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This question already has an answer here:

Now this question has many answers all over the internet, but this site gives me the power to pose my doubts in front of you all. Let's get straight to it: Suppose I move on a road while holding a book in my hand. I read that I am not doing any work to it, because the angle between the displacement and the motion is 90 degrees. But, I think that if the angle is 90 degrees, what is causing the book to get displaced? If the book is getting displaced, then there is some force which is causing it to move. So, work should be done.

So my question: Why is the book even getting displaced if force is not acting along the direction of motion? If it is, then why is the work done zero?

Another question(Edited): I have also read this: Suppose I hold a book and take it straight to a particular height. I do some work on it, which is transferred to it as potential energy. But if I take the same book first to the left, then to a little height; then to the right; then to a little height; and keep repeating it until I reach the same height, then same amount of potential energy is stored. How is this possible, if I run with an acceleration, while moving to the right and the left? If I am correct, then more potential energy should be transferred, isn't it?

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marked as duplicate by David Z Jul 5 '17 at 6:56

This question has been asked before and already has an answer. If those answers do not fully address your question, please ask a new question.

  • $\begingroup$ Is there an acceleration involved? If there is no acceleration then there is no net force, which in the horizontal direction can often mean there are no forces. The vertical direction is different because a force is needed to support the book against gravity. However, if there is no force, there is no work. $\endgroup$ – NeutronStar Jan 21 '16 at 15:49
  • $\begingroup$ "then there is some force which is causing it to move. So, work should be done" is not a correct implication. Work is defined as the differential form associated to the force, that can be zero despite the force not vanishing. $\endgroup$ – gented Jan 21 '16 at 16:19
  • $\begingroup$ When you move from rest, holding the book on top of your palm, the friction between your palm and the book causes the book to accelerate from rest. So there is a force acting in the direction of motion of the book. So assuming the book accelerates to some final velocity, then remains at that constant velocity, the friction of your palm does work on the book while it accelerates. Once the book reaches its final velocity, it moves at constant speed without any work done on it (until you slow down). When you slow down and stop, the energy of the book is lost as heat. $\endgroup$ – Ameet Sharma Jan 21 '16 at 16:35
  • $\begingroup$ Related: physics.stackexchange.com/q/1984/2451 and links therein. $\endgroup$ – Qmechanic Jan 21 '16 at 16:52
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    $\begingroup$ @AmeetSharma: "When you slow down and stop", the book is doing positive work on you via the static friction force, and therefore losing kinetic energy in the process. That is not a heat transfer mechanism. The energy goes into your body first as an elastic-like deformation of your body (elastic potential energy), and that energy is then redistributed in your body, increasing the internal thermal energy of your body. $\endgroup$ – march Jan 21 '16 at 19:33
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There are some missing words in your description, or the descriptions you've seen.

In moving horizontally, gravity does no work because the force and displacement are perpendicular to each other.

If you start from rest and apply a force with your hand, then your hand does work as long as your hand is applying a force. Once you reach constant velocity, your hand has to continue to apply a tiny horizontal force to overcome air resistance, but we usually ignore that and say that once a constant velocity is attained, your hand no longer applies a force, and thus your hand does no work.

So gravity never does work when the object moves horizontally. Your hand does work when the object is accelerating horizontally due to a force provided by your hand.

Your hand also does work when the object is moving horizontally with constant velocity if and only if your hand applies a force and there are other forces (friction, for example) that balance the force due to your hand, so that the net force is zero. In this case your hand does positive work and the sum of the other forces does negative work. The net work done on the object is zero (and its kinetic energy remains constant), but your hand still does work nonetheless.

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Put on your ice-skate go on some ice-sheet, hold your book and ask a friend to give you a push. Your friend will have to provide some work to make you move but once it is done you are sliding at a constant speed. This is an inertial motion: no force involved no acceleration constant speed. A displacement at constant speed do not require any force, only change in the speed do. Also: you will have to provide a force to stop your displacement.

This has been understood the first time by G. Galilei even if it was not proved that he ever practiced ice-skating...

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