# Work – Definition, Formula, Types of Work, Sample Problems

In daily life, you are doing activities like study, running speaking, hear, climbing, gossips with friends and a lot of other things. Do you know? All these activities require some energy, and you get it from your daily food.

In our day-to-day life, everyone eats food, gets energy, and does some activity which is called work. Any physical or mental activity labor consider as work in our daily life. What will be considered as work or not, it depends on how we define work. “Playing card” could be considered as work for someone and couldn’t be for another one. But in science, work has a certain definition and some conditions.

### Work

To understand work from a scientific point of view let’s take some example:

- A boy pushes a box. The box moves through some distance. In this situation, the boy exerted a force on the box and the box got displaced. In this scenario, work has been done.

- A girl pulls a box. The box moves through some distance. In this situation, the girl exerted a force on the box and the box has some displacement. In this scenario, work has been done.
- A girl lifts a box. The box gets some height. In this situation, the girl exerted a force on the box and the box is displaced. In this scenario, work has been done.

When we analyze the above conditions, we got two things common force and displacement. So we can state some conditions for work as follows:

- A force should act on an object.
- The object must have some displacement.

If any of the above condition does not occur then work is not done.

**Difference between Scientific Work and Daily Life Work**

Ram preparing for his exam. He does a lot of studies, draws diagrams, solves problems, and learns lessons. He is very “hard-working” towards his study but in the scientific definition of work, he does a small amount of work.

Consider a few more examples to clear scientific concept of work:

- A boy strongly pushes a wall. In spite of all effort by the boy, the wall doesn’t move. The boy gets tired totally. Although there is no displacement, the work done is zero.
- A girl standstill for few hours with a heavy load on her head. She is exhausted as she exerted force to stand with the load. The load hasn’t any displacement, so as the scientific definition of work, work hasn’t been done here.

### Work Definition

Let assume a constant force F applies on a box in a certain direction. The box has displaced by a distance d in the same direction as in force, then work done W by force is defined as

Work done = Force x Displacement

W = F d …(i)

In the above figure, 2 (i) states the initial position of the box whereas (ii) later position of the box.

Thus, Work done by the force is equal to the multiplication of magnitude of the force and distance moved by the box in the direction of the force.

Work is a scalar quantity, which means work has no direction. It has only magnitude.

In equation (i), If F = 1N and d = 1m then the work done by the force is 1 Nm or 1 Joule. Joule is the SI (System of International) unit of work.

Thus, 1 Joule amount of work defined as when 1 Newton force causes a 1-meter displacement in the direction of the force.

### Negative Work Vs Positive Work

If the direction of displacement is opposite to the direction of applied force then work done by the force is negative.

Let’s take one example to clear the concept of negative and positive work. A man lifts a 5 kg box to the height of 10 meters. In this situation, a force applied by a man and gravitation force mg works on the box.

- Direction of force, which is applied by man, is upward
- Direction of gravitation force is downward.
- Direction of displacement is upward.

Here the direction of force, which is applied by man, and the direction of the displacement is the same. So the work done by the force is positive. While the direction of the gravitation force and the direction of the displacement are opposite so that work done by the gravitational force is negative.

### Sample Problems

**Example 1. A force of 6N is applied to a box. The box has a displacement of 7 meters in the direction of force. What is the work done by force?**

**Solution:**

As we know, W = F d

W = 6 x 7 Joule

W = 42 Nm or Joule (Ans).

**Example 2. A man lifts a 10 kg load to the height of 7 meters. What is the work done by man and gravitation force? (Take g = 10 ms ^{-2})**

**Solution:**

Work done by a force is given by

W = F d

(i)Work done by manW = 10 × 10 × 7

= 700 Nm or Joule (Ans)

(ii)Work done by gravitation forceW = 10 × 10 x (-7)

= -700 Nm or Joule (Ans)

**Example 3. A boy is standing with a load of 7 kg on her head for 10 minutes. What is the work done by the boy? (Take g = 10 ****)**

**Solution:**

According to the given condition, the boy applies a force of 70N on the load. Although, the load has zero displacement. So word done by the boy is given as

W = 70N × 0 m

= 0 Joule (Ans)

**Example 4. Kavita applies some force on a box. The box got displaced by 2 meters in the direction of the force.** **If work done on the box by Kavita is 20 Joule then what is the force apply by Kavita?**

**Solution:**

Work done by a force is given by

W = F d

F =

Here W = 20 Joule and d = 2 meter

F =

= 10 N (Ans)

**Example 5. What is 1 Joule work?**

**Answer:**

When 1N force applied on an object and the object got displaced by 1-meter distance in the direction of force, then work done by the force is 1 Joule.