A projectile of mass mp is traveling at a constant velocity up toward a stationary disk of mass M and radius R that is free to rotate about its axis, as shown in the figure. Before impact, the projectile is traveling along a line displaced a distance b below the axis. The projectile strikes the disk and sticks to point B. Model the projectile as a point mass. (Use any of the given variables and any mathematical or physical constants as necessary.)
A projectile of mass mp is traveling at a constant velocity up toward a stationary disk of mass M and radius R that is free to rotate about its axis, as shown in the figure. Before impact, the projectile is traveling along a line displaced a distance b below the axis. The projectile strikes the disk and sticks to point B. Model the projectile as a point mass. (Use any of the given variables and any mathematical or physical constants as necessary.)
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![A projectile of mass \( m_p \) is traveling at a constant velocity \( \vec{v}_0 \) toward a stationary disk of mass \( M \) and radius \( R \) that is free to rotate about its axis, as shown in the figure. Before impact, the projectile is traveling along a line displaced a distance \( b \) below the axis. The projectile strikes the disk and sticks to point \( B \). Model the projectile as a point mass. (Use any of the given variables and any mathematical or physical constants as necessary.)
**Diagram Description:**
The diagram illustrates a projectile moving towards a disk. The disk has a radius \( R \) and mass \( M \). The projectile has a mass \( m_p \) and velocity \( \vec{v}_0 \). The projectile's path is a distance \( b \) below the axis of rotation of the disk. The point of impact on the disk is labeled as \( B \).
**Questions and Formulas:**
1. **Before impact, what is the total angular momentum magnitude \( L_0 \) of the disk-projectile system about the axis?**
\[
L_0 = m_p v_0 b
\]
- **Incorrect**
2. **What is the angular speed \( \omega \) of the disk-projectile system just after the impact?**
\[
\omega = \frac{2m_p v_0 b}{MR^2 + 2m_p R^2}
\]
- **Incorrect**
3. **What is the kinetic energy \( K_f \) of the disk-projectile system after impact?**
\[
K_f = \frac{\left(m_p v_0 b\right)^2}{MR^2 + 2m_p R^2}
\]
- **Incorrect**
4. **How much mechanical energy \( E_{\text{lost}} \) is lost in this collision?**
\[
E_{\text{lost}} = \frac{1}{2} m_p v_0^2 - \frac{\left(m_p v_0 b\right)^2}{MR^2 + 2m_p R^2}
\]
- **Incorrect**](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F1784d6b6-d0da-4ca6-88bb-f1a2aff3fb92%2F46b758a6-4dae-44e5-933f-1635a557cc74%2Fthq3bpl_processed.png&w=3840&q=75)
Transcribed Image Text:A projectile of mass \( m_p \) is traveling at a constant velocity \( \vec{v}_0 \) toward a stationary disk of mass \( M \) and radius \( R \) that is free to rotate about its axis, as shown in the figure. Before impact, the projectile is traveling along a line displaced a distance \( b \) below the axis. The projectile strikes the disk and sticks to point \( B \). Model the projectile as a point mass. (Use any of the given variables and any mathematical or physical constants as necessary.)
**Diagram Description:**
The diagram illustrates a projectile moving towards a disk. The disk has a radius \( R \) and mass \( M \). The projectile has a mass \( m_p \) and velocity \( \vec{v}_0 \). The projectile's path is a distance \( b \) below the axis of rotation of the disk. The point of impact on the disk is labeled as \( B \).
**Questions and Formulas:**
1. **Before impact, what is the total angular momentum magnitude \( L_0 \) of the disk-projectile system about the axis?**
\[
L_0 = m_p v_0 b
\]
- **Incorrect**
2. **What is the angular speed \( \omega \) of the disk-projectile system just after the impact?**
\[
\omega = \frac{2m_p v_0 b}{MR^2 + 2m_p R^2}
\]
- **Incorrect**
3. **What is the kinetic energy \( K_f \) of the disk-projectile system after impact?**
\[
K_f = \frac{\left(m_p v_0 b\right)^2}{MR^2 + 2m_p R^2}
\]
- **Incorrect**
4. **How much mechanical energy \( E_{\text{lost}} \) is lost in this collision?**
\[
E_{\text{lost}} = \frac{1}{2} m_p v_0^2 - \frac{\left(m_p v_0 b\right)^2}{MR^2 + 2m_p R^2}
\]
- **Incorrect**
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