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# Work Formula

## Work Formula in Physics

Before learning the formula of work let us know what is work and its applications. When we apply any force to an object and the object is displaced by its actual position in the direction of force then the work is said to be done. If there is no displacement in the object then the work done will be zero. Lets more simplify the definition of work with an example, suppose a box is placed at the position “p” and when we push the box in forwarding direction, that means we are applying force to the box and the box moved to the new position “q” that means its displaced from p position to q position. If the box will not displace a bit from its actual position p to new position q then the work done will be zero.

## Work Formula dimension in Physics

The formula of work is employed to calculate the work done to displace any object. Work is the product of force and displacement. Both are vector quantities, which means work is the dot product of two vectors and we have studied in physics that the dot product of two vectors produces scalar quantity.  Hence, work is a scalar quantity and its SI unit is Joule which is represented by J. The formula of work is given below:

W = F.d

W = (Fcos θ)d

Where,

W = Work done

F = Magnitude of the force applied

d = The magnitude of the displacement in the force’s direction.

θ= is the angle formed by the force and displacement.

The Joule is the SI unit of work. If one joule of work is done, the formula for work is 1 J = 1 N.m.

## Work Formula in Thermodynamics

Here we will see the work formula in thermodynamics and also we will know how to calculate work done by the compression or expansion of a gas. As we already studied, work is some sort of energy required to move an object in the direction of the force. The work in gases can be done by expansion or compression against constant external pressure. This process is also known as Pressure-Volume or PV.  Let’s calculate the work done through gases against a constant external pressure by taking reference to the formula we have studied lately.

Work = −PΔV

Where,

P = Pressure

ΔV =  Change in volume

## Work Formula in Electricity

Energy and work are correlated to each other, the transfer of mechanical energy from one object to another is known as work. It shows that the work is the movement of energy. Thus the SI unit of work and energy is the same, and the SI unit of work and energy is Joule(J). So we have covered the work done, work in thermodynamics, and work formula in terms of energy so far.

## Work Done Formula: Solved Example

Only the mugging concept in physics won’t give you much benefit, as the implementation of the concept can do. In this section we have provided some solve examples of work formulas, so students can understand better the use of them. Solve these questions which seeing their solution, if you are stuck anywhere then see the solution and solve as much as the problem you can through the internet or through the physics book. Have a look at the questions below and try to solve them.

Example 1: A force of 12 Newton is applied to a body, causing it to move 4 meters. Use the work formula to figure out how much work you’ve done.

Solution:

To find: Work done

Given: Force = 12N

Displacement = 4 m

Using Formula For Work,

W = F.d

= (12) *(4)

= 48 Nm

Answer: When a 12 Newton force displaces an object by 4 meters, 48 Nm of work is done.

Example 2: A coolie at a railway station carries a bag weighing 200 N through some distance. Calculate the work done by the coolie on the bag by using the formula for work.

Solution:

To find work done by the coolie.

Given: Weight of the bag = 200 N

In addition, the bag’s weight will act in a vertical direction, while its motion will be horizontal. As a result, the bag’s displacement in the direction of the force (weight) is zero.

d = 0

Using Formula For Work,

W = F.d

= (200)(0)

= 0 J

Answer: Work done by the coolie on the bag is zero.

Example 3: If an object is horizontally pulled across the surface by a 300 N force acting parallel to the surface, calculate the amount of work done by the force in moving the object across a distance of 14 m.

Solution:

To find: Work done by the force in moving the object through a distance of 7 m

Given: F = 300 N, d = 14 m

Since F and d are in the same direction,

θ = 0, [θ is the angle of the force to the direction of movement]

W = F × Cos θ × d

= 300× 14 × Cos 0

= 4200 J [Since Cos 0 = 1]

Answer: The amount of work done by the force in moving the object is 4200 J.

## FAQs on Work Formula

Q. What Is the Work done?

When we apply any force to an object and the object is displaced by its actual position in the direction of force then the work is said to be done. If there is no displacement in the object then the work done will be zero.

Q. What Is the Work formula?

Work is the product of force and displacement. The SI unit of work is Joule.

W = F.d

W = (Fcos θ)d

Where,

W = Work done

F = Magnitude of the force applied

d = Magnitude of the displacement in the direction of the force.

θ = is the angle between the vectors: force and displacement

Q. What is the d in the work formula?

The d represents the displacement by applying to an object. So d is the displacement in the work formula.

Q. What is the use of the Work formula?

We can use the work formula to calculate the work done, force, and displacement.

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## FAQs

### What Is the Work done?

When we apply any force to an object and the object is displaced by its actual position in the direction of force then the work is said to be done. If there is no displacement in the object then the work done will be zero.

### What Is the Work formula?

Work is the product of force and displacement. The SI unit of work is Joule.

W = F.d
W = (Fcos θ)d
Where,
W = Work done
F = Magnitude of the force applied
d = Magnitude of the displacement in the direction of the force.
θ = is the angle between the vectors: force and displacement

### What is the d in the work formula?

The d represents the displacement by applying to an object. So d is the displacement in the work formula.

### What is the use of the Work formula?

We can use the work formula to calculate the work done, force, and displacement.

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