AP Physics C: Mechanics Practice Quiz: Conservation of Linear Momentum

Correct Answer: A

Based on the provided content: 'If the net external force on the selected system is zero, the total momentum of the system is constant.'

Correct Answer: C

The selection of a system determines whether its momentum changes. By defining the system as both balls, the forces they exert on each other during the collision are internal. With no net external forces (like friction), the total momentum of the two-ball system is conserved.

Correct Answer: A

The velocity of the center of mass is calculated using the equation $\vec{v}_{cm}=\frac{\sum\vec{p}_{i}}{\sum m_{i}}$. The sum of the momenta is $\sum\vec{p}_{i} = (+10 \text{ kg·m/s}) + (-6 \text{ kg·m/s}) = 4 \text{ kg·m/s}$. The total mass is $\sum m_{i} = 8 \text{ kg}$. Therefore, $\vec{v}_{cm} = \frac{4 \text{ kg·m/s}}{8 \text{ kg}} = 0.5 \text{ m/s}$.

Correct Answer: C

The initial momentum of the system was zero. Since the explosion is an internal event with no net external forces, any change to the momentum of one piece must be balanced by an equivalent and opposite change of momentum in the other piece to keep the total momentum of the system constant at zero.

Correct Answer: B

This is a direct application of the principle that 'any change to the momentum of an object within a system must be balanced by an equivalent and opposite change of momentum elsewhere within the system.' These balanced changes are caused by Newton's Third Law pairs of internal forces.

Correct Answer: A

The equation $\vec{v}_{cm}=\frac{\sum\vec{p}_{i}}{\sum m_{i}}$ relates the center of mass velocity to the total momentum ($\sum\vec{p}_{i}$). If the total momentum is zero, and the total mass is non-zero, the velocity of the center of mass must also be zero.

Correct Answer: C

The system is the person, skateboard, and ball. Initially, the total momentum is zero. Since throwing the ball is an internal action and there are no net external forces (frictionless), the total momentum must remain zero. The forward momentum of the ball must be balanced by an equivalent and opposite momentum of the person and skateboard.

Correct Answer: C

The selection of the system is critical. If the system is only the rocket, the force exerted by the expelled gas is an external force. This net external force changes the rocket's momentum. If the system were defined as the rocket *and* the expelled gas, the total momentum would be conserved.

Correct Answer: C

If the net external force on a system is zero, its total momentum is constant. According to the equation $\vec{v}_{cm}=\frac{\sum\vec{p}_{i}}{\sum m_{i}}$, if the total momentum ($\sum\vec{p}_{i}$) and total mass ($\sum m_{i}$) are constant, the velocity of the center of mass ($\vec{v}_{cm}$) must also be constant.

Correct Answer: B

The provided content explicitly states, 'If the net external force on the selected system is zero, the total momentum of the system is constant.' This is the fundamental condition for conservation of linear momentum.

Correct Answer: C

The system is defined as only the cart. The push from the student is a force originating from outside the system, making it a net external force. The presence of a net external force means the system's momentum will change.

Correct Answer: C

The equation for the center of mass velocity, $\vec{v}_{cm}=\frac{\sum\vec{p}_{i}}{\sum m_{i}}$, can be rearranged to find the total momentum, $\sum\vec{p}_{i} = (\sum m_{i}) \vec{v}_{cm}$. The total momentum is (20 kg) * (5 m/s) = 100 kg·m/s to the right.

Correct Answer: C

This directly follows the principle that 'In the absence of net external forces, any change to the momentum of an object within a system must be balanced by an equivalent and opposite change of momentum elsewhere within the system.' The explosion is an internal event.

Correct Answer: C

In deep space, the net external force on the two-asteroid system is effectively zero. Therefore, the total momentum of the system is constant. Since $\vec{v}_{cm}=\frac{\sum\vec{p}_{i}}{\sum m_{i}}$, and both the total momentum and total mass are constant, the velocity of the center of mass must also remain constant.