NEWTON'S LAW OF MOTION Physical State V=0 (Rest) V=constant (uniform motion) # Inertia It oppose the cause of change in state of a body. Inertia ∝ Mass It can be compared, but can't be measured. Inertia is not a physical quantity. Unitless & dimensionless. # Types of Inertia Inertia of rest -> Speed Inertia of Motion -> direction Normal Reaction Contact force Always in pair (equal & opposite) Perpendicular to contact surface E.g. -> Weighing Machine (Measure normal) Tension force On stretched string Always from contact point Ideal (massless) string -> 'T' is same at all point SPRING FORCE f = kx (Restoring force) Always act towards mean Ideal spring -> same force at all point. Fspring = kx = k(lf - lo) k = Spring constant x = compression or Elongation Fs1 --> Fs2 --> Fs1 = Fs2 Fs1 <-- Fs2 <-- Fs1 = Fs2 Fs1 --> Fs2 <-- Fs1 ≠ Fs2 Fs1 --> Fs2 <-- Fs1 + Fs2 = Fs NEWTON'S 1st LAW OF MOTION Law of inertia / Law of equilibrium Fnet = 0 Qualitative definition of Motion If ΣFx=0 --> ax=0 If ΣFy=0 --> ay=0 "If net force acting on body is zero, then it will continue its state". Equilibrium Object at Rest (static) Object at Motion (const. velocity) (dynamic equilibrium) Free body diagram [F.B.D] (1) Represent the body by a point. (2) Identify all forces on the body. (3) Represent all the forces in vector. (4) Apply Law of Motion. MOMENTUM (P) Motion contained in a body along velocity. P = mv change in momentum (ΔP) [ΔP = Pf - Pi = m(Vf - Vi)] Tension force (2) --> m --> Vf = mv (+i) Pf = mv (+j) ΔP = mv(î-ĵ) |ΔP| = sqrt(2)mv (3) 'θ' with Horizontal ΔP = -2mv cosθ |ΔP| = 2mv cosθ 'θ' with vertical ΔP = -2mv sinθ |ΔP| = 2mv sinθ Newton's 2nd Law "in time t" Favg = ΔP/Δt = (Pf-Pi)/(Δt) = m(Vf-Vi)/Δt F = dP/dt (Slope of P-t graph) ΔP = ∫Fdt (Area of F-t) F = dP/dt (Slope of P-t) F = dP/dt = d(mv)/dt F = d(mv)/dt (general form) If m=const --> F = m(dv/dt) = ma If v=const (m=variable) --> F = v(dm/dt) direction of Fnet always along Accn. IMPLUSE I = ΔP (change in momentum) Vector quantity along direction of force. Big force (F↑), Small duration(t↓) Impulse = ΔP = ∫[от t1 до t2] Fdt Newton's 3rd Law There is equal & opposite reaction for every action. Action-Reaction pair At same instant, diff body Equal magnitude, diff. direction Having same nature. All the three laws of Newton are independent of each other. # Conservation of Momentum (x) Fext=0 ; Px --> Conserved (y) Fext=0 ; Py --> Conserved (system) Fext=0 ; P_sys --> conserved. # Gun-bullet system Mass of gun = M Mass of bullet = m Velocity of gun = Vg Velocity of bullet = Vb Tension force Vg = -mUb/M Recoil velocity of gun Force on 1 bullet = m(dVb/dt) = Fg Force on N Bullet = N*m(dVb/dt) = Fg Force of N-Bullet = N*mUb Fg = n m Vb n = no. of bullet/time K.E. = p²/2m |Pgun| = |Pbullet| = same K.E. gun = (P²/2M) K.E. bullet = (P²/2m) K.E. bullet > K.E. gun Rocket Repulsion Initial mass = mo Fuel burning rate = dm/dt Velocity of exhaust = u Fnet = Fup - mo g Fnet = u dm/dt Fnet = u dm/dt - mo g a = Fnet/mo = (u dm/dt)/mo - g Accn after time t at = (u dm/dt)/ (mo - (dm/dt)t) - g