These are some of my question related to work and energy- 1)W is proportional to Force W is proportional to displacement Therefore, W=Fs My question is why do we have to multiply F and s.Why can't we add them.Why can't the formula be W=F+s 2)In space if you were to push an object it would keep on going.Displacement could be infinite.Therefore, the work you did would be infinite and therefore your energy as well.How can you have infinite energy? 3)Suppose you have 2 balls of the same mass.One is already in motion while the other is at rest.You apply a force F on Both the balls for the same time period.If you calculate the work done in both the cases the work done in the first case would be greater because the distance travelled in the time in which the force was applied would be greater as the ball was aleady in motion.Shouldn't the work be the same?If you were to push 2 identical balls with the same force how would you use greater energy in one case.Isn't the extra displacement because the ball was already in motion due to a previous force? 4)The derivation for the formula for potential energy in my book goes like this- The potential energy of an object above the ground is equal to the work done in raising it from the ground to that point against the force of gravity.So the displacement would be its height from the ground h.The minimum force required to raise the object would be mg.Therefore P.E=mgh.How can the minimum force required to lift the object be mg.The weight of the object would also be mg amd the two forces should cancel each other out.Yet they say that the object is raised with no force.How? 5)Suppose you raise an object to a certain height.Its P.E would be mgh.But now if you were to dig a pit directly under the ball the height would increase and therefore, so would the P.E.But no work was done on the ball and still there was an increase in energy.My book says change in energy of a body=work done on that body.But in this case no work was done and still there was an increase in energy.How? 6)Imagine two people standing opposite to each other.hey both begin to push each other with same force.After some time they would both feel tired but as there was no displacement there was no work done.So where did there energy go?Doesn't this violate the law of conservation of energy? 7)In my book when introducing the concept of power they say-"Imagine two people A and B of same mass.They both cover a distance s but A does it in 15 seconds while B does it in 20 seconds.Work done is same but A does it in a shorter time.Who would you say is more powerful?" My question is -How can the work done be the same.If A reaches faster then he must have used greater force so as to accelerate faster.How is Work the same? 8)My book says P.E does not matter on the path taken to reach the point.But suppose you were to raise an object to a height h but not straight up through say a staircase.Wouldn't the work done on the object be more than if you were to raise it straight up as the diagonal path would be longer than the straight path so displacement would be more? 9)If you place your hand in hot water your hand warms up.There is transfer of energy.My book says change in energy of a body=work done on that body.So whats the work done?