Author: dexter

Problem Statement Solve the momentum/collision problem: Solve the momentum/collision problem: Mass m (velocity v) makes head-on elastic collision with stationary mass M. Find energy transferred. Moving: mass m, velocity v Stationary: mass M $$V_M=\frac{2mv}{m+M},\quad \Delta T=\tfrac{1}{2}MV_M^2$$ Step 1: V_M = 2mv/(m+M). Step 2: ΔT = ½M·4m²v²/(m+M)². St Given Information Masses $m_1$, $m_2$ and initial velocities…

Problem Statement Solve the momentum/collision problem: Solve the momentum/collision problem: Mass m₁ (> m₂) moving at v₀ hits stationary m₂ elastically. Find maximum deflection angle of m₁. m₁ > m₂ Initial velocity v₀, m₂ at rest Elastic collision $$\sin\theta_{max}=\frac{m_2}{m_1}$$ Step 1: CM velocity: V = m₁v₀/(m₁+m₂). Step 2: Speed of m₁ in CM frame Given…

Problem Statement Solve the work-energy problem: Solve the work-energy problem: Two particles of masses m₁, m₂ with lab velocities v₁, v₂. Find KE in the CM frame. Masses m₁, m₂ Lab velocities v₁, v₂ $$\tilde{T}=\tfrac{1}{2}\mu v_{rel}^2,\quad \mu=\frac{m_1m_2}{m_1+m_2}$$ Step 1: v_rel = |v₁ − v₂|. Step 2: μ = m₁m₂/(m₁+m₂) (reduced mass). Step 3: Given Information…

Problem Statement Simple pendulum (length l) in car accelerating horizontally at a. Find equilibrium angle and oscillation frequency. Given Information All quantities, constants, and constraints stated in the problem above Physical constants used as needed (see Concepts section) Physical Concepts & Formulas This problem draws on fundamental physical principles. The key is to identify which…

Problem Statement Solve the Newton’s Laws / mechanics problem: Ball of mass m falls from height h onto spring (stiffness k). Find maximum compression x. All quantities, constants, and constraints stated in the problem above Physical constants used as needed (see Concepts section) This problem draws on fundamental physical principles. The key is to identify…