44 Questions
What is the equation for the velocity of the center of mass of a system of particles?
$v_{S_{CM}} = \frac{1}{M} \sum_{i} m_i v_{S_i}
What is the equation for the total linear momentum of a system of particles?
$p_{S_{tot}} = M v_{S_{CM}}
What is the equation for the acceleration of the center of mass of a system of particles?
$a_{S_{CM}} = \frac{1}{M} \sum_{i} m_i a_{S_i}
What is the equation for the net force on particle i in a system of particles?
$F_{S_i}$
What type of forces can act on a particle in a system?
Both external forces and internal forces
According to Newton's third law, how does the internal force exerted by particle 1 on particle 2 compare to the internal force exerted by particle 2 on particle 1?
Equal in magnitude and opposite in direction
What is the equation for the velocity vector of a position vector?
$\frac{d}{dt}(\vec{r}{S{CM}}) = \vec{v}{S{CM}}
What is the equation for net external force on a system of particles?
a F_S_{ext} = M a_S_{CM} (9.39)
What is the equation that relates impulse and momentum for a system of many particles?
Dp_S_{tot} = I_S (9.40)
What is the equation for the isolated system model for momentum of a system of many particles?
Dp_S_{tot} = 0 (9.41)
When is the total linear momentum of a system of particles conserved?
If no net external force is acting on the system (a F_S_{ext} = 0)
What is the condition for the center of mass of an isolated system to remain at rest?
If there is no net force on the system
What happens to the center of mass of a system when a swimmer dives horizontally off a raft?
The center of mass of the system remains at rest
What is the magnitude of the linear momentum of the diver compared to that of the raft?
Equal
What is the direction of the linear momentum of the diver compared to that of the raft?
Opposite
True or false: The velocity of the center of mass of a system of particles is equal to the sum of the velocities of each individual particle.
True
True or false: The total linear momentum of a system of particles is equal to the total mass multiplied by the velocity of the center of mass.
True
True or false: The acceleration of the center of mass of a system of particles is equal to the sum of the accelerations of each individual particle.
True
True or false: The net force on particle i in a system of particles is equal to the product of its mass and acceleration.
True
True or false: The internal force exerted by particle 1 on particle 2 is equal in magnitude and opposite in direction to the internal force exerted by particle 2 on particle 1.
True
True or false: The external forces acting on a particle in a system can affect its linear momentum.
True
True or false: The center of mass of an isolated system will remain at rest if the net external force on the system is zero.
True
True or false: The net force on a system of particles is caused only by external forces.
True
True or false: The center of mass of a system of particles moves like an equivalent particle of mass M would move under the influence of the net external force on the system.
True
True or false: The impulse imparted to a system of many particles by external forces is equal to the change in momentum of the system.
True
True or false: If the net external force on a system of particles is zero, then the total linear momentum of the system is conserved.
True
True or false: If the center of mass of an isolated system consisting of two or more members is at rest, then the center of mass of the system remains at rest if there is no net force on the system.
True
True or false: The linear momentum of the diver is equal in magnitude to that of the raft, but opposite in direction.
True
True or false: The equation for the acceleration of the center of mass of a system of particles is $a_{S_{CM}} = \frac{1},{M} \sum_{i=1}^{n} m_i a_{i}$, where $M$ is the total mass of the system and $m_i$ is the mass of particle $i$.
False
True or false: The equation for the velocity of the center of mass of a system of particles is $v_{S_{CM}} = \frac{1},{M} \sum_{i=1}^{n} m_i v_{i}$, where $M$ is the total mass of the system and $m_i$ is the mass of particle $i$.
True
Which one of these is the correct equation for the velocity of the center of mass of a system of particles?
$v_{S_{CM}} = \frac{1},{M} \sum_{i=1}^{n} m_i v_{i}$
What is the equation for net external force on a system of particles?
$F_{S_{ext}} = \sum_{i=1}^{n} F_{i}$
True or false: The net force on particle i in a system of particles is equal to the product of its mass and acceleration.
True
True or false: If the center of mass of an isolated system consisting of two or more members is at rest, then the center of mass of the system remains at rest if there is no net force on the system.
True
What is the equation for the acceleration of the center of mass of a system of particles?
$a_{S_{CM}} = \frac{1},{M} \sum_{i=1}^{n} m_i a_{i}$
True or false: The total linear momentum of a system of particles is equal to the total mass multiplied by the velocity of the center of mass.
True
What is the equation for the net force on particle i in a system of particles?
$F_{S_{i}} = m_i a_{i}$
Which equation represents the net external force on a system of particles?
$F_{S_{\text{ext}}} = M \cdot a_{S_{\text{CM}}}$
Which equation represents the acceleration of the center of mass of a system of particles?
$a_{S_{\text{CM}}} = \frac{1}{M} \sum_{i=1}^{n} m_i \cdot a_{i}$
Which equation represents the impulse imparted to a system of many particles by external forces?
$I_S = \Delta p_{S_{\text{tot}}}$
Which equation represents the isolated system model for momentum of a system of many particles?
$\Delta p_{S_{\text{tot}}} = 0$
What is the condition for the center of mass of an isolated system to remain at rest?
The net external force on the system is zero
What is the equation for the total linear momentum of a system of particles?
$p_{S_{\text{tot}}} = \sum_{i=1}^{n} m_i \cdot v_{i}$
What is the equation that relates impulse and momentum for a system of many particles?
$\Delta p_{S_{\text{tot}}} = I_S$
This quiz explores the concept of the center of mass in systems of multiple particles. Learn about the physical significance and utility of the center of mass and its time derivative. Test your understanding with this quiz!
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