**Physics Problem: Collision and Final Velocity Calculation****Problem Statement:**A billiard ball (1 kg) and a big piece of chewing gum (0.2 kg) are moving towards each other. The billiard ball has an initial velocity of 4 m/s to the right, and the chewing gum has a velocity of 20 m/s to the left. What is the final velocity of both the chewing gum and the billiard ball when they stick together after colliding?**Solution Approach:**To solve this problem, we use the principle of conservation of momentum. According to the law of conservation of momentum, the total momentum of a system before a collision is equal to the total momentum of the system after the collision, provided no external forces act on the system.**Step 1: Calculate Initial Momentum**The initial momentum (p_initial) is the sum of the momenta of both the billiard ball and the chewing gum.Momentum of billiard ball, \( p_{1} = \text{mass} \times \text{velocity} \)\[ = 1\, \text{kg} \times 4\, \text{m/s} \]\[ = 4\, \text{kg m/s} \](Direction is to the right)Momentum of chewing gum, \( p_{2} = \text{mass} \times \text{velocity} \)\[ = 0.2\, \text{kg} \times (-20)\, \text{m/s} \]\[ = -4\, \text{kg m/s} \](Direction is to the left, thus negative)Total initial momentum:\[ p_{initial} = p_{1} + p_{2} \]\[ = 4\, \text{kg m/s} + (-4\, \text{kg m/s}) \]\[ = 0\, \text{kg m/s} \]**Step 2: Calculate Final Momentum**When the billiard ball and chewing gum stick together, their final momentum (p_final) must equal the initial momentum due to conservation of momentum.\[ p_{final} = p_{initial} = 0\, \text{kg m/s} \]**Step 3: Determine Final Velocity**Let \( v_f \) be the final velocity of the combined mass (billiard ball + chewing gum).The combined mass \( m_{total} = m_{

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A billiard ball (1kg) and a big piece of chewing gum (0.2kg) are moving at each other. The billiard ball has an initial velocity of 4 m/s to the right, and the chewing gum has a velocity of 20 m/s to the left. What is the final velocity of both the chewing gum and the billiard ball when they stick together after colliding?

A billiard ball (1kg) and a big piece of chewing gum (0.2kg) are moving at each other. The billiard ball has an initial velocity of 4 m/s to the right, and the chewing gum has a velocity of 20 m/s to the left. What is the final velocity of both the chewing gum and the billiard ball when they stick together after colliding?

College Physics

11th Edition

ISBN:9781305952300

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter1: Units, Trigonometry. And Vectors

Section: Chapter Questions

Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...

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