A three-part walkthrough of kinetic energy and collisions. It starts with a quick calculation of kinetic energy from mass and velocity, then works through a partially elastic collision using momentum conservation and the coefficient of restitution to find final velocities and energy lost, and finishes with a practice problem on a perfectly inelastic collision where objects stick together. Useful for students learning momentum, restitution, and energy loss in collisions.
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Scene 1: Quick Check (Kinetic Energy)On-Screen Title: Quick Check: Calculating Kinetic EnergyQuestion: A cart of mass $2.0\text{ kg}$ moves with a velocity of $4.0\text{ m/s}$. Calculate its kinetic energy in Joules. Answer:Formula: $E_k = \frac{1}{2}mv^2$ Calculation: $E_k = \frac{1}{2} \times 2.0 \times (4.0)^2 = \mathbf{16\text{ J}}$ Scene 2: Worked Example (Restitution and Lost Energy)On-Screen Title: Worked Example: Final Velocities and Lost EnergyQuestion: Small sphere A ($1.0\text{ kg}$) moves right at $4.0\text{ m/s}$ and collides with stationary sphere B ($1.5\text{ kg}$). The coefficient of restitution is $0.25$. Find: (a) The final velocities of both spheres after collision in $\text{m/s}$, (b) The lost mechanical energy in Joules (taking right as positive). Answer:(a) Using momentum and restitution equations: $v_{Af} = -0.40\text{ m/s}$, $v_{Bf} = \mathbf{2.4\text{ m/s}}$. (b) Lost Energy: $\Delta E_k = E_{k,initial} - E_{k,final} = \mathbf{6.0\text{ J}}$. Scene 3: Try It Yourself (Inelastic Sticking Collision)On-Screen Title: Practice: Sticking Collision and Energy LossQuestion: Small sphere A ($2.0\text{ kg}$) moves right at $4.0\text{ m/s}$ and collides with stationary sphere B ($3.0\text{ kg}$). They stick together. Find the final velocity and the lost kinetic energy in Joules. Answer:(i) Final velocity: $(2.0 + 3.0)v_f = (2.0)(4.0) \implies v_f = \mathbf{1.6\text{ m/s}}$. (ii) Initial $E_k = \frac{1}{2}(2)(4)^2 = 16\text{ J}$; Final $E_k = \frac{1}{2}(5)(1.6)^2 = 6.4\text{ J}$. Lost Energy = $16 - 6.4 = \mathbf{9.6\text{ J}}$. Scene 4: Try It (a) - Head-on Collision with RestitutionOn-Screen Title: Try It (a): 1D Collision with RestitutionQuestion: Sphere A ($2.0\text{ kg}$) moving right at $4.0\text{ m/s}$ collides with sphere B ($1.0\text{ kg}$) moving left at $6.0\text{ m/s}$. After collision, A moves right at $1.0\text{ m/s}$ and B moves right at $4.0\text{ m/s}$ (right is positive, $e = 0.5$). (i) Deduce that momentum is conserved, (ii) Find the lost kinetic energy in Joules. Answer:(i) Initial momentum = $(2)(4) + (1)(-6) = +2\text{ kg}\cdot\text{m/s}$; Final momentum = $(2)(1) + (1)(4) = +2\text{ kg}\cdot\text{m/s}$ (Conservred). (ii) Initial $E_k = 16 + 18 = 34\text{ J}$; Final $E_k = 1 + 8 = 9\text{ J}$; Lost Energy = $\mathbf{25\text{ J}}$. IMPORTANT LANGUAGE RULE: All on-screen text must be in Arabic EXCEPT mathematical equations, formulas, laws, symbols, variables, and numerical expressions. Keep every equation, formula, and law exactly as provided, without translating or changing it. Translate only the explanatory text, headings, labels, and descriptions into Arabic. Arabic text must use proper RTL direction and correct Arabic typography. Do not use English text anywhere else on the screen. Audience: student