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.