Two identical carts and of masses and respectively are held together on a smooth…

PHYSICS · Subjective · CBSE · Physics · Laws of Motion · Laws of Motion

Problem

Two identical carts AA and BB of masses 2 kg2\,\text{kg} and 3 kg3\,\text{kg} respectively are held together on a smooth horizontal track by a light spring compressed between them. A light thread keeps the spring compressed so that the system is at rest relative to the ground. (a) Immediately after the thread is burnt, explain whether any external forces act on the system of the two carts and the spring. (b) Prove that the total linear momentum of the two-cart system remains constant during the expansion of the spring. (c) If the spring had been compressed so that it stored 10 J10\,\text{J} of potential energy, calculate the speeds of the two carts after they lose contact with the spring. (Neglect the mass of the spring and any rotational effects.)

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