Newton's 2nd Law for a Particle

Newton’s 2 nd LawLecture 18ME 231: Dynamics

Question of the DayWhich defensive player generates thelargest tackling force?DB 5’-11” 203 lb (92 kg)4.35 s 40-yd dasha = 33.63 m/s 2ME 231: DynamicsLB 5’-10” 224 lb (101 kg)4.94 s 40-yd dasha = 29.60 m/s 22

Outline for Today Question of the day Kinetics: cause of motion Possible solutions to kinetics problems Force:acceleration ratio experiment Newton’s 2 nd Law for a particle Force and mass units Newton’s 2 nd Law for a system of particles Answer your questions!ME 231: Dynamics3

Where are we in the course?Concept: What is dynamics?Chapters 1, 2, 6 Chapters 3, 5, 7, 8Kinematics Kinetics DynamicsRelationshipamong position,velocity, andaccelerationRelationshipamong forces(andmoments)andaccelerationME 231: Dynamics4

Kinetics: Cause of MotionConcept: What is kinetics?ME 231: Dynamics 5

Kinetics: Cause of MotionConcept: What is kinetics?ME 231: Dynamics 6

Kinetics: Cause of MotionConcept: What is kinetics?Kinetics: The study of the relationsbetween unbalanced forces (andmoments) and the resulting changesin motion.ME 231: Dynamics 7

Kinetics: Cause of Motion?Concept: What is kinetics?ME 202Chapters 1, 2, 6 Chapters 3, 4, 5, 7, 8Statics Kinematics KineticsRelationshipamong forces(and moments)and equilibriumRelationshipamong position,velocity, andaccelerationRelationshipamong forces(andmoments)andaccelerationME 231: Dynamics8

Possible Solutions to Kinetics Problems Direct application of Newton’s 2nd Law– force-mass-acceleration method– Chapters 3 and 7 Use of impulse and momentum methods– Chapters 5 and 8 Use of work and energy principles– Chapter 4ME 231: Dynamics9

Force:Acceleration Ratio Experiment Force:acceleration ratio is constant This constant is a measure of inertiaof the particle (resistance to rate ofchange in velocity) Acceleration in the direction of forceF 1 F 2 F 3CFFF1 2 3 kma1a2a3ME 231: Dynamics10

Newton’s 2 nd Law for a ParticleF ma Customary to take k = 1 Assumes a kinetic system of units whereforce, mass, and acceleration units are notindependentSIN, kg, and m/s 2 U.S. Customarylbf, slug, and ft/s 2 Absolute kinetic system: force is dependenton the absolute value of mass (N = kg·m/s 2 ) Gravitational kinetic system: mass isderived from force as determined fromgravitational attraction (slug = lbf·s 2 /ft)ME 231: Dynamics11

Force and Mass Units: Free-Fall ExperimentF maForce of gravitational attraction (W) is weightSI: Mass m = 1 kg, weight W = 9.81 N, and accelerationa = 9.81 m/s 2U.S. Customary: Mass m = 1 slug (or 1 lbm), weight W= 32.2 lbf (or 1 lbf), and acceleration a = 32.2 ft/s 2ME 231: Dynamics12

Force and Mass Units: Newton’s 2 nd LawF ma Simple example: accelerate an object of massm along the horizontal with a force F SI: Mass in kg, force in N (kg·m/s 2 ), andacceleration in m/s 2 U.S. Customary: Mass in slug (lbf·s 2 /ft) or lbm,force in lbf, and acceleration in ft/s 2ME 231: Dynamics13

Newton’s 2 nd Law: ExerciseF maDuring a brake test, a 1500 kg car with a speedof 100 km/h is stopped with a constantdeceleration in a distance of 50 m.Determine the braking force F.ME 231: Dynamics14

Newton’s 2 nd Law of a System of ParticlesF1 F2 F3f1 f2 f3m rii F f m rii F m ror Fma Fx ma x F mya y Fz mazME 231: Dynamics15

Outline for Today Question of the day Kinetics: cause of motion Possible solutions to kinetics problems Force:acceleration ratio experiment Newton’s 2 nd Law for a particle Force and mass units Newton’s 2 nd Law for a system of particles Answer your questions!ME 231: Dynamics17

For Next Time… Begin Homework #7 due 10/17 Read Chapter 3, Section 3.1ME 231: Dynamics18