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The general work definition is an activity with a mental or physical effort to achieve a goal or result.

We are doing work when we push or pull a heavy load or raise it off the floor, but a man carrying a heavy load and standing still is not doing work according to the scientific concept of work.

Energy is another word we commonly use. In the sense that a person who is feeling very enthusiastic is capable of doing a lot of work, energy is normally correlated with work completed. In this way, energy is characterised as the ability to perform work.

Work meaning in Physics is “Energy transfer that occurs when an object is displaced over a distance by an external force, at least part of which is exerted in the direction of displacement”.

Mathematical work definition science is Force multiplied by displacement.

W= F x d

Where W is the work, F is the magnitude of the force, d is the displacement.

When a force is applied, it is said to do positive work if it has a part in the direction of the point of application's displacement. If a force has a part that is opposite the direction of displacement at the point of application, it does negative work.

Joule (J) is the SI unit of work, and it is defined as the amount of work needed to exert a force of one newton over a distance of one metre.

The Newton-metre, erg, foot-pound, kilowatt-hour, litre-atmosphere, and horsepower-hour are non-SI units of work.

How to define work done in physics?

The definition of work done in physics refers to both the force applied to the body and the displacement of the body.

Consider a block on a horizontal frictionless surface. A constant force F is acting on this block. The action of this force is to drive the body in a straight line in the direction of force over a distance d.

W= F x d

Where F is the force acting on the block and d is the displacement of the block.

The product of the magnitude of the applied force and the distance travelled by the body equals the work done by this force.

If the force acting on the block is constant, but the force's direction and the displacement induced by it are not the same. Force F acts at an angle θ to the displacement d in this case. Fcosθ is the affective component of force along the displacement direction, and it is this component of a force that causes the block to move in the given direction.

There work done by the force F acting at an angle θ to the displacement d is given by,

W = F x cosθ x d

1. Force Acting on the Body:

At constant displacement and the constant angle between force and displacement, work is directly proportional to the acting force.

2. Displacement of the Body:

At constant force and the constant angle between force and displacement, work is directly proportional to displacement.

3. The Angle Between Force and Displacement:

At constant force and constant displacement, work is directly proportional to the cosine of the angle between the force and the displacement.

1. When the angle between the force and displacement is zero that is when the direction of force is the same as the direction of displacement. In this case, the work done is maximum.

W = F x cos 00 x d = F x d (cos 00 = 1)

2. When the angle between the force and displacement is 900 that is the direction of force is perpendicular to the direction of displacement. In this case, the work done is zero.

W = F x cos 900 x d = 0 (cos 900 = 0)

Work is said to be a positive work when force is applied to the object that is

0 ≤ θ < 90^{o}Work is said to be negative work when force is applied by the object that is

180 ≤ θ < 90^{o}

In this article till now we got to know what is work, the work definition of science mathematically, and the definition of work done in physics.

Let us solve some basic problems on Work to understand the concepts more clearly.

1. A Body is Displaced 2m When a Force of 10 KN is Applied. Calculate the Work Done on the Body.

Ans: Work done is given by force multiplied by displacement. So work done will be

W = F x d

Where F = 10 KN = 10000N, and d = 2m

Substituting the values in the formula we get

W = 10000 x 2 = 20000 Nm or 20000 J.

So the work done on the body is 20000 J.

2. A Student is Pulling a Box Over an Inclined Plane With a Force of 15 KN. If the Body is Displaced to 3m With an Inclination of 600. Calculate the Work Done By the Student on the Body.

Ans: The force applied by the student to pull a box over the inclined plane is F = 15 KN = 15000 N.

The body is displaced by 3m so d = 3m. The angle of inclination between the force and displacement is θ = 600.

So the work done formula is W = F x cosθ x d

Substituting the values in the formula we get

W = 15000 x cos 600 x 3

cos 600 = ½

So W = 15000 x (½) x 3 = -22500 Nm or -22500 J.

Here the student is pulling the box, so the box does work on the student. Therefore the work done is negative.

The work done by the student on the body is -22500 J.

Work has a different significance in science than it does in real life. Work does not imply that a difficult job has been completed. The acting force and the displacement in the direction of the force are the two conditions for work to be performed in physics.

FAQ (Frequently Asked Questions)

1. What is Work Definition?

Ans: Work describes the energy transfer that happens when an object is displaced over a distance by an external force that is applied in at least part of the displacement direction.

2. What is Work Done? Explain with the Mathematical Notation.

Ans: When energy is transferred from one form to another, work is said to be done. When a force causes an object to move, it defines work done.

Work done by the force F acting at an angle θ to the displacement d is given by,

W = F x cosθ x d

If θ = 0^{o} then the work done is maximum.

If θ = 90^{o} then the work done is zero.

3. What are the Different Units of Work?

Ans: The SI unit of work is Joule (J). The non-SI unit of work is Newton-metre, erg, the foot-pound, kilowatt-hour, litre-atmosphere, and horsepower-hour.