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If the force $$F=3i +4j $$ moves a body from the position $$A(2 , 3)\ \mathrm{to}\ B(7 , 6) $$ .Evaluate the change in the potential energy of the body . My turn: The work done by the force =$$(3,4) • (5 , 3)= 27$$ $$\delta PE + \delta KE = W $$ But I think the given is not enough to evaluate the change in the the kinetic energy ?

J W
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Hussien Mohamed
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1 Answers1

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This is a physics question. There are two parts to this problem. One is the force. The force moving an object from point $A$ to point $B$ will do some work, which you already calculated. Then there is an object that moves under the influence of that force. When the object moves from point $A$ to point $B$ it changes its' potential energy. They are equal in magnitude, but opposite in sign. If the object moves only under the influence of the force, it will lose potential energy, but it will be transformed into kinetic energy. Think of it like action and reaction. The two happen on different entities. Therefore $$W=-\Delta U =\Delta K$$ Note that $W=-\Delta U$ is always true, but the second part is not necessary. One can have additional forces in the system, to compensate for the loss in potential energy, without increase in kinetic energy. To give an example: hold a ball with your hand extended above your head. Then lower it slowly and stop. The ball lost potential energy (the gravity did some work), but your hand also did some work in the opposite direction, so the kinetic energy at the end is still $0$.

Andrei
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  • I think the example you have mentioned is different little bit because our situation has one force only but the example has two opposite forces their resultant vanishes . So i think it would be a change in the KE @Andrei – Hussien Mohamed May 13 '19 at 14:36
  • Indeed, as I've mentioned in the answer. You fully transform the potential energy into kinetic energy only if no other forces are present. But the work done by the force, and potential energy relationship is always true, independent of other forces. I can put a spring in a gravitational field, and the gravitational potential energy does not depend on the elastic force, and the elastic potential energy does not depend on the gravity. But the kinetic energy depends on both, as well as any non-conservative processes, such as friction. – Andrei May 13 '19 at 14:43
  • I think i am confused little bit between the general formula of the work-energy principle equation $$\delta U + \delta K = W $$ and the special case of it $$\delta U = -W$$ i do not know which one i have to use it ?@Andrei – Hussien Mohamed May 13 '19 at 17:48
  • The second. The work done by the force will change the potential energy due to that force only. In the example above, work done by the elastic force will change only elastic potential energy, and work done by gravitational force will change only gravitational potential energy. The first formula should apply when you have potential energy that transforms into kinetic energy and some part that is lost to other (maybe non-conservative) forces, such as friction. – Andrei May 13 '19 at 18:00
  • Why do you assume that the force is an elastic force (conservative) ? @Andrei – Hussien Mohamed May 13 '19 at 22:28
  • Your force is constant, like gravity near the surface of the Earth. In fact, with the right choice of reference axes and units, it is exactly that. So it is conservative – Andrei May 14 '19 at 00:43
  • Do you mean that any constant force is conservative ?!@Andrei – Hussien Mohamed May 14 '19 at 05:59
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    Yes. Direction must also be constant – Andrei May 14 '19 at 11:53
  • Why do not we consider the constant friction force is conservative ? @ Andrei – Hussien Mohamed May 14 '19 at 21:19
  • Let us continue this discussion in chat. – Andrei May 14 '19 at 21:19
  • You are welcome but how can i join the chat ? @Andrei – Hussien Mohamed May 15 '19 at 07:10