This animation walks through worked problems on perfectly inelastic collisions, where two objects stick together after impact. It shows how to apply conservation of momentum to find the common final velocity, then compares initial and final kinetic energy to calculate the energy lost to deformation and heat. Multiple examples with spheres and carts reinforce the method step by step. Useful for physics students and teachers covering momentum, collisions, and energy conservation in mechanics.
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Scene 5: Try It (b) - Perfectly Inelastic Collision (Sticking)On-Screen Title: Try It (b): Perfectly Inelastic CollisionQuestion: Sphere A ($2.0\text{ kg}$) moving right at $4.0\text{ m/s}$ collides with stationary sphere B ($3.0\text{ kg}$) and they stick together (right is positive). (i) Find the final velocity of the spheres, (ii) Find the lost kinetic energy after collision in Joules. Answer:(i) $v_f = \frac{(2.0)(4.0)}{2.0 + 3.0} = \mathbf{1.6\text{ m/s}}$. (ii) Initial $E_k = 16\text{ J}$; Final $E_k = 6.4\text{ J}$; Lost Energy = $\mathbf{9.6\text{ J}}$. Scene 6: Exam-Style QuestionOn-Screen Title: Exam-Style Question: Carts Sticking TogetherQuestion: Cart A ($1.0\text{ kg}$) moving at $4.0\text{ m/s}$ collides with stationary cart B ($1.5\text{ kg}$) and they stick together. (a) Find the final velocity of the stuck carts, (b) Calculate the lost kinetic energy after collision. Answer:(a) $v_f = \frac{(1.0)(4.0)}{1.0 + 1.5} = \mathbf{1.6\text{ m/s}}$. (b) Initial $E_k = \frac{1}{2}(1)(4)^2 = 8.0\text{ J}$; Final $E_k = \frac{1}{2}(2.5)(1.6)^2 = 3.2\text{ J}$; Lost Energy = $\mathbf{4.8\text{ J}}$. Scene 7: Exercise (a) - Momentum and Energy LossOn-Screen Title: Exercise (a): Momentum Conservation and Energy LossQuestion: Sphere A ($2.0\text{ kg}$) moving right at $8.0\text{ m/s}$ collides with sphere B ($1.0\text{ kg}$) moving ahead at $2.0\text{ m/s}$. After collision, A moves right at $5.0\text{ m/s}$ and B moves right at $8.0\text{ m/s}$. (i) Deduce that momentum is conserved, (ii) Find the lost kinetic energy after collision in Joules. Answer:(i) Initial momentum = $(2)(8) + (1)(2) = 18\text{ kg}\cdot\text{m/s}$; Final momentum = $(2)(5) + (1)(8) = 18\text{ kg}\cdot\text{m/s}$ (Conserved). (ii) Initial $E_k = 64 + 2 = 66\text{ J}$; Final $E_k = 25 + 32 = 57\text{ J}$; Lost Energy = $\mathbf{9\text{ J}}$. 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