Work Formula

The formula for work is used to calculate the work. Before we learn the formula, let us recall what work means. Work is said to be done when we apply a force on an object and the object experiences displacement. If the displacement in the direction of force is zero then the work done becomes zero. The formula for work is used to calculate work done in moving an object. Let us learn more about the formula for work along with solved examples in the following section. 

What is Formula For Work?

The formula for work is used to calculate the work done to displace any object. Work is the product of the force applied and displacement in the direction of the force applied. Work is the dot product of the two vectors: force and displacement. Thus work is a scalar quantity. SI unit of work is Joule (J).

Work Formula

The formula for Work can be expressed as, 

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

SI unit of work is Joule (J). If 1 joule of work is done then the formula for work comes out to be 1 J = 1 N.m

Derivation of Work Formula

Consider a block placed on a frictionless horizontal floor acted upon by a constant force F due to which this block moves through a distance d in a straight line in the direction of the force.
 

In general, the work done by force F is equal to the change in kinetic energy

W = (1/2)mv² - (1/2) mu² = 1/2m(v²-u²)

Applying v²-u² = 2as

W = (1/2)m(2as)

W = mas

Since F = ma (Newton's 2nd law), thus W = Fs. (s=d=displacement)

Now, if the effective component of force along the direction of displacement is Fcosθ responsible for the displacement of any object in the given direction, then work done by the force F in displacing the body through displacement d is, W=(|F|cosθ)|d| 

Examples Using Formula For Work

Example 1: 10 Newton of force is applied on a body which displaces it by 2 meters. Calculate the work done by using the formula for work.
Solution: 

To find: Work done

Given: Force (F) = 10N

Displacement (d) = 2 m

Using Formula For Work,

W = F.d

= (10)(2)

= 20Nm

Answer: 20 Nm of work is done when a 10 Newton of force displaces an object by 2 meters.

Example 2: A coolie at a railway station carries a bag weighing 100 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 = 100N

Also, the weight of the bag will be acting in the vertical direction and its motion is in the horizontal direction. So the displacement of the bag in the direction of the force (weight) is zero.

d = 0

Using Formula For Work,

W = F.d

= (100)(0)

= 0 J

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

Example 3: Calculate the amount of work done by the force in moving the object through a distance of 7 m if an object is horizontally dragged across the surface by a 150 N force acting parallel to the surface.
Solution: 

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

Given: F = 150 N, d = 7 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

= 150× 7 × Cos 0

= 1050 J [Since Cos 0 = 1]

Answer: The amount of work done by the force in moving the object is 800 J.