We use the word ‘work’ in our everyday language to describe any physical or mental labour and a variety of activities such as writing, reading, or eating. However, in physics, the term ‘work’ refers to the displacement caused by force. 

Only when a body moves under the effect of a force is stated to be work done. The work done is zero if the body does not move when a force is applied to it. Thus, work is considered done only when a force is applied to a body that causes it to move. 

For instance, a man pushing a car, a horse dragging a cart, or a cyclist cycling a bicycle.

Here, we explore the concept of calculation of work done by force with the help of examples.

How to Calculate Work Done by Force

The quantity of work performed is determined by the size of the applied force and the magnitude of the displacement. The amount of work done by a force is equal to the product of the force and the displacement of the point of application of the force in the direction of the force.

Work Done Formula:

Work = Force x displacement of the point of application of the force in the direction of force

Thus, the formula of work done is,

W = FS + cosθ

F = Force

S = Displacement

θ = angle between F and S

The joule (J) is the SI unit for work and energy, with 1 J equaling 1 N m = 1 kg m2/s2.

Classification of Work Done

Work done can be classified into positive work, negative work, or zero work.

1. Positive Work:

When force and displacement are in the same direction, the work done on an item is positive. Force and displacement act in the same direction when an object moves on a horizontal surface. As a result, the work done is positive. The force and motion are both moving in the same direction.

Example: Riding a skateboard, throwing a stone, riding a bicycle, etc.

2. Negative Work:

When force and displacement are in opposite directions, the work done is considered to be negative work. The force of gravity acts in the downward direction when an object is hurled upwards, whereas displacement acts in the upward direction. The force and motion directions are at an angle of 180 degrees.

Example:

• Negative work is done on a see-saw because we apply downward power while the person seated opposite us is displaced higher.
• When we pull water from a well, we are doing negative work since we are pulling the rope downwards, yet the bucket is being shifted upwards.

3. Zero Work:

When force and displacement are perpendicular to each other or when either force or displacement is zero, the work done is zero. Force is applied, but there is no displacement since the direction of force and motion are at a straight angle, i.e. 90 degrees.

Example:

• If you press against a wall and it does not move. There is no work to be done.
• You spend hours sitting in a chair. There is no work done since there is no motion.

Practical Examples Through Application of Formula

Q1. A force of 10 N acts across a distance of 10 m in the force’s direction. Calculate how much work the force has done?

Ans.

Force and displacement are both in the same direction here. So, using the formula for work done, the force’s work is calculated as follows:

W = F × d = 10 × 10 = 100J

Q2. A rope that makes a 30° angle with the horizontal drags a box along the floor. The rope exerts a force of 100 N, and the box is dragged for 10 meters. Calculate how much work the force has done?

Ans.

Here, the force and displacement are at a 60-degree angle. As a result, the force’s work is completed.

W = F × d cosθ = 100 × 10 × .5 = 500J

Q3. Anil is in the eleventh grade. He noticed an elderly man attempting but failing to keep his box on the roof of a bus. Anil took his box and placed it on the bus’s roof. The elderly gentleman thanked anil. Based on the given passage, respond to the following questions:

1. Is Anil’s work on the bus roof positive or negative?
2. Is gravity doing positive or negative work on the box?

Ans. 

1. Positive 
2. Negative 

Q3. Solve both parts:

1. What exactly is power?
2. How can you tell the difference between a kilowatt and a kilowatt-hour? In the state of Karnataka, the Jog falls are about 20 meters high. In a minute, 2000 tonnes of water pour from it. If all of this energy can be used, calculate the corresponding power. (g = 10 milliseconds-2)

Ans. 

1. The rate at which work is completed is referred to as power.
2. The kilowatt is a power unit, and a kilowatt-hour is an energy unit.

Given, height, h = 20 m

Mass per unit time,

m/t = 2000 tonnes per minutes = 2000 × 10360 kg/s

Power P = Wt = mght = 2000 × 10360 = 10 x 20

∴ P = 6.67 x 106 W = 6.67 MW

Q4. Four men carry and hold a 250 kg box to a height of 1 m. 

1. How much work is done by men in lifting the box without elevating or lowering it?
2. How much work do they use simply holding it?

Ans.

Given, the mass of the block, m = 250 kg

Height, h = 1 m

1. Work done in lifting,

W = Fs = mgh = 250 x 10 x 1

W = 2500 J

1. Work done in holding, W = 0

Q5. A ball is thrown from a height of ten meters. How high can the ball bounce back if the energy of the ball is lowered by 40% after it hits the ground? (g 10 m/s2)

Ans.

Given,

Height, h = 10

If the ball’s energy is lowered by 40%, its remaining energy is 60% of its initial value. 

As a result, the ball will rebound to 60% of its original height.

h = 60100 x 10 m

∴ h = 6m

Conclusion

Work done is one of the fundamental chapters taught in Physics, and it is critical to grasp the ideas so that your foundation is strong and you can answer any question presented in tests. 

Vedantu is here to help you along your learning path by giving summary notes, a list of important questions, and a unified plan to excel in examinations, all of which are provided by our panel of expert teachers.