# Work, positive work and negative work

#### What is Work? How does Physics define it?

Something that is considered a work in daily life may not be considered a work when it comes to physics. Take the job of a watchman for example. Even if he barely moves, he is said to have completed his task at the end of the day in daily life terms. But it’s not the same in the language of Physics. Some will opine that an object has to move to do some work according to physics. Well, it is not 100% correct either. (This article is on the topics Work, positive work and negative work.)

Actually, in order to do some work in Physics, you have to fulfill three conditions:

(1) You have to apply a force on a body

(2) It will have to move

(3) But the direction of movement must not make 90 degrees angle with that of the force applied.

That’s why work (usually denoted by the letter W) is expressed as: W=FScosθ

So work done is the product of the magnitude of force, that of the displacement and the cosine of the angle between the force and the displacement. If any of the above-mentioned three quantities becomes zero, the work done becomes zero as well.

#### Consider these three cases of work done being zero

First of all consider a case where F=0, S≠0. In the space, far far away from the earth and all other planets and stars, there might be place where the gravitational field is absolutely zero. In a place like that, if an asteroid or any other object is moving with a constant speed (constant speed is expected since no force is acting on the object), then no work is done on the object although displacement is not zero (S≠0). Because in this case no force is acting on the object (F=0). (This article is on the topics Work, positive work and negative work.)

Second of all we will consider a case where F≠0, S=0. Suppose that you’re pushing/pulling an object with no avail, i.e. you failed to move it. So the displacement is zero in this case although the applied force is not. That’s why the product FScosθ will have a zero value as a whole. Thirdly we are going to consider a case where neither the force nor the displacement is zero, still the work done is zero. In such cases the quantity cosθ (which is the cosine of the angle between the force and the displacement) is zero.

The orbital path of the moon around the earth is fairly (or exactly) round. That’s why every moment the incremental displacement takes place in a direction perpendicular to that of the gravitational force on the moon by the earth. So θ=90 degrees and cosθ=0; hence the work done by the gravitational pull is zero. In this case the gravitational pull acts like a centrifugal force. When a body revolves around in a circular path the work done by the centripetal force is always zero. (This article is on the topics Work, positive work and negative work.)

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#### Positive work and negative work

Now that we have explained ‘Work’ enough, let’s come to know what positive work and negative work are. When the angle between the force and the displacement is less than 90 degrees, then the work is found positive, that’s why such work is called positive work. This sort of work is also called ‘Work by force’. On the other hand, when the angle between the force and the displacement is greater than 90 degrees, then the work is found negative, that’s why such work is called negative work. This sort of work is also called ‘Work against force’. (This article is on the topics Work, positive work and negative work.)

Suppose you’re pulling or pushing a trolley and it is moving in the direction you intend it to, then your work done on the trolley is definitely positive. Again, you’re holding a duster and moving it upwards vertically. Positive work is done for the force you’re applying on it, but negative work is done by its weight (gravitational pull); because in that case the angle between the gravitational pull and the displacement is 180 degrees and cos180= -1. So whether positive or negative work is done depends on which force is being considered.