Q: A 1.50 $$\times$$ $$10^3 kg $$car collides with a wall and rebounds. Its initial velocity is $$-15.0 m/s $$and its final velocity is $$+2.60 m/s. $$What is the impulse delivered to the car?

$$I = 1.50 \times 10^3$ \times (2.60 - (-15.0)) = 2.64 \times 10^4$ kg·m/s

Q: A 75-kg passenger in a car traveling at 27 m/s comes to rest in 0.010 s after hitting an unpadded dashboard. What is the average force experienced by the passenger?

$$F_{avg} = \frac{m(v_f - v_i)}{\Delta t} = \frac{75 \times (0 - 27)}{0.010} = -2.0 \times 10^5$ N

Question 1

Which of the following best describes the impulse delivered to an object when a force acts on it over a time interval $$\Delta t$$?

Accepted Answer

Impulse is the area under the force versus time curve.

Question 2

A 1.50 $$	imes$$ $$10^3 kg $$car collides with a wall and rebounds. Its initial velocity is $$-15.0 m/s $$and its final velocity is $$+2.60 m/s. $$What is the impulse delivered to the car?

Accepted Answer

$$I = 1.50 	imes 10^3$ 	imes (2.60 - (-15.0)) = 2.64 	imes 10^4$ kg·m/s

Question 3

In a real-life collision, why do seat belts and airbags reduce injuries?

Accepted Answer

They increase the time over which the force acts, reducing the average force.

Question 4

Which equation correctly expresses the impulse-momentum theorem?

Accepted Answer

$$\vec{F} \cdot \Delta t = \Delta \vec{p} = m \vec{v}_f - m \vec{v}_i$$

Question 5

A collision between two objects is perfectly elastic. Which of the following statements is true?

Accepted Answer

Both momentum and kinetic energy are conserved.

Question 6

Two cars collide at an intersection. Car A (1.50 $$	imes$$ $$10^3 kg) $$moves east at 25.0 m/s, and Car B (2.50 $$	imes$$ $$10^3 kg) $$moves north at 20.0 m/s. If they stick together after the collision, what is the magnitude of their final velocity?

Accepted Answer

$$v_f = \sqrt{\left(\frac{m_A v_A}{m_A + m_B}\$$right)^2$$ + \left(\frac{m_B v_B}{m_A + m_B}\$$right)^2$$}$$

Question 7

Which of the following is NOT a characteristic of a perfectly inelastic collision?

Accepted Answer

Kinetic energy is conserved.

Question 8

A force $$F(t)$$ acts on an object for a time interval $$[t_i, t_f]. $$How is the impulse $$I$$ related to the force?

Accepted Answer

$$I = \int_{t_i}^{t_f} F(t) \, dt$$

Question 9

In a two-dimensional collision, which principle must be applied to both the x and y components of momentum?

Accepted Answer

Conservation of momentum

Question 10

A 75-kg passenger in a car traveling at 27 m/s comes to rest in 0.010 s after hitting an unpadded dashboard. What is the average force experienced by the passenger?

Accepted Answer

$$F_{avg} = \frac{m(v_f - v_i)}{\Delta t} = \frac{75 	imes (0 - 27)}{0.010} = -2.0 	imes 10^5$ N

Question 11

Which scenario demonstrates conservation of momentum but not conservation of kinetic energy?

Accepted Answer

A perfectly inelastic collision where two objects stick together.

Question 12

In the ballistic pendulum experiment, a bullet of mass $$m_1$$ embeds in a block of mass $$m_2. If $$the combined system rises to height $$h$$, what equation relates the initial speed of the bullet $$v_{1i} to$$ $$h$$?

Accepted Answer

$$v_{1i} = \frac{(m_1$ + m_2$)}{m_1$} \sqrt{2gh}$$

Question 13

Which of the following is a correct statement about Newton's third law in the context of collisions?

Accepted Answer

The force exerted by object 1 on object 2 is equal in magnitude and opposite in direction to the force exerted by object 2 on object 1.

Question 14

A system of two objects undergoes a collision. Which condition must be met for the total momentum of the system to be conserved?

Accepted Answer

No net external force acts on the system.

Question 15

Which of the following best describes the relationship between momentum and kinetic energy for an object of mass $$m$$ and momentum $$p$$?

Accepted Answer

$$KE = \frac{p^2$}{2m}$$

Question 16

In a collision, why is it important to pay attention to the signs of velocity components when applying conservation of momentum?

Accepted Answer

Because direction determines whether velocities add or subtract in the momentum equation.

Question 17

Which of the following is a real-world example of a nearly elastic collision?

Accepted Answer

Collisions between atomic and subatomic particles.

Question 18

A Newton's cradle (five balls suspended in a row) demonstrates which physical principle?

Accepted Answer

Conservation of linear momentum.

Question 19

In a two-dimensional collision, if object 1 moves along the x-axis and object 2 moves along the y-axis, what is the direction of the combined velocity after a perfectly inelastic collision?

Accepted Answer

The combined velocity points in a direction given by $$	an 	heta = \frac{v_{2i} m_2$}{v_{1i} m_1$}.$$

Chapter 9: Momentum – Impulse, Collisions, and Conservation Laws

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