Evaluate the change in the potential energy

Question

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 ?

Answer 1

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 $0$.