Dynamics: Kinetics - Concept Map
Kinetics: Relating Forces to Motion
Related concepts
Newton's Second Law (ΣF = ma)
Sub concepts
- Free Body Diagram (FBD) construction
- Force summation along motion direction
- Mass and acceleration relationship
- D'Alembert's Principle (inertia force -ma)
- Friction forces (F = μN)
Relationship to central
Foundation principle connecting forces to acceleration; direct application of Newton's laws
Work–Energy Principle
Sub concepts
- Work definition (U = Fd cos θ)
- Kinetic energy change (ΔKE = ½mv₂² - ½mv₁²)
- Work by gravity (U = ±Wh)
- Work by springs (U = ½k(x₁² - x₂²))
- Friction work (negative: U_f = -μNd)
- Conservation of energy (KE₁ + PE₁ = KE₂ + PE₂)
Relationship to central
Alternative approach linking forces and motion through energy; used when distance and speed are primary variables
Impulse–Momentum Principle
Sub concepts
- Impulse definition (ΣF·Δt)
- Linear momentum (p = mv)
- Change in momentum (Δp = m·Δv)
- Momentum conservation (no external impulse)
- System analysis
Relationship to central
Time-based approach to relating forces and motion; essential for collision and impact problems
Impact and Coefficient of Restitution
Sub concepts
- Momentum conservation in collisions
- Coefficient of restitution (e = separation/approach)
- Perfectly elastic impact (e = 1, KE conserved)
- Perfectly plastic impact (e = 0, bodies unite)
- Signed velocity convention along line of impact
Relationship to central
Specialized application of momentum conservation for collision analysis; determines post-impact velocities
Curvilinear Kinetics
Sub concepts
- Tangential acceleration (a_t along path)
- Normal acceleration (a_n = v²/r toward center)
- Tangential force equation (ΣF_t = ma_t)
- Normal force equation (ΣF_n = mv²/r)
- Banking of roads and curves
- Looping and centrifugal effects
Relationship to central
Extension of Newton's second law to curved paths; critical for infrastructure applications (banking, circular motion)
Problem-Solving Strategy
Sub concepts
- Identify given variables (force, distance, time, velocity)
- Select appropriate principle
- Draw FBD if using Newton's second law
- Apply conservation laws
- Solve for unknowns systematically
Relationship to central
Framework for selecting the correct kinetics approach based on problem variables
Concept connections
- Newton's Second LawD'Alembert's PrincipleD'Alembert recasts Newton's second law as pseudo-equilibrium by adding inertia force -ma, transforming dynamics into statics
- Work-Energy PrincipleConservation of EnergyEnergy conservation is a special case of work-energy when only conservative forces act (no friction or external work)
- Impulse-Momentum PrincipleMomentum ConservationMomentum conservation is a special case when external impulse is zero (no net external forces)
- Coefficient of RestitutionImpulse-Momentum PrincipleCoefficient of restitution equation provides second equation needed to solve collision problems along with momentum conservation
- Curvilinear KineticsNewton's Second LawCurvilinear kinetics applies Newton's second law by resolving it into tangential and normal components for curved paths
- Friction ForcesWork-Energy PrincipleFriction does negative work (U_f = -μNd), reducing mechanical energy; always included in work calculations
- Newton's Second LawCurvilinear KineticsNormal force equation (ΣF_n = mv²/r) derived from Newton's second law applied to circular path requirement
- Work by Applied ForceWork by GravityBoth contribute to total work; gravity work depends only on height change (conservative), applied force depends on path (if variable)
- Free Body DiagramNewton's Second LawFBD is essential prerequisite for applying Newton's second law; identifies all forces to be summed
- Problem-Solving StrategyNewton's Second LawStrategy guides when to select Newton's second law (force-acceleration problems)
- Problem-Solving StrategyWork-Energy PrincipleStrategy guides when to select work-energy (distance-velocity problems)
- Problem-Solving StrategyImpulse-Momentum PrincipleStrategy guides when to select impulse-momentum (time-velocity problems)
- Impact ProblemsNewton's Second LawImpact analysis provides post-collision conditions that may serve as initial conditions for subsequent motion analysis using Newton's second law
- Spring WorkPotential EnergySpring work is negative of change in elastic potential energy (U_spring = -ΔPE_elastic)
- Tangential AccelerationNormal AccelerationBoth components act simultaneously on curved paths; tangential changes speed, normal changes direction
- Banking of RoadsCurvilinear KineticsBanking angle designed to provide necessary centripetal force through combination of normal force and friction
- Momentum ConservationCoefficient of RestitutionTogether they form system of equations to solve collision problems; momentum provides first equation, e provides second
- Kinetic Energy ChangeWork-Energy PrincipleChange in kinetic energy equals total work done on the body (fundamental theorem of work-energy)
- Friction ForcesNewton's Second LawFriction is a force that must be included in force summation; depends on normal force (F = μN)
- Centripetal ForceNormal Force EquationCentripetal force is the net normal force required to maintain circular motion (ΣF_n = mv²/r)
Diagrams
Dynamics: Kinetics - Complete Concept Hierarchy
Comprehensive mind map showing the hierarchical structure of kinetics concepts, organized around the five major approaches: Newton's second law, work-energy, impulse-momentum, impact analysis, and curvilinear motion. Each branch breaks down into specific sub-concepts and applications relevant to PRC licensure-level problems.
Kinetics Problem-Solving Decision Tree
Decision tree flowchart for selecting the correct kinetics principle based on the problem variables. This guides students through systematic problem identification and solution pathways, mimicking the step-by-step board-exam approach. The flowchart incorporates all five major kinetics methods and verification.
Work-Energy Analysis Process for Kinetics Problems
Step-by-step flowchart for solving kinetics problems using the work-energy principle. Shows decision points for different force types and application of energy conservation vs. work-energy theorem. Critical for problems where distance and velocity are the primary variables.
Collision Analysis Process Using Impulse-Momentum
Systematic flowchart for collision and impact problems using impulse-momentum principle. Emphasizes critical aspects: proper sign convention for velocities, momentum conservation, and coefficient of restitution application. Essential for board-exam collision problems.
Curvilinear Kinetics: Normal and Tangential Force Resolution
Flowchart for analyzing curvilinear motion problems by resolving forces into tangential and normal components. Shows decision points for different curve geometries (banked roads, vertical loops, hills/valleys). Essential for infrastructure-related problems in the Civil Engineer Licensure Exam.
Kinetics Principle Selection State Diagram
State diagram showing the logical progression of kinetics problem-solving. Illustrates how different problem types transition to their appropriate solution methods, with feedback loops for error checking. Demonstrates the interconnected nature of kinetics principles and decision-making pathways.
Free Body Diagram Construction for Kinetics Problems
Step-by-step flowchart for constructing Free Body Diagrams (FBD), the critical first step in applying Newton's second law. Shows systematic identification of all forces (contact and body forces) and proper representation. Essential skill for kinetics problem-solving in the Civil Engineer Licensure Exam.