Q: A 1200 kg car is traveling north at 8 m/s, and a 900 kg car is traveling east at 10 m/s. What is the magnitude of the total momentum of the system consisting of both cars?

$$\sqrt{(1200 \times 8)^2$ + (900 \times 10)^2$} = \sqrt{(9600)^2$ + (9000)^2$} = \sqrt{92160000 + 81000000} = \sqrt{173160000} \approx 13160\ \mathrm{kg\ m/s}$$

Q: A 200 g tennis ball moving at 10 m/s bounces off a wall and returns at 10 m/s in the opposite direction. What is the magnitude of the change in its momentum?

$$\Delta p = m(v_f - v_i) = 0.2\ \mathrm{kg} \times (-10 - 10)\ \mathrm{m/s} = 0.2 \times (-20) = -4\ \mathrm{kg\ m/s}$$; magnitude is $$4\ \mathrm{kg\ m/s}$$

Q: A small rocket is launched straight up. At a certain instant, its velocity is $$120\ \mathrm{m/s}$$, its mass is $$48\ \mathrm{kg}$$, it is accelerating at $$18\ \mathrm{m/s^2$}$$, and it is losing mass at a rate of $$0.50\ \mathrm{kg/s}. $$What is the net force on the rocket at this instant?

$$F_{\mathrm{net}} = m a + v \frac{dm}{dt} = 48 \times 18 + 120 \times (-0.5) = 864 - 60 = 804\ \mathrm{N}$$

Q: Two billiard balls, each of mass $$0.5\ \mathrm{kg}$$, collide head-on. The red ball moves at $$3\ \mathrm{m/s} to $$the right, and the blue ball moves at $$-5\ \mathrm{m/s} to $$the left. After the collision, the blue ball moves at $$2\ \mathrm{m/s} to $$the right. What is the velocity of the red ball after the collision?

$$v_{\mathrm{red, f}} = \frac{(0.5 \times 3) + (0.5 \times -5) - (0.5 \times 2)}{0.5} = \frac{1.5 - 2.5 - 1}{0.5} = \frac{-2}{0.5} = -4\ \mathrm{m/s}$$

Question 1

A 1200 kg car is traveling north at 8 m/s, and a 900 kg car is traveling east at 10 m/s. What is the magnitude of the total momentum of the system consisting of both cars?

Accepted Answer

$$\sqrt{(1200 	imes 8)^2$ + (900 	imes 10)^2$} = \sqrt{(9600)^2$ + (9000)^2$} = \sqrt{92160000 + 81000000} = \sqrt{173160000} \approx 13160\ \mathrm{kg\ m/s}$$

Question 2

Which of the following best describes the difference between momentum and kinetic energy for a moving object?

Accepted Answer

Momentum is a vector quantity ($$\vec{p} = m\vec{v}$$), while kinetic energy is a scalar ($$K = \frac{1}{2}mv^2$).

Question 3

A 200 g tennis ball moving at 10 m/s bounces off a wall and returns at 10 m/s in the opposite direction. What is the magnitude of the change in its momentum?

Accepted Answer

$$\Delta p = m(v_f - v_i) = 0.2\ \mathrm{kg} 	imes (-10 - 10)\ \mathrm{m/s} = 0.2 	imes (-20) = -4\ \mathrm{kg\ m/s}$$; magnitude is $$4\ \mathrm{kg\ m/s}$$

Question 4

The impulse-momentum theorem states that the change in momentum of an object is equal to:

Accepted Answer

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

Question 5

A force acts on an object for $$5.0\ \mathrm{ms}$$, imparting an impulse of $$10.0\ \mathrm{N\cdot s}. $$What is the average force exerted on the object?

Accepted Answer

$$F_{\mathrm{avg}} = \frac{J}{\Delta t} = \frac{10.0}{0.005} = 2000\ \mathrm{N}$$

Question 6

A small rocket is launched straight up. At a certain instant, its velocity is $$120\ \mathrm{m/s}$$, its mass is $$48\ \mathrm{kg}$$, it is accelerating at $$18\ \mathrm{m/s^2$}$$, and it is losing mass at a rate of $$0.50\ \mathrm{kg/s}. $$What is the net force on the rocket at this instant?

Accepted Answer

$$F_{\mathrm{net}} = m a + v \frac{dm}{dt} = 48 	imes 18 + 120 	imes (-0.5) = 864 - 60 = 804\ \mathrm{N}$$

Question 7

Which of the following is an example of a system where the mass is not constant?

