-second, or one watt/second. The energy required to complete this action is exactly one watt. Therefore, one joule is the work done, or energy expended, when a force of one newton acts through a distance of one meter. Work occurs through a force acting over a distance. This energy expenditure is equal to exactly one watt. One newton is the force, one kilogram is the mass, and one meter is the distance moved in one second time one joule is the energy expended, or work done, in this action. Essentially, a one-newton force, acting on a one-kilogram mass, will accelerate that 1-kg mass through one meter in one second. One joule is equivalent to the energy expended, or work done, by a force of one newton accelerating a one-kilogram mass through a distance of one meter in one second. Let’s state, and restate, the elementary concepts regarding this definition. The question asked for the definition of a joule. ThenĮach mass now has the same amount of momentum, but if you calculate out the energy, the smaller mass has significantly more energy ( $0.5J$ vs $0.0005J$) Suppose instead we applied a force of 1N for 1 second to each mass. So the larger mass has significantly more momentum, even though they have the same amount of energy. Taking your example of $m_1 = 1 \space kg$ and $m_2 = 1000 \space kg$, we can calculate that after the application of 1 Joule of work each mass will be traveling at $v = \sqrt$, so It just turns out that something is momentum, not energy. It's understandable that since the bigger mass experiences the force for a longer time, it feels like it should have more something than the smaller mass. I would just like to offer a perspective that doesn't focus so much directly on work/energy. We are too darn inefficient and so much is going on beneath our surfaces for us to be relied upon. Of this reason it is unwise to rely on the human feeling when we are talking about energy usage in science. But all that extra energy is not spent as work on the object, it is just spent on compressing and elongating muscle fibres, on increasing heart rate and respiration, on adrenalin flows and circulation etc. So pushing for a longer time does correspond to more energy being spent. Our human bodies spend energy just to produce a force. But this is of another reason: this is due to our inefficient human bodies and not due to more energy being given to the pushed object. You can clearly feel more energy being spent. It does feel tougher to push on something over a longer time. The duration that the force acts over has no influence on the energy being spent on the object, the work that is being done.īut you might still object to this answer. But it doesn't matter if the book started from rest and now falls while slowly speeding up, or if the book was thrown down with high initial speed so that it reaches the ground much faster - in both cases gravity did the same amount of work, spent the same amount of energy. Only when the book falls is work done by pulling it further down. It is constantly pulling in the book on the shelf - but no energy is spent, no work is done. Just because it takes more time doesn't mean more energy is spent. How is it the same amount of work done if I have to be pushing on that 1000kg object a lot longer than the 1kg object to move it over a metre?
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