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WORK AND ENERGY

• Presented by: Group 4

INTRODUCTION

• Overview of key concepts: Work, Energy, Conservation of Energy, and Power in Mechanical Systems

PRINCIPLE OF WORK

What is Work?

• Definition: Work is the application of force across a distance.

• Energy expended when an object is moved against a resisting force.

• Fundamental concept crucial to physics and engineering, with broader implications.

How Do We Apply the Principle of Work?

• Force and Displacement:

  • Work requires a force causing an object to move; without movement, no work is done even if force is applied.

• Direction of Force Matters:

  • The force must align with the direction of displacement for work to be done.

  • Only the component of the force in the direction of motion contributes to work when at an angle.

Formula of the Principle of Work

• Work (W) is measured in joules (J)

• Force (F) is measured in newtons (N)

• Distance (d) is measured in meters (m)

• Formula: W = F × d × cos(θ)

  • θ: Angle between the force and motion direction in degrees.

PRINCIPLE OF ENERGY

What is Energy?

• Definition: Energy is the capacity of objects or substances to perform work or create changes in the environment.

• Two Types of Energy:

  • Kinetic Energy

  • Potential Energy

What is Kinetic Energy?

• Definition: Energy possessed by a moving object.

• Factors: Speed (velocity), mass impact energy - faster or heavier = more kinetic energy.

• Formula:

  • KE = ( \frac{1}{2} mv^2 )

  • KE = Kinetic energy (in joules, J)

  • m = Mass (in kilograms, kg)

  • v = Velocity (in meters per second, m/s)

What is Potential Energy?

• Definition: Energy an object holds due to its position, state, or configuration.

• Related to object’s capacity to do work based on location or structure.

• Example: Falling object or released compressed spring releases potential energy.

Formula of Potential Energy

• Gravitational Potential Energy Formula:

  • PE_gravitational = mgh

  • PE = Gravitational potential energy (in joules, J)

  • m = Mass (in kg)

  • g = Acceleration due to gravity (9.81 m/s² on Earth)

  • h = Height above reference point (in meters, m)

CONSERVATION OF ENERGY

What is Conservation of Energy?

• Principle: Energy cannot be created or destroyed; it can only be transformed from one type to another.

• Examples include:

  • Falling objects

  • Roller coasters

  • Bouncing balls

PRINCIPLE OF POWER IN MECHANICAL SYSTEMS

What is Power in Mechanical Systems?

• Definition: Power measures the rate of doing work; a result of force and motion.

• Power can be expressed as the product of force and velocity or torque and angular velocity.

Formula of Mechanical Systems

• General Formula:

  • P = W / t

    • P = Power (in Watts, W)

    • W = Work done (in Joules, J)

    • t = Time taken (in seconds, s)

• Force and Velocity:

  • P = F × v

    • F = Force applied (in Newtons, N)

    • v = Velocity (in meters per second, m/s)

• Torque and Angular Velocity (Rotational Systems):

  • P = T × w

    • T = Torque (in Newton-meters, Nm)

    • w = Angular velocity (in radians per second, rad/s)

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