A worked problem set applying conservation of momentum to cart collisions on a frictionless track. Each scene presents a question, then solves it step by step: a perfectly inelastic collision where two carts stick together, and a partially solved collision where one cart's final velocity is unknown and must be found, including direction reversal. Useful for students practicing momentum equations before a physics exam.
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Scene 7: Exam-Style QuestionOn-Screen Title: Exam-Style Question: Inelastic Cart CollisionQuestion: A cart of mass $1.5\text{ kg}$ moving at $2.0\text{ m/s}$ collides head-on with a stationary cart of mass $0.50\text{ kg}$ on a smooth track, and they move together. Find the final velocity of the stuck carts in $\text{m/s}$. Answer:$(1.5 + 0.50)v_f = (1.5)(2.0) + (0.50)(0)$ $2.0 v_f = 3.0$ $v_f = \mathbf{1.5\text{ m/s}}$ Scene 8: Exercise (a)On-Screen Title: Exercise (a): Sticking CollisionQuestion: Body A ($2.0\text{ kg}$) moving in the positive direction at $3.0\text{ m/s}$ collides with stationary body B ($1.0\text{ kg}$) and they stick together. Find the velocity after collision in $\text{m/s}$. Answer:$(2.0 + 1.0)v_f = (2.0)(3.0) + (1.0)(0)$ $3.0 v_f = 6.0$ $v_f = \mathbf{2.0\text{ m/s}}$ Scene 9: Exercise (b)On-Screen Title: Exercise (b): Moving Carts CollisionQuestion: Cart A ($2.0\text{ kg}$) moving at $4.5\text{ m/s}$ collides with cart B ($5.0\text{ kg}$) moving at $0.40\text{ m/s}$ in the same direction. If cart B moves at $2.6\text{ m/s}$ in its original direction after collision, find cart A's speed and direction after collision. Answer:$(2.0)(4.5) + (5.0)(0.40) = (2.0)v_{Af} + (5.0)(2.6)$ $9.0 + 2.0 = 2.0 v_{Af} + 13.0 \implies 2.0 v_{Af} = -2.0$ $v_{Af} = \mathbf{-1.0\text{ m/s}}$ (Magnitude $1.0\text{ m/s}$, opposite direction). 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