1. WORK, ENERGY AND POWER

Work, Energy & Power

• Instructor: Dr. I.J. Lugendo

Page 2: Understanding Work

• Definition of Work: Work is defined as the product of force and distance moved in the direction of the force.

• Key Equation: [ W = F imes d ]

  • Only the force component in the direction of motion counts.

• Units: The unit of work is Joules (J).

Page 3: Scalar Dot Product

• Scalar: A scalar is a quantity that has no direction.

• Work Calculation: Work can be derived by multiplying the force (F) by the displacement (d), yielding energy, which is also a scalar quantity.

• Dot Product: The scalar dot product requires F and d to be parallel. Adjusting with cosine ensures this parallel relationship.

• Basic equation: [ W = F imes d ]

• Area: In terms of geometry, Area = Base x Height.

Page 4: Direction Matters

• Force Direction: Only the force in the direction of the motion contributes to work.

• Key Equation: [ W = d imes F imes ext{cos} heta ]

Page 5: Components of Work

• Horizontal and Vertical Forces:

  • The vertical component of force does not contribute to horizontal displacement work.

  • Positive Work: When force and displacement are in the same direction (angle = 0°).

  • Negative Work: When force and displacement are in opposite directions (angle = 180°).

  • Zero Work: When force and displacement are perpendicular (angle = 90°).

Page 6: Work Done in Lifting

• Lifting work: [ W = F imes d_y = MgH ]

• This calculates work done by a person lifting a box.

Page 7: Work in Lowering

• Work can be both positive and negative based on direction.

• Lowering a box results in negative work: [ W = - MgH ].

Page 8: Work by Gravity

• Work done by gravity is defined:

  • Positive when dropping an object: [ F_g = - Mg imes d_y = - H ]

Page 9-10: Example Problems

• Solved problem involves forces and angles with calculations for mass and theta.

• Understanding of positive, negative, and zero work based on force and displacement relevant to angles.

Page 11-20: Variable Forces and Work

• Area under force-distance curve computes work when force is not constant.

• Encompasses graphical representations of forces and work.

Page 21-24: Energy Basics

• Work produces energy change. Factors include force application and object movement.

• Energy is defined through various examples that illustrate potential to do work.

• Types of Energy: Expressed in Joules (J); conversion rates like 4.19 J = 1 calorie.

• Work also represents the scalar dot product between force and displacement.

Page 25-28: Mechanical Energy

• Mechanical energy consists of two forms:

  • Potential Energy (PE): Energy of position, calculated as [ PE = mgh ]

  • Kinetic Energy (KE): Energy of motion, given by [ KE = \frac{1}{2} mv^2 ]

    • KE increases dramatically with velocity (squared).

Page 29-32: Law of Conservation of Energy

• Energy transforms but is neither created nor destroyed (Law of Conservation).

• Demonstrates the transformation between potential and kinetic energy.

Page 33-36: Work-Energy Theorem

• Change in gravitational potential energy equals work needed to change height.

• Both kinetic energy and work relate directly, as [ W = \Delta KE ].

Page 37-38: Applications of Work-Energy Theorem

• Connects kinematics with Newton's laws to derive the work-energy theorem,

  • If work is done, there is a change in energy.

Page 39-40: Real-World Applications

• Example problems illustrate energy loss through friction and necessary calculations for various physics scenarios.

Page 41-44: Potential Energy in Motion

• Lifting and throwing scenarios demonstrate potential and kinetic energy relationships, along with work done while moving.

Page 45-47: Example Scenarios

• Detailed analysis of energy conservation through different positions and motions with calculations.

Page 48-50: Spring Dynamics

• Hooke's Law: Describes the force significance in elastic behavior, specifically in springs.

Page 51-56: Elastic Potential Energy

• Work done on springs results in stored energy known as elastic potential energy,

  • Derived from force versus displacement graphs, illustrating energy relationships with springs.

Page 57-62: Understanding Power

• Power: Defined as the rate of doing work or using energy.

• Key formulas: [ P = \frac{W}{t} ]; various units demonstrated.

• Practical examples relate power consumption in systems and calculations utilizing force over distance.