Why Work is a Scalar Quantity: Exploring the Reason

[abrowaqas]

We know that work is the dot product between force and displacement .. so dot product always gives scalar (horizontal projection etc) hence work is a scalar quantity?

I want the reason behind it...

we always do work in specific direction..

suppose a man in appliying force at the angle of 30 in the horizontal distance to cover displacement of 3m... hence he is doing work in the direction of displacement..

clearly stated from this example that work always has direction.. then

why it is scalar quantity ? in its actual sense..

 

[hamsterman]

Work is a difference of energies. It might be tempting to say that kinetic energy is a vector, but it would make no sense for potential, heat and etc.

 

[Dale]

we always do work in specific direction..

suppose a man in appliying force at the angle of 30 in the horizontal distance to cover displacement of 3m... hence he is doing work in the direction of displacement..

Is he doing work in the direction of the displacement or in the direction of the force? Why?

What about a pulley? Do pulleys violate the conservation of energy by changing direction? How can you avoid having a pulley change the direction of work in your proposal?

 

[Khashishi]

The work doesn't depend on the direction. You can always change the direction of the applied force using machines like pulleys and such. It doesn't matter which way you pull.

 

[abrowaqas]

DaleSpam..
i got the point of your questions. but u quote examples both are related to the circular motion ...
what about the work in the rectilinear motion ?

 

[Dale]

Huh? Neither of my questions were about circular motion.

 

[mikeph]

It just doesn't make sense given its definition, its a dot product which is F1x1 + F2x2, that's a scalar; its units are Joules, how can an energy have a direction? Would two energies with equal magnitude and opposite direction sum to zero in this world? Doesn't that violate conservation? How do you pick what direction work points in? Is it parallel to F or x? What if you know the work done by a system is equal to heat lost? Is heat a vector as well?

It shouldn't need explaining, it's defined that way. But the above should convince you that alternate definitions lead to big problems.

 

[abrowaqas]

Thanks mLkey W.
You gave good explanation . I got it ..

 

[jtbell]

Note that besides kinetic energy, we have another motion-related quantity which is a vector, namely momentum. Just as an object's kinetic energy changes because of the net work done on it, so does the object's momentum change because of the net impulse acting on it (force x time in the simplest case). And impulse is a vector, like momentum is.

 

[victor.raum]

Recall that work is defined as a discrete change in energy, so you're question really boils down to "why is energy a scalar quantity." The answer to that question is simple. Energy is all about a physical system's positional configuration with relation to the forces in play, like for example the location of an object in a gravitational field. A physical system can have many different configurations which all share the same energy value. To continue with the example, an object at a distance $d$ from a gravitational source has some energy value. Yet, there are lots of ways to place an object at a distance of $d$ from said source. Namely, you can place it anywhere on a sphere of radius $d$ (with the source in the center). Naturally this sort of configuration-energy will be a scalar with no direction. If that physical system converts the positional energy into motion (kinetic) energy, the the motion energy must be scalar by inheritance.

 

[kmarinas86]

If you want to give energy a "direction", then the sum of that energy in a system is simply the "gross kinetic energy" of that system. Potential energy in that sense is simply energy not having a net direction. This can be of an unknown arbitrary amount (at least E=mc^2). Of course, whether energy has a net direction or not is relative to an observer, so what looks like potential energy in one frame looks like kinetic energy in another frame.