How to calculate the Total Work Done? (original) (raw)

Last Updated : 23 Jul, 2025

The total work done can simply calculated by multiplying the force applied by the total displacement. The formula for calculating total work done is Fscosθ, where F is the force, s is displacement and cosθ is the angle between Force and displacement. Total work done will be maximum in case F and s are in the the same direction i.e. cosθ is 0 degree as cos 0 = 1. In this article, we will discuss what is work, how to calculate total work done and some problems with the concept.

What is Work Done?

If and only if a force is exerted on a body and the body is moved to a particular displacement as a result of the exerted force, the action is called "work done."

It is denoted by "W". It is measured in Joules(J).

The formula of work done would be: W = F ⋅ s ⋅ cosθ

How to Calculate Work Done?

When the point of application of a force moves along the force's path of action, work is completed. The force's line of action is a line drawn in the force's direction from the place of application. Assume a constant force vector F acts on an object, causing it to move through a displacement vector s in a direction parallel to the force's line of action.

• **Step 1: Identify the magnitude of the force applied to the object.
• **Step 2: Determine the distance over which the force is applied.
• **Step 3: Measure the angle between the direction of the force and the direction of the displacement.
• **Step 4: Use the formula **W = Fscosθ to calculate the work done.

So, the Work Done W will be,

**W = F.s

Where:

• **W is the work done,
• **F is the force applied,
• **s is the displacement of the object

**W = Fscosθ

Where:

• **F is the magnitude of the force,
• **s is the magnitude of the displacement,
• **θ is the angle between the force and displacement vectors.

Work completed is a scalar quantity. It uses SI units as Joule (J). When the point of application of the force is moved by 1 m and the force has a component of 1 N in the displacement direction, 1 joule of work is done.

If the force is a function of position x rather than a constant, the work done by the force to move the object from position x 1 to position x 2 is given by,

W=\int^{x_2}_{x_1}F(x)\text{d}x

If a force vs. distance graph is produced, the labor required to move an object from x1 to x2 is equal to the area beneath the graph between x=x1 and x=x2.

Sample Problems on Calculation of Work Done

**Problem 1: A child in a toy cart being pulled ahead by a buddy at a playground, who pushes the cart forward with a force of 60 N along a rope linked to the cart. The rope forms a 35° angle with the ground. Calculate the amount of work done by the child's playmate to propel the child 20 meters forward.

**Solution:

Given,

Force F = 60 N

θ = 35°

s = 20 m

Using Work Done formula,

W = Fscosθ

= (60)(20)(cos35°)

= 60 × 20 × 0.8192

So, the Work Done is 983 J.

**Problem 2: A 15-meter displacement is produced by pulling a box with a force of 25 N. Find the work done by the force if the angle between the force and the displacement is 30°.

**Solution:

Given,

Force F = 25N

s = 15 m

θ = 30°

Using Work Done Formula,

W = Fscosθ

= (25)(15)(cos30°)

= 324.76

So, the Work Done is **324.76 J.