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" »

Understanding Direct Current (DC)

Direct Current (DC) is the electric current flowing consistently in the same direction. The flow of current is determined by three interrelated quantities, the first being the potential difference across the circuit, often referred to as electromotive force or voltage.

Power Generators

A power generator consists of a rotating coil of wire inside a magnet. The magnet is known as the stator, while the rotating loop is called the rotor.

Classification of Generators

Generators are classified based on the currents they produce and their circuit configurations:

• Electromechanical generators
• Electrochemical generators
• Photovoltaic generators
• DC generators
• AC generators

Direction of Electric Current

When an external voltage source... Continue reading "Understanding Direct Current, Ohm's Law, and Electrical Resistance" »

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

CRT Screen Dimensions

The dimensions of the CRT screen are now standard in most instruments, measuring 10 cm in the horizontal axis (X) by 8 cm in the vertical (Y). On the screen, divisions of 1 cm square are recorded, either directly on the CRT or on a superimposed part featuring a grid of 80 cm square. This grid serves as the reference for the signal representation applied to the oscilloscope.

Appliance Description

The device consists of an evacuated glass tube containing:

• An electron beam dispenser at one end.
• A screen coated with phosphorescent material at the other end.
• Two pairs of parallel plates (one horizontal and one vertical).

Beam Deviation Formula

The beam deviation experienced is defined as:

y = (1/2) * (m/d) * (v0^2) * (E/V)

RMS Voltage

The Cartesian Scientific Method

The Scientific Method is a strict deductive method, particularly involving the idea of God as the creator and curator of the world and the immutability of certain innate ideas existing in the human mind, hitherto the prescient procedure of experience. It comes in addition to the cause and effect in physics, as it is a long series of deductive chains ordered by the prime causes. The concept of cause becomes substance next to the second key concept of Cartesianism, but that inference has limited contingents arrived at in moments and can no longer be deducted towards their cause; that is when experience intervenes to determine regarding its effects, which are those that are actually performed. Experience is valuable... Continue reading "Descartes' Scientific Method and Cartesian Physics" »

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