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 beexpressed 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 movesthrough 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 objectin the given direction, thenwork done by the force F in displacing the body through displacement d is, W=(|F|cosθ)|d|
Want to find complex math solutions within seconds?
Use our free online calculator to solve challenging questions. With Cuemath, find solutions in simple and easy steps.
Book a Free Trial Class
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: Calculatethe amount of work done by the force in moving the object through a distance of 7mif an object is horizontally dragged across the surface by a 150N force acting parallel to the surface.
Solution:
To find: Work done by the force in moving the object through a distance of 7m
Given:F = 150 N, d = 7m
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
= 1050J [Since Cos 0 = 1]
Answer: The amount of work done by the force in moving the object is 800 J.
FAQs on Formula forWork
What is the Work Formula?
The formula for work is defined asthe formula tocalculate the work done in moving an object. Work doneis equal to the product of the magnitude of applied force and the distancethe body moves from its initial to the final position. Mathematically Work done Formula isgiven as, W = Fd
What are the Versions of the Work Formula?
Mathematically, the concept of work done Wequals the force f times the distance (d), that isW = f. d and if theforce is exerted at an angle θ to the displacement, then work done is calculated as W = f . d cos θ.
What are the Applications of the Work Formula?
Work formula has numerous applications, such as to compute work done, force, or displacement in any problem.
What is d in Work Formula?
In the work formula W = F. d, d is the displacement as in how much the object has moved from its initial place.
