WORK, POWER AND ENERGY

1. Introduction

In engineering mechanics, work, power, and energy are closely related concepts that describe the effect of forces on bodies in motion. These concepts are essential for analyzing machines, structures, engines, lifting devices, and mechanical systems. They help engineers determine how much effort is required to perform a task and how efficiently energy is used.

2. Work

2.1 Definition of Work

Work is said to be done when a force acting on a body causes displacement in the direction of the force.$$\text{Work} = \text{Force} \times \text{Displacement}$$Work=Force×Displacement $$W = F \times s$$W=F×s

Where:

• $F$F = Force (N)
• $s$s = Displacement (m)

2.2 Units of Work

• SI unit: Joule (J)
• 1 Joule = Work done by a force of 1 N moving a body through 1 m

2.3 Types of Work

1. Positive Work
   • Force and displacement are in the same direction
   • Example: Pulling a trolley forward
2. Negative Work
   • Force acts opposite to displacement
   • Example: Friction acting on a moving body
3. Zero Work
   • No displacement or force is perpendicular to displacement
   • Example: Carrying a load on a horizontal road

2.4 Work Done by a Variable Force

When force varies with displacement, work is equal to the area under the force–displacement curve.

3. Power

3.1 Definition of Power

Power is defined as the rate of doing work.$$\text{Power} = \frac{\text{Work Done}}{\text{Time}}$$$$P = \frac{W}{t}$$

3.2 Units of Power

• SI unit: Watt (W)
• 1 Watt = 1 Joule/second
• Practical unit: Horsepower (HP) $$1 \, \text{HP} = 746 \, \text{W}$$1HP=746W

3.3 Power in Terms of Force and Velocity

$$P = F \times v$$P=F×v

Where:

• $F$F = Force (N)
• $v$v = Velocity (m/s)

3.4 Types of Power

1. Average Power – Work done over a time interval
2. Instantaneous Power – Power at a particular instant

4. Energy

4.1 Definition of Energy

Energy is the capacity of a body to do work.

4.2 Units of Energy

• SI unit: Joule (J)

5. Types of Mechanical Energy

5.1 Kinetic Energy (KE)

Definition

Kinetic energy is the energy possessed by a body due to its motion.$$\text{Kinetic Energy} = \frac{1}{2} m v^2$$Kinetic Energy=21​mv2

Where:

• $m$m = mass (kg)
• $v$v = velocity (m/s)

5.2 Potential Energy (PE)

Definition

Potential energy is the energy possessed by a body due to its position or configuration.$$\text{Potential Energy} = m g h$$Potential Energy=mgh

Where:

• $g$g = acceleration due to gravity
• $h$h = height (m)

6. Work–Energy Principle

Statement

The work done by all forces acting on a body is equal to the change in kinetic energy of the body.

$$W = KE_{final} – KE_{initial}$$

Importance

• Simplifies motion analysis
• Useful in solving problems involving forces and velocities

7. Conservation of Energy

Law of Conservation of Energy

Energy can neither be created nor destroyed, but it can be transformed from one form to another.

For a closed system:$$\text{Total Energy} = \text{Constant}$$Total Energy=Constant

Example

Potential energy converting into kinetic energy when a body falls freely.

8. Relation Between Work, Power, and Energy

Quantity	Definition	Formula
Work	Force × displacement	$W = F s$W=Fs
Power	Rate of doing work	$P = \frac{W}{t}$P=tW​
Energy	Capacity to do work	$E = W$E=W

9. Engineering Applications

• Design of engines and motors
• Lifting machines like cranes and elevators
• Vehicle motion and braking systems
• Power transmission in shafts
• Structural and machine efficiency analysis

10. Practical Examples

• A motor lifting a load → Work and power
• Moving car → Kinetic energy
• Water in dam → Potential energy
• Machines converting fuel energy into mechanical work