As part of a carnival game, a \( m_b = 0.453 \, \text{kg} \) ball is thrown at a stack of 15.8 cm tall, \( m_o = 0.383 \, \text{kg} \) objects and hits with a perfectly horizontal velocity of \( v_{b,i} = 11.8 \, \text{m/s} \). Suppose that the ball strikes the topmost object. Immediately after the collision, the ball has a horizontal velocity of \( v_{b,f} = 4.35 \, \text{m/s} \) in the same direction, the topmost object has an angular velocity of \( \omega_o = 5.23 \, \text{rad/s} \) about its center of mass, and all the remaining objects are undisturbed. Assume that the ball is not rotating and that the effect of the torque due to gravity during the collision is negligible.If the object's center of mass is located \( r = 11.1 \, \text{cm} \) below the point where the ball hits, what is the moment of inertia \( I_o \) of the object about its center of mass?\( I_o = \boxed{\phantom{1234567890}} \, \text{kg} \cdot \text{m}^2 \)What is the center of mass velocity \( v_{o,cm} \) of the tall object immediately after it is struck?\( v_{o,cm} = \boxed{\phantom{1234567890}} \, \text{m/s} \)**Diagrams Explanation:**1. **Top Diagram:** - A ball with velocity \( v_{b,i} \) is approaching a stack of objects. The ball is shown on the left, heading towards a stack of three identical-looking objects, indicating the initial condition before the collision.2. **Bottom Diagram:** - After the collision, the ball moves in the same direction with reduced velocity \( v_{b,f} \). - The top object is shown tilted with an angular velocity \( \omega_o \), representing its rotation after being struck. - This diagram illustrates the system's dynamics immediately following the collision.

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As part of a carnival game, a mb = 0.453 kg ball is thrown at a stack of 15.8 cm tall, mo = 0.383 kg objects and hits with a perfectly horizontal velocity of vp,i = 11.8 m/s. Suppose that the ball strikes the topmost object. Immediately after the collision, the ball has a horizontal velocity of vo.f = 4.35 m/s in the same direction, the topmost object has an angular velocity of @. = 5.23 rad/s about its center of mass, and all the remaining objects are undisturbed. Assume that the ball is not rotating and that the effect of the torque due to gravity during the collision is negligible. If the object's center of mass is located r = 11.1 cm below the point where the ball hits, what is the moment of inertia I, of the object about its center of mass? I, = kg m2 What is the center of mass velocity vo.cm of the tall object immediately after it is struck? Vo,cm = m/s

As part of a carnival game, a mb = 0.453 kg ball is thrown at a stack of 15.8 cm tall, mo = 0.383 kg objects and hits with a perfectly horizontal velocity of vp,i = 11.8 m/s. Suppose that the ball strikes the topmost object. Immediately after the collision, the ball has a horizontal velocity of vo.f = 4.35 m/s in the same direction, the topmost object has an angular velocity of @. = 5.23 rad/s about its center of mass, and all the remaining objects are undisturbed. Assume that the ball is not rotating and that the effect of the torque due to gravity during the collision is negligible. If the object's center of mass is located r = 11.1 cm below the point where the ball hits, what is the moment of inertia I, of the object about its center of mass? I, = kg m2 What is the center of mass velocity vo.cm of the tall object immediately after it is struck? Vo,cm = 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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