Newton's Laws of Motion Short Notes PDF

# NEWTON'S LAW OF MOTION ## Physical State - Rest (v=0) - Uniform motion (v=constant) ### Inertia - It opposes the cause of change in the state of a body. - It can be compared, but can't be measured. - Inertia is not a physical quantity. - It is a unitless and dimensionless quantity. ### Types...

# NEWTON'S LAW OF MOTION ## Physical State - Rest (v=0) - Uniform motion (v=constant) ### Inertia - It opposes the cause of change in the state of a body. - It can be compared, but can't be measured. - Inertia is not a physical quantity. - It is a unitless and dimensionless quantity. ### Types of Inertia 1. Inertia of rest: Speed 2. Inertia of motion: Direction ## Tension force - On stretched string - Always from contact point - Ideal (massless) string 'T' is same at all points ## Normal Reaction - Contact force - Always in pair (equal & opposite) - Perpendicular to contact surface. - e.g. Weighing Machine (Measure normal) ## Spring force - Restoring force - Always act towards mean. - Ideal spring→ same at all point. - fspring = kx = k(l'-l0) - k= Spring constant - x = compression or elongation. ## NEWTON'S 1st LAW OF MOTION - Law of inertia / Law of equilibrium - fnet = 0 - Qualitative definition of motion - Σfx = 0 → ax = 0 - Σfy = 0 → ay = 0 - "If net force acting on a body is zero, then it will continue its state!"-- Equilibrium - Object at rest (static) - Object at motion (constant velocity) (dynamic equilibrium) ### Free body diagram [f.B.D] - Represent the body by a point. - Identify all forces on the body. - Represent all the forces in vector. - 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) ## Newton's 2nd Law - "in time 't'" - ΔP = Pf - Pi = m(Vf - Vi) - Favg = ΔP / Δt - Favg = (1/Δt) ΔP - At time 't' - finst = dp/dt (slope of P-t graph) - ΔP = ∫Fdt (Area of f-t) - F = dP/dt = (slope of P-t) - F = d/dt (mv) ## F = ma + v dm/dt (general form) - If M=const - dm/dt = 0 - F=ma - If M(constant) (M-variable) - F = (dm/dt)v - Direction of fret always along Acc? ## Impulse - I = ΔP (change in momentum) - Vector quantity along direction of force. - Big force(F↑), small duration(t↓) - Impulse = ΔP = ∫Fdt ## Newton's 3rd Law - There is equal & opposite reaction for every action. - Action Reaction pair - At same instant, different body - Equal magnitude, different direction - Having same nature. - All the three laws of Newton are independent of each other. ## Conservation of Momentum 1. Σfext = 0; Px Conserved 2. Σfext = 0 ; Py conserved 3. (system) Σfext = 0; Psys conserved ## Gun-bullet system - Mass of gun = M - Mass of bullet = m - velocity of gun = Va - velocity of bullet = VB ## Recoil velocity of gun - Vg = -MUB/M - Force on 1 Bullet = MUB - Force on N Bullet = NMUB - Force on N Bullet = nMVB - n = no. of Bullet ## Rocket Repulsion - initial mass = mo - fuel burning rate = dm/dt - velocity of exhaust = u - Fnet = Fup-mog - Fnet = udm/dt - mog - a = Fnet/mo = udm/dt-g/mo - at = udm/dt - g/mo(dt) - mt = mo - (dm/dt)*t ## PULLING TENSION - a = Fnet/(M1+M2) - T = (M2+M3)a - T = (M2+M3)g ## PUSHING CONTACT FORCE - a = Fnet/(M1+M2+M3) - N1= (Mi+M2)f/(Mi+M2+M3) ## LIFT SYSTEM - N = m(g±a) - free fall → N=0 - a = 0 → N = mg - Accelerating upward → N = m(g+a) - Retarding downward → N = m(g-a) - Accelerating downward → N = m(g-a) - Retarding upward → N = m(g+a) ## Pulley Block system - Let M = M2+M3 - a = (M-M1)g/(M1+M) - T = 2M1M2g/(M1+M) - If M >>> M1 - T = 2M1g ## Pseudo force (fc) - Act in non-inertial frame only - Opposite to the acceleration of travel. - Rest, uniform motion (fc not applicacble) - Accelerating, deceleration (fc applicable) ## Friction - Contact force, parallel to contact surface - Depend upon N. - Oppose relative motion. ### Types of friction #### Static Friction - Self adjustable force - Always equal to applied force - Only when tendency of motion object is at rest. #### Limiting friction force - Depends on nature of contact surface (μ) - Does not depend on area of contact surface - Max. static friction - Force required to move body about to move - FL = μsN #### Kinetic friction - Sliding friction - Moving when there is relative motion less then limiting friction - μs>μk generally ### MR. Star 1. First Calculate fe = μLN 2. Compare f with fe - f<fe Body don't move - f = fe Body about to move - f>fl: Now body start moving - Frictional force = Kinetic friction. ## 2-Blocks system - Calculate limiting (fl) - fL1 = μ1N1 - fL2 = μ2N2 - F < fL1+fL2 Body don't move - a = 0 - F > fL1+fL2 Body will move - a = (F-fL1+fL2) / (M1+M2) - T - draw F.B.D of M2 - T = (f-fL1) + M2a ## Block over Block - amax = μg (M1/M1+M2) - a = f / (M1+M2) - Case 1: amax > a - Body will move together with a' - Frictional force = fs = f (applied) - fs = μ2a - Case I: amax = a; About to slip - Case III: amax < a; Move with diff. a - (Draw separate F.B.D) - M2 → fk = μ2a - M1 → f-fk = m1a - amax = μg (M1/M1+M2) - a = f / (M1+M2) ## Angle of repose θ - tan θ = μ - N = Mgcos θ - Mgsinθ = fs - Mgsinθ = μNcosθ - tan θ = μ - μ > tanθ → Object don't move - μ = tanθ → About to move - μ < tanθ → start Moving - fk = μk mg cos θ - a = gsinθ - μk gcosθ