College Physics
11th Edition
ISBN: 9781305952300
Author: Raymond A. Serway, Chris Vuille
Publisher: Cengage Learning
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As part of a carnival game, a ?b=0.503 kgmb=0.503 kg ball is thrown at a stack of 22.8 cm22.8 cm tall, ?o=0.363 kgmo=0.363 kg objects and hits with a perfectly horizontal velocity of ?b,i=11.6 m/s.vb,i=11.6 m/s. Suppose that the ball strikes the topmost object. Immediately after the collision, the ball has a horizontal velocity of ?b,f=3.35 m/svb,f=3.35 m/s in the same direction, the topmost object has an
If the object's center of mass is located ?=16.0 cmr=16.0 cm below the point where the ball hits, what is the moment of inertia ?oIo of the object about its center of mass?
![## Problem Description
As part of a carnival game, a ball with mass \( m_b = 0.503 \, \text{kg} \) is thrown at a stack of objects each with a height of 22.8 cm and a mass \( m_o = 0.363 \, \text{kg} \). The ball is thrown with a perfectly horizontal velocity of \( v_{b,i} = 11.6 \, \text{m/s} \). It strikes the topmost object in the stack. Immediately after the collision, the ball has a reduced horizontal velocity of \( v_{b,f} = 3.35 \, \text{m/s} \) in the same direction. The topmost object receives an angular velocity \( \omega_o = 2.03 \, \text{rad/s} \) about its center of mass, while the other objects remain undisturbed. Assume the ball is not rotating and that gravitational torque effects during the collision are negligible.
### Moment of Inertia Calculation
The center of mass of the object is located a distance \( r = 16.0 \, \text{cm} \) below the point where the ball impacts. Determine the moment of inertia \( I_o \) of the object about its center of mass.
\[ I_o = \underline{\hspace{2cm}} \, \text{kg}\cdot\text{m}^2 \]
### Center of Mass Velocity Calculation
Determine the velocity \( v_{o,cm} \) of the center of mass of the topmost object immediately after being struck by the ball.
\[ v_{o,cm} = \underline{\hspace{2cm}} \, \text{m/s} \]
## Diagrams
1. **First Diagram**:
- Illustrates the setup before collision, showing the ball approaching the top of a stack of three objects, aligned vertically. Arrow indicates the initial horizontal velocity \( v_{b,i} \).
2. **Second Diagram**:
- Depicts the situation immediately after the collision. The ball's reduced velocity \( v_{b,f} \) is indicated. The top object is shown with angular velocity \( \omega_o \), rotating about its center of mass, and the new velocity direction is shown with an arrow.](https://content.bartleby.com/qna-images/question/31ba52e1-bc06-4f7d-82d8-069c42f67e2b/16c3b858-9a86-472f-9933-37ab9f77bb66/9y069kr_processed.png)
Transcribed Image Text:## Problem Description
As part of a carnival game, a ball with mass \( m_b = 0.503 \, \text{kg} \) is thrown at a stack of objects each with a height of 22.8 cm and a mass \( m_o = 0.363 \, \text{kg} \). The ball is thrown with a perfectly horizontal velocity of \( v_{b,i} = 11.6 \, \text{m/s} \). It strikes the topmost object in the stack. Immediately after the collision, the ball has a reduced horizontal velocity of \( v_{b,f} = 3.35 \, \text{m/s} \) in the same direction. The topmost object receives an angular velocity \( \omega_o = 2.03 \, \text{rad/s} \) about its center of mass, while the other objects remain undisturbed. Assume the ball is not rotating and that gravitational torque effects during the collision are negligible.
### Moment of Inertia Calculation
The center of mass of the object is located a distance \( r = 16.0 \, \text{cm} \) below the point where the ball impacts. Determine the moment of inertia \( I_o \) of the object about its center of mass.
\[ I_o = \underline{\hspace{2cm}} \, \text{kg}\cdot\text{m}^2 \]
### Center of Mass Velocity Calculation
Determine the velocity \( v_{o,cm} \) of the center of mass of the topmost object immediately after being struck by the ball.
\[ v_{o,cm} = \underline{\hspace{2cm}} \, \text{m/s} \]
## Diagrams
1. **First Diagram**:
- Illustrates the setup before collision, showing the ball approaching the top of a stack of three objects, aligned vertically. Arrow indicates the initial horizontal velocity \( v_{b,i} \).
2. **Second Diagram**:
- Depicts the situation immediately after the collision. The ball's reduced velocity \( v_{b,f} \) is indicated. The top object is shown with angular velocity \( \omega_o \), rotating about its center of mass, and the new velocity direction is shown with an arrow.
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