Is there work done when the force applied is directed opposite to the displacement of the object

What is the difference between work done by a force and work done against a force?How would we calculate the two and what is the mathematical relation between the two.
Please help. Thanks.

Sounds like a bit of semantics. Can you give some examples of exactly what you mean?

Sounds like a bit of semantics. Can you give some examples of exactly what you mean?

Sounds like a bit of semantics. Can you give some examples of exactly what you mean?

For example, we can easily calculate the work done by the force of gravity in moving an object up or down an inclined plane by using the expressions W=FSCostheta or W=(-)mgh but how would we calculate the work done against the force or gravity? And what exactly does 'work done against the force of gravity' (or friction or any other force for that matter) mean?

But when work is involved, there is always something exerting a force on something else.

The terminology is a bit loose, but prevalent. Here's an example: You lift a box (at constant speed) a distance h. There are two forces acting on the box: gravity and the force exerted by you. The work done by gravity (as you well know) is -mgh; the work done by you, which you could think of as work done 'against gravity' is mgh.

But when work is involved, there is always something exerting a force on something else.

How is work done by the person equal to mgh?

If they exert a force greater than mg, then the work they do 'against gravity' would be the same, but they will be doing additional work to increase the kinetic energy of the box.

Simply put and according to Thermodynamics: if you supply energy through work, then work is taken as positive and when work is done by the system, it is taken as negative. If you have various forces on a system, the whole thing boils down to what force you're talking about. Producing or consuming? Then work has the appropriate sign.

The work done by the force F1 is done against a force F2 when the forces F1 and F2 are directed in opposite sides one to other.

The force they exert = mg and the distance over which they exert it = h. Work = mgh.

If they exert a force greater than mg, then the work they do 'against gravity' would be the same, but they will be doing additional work to increase the kinetic energy of the box.

The work done by the force F1 is done against a force F2 when the forces F1 and F2 are directed in opposite sides one to other.

Simply put and according to Thermodynamics: if you supply energy through work, then work is taken as positive and when work is done by the system, it is taken as negative. If you have various forces on a system, the whole thing boils down to what force you're talking about. Producing or consuming? Then work has the appropriate sign.

The force they exert = mg and the distance over which they exert it = h. Work = mgh.

If they exert a force greater than mg, then the work they do 'against gravity' would be the same, but they will be doing additional work to increase the kinetic energy of the box.

Also, how is the force the person exerts=mg.

So technically, the body shouldn't move?

So technically, the body shouldn't move?

In order to move the object, use a force greater then mg. When you are satisfied with its position, use a force slightly less than mg until the object is at rest.

So how is it possible for the force applied by the person to be equal to the gravitational force?

Now, since the net force is 0, the person will move with constant velocity v.

But then wouldn't we have to keep two forces in mind while calculating the work done?

Yes. But if the initial force is infinitesimally greater than mg and is applied for an instant only, just to break the inertia and set the body into motion, it can be considered 0. Of course, the velocity attained is also very small.

So, when we consider the force applied by the person to be zero, and we calculate work done, we are just calculating the work done in moving the body against gravity,

When the body is set into motion and the net force on the body becomes 0, it will move up with constant velocity v. The actual energy at a height h will be E=mgh+mv2/2. But since v→0 as the initial force was infinitesimally greater than mg and was applied just for an instant,
E=mgh+lim(v→0) mv2/2.
∴E=mgh.

the work done on a body against a force is the work required to move the body against the force?

when the forces F1 and F2 are directed in opposite sides one to other

When the body is set into motion and the net force on the body becomes 0, it will move up with constant velocity v. The actual energy at a height h will be E=mgh+mv2/2. But since v→0 as the initial force was infinitesimally greater than mg and was applied just for an instant,
E=mgh+lim(v→0) mv2/2.
∴E=mgh.

No. Absolutely. It does not metter were the body is moving. Sadnifficant is only:

And it means that the F1 works aganist to F2 and F2 works aganist to F1. Have you ever seen an arm-wrestling fight?

We are concluding all of this assuming friction and air resistance are absent, right?

Consider a box placed on a smooth surface and a man is pushing it with force F. If the box moves through a distance s, work done "on the block"=F.s and is positive. If the box were moving with some velocity v and the man applied an opposing force F, the block will decelerate and stop. Here also, work is done "on the block by the man" , but F and s are in opposite direction, hence work done is negative here. Whoever applies force, does the work. If a man is moving a body up against gravity such that net force on it is 0, this means mg=Fman.
Since F(man) and s are in the same direction, work done by the man is positive and man loses muscular energy. Work done by gravity is negative since mg and s are opposite in direction. Hence, the body will gain same amount of PE. K.E. of the body will be 0 as discussed earlier( or it is unaffected, if present).

Also, how is the force the person exerts=mg.
Technically, the gravitational force=mg. If the force the person is applying is equal to mg, then the gravitational force and the person's force would cancel out leaving a net force of zero. So technically, the body shouldn't move?

When the net force is zero, the velocity is constant, not necessarily zero. If you lift the box at constant speed you'll need to exert a force equal to its weight.

You do. Do not think about friction or resistance or reactions yet. If the force makes work and exists anoter force that is directed in opposit to it, that means that both work aganist one to each other. That is much more easily than you think now. Just relax and imagine the arm-wrestling.

Consider a box placed on a smooth surface and a man is pushing it with force F. If the box moves through a distance s, work done "on the block"=F.s and is positive. If the box were moving with some velocity v and the man applied an opposing force F, the block will decelerate and stop. Here also, work is done "on the block by the man" , but F and s are in opposite direction, hence work done is negative here. Whoever applies force, does the work. If a man is moving a body up against gravity such that net force on it is 0, this means mg=Fman.
Since F(man) and s are in the same direction, work done by the man is positive and man loses muscular energy. Work done by gravity is negative since mg and s are opposite in direction. Hence, the body will gain same amount of PE. K.E. of the body will be 0 as discussed earlier( or it is unaffected, if present).

But, as cnh1995 said, for the body to be set into motion, the initial force has to be in infinitesimally greater than mg, just at that instant.. After that, to maintain constant speed, we need to apply a force equal to (mg). Right?

But, as cnh1995 said, for the body to be set into motion, the initial force has to be in infinitesimally greater than mg, just at that instant.

Though work is only done when there is displacement of the body

Can work done against gravity be negative? (In the sense that the angle between displacement and force is zero)