This is not because there is inherently no displacement Again, imagine pushing on a block downwards, so it does not move at all. This is because the normal force is pushing back at you, so there is no net force on the object at all.
That is in fact why it does not move. So depending on what direction you push on an object and subsequently accelerates , you can define work to be positive or negative. This depends on your choice of coordinate system. But to reiterate - work will only be positive or negative.
It will never have a direction associated with it. When we say "work done does not depend on direction" we only mean the direction in which we measure --that is the orientation of our co-ordinate system. We definitely do not mean the relative direction between the force and the displacement.
For a quantity to be a scalar, we should have a fixed value for it which does not depend on the direction of our co-ordinate system. A vector does not fulfil this criterion. For example, if you were to rotate your co-odinate system then the Force vector's components will change and so will the displacement vector's components the vectors of course remain same just our components change.
But their inner product will still remain the same. This inner product is defined to be the work done by the force. Now, physically speaking why should we expect work to be a scalar? This is a deeper question. Work done on a system changes the energy of that system. And energy should be an invariant quantity that does not depend upon how different observes orient their co-ordinate systems.
Because if it does then we will have to prefer one orientation of a co-ordinate system over other and we simply don't see this to be the case in our universe. Therefore, the amount of work done by a force as measured by different observers is also defined in such a way. You might have some other perspective thinking that a scalar quantity is not that, that does not depend on directions of vector quantities, no matter which vectors. Every scalar quantity which is the result of an inner product of two vector quantities depends on those vectors, so on their direction, off course.
But its still a scalar quantity that does not have a direction What makes a quantity scalar or vector in physics is its 'nature' by definition this is to say that quantities are, a priori scalars or vectors. The algebra comes after Sign up to join this community. The best answers are voted up and rise to the top. Work is a scalar quantity because it is the dot product of two vectors Force and displacement. Dot product of two vectors becomes scalar quantity. So, work done has only magnitude but not direction.
Work done may be positive, negative or zero. This does not mean that it has a direction. It depends on the reference we choose. Recommend 0 Comment 0. Gaurav Singh. Janhavi Govinda rao. S where F is the force applied and S the displacement. The dot product of two vectors is a scalar and not a vector. Work does not combine as a vector because work is a form of energy. According to the law of conservation of energy, the energy in any closed system adds up to a constant. So, energy expenditures add as scalars rather than vectors.
So, the law of conservation of energy implies that energy expenditures add as scalars: add as magnitudes only, regardless of direction. That is why work is a scalar and not vector. But quantity like displacement need us to define direction as displacement of 20m doesn't specify which direction the 20m is , which is necessary as displacement is shortest distance between two points and it couldn't be in any direction.
For Work , for example, if we do 10 J work when we push object to 10m in east and then when we push 10 m in West with say 15 Joule, the total work would be 25 Joule here we are not bothered here about direction as it doesn't add any extra information. Please note if force is in opposite direction to displacement then work is negative. Sign up to join this community. The best answers are voted up and rise to the top.
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