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# Calculating the Final Speed of Colliding Carts: Inelastic Collision Analysis

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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?

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The carts colliding inelastically and sticking together is an example of conservation of momentum, where the total momentum before the collision must equal the total momentum after the collision. Before the collision, the total momentum is: Initial momentum = Momentum of the 3 kg cart + Momentum of the 5 kg cart = (3 kg * 4 m/s) + (5 kg * 2 m/s) = 12 kg m/s + 10 kg m/s = 22 kg m/s After the collision, the total momentum is: Final momentum = (3 kg + 5 kg) * V (V is the velocity after collision) So, the final momentum should also be equal to 22 kg m/s. Let's set the final momentum equal to the initial momentum and solve for V: (3 kg + 5 kg) * V = 22 kg m/s 8 kg * V = 22 kg m/s V = 22 kg m/s / 8 kg V = 2.75 m/s So, the speed of the carts after they collide and stick together is 2.75 m/s.

March 22, 2024, 10:23 a.m.

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