3. Dynamics

Dynamics Newton’s 1st Law of Motion – A body at rest will remain as rest and a body in motion will continue in motion at constant velocity unless a net force acts on it. Newton’s 2nd Law of Motion – Rate of change of momentum of a body is proportional to the net force acting on it and the direction of momentum change is in the direction of the net force. Equations Graphs Net force, dpF dt As Momentum, p mv , d( mv )F dt dv dmF m v dt dt Constant m F ma  Free Body Diagram  Sum of Forces Equation Constant v dmFv dt 1. Flow Rate Problem Constant m problems (Free Body Diagram + Sum of Forces Equation) Lift Connected Bodies Incline Plane Equilibrium, N = W F N W 0   Accelerate up, N > W F N W ma   Accelerate down, N < W F N W ma   Same acceleration for both  ABF F m m a   For object A, A AB AF F F m a   For object B, B BA BF F m a Acceleration along plane, F mg sin ma , N mg cos  F t Δt Area = Impulse = F p t Gradient Δp Δt N W F mA mB FBA FAB N θ W mg sin θ mg cos θ

Flow Rate Problems (Free Body Diagram + Sum of Forces Equation) Water Hose Helicopter Mass on moving Belt Impact force on wall: dmFv dt 2d( AL g ) dLF v v.A g v A gdt dt     Force required to move sand, dmFv dt dm dt  Rate of mass falling Conservation of Linear Momentum – Total sum of momentum is conserved in collision General Inelastic Collision Before Collision: *ub is negative *ub is positive *ub is zero *explosion case By Principle of Conservation of Linear Momentum, a a b b a a b bm u m u m v m v   Elastic Collision Perfectly Inelastic Collision Equation 1: a a b b a a b bm u m u m v m v   Equation 2: a b b au u v v    Sum of kinetic energy is conserved  Relative speed of approach is equal to Relative speed of separation Equation 1: a a b b a a b bm u m u m v m v   Equation 2: abvv  Object stick together after collision Newton’s 3rd Law of Motion – Whenever a force acts on a body, an equal but oppositely directed force of the same kind acts on another body. Action-Reaction pair forces 1. are equal in magnitude. 2. are opposite in direction 3. act on two different bodies 4. are of the same nature. Wall Lift W Rotor Top View Circular Area, A Column of Air ma mb ua ub ma mb ua ub ma mb ua ub = 0 ma mb ua = ub = 0