you have to push a big and heavy box to a distance think away which will make this task easier
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The force that apply on the object
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Work is force times distance. Force without movement means no work. The error here is confusing external (or summed-up) work, for all work.
In the simplest analysis of your problem, nothing moves therefore no work was done, and this is correct, but only for the global view. No work was done on the heavy object. No work was done on (or by) you as a whole.
Internally, there is a different story. When you use your muscles, you engage muscle fibers to twitch together. A muscle contraction is a whole bunch of muscle fibers twitching and then relaxing, and repeating. The harder the contraction, the more fibers are involved and the more rapidly they repeat that cycle.
So if you push really hard on the heavy object, inside of your muscles, a ton of work is happening (or more accurately, a foot-ton, or perhaps, a mile-pound). This can be true even while you are doing no work externally.
Your muscle fibers are always doing work—even at rest. Each fiber randomly twitches. How much this happens determines what is called your muscle-tone. Flabby muscles are made of fibers that don't twitch that much.
Regarding some other answers here:
The spring notion is interesting but misses the point. The energy you consume in pushing on a spring will not be explained by one single deflection of that spring, and when that spring returns, it will not return the energy to your muscle fibers. The longer you hold that spring compressed, without moving, the more movement you get in your muscle fibers, doing more internal work, and consuming energy to match.
The generation of heat it simply an expression of work occurring at the atomic level.
Is work the same as energy? No but they do always have to balance. If work is done energy is always used. If energy is used, work is always done somewhere. Perhaps not where you think, or where you want it. This is just conservation of energy: energy can never be created or destroyed (ignoring nuclear reactions, where e=mc^2 covers the conservation), energy just moves matter around. You can also think of work as just a meta-concept for energy, from a specific point of view. Work is a way of accounting for energy when it is transferred to or from the object you are considering.
In the simplest analysis of your problem, nothing moves therefore no work was done, and this is correct, but only for the global view. No work was done on the heavy object. No work was done on (or by) you as a whole.
Internally, there is a different story. When you use your muscles, you engage muscle fibers to twitch together. A muscle contraction is a whole bunch of muscle fibers twitching and then relaxing, and repeating. The harder the contraction, the more fibers are involved and the more rapidly they repeat that cycle.
So if you push really hard on the heavy object, inside of your muscles, a ton of work is happening (or more accurately, a foot-ton, or perhaps, a mile-pound). This can be true even while you are doing no work externally.
Your muscle fibers are always doing work—even at rest. Each fiber randomly twitches. How much this happens determines what is called your muscle-tone. Flabby muscles are made of fibers that don't twitch that much.
Regarding some other answers here:
The spring notion is interesting but misses the point. The energy you consume in pushing on a spring will not be explained by one single deflection of that spring, and when that spring returns, it will not return the energy to your muscle fibers. The longer you hold that spring compressed, without moving, the more movement you get in your muscle fibers, doing more internal work, and consuming energy to match.
The generation of heat it simply an expression of work occurring at the atomic level.
Is work the same as energy? No but they do always have to balance. If work is done energy is always used. If energy is used, work is always done somewhere. Perhaps not where you think, or where you want it. This is just conservation of energy: energy can never be created or destroyed (ignoring nuclear reactions, where e=mc^2 covers the conservation), energy just moves matter around. You can also think of work as just a meta-concept for energy, from a specific point of view. Work is a way of accounting for energy when it is transferred to or from the object you are considering.
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