Consider a system consisting of three particles: m = 3 kg, v = < 9, -4, 14 > m/s m2 = 9 kg, v2 = < -13, 7, -6 > m/s m3 = 4 kg, v3 -< -24, 35, 21 > m/s (a) What is the total momentum of this system? F tot = kg · m/s (b) What is the velocity of the center of mass of this system? cm = m/s (c) What is the total kinetic energy of this system? Krot = (d) What is the translational kinetic energy of this system? Ktrans = (e) What is the kinetic energy of this system relative to the center of mass? Krel = One way to calculate Krej is to calculate the velocity of each particle relative to the center of mass, by subtracting the center-of-mass velocity from the particle's actual velocity to get the
Consider a system consisting of three particles: m = 3 kg, v = < 9, -4, 14 > m/s m2 = 9 kg, v2 = < -13, 7, -6 > m/s m3 = 4 kg, v3 -< -24, 35, 21 > m/s (a) What is the total momentum of this system? F tot = kg · m/s (b) What is the velocity of the center of mass of this system? cm = m/s (c) What is the total kinetic energy of this system? Krot = (d) What is the translational kinetic energy of this system? Ktrans = (e) What is the kinetic energy of this system relative to the center of mass? Krel = One way to calculate Krej is to calculate the velocity of each particle relative to the center of mass, by subtracting the center-of-mass velocity from the particle's actual velocity to get the
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ISBN:9781305952300
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Chapter1: Units, Trigonometry. And Vectors
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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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![### System of Particles Analysis
Consider a system consisting of three particles:
- **Particle 1:** Mass \( m_1 = 3 \, \text{kg} \), Velocity \( \vec{v}_1 = \langle 9, -4, 14 \rangle \, \text{m/s} \)
- **Particle 2:** Mass \( m_2 = 9 \, \text{kg} \), Velocity \( \vec{v}_2 = \langle -13, 7, -6 \rangle \, \text{m/s} \)
- **Particle 3:** Mass \( m_3 = 4 \, \text{kg} \), Velocity \( \vec{v}_3 = \langle -24, 35, 21 \rangle \, \text{m/s} \)
#### Exercises:
(a) **Total Momentum of the System**
\[
\vec{p}_{\text{tot}} = \underline{\hspace{3cm}} \, \text{kg} \cdot \text{m/s}
\]
(b) **Velocity of the Center of Mass**
\[
\vec{v}_{\text{cm}} = \underline{\hspace{3cm}} \, \text{m/s}
\]
(c) **Total Kinetic Energy of the System**
\[
K_{\text{tot}} = \underline{\hspace{3cm}} \, \text{J}
\]
(d) **Translational Kinetic Energy of the System**
\[
K_{\text{trans}} = \underline{\hspace{3cm}} \, \text{J}
\]
(e) **Kinetic Energy Relative to the Center of Mass**
\[
K_{\text{rel}} = \underline{\hspace{3cm}} \, \text{J}
\]
#### Key Concept:
To calculate \( K_{\text{rel}} \), determine the velocity of each particle relative to the center of mass by subtracting the center-of-mass velocity from the particle's actual velocity. Then calculate the corresponding kinetic energies and add them up. Alternatively, consider the energy relationships in a multiparticle system to simplify the calculation.
(Note: You can verify your result with a detailed calculation if desired.)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F97aba9c2-7733-43fc-8cda-64b1db1637bb%2F1019d590-9932-41cf-8e98-8709e7dae6c3%2Fyfv6z26_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### System of Particles Analysis
Consider a system consisting of three particles:
- **Particle 1:** Mass \( m_1 = 3 \, \text{kg} \), Velocity \( \vec{v}_1 = \langle 9, -4, 14 \rangle \, \text{m/s} \)
- **Particle 2:** Mass \( m_2 = 9 \, \text{kg} \), Velocity \( \vec{v}_2 = \langle -13, 7, -6 \rangle \, \text{m/s} \)
- **Particle 3:** Mass \( m_3 = 4 \, \text{kg} \), Velocity \( \vec{v}_3 = \langle -24, 35, 21 \rangle \, \text{m/s} \)
#### Exercises:
(a) **Total Momentum of the System**
\[
\vec{p}_{\text{tot}} = \underline{\hspace{3cm}} \, \text{kg} \cdot \text{m/s}
\]
(b) **Velocity of the Center of Mass**
\[
\vec{v}_{\text{cm}} = \underline{\hspace{3cm}} \, \text{m/s}
\]
(c) **Total Kinetic Energy of the System**
\[
K_{\text{tot}} = \underline{\hspace{3cm}} \, \text{J}
\]
(d) **Translational Kinetic Energy of the System**
\[
K_{\text{trans}} = \underline{\hspace{3cm}} \, \text{J}
\]
(e) **Kinetic Energy Relative to the Center of Mass**
\[
K_{\text{rel}} = \underline{\hspace{3cm}} \, \text{J}
\]
#### Key Concept:
To calculate \( K_{\text{rel}} \), determine the velocity of each particle relative to the center of mass by subtracting the center-of-mass velocity from the particle's actual velocity. Then calculate the corresponding kinetic energies and add them up. Alternatively, consider the energy relationships in a multiparticle system to simplify the calculation.
(Note: You can verify your result with a detailed calculation if desired.)
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