Q: Two ice skaters, Skater A (mass $$60\ \mathrm{kg}) $$and Skater B (mass $$40\ \mathrm{kg}$$), stand at rest on a frictionless ice surface. They push off each other and Skater A moves to the right at $$3\ \mathrm{m/s}. $$What is Skater B's velocity after the push?

$$4.5\ \mathrm{m/s}$$ $$\ \text{to the left}$$

Question 1

Which of the following statements best describes the motion of the center of mass of a system after an internal explosion (such as a firework exploding in midair), assuming only gravity acts externally and air resistance is negligible?

Accepted Answer

The center of mass will move in a parabolic trajectory, as if the explosion had not occurred.

Question 2

A 2 kg object moving at $$5\ \mathrm{m/s}$$ collides with and sticks to a 3 kg object at rest. What is the final velocity of the combined mass immediately after the collision?

Accepted Answer

$$2\ \mathrm{m/s} to $$the right

Question 3

Which of the following is a necessary condition for the conservation of linear momentum in a system?

Accepted Answer

The net external force acting on the system must be zero.

Question 4

A bullet of mass $$10\ \mathrm{g} is $$fired horizontally at $$400\ \mathrm{m/s}$$ into a stationary block of mass $$390\ \mathrm{g} on a $$frictionless surface. The bullet embeds in the block. What is the speed of the block and bullet immediately after the collision?

Accepted Answer

$$10\ \mathrm{m/s}$$

Question 5

Two ice skaters, Skater A (mass $$60\ \mathrm{kg}) $$and Skater B (mass $$40\ \mathrm{kg}$$), stand at rest on a frictionless ice surface. They push off each other and Skater A moves to the right at $$3\ \mathrm{m/s}. $$What is Skater B's velocity after the push?

Accepted Answer

$$4.5\ \mathrm{m/s}$$ $$\ 	ext{to the left}$$

Question 6

A rocket at its maximum height explodes into two identical fragments. One fragment lands a distance $$D$$ from the launch point. If the center of mass lands at $$2D$$, where does the second fragment land?

Accepted Answer

$$3D$$

Question 7

Which of the following best describes an elastic collision?

Accepted Answer

Both momentum and kinetic energy are conserved.

Question 8

A lithium ion moves to the right and breaks into two fragments: one moves to the right, the other moves straight up. Is momentum conserved in this process?

Accepted Answer

No, because the final momentum is not in the same direction as the initial momentum.

Question 9

In a two-dimensional collision, which of the following must be true for momentum conservation to apply?

Accepted Answer

Momentum must be conserved separately along each axis with no net external force in that direction.

Question 10

A car of mass $$m_1$$ moving at velocity $$v_1$$ collides and sticks to a stationary car of mass $$m_2. $$What is the ratio of the final kinetic energy to the initial kinetic energy?

Accepted Answer

$$\left(\dfrac{m_1$}{m_1$ + m_2$}\$$right)^2$$

Question 11

Which of the following is true about internal forces in a system when considering the motion of the center of mass?

Accepted Answer

Internal forces do not affect the motion of the center of mass.

Question 12

A $$0.2\ \mathrm{kg}$$ ball is thrown horizontally at $$10\ \mathrm{m/s}$$ and experiences no air resistance. What is the horizontal component of its momentum after $$2$$ seconds?

Accepted Answer

$$2\ \mathrm{kg\cdot m/s}$$

Question 13

During a collision, the force between two objects varies with time. The impulse delivered to an object is equal to:

Accepted Answer

The area under the force versus time curve.

Question 14

A $$5\ \mathrm{kg}$$ object moving at $$2\ \mathrm{m/s}$$ collides elastically with a $$3\ \mathrm{kg}$$ object at rest. Which of the following is true immediately after the collision?

Accepted Answer

The total kinetic energy is the same as before the collision.

Question 15

Which of the following best describes a completely inelastic collision?

Accepted Answer

The objects stick together and move with a common velocity after collision.

Question 16

A projectile is launched and moves under gravity alone. Which statement is correct regarding the conservation of momentum?

Accepted Answer

Momentum is conserved in the horizontal direction because there is no external force in that direction.

Question 17

If the net external force on a system is not zero, which of the following is true?

Accepted Answer

The system's momentum changes over time.

Question 18

In a collision, the impulse delivered to an object is equal to:

Accepted Answer

The change in the object's momentum.

Question 19

Which of the following is NOT a requirement for using the center of mass equation $$x_{CM} = \dfrac{\sum m_i x_i}{\sum m_i}$$?

Accepted Answer

All masses must be point particles.

Question 20

Which of the following statements about kinetic energy in collisions is correct?

Accepted Answer

Kinetic energy is conserved only in elastic collisions.

Linear Momentum, Center of Mass, and Collisions: Study Notes

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