suppose i jump from ground then work done by normal is zero as point of application displacement is zero(work is doneby internal forces) but during the pushing part COM has upwards displacement then shouldn't work be done if apply force on COM ??
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$\begingroup$ but shouldn't it be as normal acts on the feet and its displacement is zero while normal is acting? $\endgroup$– Us18Commented Feb 15, 2017 at 14:36
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$\begingroup$ but is we assume our body as a system then normal is ext force and there is displacement of centre of mass $\endgroup$– Us18Commented Feb 15, 2017 at 14:41
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$\begingroup$ C.O.M has nothing to do here. The normal force is acting on particles in your body which don't move. These particles then transfer the force to the adjacent particles (which remain at rest too). Your muscles use the particles at rest to apply a force so that it applies a force in the opposite direction which sends you upwards. $\endgroup$– YashasCommented Feb 15, 2017 at 14:42
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$\begingroup$ i understand that but if i assume my body as system then work done by normal should be N × displacement of COM shouldn't it be ?? $\endgroup$– Us18Commented Feb 15, 2017 at 15:00
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2 Answers
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When you jump, your legs don't leave the ground instantaneously.
When you bend, you do work on your body (your muscles are applying force and your center of mass gets displaced). Your muscles do work against the gravity to slow your downward motion down.
After you bend completely, you try to jump. In the process, your muscles begin to move your body upwards. Your body is being displaced and you jump (you are gaining kinetic energy). At one point, your body has sufficient velocity and momentum that you can left your legs.
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$\begingroup$ I would say that Normal Force did not act on you ( by did not act I mean it never caused displacement) . You press a book by your finger and remove it quickly moving it upwards. Both while pushing or pulling its the muscles that push or pull. At the instant you leave the ground N =0 . It does no work . All the work was due to the pulling. The pencil example that I gave had an impulse acted on it and was apparently misleading ! Your bending example is better . It shows the pulling force ! $\endgroup$ Commented Feb 15, 2017 at 19:05
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Normal force doesn't do work . You are thinking right that your Center of Mass has got a displacement and it's the displacement of the center of mass which counts in the equation.
What your are not seeing is that The Normal Force doesn't last during the interval of displacement . Infact Displacement begins after Normal Force has gone down to 0.
For eg: You hit a pencil . During the time of your hit the pencil displaces only a very small amount. And that displacement causes the work done by you. After that ( without friction ) the pencil moves with a constant velocity.
Here the Normal Force doesn't even cause the displacement . Its your muscles.
Consider a block on an inclined plane . You apply force horizontally to the plane . The normal force being perpendicular to the displacement doesn't do any work. But its the vertical component of normal force the cause the block to rise. Effectively the Normal Force has caused your applied force to raise the block ( your applied force doesn't raise it directly ).
Similarly the normal force here causes you muscles ti do the work .
answered Feb 15, 2017 at 15:16
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$\begingroup$ I am kneeling down. I start moving upwards. My legs are still in contact with the ground. There is a normal force (not $mg$ but also not zero). My center of mass is displaced. $\endgroup$– YashasCommented Feb 15, 2017 at 15:43
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$\begingroup$ @YashasSamaga Yes I knew that point that's why I wrote the last line that Normal Force doesn't cause the displacement . Its the muscular force ! $\endgroup$ Commented Feb 15, 2017 at 15:45
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$\begingroup$ @YashasSamaga On thinking , his point is also right. That when I bend down trying to jump there is a normal force which acts for a small time . I have added to my answer. Have a go at it ! $\endgroup$ Commented Feb 15, 2017 at 15:53