Work done by a content force and a variable force

Introduction 

Every day, we are indulged in hundreds of different types of work, including walking, rolling, sleeping, eating, pushing, laying, and others. Have you noticed something common in all the work you do every day? Well, the common thing in all the work done is the force applied. For example, every time you push a box, a force “F” is applied to cover the distance “D.” Therefore, it can be said that whatever you do, you require force. 

In this article, you will understand work done by a constant force and a variable force. 

What is Work Done in Physics? 

Every time we give thrust to the block with force “F”, the body covers a certain distance with some acceleration. Also, its speed tends to fall and rise depending on the direction of the force applied. As the speed declines or increases, the system’s kinetic energy alters. In case positive work is done, the energy increases; however, the energy tends to decrease if negative work is done. The SI unit of the work done is Joule. 

Types of Work Done 

There are mainly three types of work done. These include: 

• Positive work – The positive work done can be defined if the force can change the direction of an object. 
• Negative work – In case the displacement and force are in a completely reverse position, it is termed negative work. 
• Zero work – In case the force direction and the displacement are both perpendicular to one another, the work done by the object force will be termed as zero work. 

Derivation of Work Done 

As discussed earlier, the work done by the force “F” is the same as the changes in the kinetic energy. Hence, we can say that

W = final kinetic energy – initial kinetic energy

W = KEf – KEi

W = (½)mv2 – (½)mu2 = (½)m (v2 – u2) …… (1) 

As per the motion’s third equation, 

v2 – u2= 2as ….(2)

Substituting equation (2) in (1), we get:

W = (½)m(2as)

Also, W = mas

According to Newton’s second law, F = ma

Now, substituting for F,

We get W = F.s

So the work done is equal to the product of force and displacement.

We know that force and displacement are vector quantities and their dot product will be a scalar quantity, so that work done is a scalar quantity and its unit is joule (J).

If the applied force and displacement are not parallel to each other then work done is given by following formula

W = Fs cos θ

Here θ is the angle between force and displacement. Maximum work done will be at θ = 0. At θ = 90, work done W = 0.

Example 1: A box is pushed by force 50 N. Due to this force box displaced 12 m from its initial position. Find the value of work done.

Solution: Given force F = 50 N

Displacement s = 12 m

Work done W = F.s

W = 50 N x 12 m

W = 600 J

So work done is 600 J to push the box.

Example 2: A man is applying a force of magnitude 10 N on a box. If the box is moved 25 m due this force and angle between force and displacement is 60, then calculate the value of force.

Solution: Given Force F = 10 N

Displacement s = 25 m

Angle  θ = 60

Work done W = Fs cos θ

W = 10 N x 25 m x cos(60)

W = 125 N

What is Constant Force and Variable Force? 

Work done by the force can further be divided into two different categories. These include the work done by the constant force and the work done by the variable force. In the constant force, the direction and the magnitude of the force remain the same or unaltered. Here, the work is the same as the force applied (F) multiplied by Δx displacement. 

Hence we can say, W = F x Δx 

As compared to the constant force, the work done by the variable force is more complicated. In variable force, the force’s direction and magnitude can change at any point in time. The most common example of variable force is the work we do every day. 

In variable force, integral calculus is important for calculating the work done. 

W = F.Δx,

where F is the work done by a constant force of magnitude, and

Δx is the displacement of an object

Conclusion 

With this, we end our study material on work done by a constant force and a variable force. Every day, we are indulged in hundreds of different types of work, including walking, rolling, sleeping, eating, pushing, laying, and others. Positive work, negative work, and zero work are three types of work done.