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enter image description here

According to the diagram, we know that if we apply a respectively force of 3N and 4N in the relative direction, then the resultant force will be 5N on its direction. But it's that means some of the energy lost to the surrounding? We applied a total force of 7N but the resultant force is only 5N, doesn't it prompt that there are some energy lost ?

Qmechanic
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ZhangJin
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    the direction of your 5N force is incorrect – Bob D Dec 27 '23 at 15:34
  • Forces are not energy. Forces that cause displacements do work which transfers energy. – Bob D Dec 27 '23 at 15:36
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    Does this answer your question? Where am I confused about force addition? – Kyle Kanos Dec 27 '23 at 15:36
  • I had a nearly complete answer when this closed, but I can at least offer a comment. Force is not the same thing as energy. Work done (energy) is equal to the force applied in the direction of travel multiplied by the distance traveled. (there's no travel in the picture shown). There's a dot product (or a cosine) in the formula. If you look at the work done by the 5N force on any path, and you look at the sum of the works done by the 3N and the 4N forces along the same path, you will find that they are equal amounts of work. – Cort Ammon Dec 27 '23 at 16:19
  • @CortAmmon it was closed as a duplicate of an earlier question that asks the same question (even using the same values for the forces!). You should post your answer in the linked duplicate – Kyle Kanos Dec 27 '23 at 16:55
  • I mean some energy must be applied to generate a force of 3N and 4N, but the outcome is less than the energy we have put in in case there's no energy lost to the surrounding. Why does this happening ? – ZhangJin Dec 28 '23 at 14:22
  • @ZhangJin 0 energy is required to generate a force. Energy is only needed for a force applied when moving a distance. The best example being of this is gravity. Consider a heavy book lying on a desk. It certainly applies a force to the desk, but no energy is needed unless the book is moved up or down. – Cort Ammon Dec 30 '23 at 16:32
  • @CortAmmon So the conclusion is energy is not depends on force and there's no relation between force and energy. Is that correct ? – ZhangJin Jan 01 '24 at 06:23
  • @ZhangJin I'd say that energy and force are not proportional. There is a relationship, but its a little more complicated. You can have one without the other. You need a force and motion (in the direction of the force), and then the work (energy) exerted by the force is the force multiplied by that distance. If there's no motion, then there's no work/energy. – Cort Ammon Jan 01 '24 at 20:56
  • Got it, thanks. – ZhangJin Jan 02 '24 at 14:43

1 Answers1

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First of all, the diagram has issues. Note how the angle is expressly $>90$ degrees and so the longest arrow is $>\sqrt{4^2 +3^2}$.

In words, the force vector labeled “5N” is not $5N$ of force. The only way this could happen is if the angle between the two vectors was exactly $90$ degrees.

As an aside, the “energy” to be considered here is likely work done which is $\int{\bf F}\cdot d{\bf r}$ but we can’t really discuss this in this context without knowing details about the path the particle is taking. We don’t really have a physical picture here, just a force diagram.

It doesn’t really make sense to consider energy in this context (as the question is posed).

JohnA.
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