Question 1

Which of the following best describes the impulse-momentum theorem?

Accepted Answer

The change in momentum of a particle during a time interval is equal to the impulse of the net force acting on it: $\Delta p = J = \int F_{	ext{net}} dt$.

Question 2

A basketball of mass $m$ falls from a height of $5\ 	ext{m}$ and bounces up to $4\ 	ext{m}$. Neglecting air resistance, what is the magnitude of the impulse delivered by the floor to the ball?

Accepted Answer

$J = m \left( \sqrt{2g(5)} + \sqrt{2g(4)} \right)$

Question 3

In a perfectly inelastic collision between two objects, which of the following statements is true?

Accepted Answer

Momentum is conserved, but kinetic energy is not.

Question 4

Two blocks, A ($1.00\ 	ext{kg}$) and B ($3.00\ 	ext{kg}$), are released from rest after compressing a spring between them on a frictionless surface. After release, what is the ratio of the kinetic energy of block A to block B?

Accepted Answer

$9$

Question 5

Which equation correctly expresses the conservation of momentum for a two-particle system in one dimension during a collision?

Accepted Answer

$m_A v_{A1} + m_B v_{B1} = m_A v_{A2} + m_B v_{B2}$

Question 6

A polystyrene ball of mass $m_p$ is placed on top of a basketball of mass $m_b$ ($m_b \gg m_p$). Both are dropped from rest, with the bottom of the basketball at height $h$ and the polystyrene ball at $h + d$. Assuming an elastic collision, to what height does the polystyrene ball bounce?

Accepted Answer

$2h + d$

Question 7

Which of the following is true for an elastic collision in one dimension?

Accepted Answer

Both momentum and kinetic energy are conserved.

Question 8

The coefficient of restitution $e$ for a collision is defined as:

Accepted Answer

$e = \dfrac{v_{A2} - v_{B2}}{v_{A1} - v_{B1}}$

Question 9

A rocket expels fuel at a constant rate with exhaust velocity $v_e$. If the initial mass is $m_0$ and the final mass is $m_f$, what is the final velocity of the rocket (assuming no external forces)?

Accepted Answer

$v = v_e \ln \dfrac{m_0}{m_f}$

Question 10

Which of the following best describes the center of mass of a system of point masses?

Accepted Answer

It is the mass-weighted average position of all the particles: $x_{cm} = \dfrac{\sum m_i x_i}{\sum m_i}$.

Question 11

During a collision, the total momentum of a system is conserved if:

Accepted Answer

The net external force on the system is zero.

Question 12

A $2\ 	ext{kg}$ object moving at $3\ 	ext{m/s}$ collides elastically with a stationary $1\ 	ext{kg}$ object. What is the velocity of the $1\ 	ext{kg}$ object after the collision?

Accepted Answer

$4\ 	ext{m/s}$

Question 13

Which formula gives the velocity of the center of mass for a two-particle system?

Accepted Answer

$v_{cm} = \dfrac{m_A v_A + m_B v_B}{m_A + m_B}$

Question 14

A collision between two cars is analyzed. If the cars stick together after the collision, what type of collision is this?

Accepted Answer

Perfectly inelastic

Question 15

A $0.5\ 	ext{kg}$ ball moving at $2\ 	ext{m/s}$ collides inelastically with a $0.5\ 	ext{kg}$ ball at rest. What is their final velocity after the collision?

Accepted Answer

$1\ 	ext{m/s}$

Question 16

Which of the following is the correct expression for the impulse delivered by a force $F(t)$ over a time interval $[t_1, t_2]$?

Accepted Answer

$J = \int_{t_1}^{t_2} F(t) dt$

Question 17

A rocket with mass $m$ expels fuel at a rate $\dfrac{dm}{dt}$ with exhaust velocity $v_e$. What is the thrust produced by the rocket?

Accepted Answer

$F = v_e \dfrac{dm}{dt}$

Question 18

In a real-world car accident, why is the impulse delivered to the passengers reduced by airbags?

Accepted Answer

Airbags increase the time over which the force acts, reducing the average force according to $J = F_{	ext{avg}} \Delta t$.

H8

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