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7. Two carts collide on a level, frictionless track. Just before they collide, the 370 g cart had a velocity of 1.7 m/s & and the 600 g cart had a velocity of -1.7 m/s ê. If they stick together, what will their velocity be just after the colli- sion?

7. Two carts collide on a level, frictionless track. Just before they collide, the 370 g cart had a velocity of 1.7 m/s & and the 600 g cart had a velocity of -1.7 m/s ê. If they stick together, what will their velocity be just after the colli- sion?

College Physics
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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**Questions** 1. (a) What does it mean to say that momentum is a conserved quantity? (b) Under what circumstance(s) will the change in momentum of a system be zero? 2. A system contains two objects. Object 1 has a mass of 220 g and is moving with a velocity \( (15 \, \text{m/s}) \hat{x} \). Object 2 has a mass of 150 g. What must the velocity of object 2 be for the total system momentum to be zero? 3. Express the vector \( \vec{A} = 41 \, \text{m/s} \, @ \, -47^\circ \) in terms of its components. 4. If they are sensible computations, complete the calculations given below. If the requested calculation does not make sense, explain what makes it nonsense. (a) \[ \begin{bmatrix} 21 \, \text{kg} \\ 14 \, \text{kg} \end{bmatrix} - \begin{bmatrix} -12 \, \text{m/s} \\ 22 \, \text{m/s} \end{bmatrix} \] (b) \( 6.0 \, \text{s} \) \[ \begin{bmatrix} 4.0 \, \text{m/s} \\ -8.0 \, \text{m/s} \end{bmatrix} + \begin{bmatrix} -22 \, \text{m} \\ 46 \, \text{m} \end{bmatrix} \] 5. Sketch a graph of velocity as a function of time for an object that is located at \( x = 3 \, \text{m} \) at \( t = 0 \) and is moving at a constant velocity of \( (-2.0 \, \text{m/s}) \hat{x} \). Make sure to label your axes, including appropriate scales and units to show at least 4 seconds of time. 6. Similarly, sketch a graph of position as a function of time for the object in question 5. 7. Two carts collide on a level, frictionless track. Just before they collide,
Transcribed Image Text:**Questions** 1. (a) What does it mean to say that momentum is a conserved quantity? (b) Under what circumstance(s) will the change in momentum of a system be zero? 2. A system contains two objects. Object 1 has a mass of 220 g and is moving with a velocity \( (15 \, \text{m/s}) \hat{x} \). Object 2 has a mass of 150 g. What must the velocity of object 2 be for the total system momentum to be zero? 3. Express the vector \( \vec{A} = 41 \, \text{m/s} \, @ \, -47^\circ \) in terms of its components. 4. If they are sensible computations, complete the calculations given below. If the requested calculation does not make sense, explain what makes it nonsense. (a) \[ \begin{bmatrix} 21 \, \text{kg} \\ 14 \, \text{kg} \end{bmatrix} - \begin{bmatrix} -12 \, \text{m/s} \\ 22 \, \text{m/s} \end{bmatrix} \] (b) \( 6.0 \, \text{s} \) \[ \begin{bmatrix} 4.0 \, \text{m/s} \\ -8.0 \, \text{m/s} \end{bmatrix} + \begin{bmatrix} -22 \, \text{m} \\ 46 \, \text{m} \end{bmatrix} \] 5. Sketch a graph of velocity as a function of time for an object that is located at \( x = 3 \, \text{m} \) at \( t = 0 \) and is moving at a constant velocity of \( (-2.0 \, \text{m/s}) \hat{x} \). Make sure to label your axes, including appropriate scales and units to show at least 4 seconds of time. 6. Similarly, sketch a graph of position as a function of time for the object in question 5. 7. Two carts collide on a level, frictionless track. Just before they collide,
## Review of Formulas ### Kinematics and Dynamics - **Displacement Formula:** \[ \Delta \vec{r} = \vec{v}_{\text{avg}} \Delta t \quad (\text{how far, how fast, how long}) \] - **Momentum and Kinetic Energy:** \[ \vec{p} = m \vec{v} \] \[ K = \frac{1}{2} m v^2 \] - **Force:** \[ \vec{F} = \frac{d}{dt} \vec{p} \quad \text{or} \quad \vec{F} = \frac{\Delta \vec{p}}{\Delta t} \] ### Relative Velocity - **Velocity of an object B relative to an object E (Earth):** \[ \vec{v}_{Eb} = \vec{v}_{Es} + \vec{v}_{sb} \] \[ \vec{v}_{Eb} = -\vec{v}_{bE} \] ### Center of Mass - **Position and Velocity of Center of Mass:** \[ \vec{r}_{cm} = \frac{m_1 \vec{r}_1 + m_2 \vec{r}_2 + \ldots}{m_1 + m_2 + \ldots} \] \[ \vec{v}_{cm} = \frac{\vec{p}_{\text{tot}}}{m_{\text{tot}}} = \frac{m_1 \vec{v}_1 + m_2 \vec{v}_2 + \ldots}{m_1 + m_2 + \ldots} \] ### Momentum Conservation - **Momentum Exchange:** \[ \vec{p}_{\text{final}} = \vec{p}_{\text{initial}} + \Delta \vec{p}_{\text{in}} - \Delta \vec{p}_{\text{out}} \] ### Isolated System - **Conservation of Total Momentum:** \[ \vec{p}_{\text{tot}_i} = \vec{p}_{\text{tot}_f} \] - **Momentum
Transcribed Image Text:## Review of Formulas ### Kinematics and Dynamics - **Displacement Formula:** \[ \Delta \vec{r} = \vec{v}_{\text{avg}} \Delta t \quad (\text{how far, how fast, how long}) \] - **Momentum and Kinetic Energy:** \[ \vec{p} = m \vec{v} \] \[ K = \frac{1}{2} m v^2 \] - **Force:** \[ \vec{F} = \frac{d}{dt} \vec{p} \quad \text{or} \quad \vec{F} = \frac{\Delta \vec{p}}{\Delta t} \] ### Relative Velocity - **Velocity of an object B relative to an object E (Earth):** \[ \vec{v}_{Eb} = \vec{v}_{Es} + \vec{v}_{sb} \] \[ \vec{v}_{Eb} = -\vec{v}_{bE} \] ### Center of Mass - **Position and Velocity of Center of Mass:** \[ \vec{r}_{cm} = \frac{m_1 \vec{r}_1 + m_2 \vec{r}_2 + \ldots}{m_1 + m_2 + \ldots} \] \[ \vec{v}_{cm} = \frac{\vec{p}_{\text{tot}}}{m_{\text{tot}}} = \frac{m_1 \vec{v}_1 + m_2 \vec{v}_2 + \ldots}{m_1 + m_2 + \ldots} \] ### Momentum Conservation - **Momentum Exchange:** \[ \vec{p}_{\text{final}} = \vec{p}_{\text{initial}} + \Delta \vec{p}_{\text{in}} - \Delta \vec{p}_{\text{out}} \] ### Isolated System - **Conservation of Total Momentum:** \[ \vec{p}_{\text{tot}_i} = \vec{p}_{\text{tot}_f} \] - **Momentum
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