Accepted Answer

A rocket burning fuel as it accelerates upward.

Question 8

In a totally inelastic collision, two objects stick together after colliding. Which of the following statements is true?

Accepted Answer

Momentum is conserved, but kinetic energy is not.

Question 9

Two billiard balls, each of mass $$0.5\ \mathrm{kg}$$, collide head-on. The red ball moves at $$3\ \mathrm{m/s} to $$the right, and the blue ball moves at $$-5\ \mathrm{m/s} to $$the left. After the collision, the blue ball moves at $$2\ \mathrm{m/s} to $$the right. What is the velocity of the red ball after the collision?

Accepted Answer

$$v_{\mathrm{red, f}} = \frac{(0.5 	imes 3) + (0.5 	imes -5) - (0.5 	imes 2)}{0.5} = \frac{1.5 - 2.5 - 1}{0.5} = \frac{-2}{0.5} = -4\ \mathrm{m/s}$$

Question 10

A particle at rest with mass $$3.0\ \mathrm{g}$$ explodes into three fragments. $$m_1 = 0.7$$\ \mathrm{g}$$ moves at 2.8$$\ \mathrm{m/s}$$ to the right, m_2$ = 1.3\ \mathrm{g}$$ moves at $$1.5\ \mathrm{m/s}$$ downward. What is the velocity (magnitude and direction) of $$m_3$$?

Accepted Answer

$$\vec{v}_3 = \frac{-(m_1$ \vec{v}_1 + m_2$ \vec{v}_2)}{m_3$}$$; $$m_3 = 3.0 - 0.7 - 1.3 = 1.0$$\ \mathrm{g}$$; $$\vec{v}_3 = \frac{-(0.7 	imes 2.8\ \hat{i} + 1.3 	imes 1.5\ \hat{j})}{1.0}$$; $$= \frac{-(1.96\ \hat{i} + 1.95\ \hat{j})}{1.0} = -1.96\ \hat{i} - 1.95\ \hat{j}\ \mathrm{m/s}$$; magnitude $$\approx 2.77\ \mathrm{m/s}$$ at 225$$^\circ$$ from the positive x-axis.

Question 11

Which of the following best describes an isolated system in the context of momentum conservation?

Accepted Answer

A system with no net external forces acting on it.

Question 12

In a one-dimensional elastic collision between two objects of equal mass, where one is initially at rest, what happens to their velocities after the collision?

Accepted Answer

The moving object comes to rest, and the stationary object moves with the initial velocity of the first.

Question 13

A $$100\ \mathrm{g}$$ red ball traveling at $$10\ \mathrm{m/s}$$ collides head-on with a $$100\ \mathrm{g}$$ green ball at rest. If the collision is perfectly elastic, what is the final velocity of each ball?

Accepted Answer

Red ball: $$0\ \mathrm{m/s}$$, Green ball: $$10\ \mathrm{m/s}$$

Question 14

A car of mass $$1200\ \mathrm{kg}$$ moving at $$8\ \mathrm{m/s}$$ north collides with a $$900\ \mathrm{kg}$$ car moving at $$10\ \mathrm{m/s}$$ east. If they stick together after the collision, what is the speed of the combined mass immediately after the collision?

Accepted Answer

$$v = \frac{\sqrt{(1200 	imes 8)^2$ + (900 	imes 10)^2$}}{1200 + 900} = \frac{13160}{2100} \approx 6.27\ \mathrm{m/s}$$

Question 15

Which of the following statements about elastic and inelastic collisions is correct?

Accepted Answer

In elastic collisions, both momentum and kinetic energy are conserved; in inelastic collisions, only momentum is conserved.

Question 16

A force $$F_x(t) = (-t^2$ + 6t) N $$acts on an object from $$t = 0 to$$ $$t = 6 s. $$What is the total impulse delivered to the object?

Accepted Answer

$$J = \$$int_0$$^6 (-t^2$ + 6t)\,dt = \left[ -\frac{1}{3}t^3$ + 3t^2$ ight]_0^6$ = \left( -\frac{1}{3} 	imes 216 + 3 	imes 36 ight) = (-72 + 108) = 36\ \mathrm{N\cdot s}$$

Question 17

Which of the following best explains why the area under a force vs. time ($$F$$-$$t) $$graph represents impulse?

Accepted Answer

Because impulse is defined as the integral of force over time: $$J = \int F\,dt$$

Conservation of Linear Momentum and Impulse: Study Notes

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