* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
Download Document
Survey
Document related concepts
Inertial frame of reference wikipedia , lookup
Equations of motion wikipedia , lookup
Fictitious force wikipedia , lookup
Centripetal force wikipedia , lookup
Centrifugal force wikipedia , lookup
Fundamental interaction wikipedia , lookup
Modified Newtonian dynamics wikipedia , lookup
Newton's theorem of revolving orbits wikipedia , lookup
Rigid body dynamics wikipedia , lookup
Mass versus weight wikipedia , lookup
Classical central-force problem wikipedia , lookup
Transcript
PHY166 Fall 2005 4 – Newton´s laws Aristotle (384-322 b.c.) 12 century -> Latin Dominating views „Forces cause objects to move; No force – no velocity“ Aristotle disregarded friction forces Galilei (+2000 years) Questioned Aristotles „Forces cause objects to accelerate; No force – velocity constant“ v = v0 + at x = x0 + v0t + 12 at 2 Newton (1642-1727) 1687 – The mathematical Principles of Natural Philosophy (Principia) Newton´s laws: Foundation of modern Physics Relativistic mechanics v ~ c=3 ·108 m/s Newton mechanics Quantum Mechanics m ~ me ~ 10-30 kg ♦ Newton´s first law: Objects that are not subject to action of forces are moving with zero or constant velocity (follows from the second law; has historical significance – disproves Aristotle) ♦ Newton´s second law: F = ma F – force; m – mass; Unit of force: kg m/s2 = N(ewton) a – acceleration Allows to compute acceleration from force etc. Consequences: (i) First law for F=0; (ii) Statics for a=0, i.e., F =0 (important applications in engineering) Force F is the sum of all forces acting on the object: F = ∑ Fi = F1 + F2 + F3 + ... 1 i Addition of vectors 2 (Tail-to-tip) 3 Sum 2 Mass m is the measure of inertia of the object ♦ Newton´s third law: F12 = −F21 Helps to identify forces in systems of interacting bodies Two objects pressed against each other 1 F12 Example: Measuring weight with a spring scale mg F12 F21 2 2 F12 1 F21 Two objects connected by flexible thread 1 2 2 F21 – read by scale! F21 = −F12= mg mg+ F12 = 0 F12 = − mg In this way the weight W=mg is measured In isolated systems the sum of all (internal) forces is zero; Only external forces can accelerate the system as the whole Examples: • rocket • car, • smart mule • Baron Münchhausen 3 Friction • Sliding friction -> static friction • Rolling friction • Viscous friction FN F Sliding friction Surfaces are rough Ffr µFN , v ≠ 0 F fr = µ s FN , v = 0 mg µs>µ Ffr Ffr µ s FN µFN v≠0 v=0 v F 4 Rolling friction FN a v mg Viscous friction Ffr v Air or liquid Ffr=−αv 5 Inclines y FN Ffr v θ x mg For a moving block FN + ( mg ) y = FN − mg cos θ = 0 F fr , x + (mg ) x = − µFN + mg sin θ = ma 6 Problems: ♦ Two blocks joined by thread a-? F12 1 m1 F21 2 F m2 F12 - ? (tension of the thread) ♦ Apparent weight in elevator N-? a z N Scale mg 7 ♦ Pulley F 1. If a=0, F - ? (Statics) 2. If F given, a - ? F F z a Load 2F 8 y ♦ Pulling a boat Known: F, α x River f Find: pushing force f, net force α F Pole (push) Rope (pull) 9