### Physics of Pool Ball Collision**Problem Statement:**A cue ball at rest on a frictionless pool table is hit dead center by a pool stick, giving it an impulse of \( +1.25 \, \text{N} \cdot \text{s} \). The ball slides (the combination of hitting the ball dead center and no friction allows this to happen) along the table and makes a head-on elastic collision with another pool ball. If both pool balls have a mass of \( 0.156 \, \text{kg} \), determine the velocity (in m/s) of the second ball the instant after the collision.**Solution:**1. **Given Data:** - Impulse (\( J \)) = \( +1.25 \, \text{N} \cdot \text{s} \) - Mass of each pool ball (\( m \)) = \( 0.156 \, \text{kg} \)2. **Formulas:** - Impulse-Momentum Theorem: \( J = \Delta p \) where \( \Delta p \) is the change in momentum. - Momentum is given by \( p = mv \) - For an elastic collision: - Total momentum before collision = Total momentum after collision - Total kinetic energy before collision = Total kinetic energy after collision3. **Calculations:** - Impulse causes a change in momentum of the cue ball: \[ J = 1.25 \, \text{N} \cdot \text{s} = \Delta p = m \Delta v \] \[ \Delta v = \frac{J}{m} = \frac{1.25 \, \text{N} \cdot \text{s}}{0.156 \, \text{kg}} \approx 8.01 \, \text{m/s} \] - The initial velocity (\( v_1 \)) of the cue ball is: \[ v_1 = 8.01 \, \text{m/s} \] - For head-on elastic collisions where one ball is initially at rest: - The initial velocity of the struck ball (\( v_2 \)) is 0. - Velocity of the first ball after collision (\( v_1' \)) is

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A cue ball at rest on a frictionless pool table is hit dead center by a pool stick, giving it an impulse of +1.25 N · s. The ball slides (the combination of hitting the ball dead center and no friction allows this to happen) along the table and makes a head-on elastic collision with another pool ball. If both pool balls have a mass of 0.156 kg, determine the velocity (in m/s) of the second ball the instant after the collision. ]m/s

A cue ball at rest on a frictionless pool table is hit dead center by a pool stick, giving it an impulse of +1.25 N · s. The ball slides (the combination of hitting the ball dead center and no friction allows this to happen) along the table and makes a head-on elastic collision with another pool ball. If both pool balls have a mass of 0.156 kg, determine the velocity (in m/s) of the second ball the instant after the collision. ]m/s

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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