How to calculate the Total Work Done?

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.