Notes, summaries, assignments, exams, and problems for Physics

Kinematics and Motion Concepts

• Fri (Instantaneous Speed): The speed a moving body has at a specific point in its trajectory.
• Vm (Average Velocity): The quotient between displacement and the time interval used in traversing it.
• Am (Average Acceleration): The ratio between the variation of velocity experienced by the moving body at a given time interval.
• Ai (Instantaneous Acceleration): The acceleration that a moving body has at a given moment of the journey or at a point in its trajectory.
• Trajectory (Career): The line that connects all the points that the moving body has passed through during its displacement.
• Route Distance (E): The length of the path traveled.
• MCU (Uniform Circular Motion): A movement describing a moving body whose angular velocity

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Position Vector and Components

The position vector r describes an object's location in space. Its components can be expressed in Cartesian or polar coordinates:

• Position Vector: r = xi + yj
• Cartesian X-component: x = r cos θ
• Cartesian Y-component: y = r sin θ
• Magnitude of Position Vector: r = √(x2 + y2)
• Angle of Position Vector: tan θ = y / x

Displacement

Displacement (Δr) is the change in an object's position:

• Final Displacement: Δr = rfinal - rinitial

Speed and Velocity

Speed is the magnitude of velocity. Velocity is a vector quantity describing the rate of change of position:

• Average Speed: vavg = Δr / Δt
• Instantaneous Speed: v = |dr / dt|
• Average Velocity: vavg = Δr / Δt
• Instantaneous Velocity: v = dr / dt

Acceleration

Acceleration (a) is the... Continue reading "Essential Kinematics Formulas and Motion Principles" »

Law of Gravitation

Every object in the universe that has mass exerts a gravitational attraction on other objects with mass, regardless of the distance between them. According to this law, more massive objects exert a greater force of attraction. In parallel, the closer objects are, the greater the force, following an inverse square law.

Considering two masses whose size is small compared with the distance that separates them, we can summarize this in an equation or law that states that the force exerted by a given object with mass m1 on one with mass m2 is directly proportional to the product of the masses and inversely proportional to the square of the distance between them.

A force is central where the position vector r is parallel to the force... Continue reading "Fundamental Physics Concepts Explained" »

44. (a) The Young’s modulus is given by

(b) Since the linear range of the curve extends to about 2.9 × 10⁸ N/m², this is approximately the yield strength for the material.

46. Since the force is (stress × area) and the displacement is (strain × length), we can write the work integral (eq. 7-32) as

  W =

  = A (differential strain)L  = AL (differential strain)

which means the work is  (wire-area) × (wire-length) × (graph-area-under-curve).  Since the area of a triangle (see the graph in the problem statement) is  (base)(height)  then we determine the work done to be

            W = (2.00 x 10^-6 m²)(0.800 m)(1.0 × 10^-3)(7.0 × 10⁷ N/m²) = 0.0560 J .

48. 46. Since the force is (stress × area) and the displacement is (strain... Continue reading "Young's Modulus and Material Strength Calculations" »

Understanding Energy Forms

• A circulating car: Kinetic energy.
• A shining light bulb: Thermal and light energy.
• A book on a library shelf: Potential energy.
• A cat chasing a mouse: Kinetic energy.

Kinetic Energy Calculation: Bullet Example

A bullet with a mass of 15 g moving at 50 m/s.

The formula for kinetic energy (Ec) is:

Ec = 1/2 * m * v2

Calculation:

Ec = 1/2 * 0.015 kg * (50 m/s)2 = 18.75 J

Potential Energy Calculation: Crane Example

The formula for gravitational potential energy (Ep) is:

Ep = m * g * h

Calculation for a 350 kg object lifted 7 m (assuming g = 10 m/s²):

Ep = 350 kg * 10 m/s2 * 7 m = 24,500 J

Energy Transformations in Action

Observe the following scenarios and identify who loses/gains energy and the types of energy involved:

• Launching an Arrow

The Electron and Electric Current

The electron is the fundamental element of the electric current, as it has electric charge and can move from one atom to another.

Electrostatic Force (Coulomb's Law)

The force of attraction or repulsion between two charged bodies is directly proportional to the product of their charges and inversely proportional to the square of the distance that separates them.

A coulomb is the charge that a body possesses when, facing another body of the same charge at 1 meter distance in a vacuum, it repels with a force of $9.10^9$ N.

Electric Circuit Components

An electric circuit consists of a set of interconnected elements, so as to permit the permanent circulation of electric power.

• Generator: Is the device responsible for

Amplification of Light in Lasers

All lasers contain a substance that can increase the intensity of light passing through it.

The Active Medium

This substance is called the active medium and may be a solid, liquid, or gas. The mechanism by which the active medium increases the intensity will be explained later. For the moment, assume that light amplification is possible.

For example, in a YAG laser (Nd:YAG), the active medium is a Yttrium Aluminum Garnet (YAG) bar containing neodymium ions.

Understanding Gain

The factor by which the light intensity increases in the active medium is known as gain.

The gain is not constant for a particular type of medium; it depends on:

• The wavelength of light.
• The length of the active medium.
• The extent to which the active

Abbe Operation

Abbe Operation is based on the determination of the critical angle. The technique is to calibrate the device, usually with distilled water at 20ºC, by matching the shade formed by the prism surface illuminated by a brand (not recorded) in the center of the telescope. Perform the same operation with the test sample to make the correct reading of the refractive index in the eyepiece of the telescope. Since the refractive index varies with temperature, it is important to perform the measurement with the apparatus thermostatted at 20°C or at least know the temperature at which to make the determination.

Understanding Light Polarization

• Natural Light: It is a vibration in all directions perpendicular to the beam.
• Polarized Light: It

Gravitational Acceleration and Field Strength

The strength of the gravitational field depends on the amount of mass $M$ causing the field. Let us define a characteristic of the field that depends only on the mass $M$ and the distance $r$ to the point we consider.

Defining Gravitational Field Strength ($g$)

The gravitational field strength, $g$, at a point in space is the force that would act on a unit mass located at that point. Its unit is Newtons per kilogram ($N/kg$). This term is often used interchangeably with gravitational field intensity.

Calculating the Gravitational Field

To determine the gravitational field created by a point mass $M$, we place a test mass $m$ at a point $P$ in space at a distance $r$ from mass $M$. We calculate the force... Continue reading "Fundamentals of Gravitational Force and Field Calculation" »