9. Two carts are moving toward each other on a track and collide. The following table shows the data for the collision: Mass Initial velocity Final velocity Cart 1 280 g 0.60 m/s to the right 0.20 m/s to the left Cart 2 320 g 0.30 m/s to the left 0.40 m/s to the right (a) What is the coefficient of restitution of this collision? (b) Is this collision totally elastic? Explain. (c) Calculate the initial velocity of the center of mass of the system that includes both carts.
9. Two carts are moving toward each other on a track and collide. The following table shows the data for the collision: Mass Initial velocity Final velocity Cart 1 280 g 0.60 m/s to the right 0.20 m/s to the left Cart 2 320 g 0.30 m/s to the left 0.40 m/s to the right (a) What is the coefficient of restitution of this collision? (b) Is this collision totally elastic? Explain. (c) Calculate the initial velocity of the center of mass of the system that includes both carts.
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Transcribed Image Text:**9.** Two carts are moving toward each other on a track and collide. The following table shows the data for the collision:
| | Cart 1 | Cart 2 |
|--------|--------------|--------------|
| Mass | 280 g | 320 g |
| Initial velocity | 0.60 m/s to the right | 0.30 m/s to the left |
| Final velocity | 0.20 m/s to the left | 0.40 m/s to the right |
(a) What is the coefficient of restitution of this collision?
(b) Is this collision totally elastic? Explain.
(c) Calculate the initial velocity of the center of mass of the system that includes both carts.
(d) Calculate the change in total momentum of the system that includes both carts and explain whether what you find is reasonable.
(e) Calculate the change in total kinetic energy of the system that includes both carts and explain whether what you find is reasonable.
(f) Make a new table that lists the velocities of the carts relative to a reference frame that is moving 0.20 m/s ‘to the left’ according to the coordinate system used in the table above.
**10.** The map of city streets to the right shows blocks that are 40 m wide and 75 m long. A person walks along the streets from A to B in 2.0 minutes (as directly as they can while staying on the streets).
(a) What is the magnitude and direction of the person’s displacement?
(b) What is the person’s average speed?
(c) What is the person’s average velocity?
Diagram Description: The city street grid diagram depicts city blocks with dimensions of 40 m by 75 m. A path is shown indicating movement from point A to point B with a northward direction covering a distance of 200 m, then eastward covering a distance of 100 m.
**11.** The position of a 25 kg robot that is moving along a straight track in the x direction is given by the function \( x(t) = (0.001 \, \text{m/s}^4)t^4 + (-0.04 \, \text{m/s}^3)t^3 + (0.4 \, \text{m/s}^2)t^2 \) between the times \( t = 0 \) and \( t = 20 \, \text{s} \).
![**Review of Formulas**
1. **Displacement and Velocity:**
\[
\Delta \vec{r} = \vec{v}_{\text{avg}} \Delta t \quad (\text{how far, how fast, how long})
\]
2. **Momentum (p):**
\[
\vec{p} = m \vec{v}
\]
3. **Kinetic Energy (K):**
\[
K = \frac{1}{2} mv^2
\]
4. **Force (F):**
\[
\vec{F} = \frac{d\vec{p}}{dt} \quad \text{or} \quad \vec{F} = \frac{\Delta \vec{p}}{\Delta t}
\]
5. **Velocity Addition:**
\[
\vec{v}_{\text{Eb}} = \vec{v}_{\text{Es}} + \vec{v}_{\text{sb}}
\]
6. **Relative Velocity:**
\[
\vec{v}_{\text{Eb}} = -\vec{v}_{\text{bE}}
\]
7. **Center of Mass Position:**
\[
\vec{r}_{\text{cm}} = \frac{m_1 \vec{r}_1 + m_2 \vec{r}_2 + \ldots}{m_1 + m_2 + \ldots}
\]
8. **Velocity of the Center of Mass:**
\[
\vec{v}_{\text{cm}} = \frac{\vec{p}_{\text{tot}}}{m_{\text{tot}}} = \frac{m_1 \vec{v}_1 + m_2 \vec{v}_2 + \ldots}{m_1 + m_2 + \ldots}
\]
9. **Final Momentum:**
\[
\vec{p}_{\text{final}} = \vec{p}_{\text{initial}} + \Delta \vec{p}_{\text{in}} - \Delta \vec{p}_{\text{out}}
\]
**Isolated System Equations:**
- Total initial momentum equals total final momentum:
\[
\vec{p}_{](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F06512908-6534-4389-9d07-5dc7e2cbc6af%2F2839fc96-1cd1-4a3d-9d9f-cf4a7fa40f28%2Fwz2iz8k_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Review of Formulas**
1. **Displacement and Velocity:**
\[
\Delta \vec{r} = \vec{v}_{\text{avg}} \Delta t \quad (\text{how far, how fast, how long})
\]
2. **Momentum (p):**
\[
\vec{p} = m \vec{v}
\]
3. **Kinetic Energy (K):**
\[
K = \frac{1}{2} mv^2
\]
4. **Force (F):**
\[
\vec{F} = \frac{d\vec{p}}{dt} \quad \text{or} \quad \vec{F} = \frac{\Delta \vec{p}}{\Delta t}
\]
5. **Velocity Addition:**
\[
\vec{v}_{\text{Eb}} = \vec{v}_{\text{Es}} + \vec{v}_{\text{sb}}
\]
6. **Relative Velocity:**
\[
\vec{v}_{\text{Eb}} = -\vec{v}_{\text{bE}}
\]
7. **Center of Mass Position:**
\[
\vec{r}_{\text{cm}} = \frac{m_1 \vec{r}_1 + m_2 \vec{r}_2 + \ldots}{m_1 + m_2 + \ldots}
\]
8. **Velocity of the Center of Mass:**
\[
\vec{v}_{\text{cm}} = \frac{\vec{p}_{\text{tot}}}{m_{\text{tot}}} = \frac{m_1 \vec{v}_1 + m_2 \vec{v}_2 + \ldots}{m_1 + m_2 + \ldots}
\]
9. **Final Momentum:**
\[
\vec{p}_{\text{final}} = \vec{p}_{\text{initial}} + \Delta \vec{p}_{\text{in}} - \Delta \vec{p}_{\text{out}}
\]
**Isolated System Equations:**
- Total initial momentum equals total final momentum:
\[
\vec{p}_{
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