Author: dexter

Problem Statement Solve the Newton’s Laws / mechanics problem: Solve the Newton’s Laws / mechanics problem: Particle of mass m moves along y = αx² at constant speed v. Find force at x = 0. Mass m, speed v constant Curve: y = αx² $$R=\frac{(1+y’^2)^{3/2}}{|y |},\quad F_n=\frac{mv^2}{R}$$ Step 1: y’ = 2αx, y = 2α.…

Problem Statement Solve the work-energy problem: Solve the work-energy problem: Body of mass m thrown at angle α with speed v₀; speed at time t is v. Find work by drag force. Mass m, angle α, initial speed v₀ Speed at time t: v $$W_{drag} = \Delta KE – W_{gravity}$$ Step 1: W_g = mg(gt²/2…

Problem Statement Solve the work-energy problem: Solve the work-energy problem: Body of mass m hauled by F = 2(1−αh)mg. Find work by F and ΔPE over first half of total path. F = 2(1−αh)mg α > 0 Body stops when F = mg: 1−αH = ½ → H = 1/(2α). First half: h = 0…

Problem Statement Solve the work-energy problem: Solve the work-energy problem: Locomotive of mass m: v = a√s. Find force and power at distance s₀. Mass m v = a√s At distance s₀ $$w = v\frac{dv}{ds},\quad F = mw,\quad P = Fv$$ Step 1: dv/ds = a/(2√s). Step 2: w = a√s · a/(2√s) = a²/2…

Problem Statement Solve the kinematics problem: Solve the work-energy problem: Body of mass m thrown at angle θ with speed v₀. Find work by gravity in first t seconds. Mass m Launch angle θ, speed v₀ Time interval t $$W_g = -mg\Delta h,\quad \Delta h = v_0\sin\theta\cdot t – \tfrac{1}{2}gt^2$$ Step 1: Δh = v₀sinθ·t…

Problem Statement Solve the work-energy problem: Solve the work-energy problem: A particle of mass 0.5 kg moves with v = 2t² m/s. Find work done over the first 3 seconds. m = 0.5 kg v = 2t² m/s t = 0 to 3 s $$W = \Delta KE = \tfrac{1}{2}mv_f^2 – \tfrac{1}{2}mv_i^2$$ Step 1: v(0)…

Problem Statement Solve the Newton’s Laws / mechanics problem: A particle of mass m moves along a circle of radius R with normal acceleration w_n = at². Find the tangential force and the total force when the kinetic energy equals T. Mass m, radius R Normal acceleration: w_n = at² KE = T at moment…