Q: Which of the following is a correct expression for the center-of-mass velocity of a system?

$$\vec{v}_{\text{cm}} = \frac{\vec{P}}{M}$$

Question 1

A soccer ball of mass 0.5 kg is kicked and moves with a velocity of 10 m/s. What is its momentum?

Accepted Answer

$$5\ \mathrm{kg\cdot m/s}$$

Question 2

Which of the following statements is true about the conservation of momentum in a system of particles?

Accepted Answer

Momentum is conserved if the sum of external forces is zero.

Question 3

Two ice skaters, Skater A (60 kg) and Skater B (40 kg), push off each other on frictionless ice. If Skater A moves left at 3 m/s, what is Skater B's velocity?

Accepted Answer

$$4.5\ \mathrm{m/s}$$\ to\ the\ right

Question 4

Which equation correctly expresses the momentum of a system of N objects?

Accepted Answer

$$\vec{P} = \sum_{i=1}^{N} \vec{p}_i$$

Question 5

A 2-D collision occurs between two billiard balls. Which of the following is true regarding momentum conservation?

Accepted Answer

Momentum is conserved in both the x and y directions independently.

Question 6

A system consists of two objects, A and B. Which forces are considered internal?

Accepted Answer

Forces between A and B.

Question 7

If the net external force on a system is zero, what does Newton's Second Law for the system reduce to?

Accepted Answer

$$\frac{d\vec{P}}{dt} = 0$$

Question 8

A 4 kg object is at (2,6) and a 2 kg object is at (8,2). What is the x-coordinate of the center of mass?

Accepted Answer

$$4.67\ \mathrm{units}$$

Question 9

In the example of two carts on a track, initially at rest, a spring pushes them apart. If cart 1 has mass $$m_1$$ and velocity $$v_1$$, and cart 2 has mass $$m_2$$ and velocity $$v_2$$, which equation expresses momentum conservation?

Accepted Answer

$$m_1$$ $$v_1$$ + $$m_2$$ $$v_2 = 0$

Question 10

Which of the following is a correct expression for the center-of-mass velocity of a system?

Accepted Answer

$$\vec{v}_{	ext{cm}} = \frac{\vec{P}}{M}$$

Question 11

A penguin walks left on a frictionless sled, which is initially at rest. What happens to the center of mass of the penguin-sled system?

Accepted Answer

It remains the same distance from the shore.

Question 12

Which of the following is NOT a requirement for momentum conservation in a system?

Accepted Answer

The system must have constant energy.

Question 13

In a two-dimensional collision, which equations must be satisfied for momentum conservation?

Accepted Answer

$$m_1 v$$_{1,x,b} + $$m_2 v$$_{2,x,b} = $$m_1 v$$_{1,x,a} + $$m_2 v$$_{2,x,a}$$ and m_1$ v_{1,y,b} + m_2$ v_{2,y,b} = m_1$ v_{1,y,a} + m_2$ v_{2,y,a}$$

Question 14

Which of the following best describes the effect of internal forces on the total momentum of a system?

Accepted Answer

Internal forces cancel in pairs and do not affect the total momentum.

Question 15

A system of three particles has momenta $$\vec{p}_1$$, $$\vec{p}_2$$, and $$\vec{p}_3. $$What is the total momentum of the system?

Accepted Answer

$$\vec{p}_1 + \vec{p}_2 + \vec{p}_3$$

Question 16

Which formula gives the x-coordinate of the center of mass for N particles?

Accepted Answer

$$x_{	ext{cm}} = \frac{\sum_{i=1}^{N} m_i x_i}{\sum_{i=1}^{N} m_i}$$

Question 17

A system's energy changes but its momentum remains constant. What does this imply?

Accepted Answer

Internal forces are changing the energy but not the momentum.

Question 18

Which equation represents the impulse-momentum theorem for a particle?

Accepted Answer

$$\int \vec{F}_{	ext{net}} dt = \Delta \vec{p}$$

Question 19

Which of the following is true about the center-of-mass velocity in an isolated system?

Accepted Answer

It remains constant if no external forces act.

Conservation of Momentum and Center of Mass

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