Q: A $$2\ \mathrm{kg}$$ mass moves in a circle of radius $$0.5\ \mathrm{m} at a $$speed of $$4\ \mathrm{m/s}. $$What is its angular momentum about the center?

$$L = 2 \times 0.5 \times 4 = 4\ \mathrm{kg\cdot m^2$/s}$$

Q: A $$0.2\ \mathrm{kg}$$ ball moving at $$10\ \mathrm{m/s}$$ strikes a $$0.3\ \mathrm{kg}$$ ball at rest. If the collision is perfectly elastic, what is the velocity of the $$0.3\ \mathrm{kg}$$ ball after the collision?

$$v = \frac{2m_1}{m_1$ + m_2$}v_1$ = \frac{2 \times 0.2}{0.2 + 0.3} \times 10 = 8\ \mathrm{m/s}$$

Q: A $$5\ \mathrm{kg}$$ object is lifted to a height of $$2\ \mathrm{m}. $$What is its gravitational potential energy relative to the ground?

$$U = 5 \times 9.8 \times 2 = 98\ \mathrm{J}$$

Question 1

A rigid body is defined as a system of particles in which the distance between any two points remains unchanged during motion. Which of the following scenarios best illustrates a rigid body?

Accepted Answer

A solid metal disc spinning about its axis with no deformation.

Question 2

Given three masses $$m_1 = 20$$\ \mathrm{g}$$ at x = 20$$\ \mathrm{cm}$$, m_2$ = 40\ \mathrm{g} at$$ $$x = 40\ \mathrm{cm}$$, and $$m_3 = 100$$\ \mathrm{g}$$ at x = 50$$\ \mathrm{cm}$$ attached to a bar, what is the position of the center of mass x_G$?

Accepted Answer

$$x_G = 43.75\ \mathrm{cm}$$

Question 3

Which equation correctly gives the coordinates of the center of mass $$\vec{R}$$ for $$n$$ particles with masses $$m_i$$ and position vectors $$\vec{r}_i$$?

Accepted Answer

$$\vec{R} = \frac{\sum_{i=1}^n m_i \vec{r}_i}{\sum_{i=1}^n m_i}$$

Question 4

A gun of mass $$M$$ fires a bullet of mass $$m$$ horizontally. If the bullet leaves the gun with velocity $$v$$, what is the recoil velocity $$V of $$the gun (assuming no external forces)?

Accepted Answer

$$V = -\frac{m}{M}v$$

Question 5

Which statement best describes the Law of Conservation of Linear Momentum?

Accepted Answer

The total linear momentum of an isolated system remains constant if no external force acts on it.

Question 6

A figure skater spins with arms extended and then pulls them in, reducing her moment of inertia. What happens to her angular velocity, and why?

Accepted Answer

Her angular velocity increases because her moment of inertia decreases and angular momentum is conserved.

Question 7

Which of the following is the correct expression for the change in kinetic energy $$\Delta K of a $$particle due to work $$A$$ done by external forces?

Accepted Answer

$$\Delta K = A$$

Question 8

A ball of mass $$m is $$dropped from height $$h. $$Neglecting air resistance, what is its velocity $$v$$ just before hitting the ground?

Accepted Answer

$$v = \sqrt{2gh}$$

Question 9

Which of the following forces is considered conservative?

Accepted Answer

Gravitational force

Question 10

A system consists of two particles: $$m_1 = 2$$\ \mathrm{kg}$$ at (0$$,0)$$ and m_2$ = 3\ \mathrm{kg} at$$ $$(4,0). $$What is the $$x-$$coordinate of the center of mass?

Accepted Answer

$$x_{CM} = 2.4$$

Question 11

Which equation represents the conservation of mechanical energy for a system subject only to conservative forces?

Accepted Answer

$$U_i + K_i = U_f + K_f$$

Question 12

A $$10\ \mathrm{kg}$$ object is moving at $$5\ \mathrm{m/s}$$ and collides elastically with a stationary $$5\ \mathrm{kg}$$ object. What is the total momentum of the system before the collision?

Accepted Answer

$$50\ \mathrm{kg\cdot m/s}$$

Question 13

Which formula gives the instantaneous power $$P$$ delivered by a constant force $$F$$ acting on an object moving with velocity $$v$$?

Accepted Answer

$$P = Fv$$

Question 14

A $$2\ \mathrm{kg}$$ mass moves in a circle of radius $$0.5\ \mathrm{m} at a $$speed of $$4\ \mathrm{m/s}. $$What is its angular momentum about the center?

Accepted Answer

$$L = 2 	imes 0.5 	imes 4 = 4\ \mathrm{kg\cdot m^2$/s}$$

Question 15

Which of the following best describes the result of an inelastic collision between two objects?

Accepted Answer

Momentum is conserved, but kinetic energy is not.

Question 16

A $$0.2\ \mathrm{kg}$$ ball moving at $$10\ \mathrm{m/s}$$ strikes a $$0.3\ \mathrm{kg}$$ ball at rest. If the collision is perfectly elastic, what is the velocity of the $$0.3\ \mathrm{kg}$$ ball after the collision?

Accepted Answer

$$v = \frac{2m_1}{m_1$ + m_2$}v_1$ = \frac{2 	imes 0.2}{0.2 + 0.3} 	imes 10 = 8\ \mathrm{m/s}$$

Question 17

Which of the following correctly expresses the impulse $$J$$ delivered by a constant force $$F$$ acting over a time interval $$\Delta t$$?

Accepted Answer

$$J = F \Delta t$$

Question 18

A rotating wheel of moment of inertia $$I_w is $$spinning. A person sitting on a frictionless chair (moment of inertia $$I_p) $$flips the wheel, causing the person and chair to rotate in the opposite direction. Which equation describes the conservation of angular momentum in this scenario?

Accepted Answer

$$I_w \omega_w + I_p \omega_p = 0$$

Question 19

A $$5\ \mathrm{kg}$$ object is lifted to a height of $$2\ \mathrm{m}. $$What is its gravitational potential energy relative to the ground?

Accepted Answer

$$U = 5 	imes 9.8 	imes 2 = 98\ \mathrm{J}$$

Chapter 3: Laws of Conservation in Physics

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