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Illustration of two carts colliding and sticking together to show the concept of inelastic collision in physics

Inelastic Collision of Carts: Calculating Final Speed Post-Collision

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Question: A 3.00-kg cart with an initial velocity of +4.00 collides inelastically with a 5.00-kg cart with an initial velocity of +2.00 The carts stick together when they collide. What is their speed after colliding?

Asked by nevaehg

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The problem involves the concept of conservation of momentum for inelastic collisions. According to this concept, the total momentum before the collision equals the total momentum after the collision. The total momentum before the collision equals the sum of the momenta of the two carts. The momentum (p) of an object is given by the product of its mass (m) and velocity (v): p = mv. The total initial momentum (p_initial) is: p_initial = (3.00 kg * 4.00 m/s) + (5.00 kg * 2.00 m/s) = 12.00 kg*m/s + 10.00 kg*m/s = 22.00 kg*m/s. Since the carts stick together after the collision, their combined mass becomes (3.00 kg + 5.00 kg) = 8.00 kg. Let's denote the final speed of the carts after the collision as vf. According to the conservation of momentum, the total initial momentum must equal the total final momentum. Therefore: p_initial = p_final, then 22.00 kg*m/s = 8.00 kg * vf. Now let's solve this equation for vf: vf = 22.00 kg*m/s / 8.00 kg = 2.75 m/s. So, the speed of the carts after they collide is 2.75 m/s.

Answered by gpt-4

March 22, 2024, 10:22 a.m.

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This article was generated in part by one of OpenAI’s large-scale language-generation model, answering user nevaehg's question. Images were generated with OpenAI's AI model, DALL·E 2. The Internet takes ultimate responsibility for the content of this publication.
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Published: Friday, March 22, 2024

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