1. Introduction to work, Power and Energy

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

Work is said to be done when a force acting on a body causes displacement in the direction of the force.

$$\text{Work} = \text{Force} \times \text{Displacement}$$$$W = F \times s$$Where:

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

Example:

If a force of 100 N moves an object 5 m in the same direction, the work done is:

$$W = 100 \times 5 = 500\;J$$

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) $$1 \, \text{HP} = 746 \, \text{W}$$

3.3 Power in Terms of Force and Velocity

$$P = F \times v$$

Where:

• $F$ = Force (N)
• $v$ = 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

Energy is the capacity of a body or system to do work. It exists in various forms and can be transformed from one form to another, but it cannot be created or destroyed. This principle is known as the Law of Conservation of Energy.

Types of Energy

1. Kinetic Energy

The energy possessed by a body due to its motion.$$KE = \frac{1}{2}mv^2$$Where:

• m = mass of the object (kg)
• v = velocity of the object (m/s)

2. Potential Energy (PE)

The energy possessed by a body due to its position or configuration.

$PE = mgh$

Where:

• m = mass (kg)
• g = acceleration due to gravity (9.81 m/s²)
• h = height above the reference level (m)

3. Other Forms of Energy

• Thermal Energy – due to heat.
• Electrical Energy – due to electric charges.
• Chemical Energy – stored in fuels, food, and batteries.
• Nuclear Energy – stored in atomic nuclei.
• Light (Radiant) Energy – carried by electromagnetic waves.
• Sound Energy – carried by sound waves.

Unit of Energy

The SI unit of energy is the Joule (J).$$1 \text{ Joule} = 1 \text{ Newton} \times 1 \text{ meter}$$

5. Types of Mechanical Energy

5.1 Kinetic Energy (KE)

Definition

Kinetic energy is the energy possessed by a body due to its motion.

$$\text{Kinetic Energy} = \frac{1}{2} m v^2$$Where:

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

5.2 Potential Energy (PE)

Definition

Potential energy is the energy possessed by a body due to its position or configuration.

$$\text{Potential Energy} = m g h$$Where:

• $g$ = acceleration due to gravity
• $h$ = 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:$$\text{Total Energy} = \text{Constant}$$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	$W = F s$
Power	Rate of doing work	$P = \frac{W}{t}$
Energy	Capacity to do work	$E = W$

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

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Frequently asked question

1. What is work in physics?

Work is done when a force causes an object to move in the direction of the applied force. If there is no displacement, no work is done.

2. What is the SI unit of work?

The SI unit of work is the Joule (J).

• 1 Joule = 1 Newton × 1 meter (1 J = 1 N·m)

4. What is positive work?

Positive work is done when the force and displacement are in the same direction.

Example: Pulling a cart forward.

5. What is negative work?

Negative work occurs when the force acts opposite to the displacement.

Example: Friction acting on a moving object.

6. What is zero work?

Zero work is done when:

• There is no displacement.
• The force is perpendicular to the displacement (θ = 90°).

Example: Carrying a bag horizontally on a level road.

7. What is power?

Power is the rate at which work is done or energy is transferred.

8. What is the SI unit of power?

The SI unit of power is the Watt (W).

• 1 Watt = 1 Joule/second

9. What is the formula for power?

Power is calculated as:$$P=\frac{W}{t}$$

where:

• P = Power (W)
• W = Work (J)
• t = Time (s)

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External Resources:

• Work Power and Energy NPTEL Course