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

**Coulomb's Law: Quantifying Force Between Electric Charges**

The quantification of force between electric charges is attributed to Coulomb, who used a torsion balance. Coulomb's law states that the force of attraction or repulsion between two charges is proportional to the product of the charges and inversely proportional to the square of the distance between them. This can be expressed as:

F = K • (Q₁Q₂ / r²)

Where:

• F is the force
• K is Coulomb's constant
• Q₁ and Q₂ are the charges
• r is the distance between the charges

The electrical constant, K, is defined in terms of another constant called the permittivity of the medium. Coulomb's law is analogous to Newton's law of universal gravitation. Both forces are proportional to the product of the property... Continue reading "Understanding Electric and Magnetic Fields: Forces and Charges" »

Vibration: Periodic Motion

Periodic motion occurs when the magnitude that characterizes it repeats at regular intervals of time. Examples include the Moon orbiting the Earth and a piston in an internal combustion engine. In periodic motion, the period is defined as the time that passes until the motion repeats.

Oscillatory Movements

An oscillatory movement is a motion in which the path is covered in two directions. An example is a pendulum. Many oscillatory movements in nature eventually stop due to friction. These oscillations are called damped oscillations, in contrast to those that do not involve friction, which are called free oscillations.

Dynamics of Simple Harmonic Motion

Work Done by a Constant Force

The work done by a constant force is the... Continue reading "Understanding Vibrations and Harmonic Motion in Physics" »

Understanding Vehicle Dynamics: FMR, RR, RP, FMD, and FMU

FMR (Force Moving Resistance): Power required to move machines on a surface, such as through a cut or haul road. The factors determining FMR are:

FMR = RR + RP

Rolling Resistance (RR)

RR (Rolling Resistance): The force opposing the ground at the turn of a vehicle's wheels. To move, the vehicle must counteract this force.

RR = rr x factor pbv

Several factors contribute to RR, the most important being:

A. Internal Friction

Internal friction produced in the powertrain, from the engine to the tires or tracks. Mechanical components like bearings create resistance to movement.

B. Tire Flexion

Flexion of tires increases resistance due to sidewall and tread deformation during spinning. The extent of this... Continue reading "Understanding FMR, RR, RP, FMD, and FMU in Vehicle Dynamics" »

John Dalton: The First Theory of Matter

John Dalton proposed the first theory of matter.

William Crookes: Perfecting Vacuum Tubes

William Crookes (1832-1919) perfected devices using a glass tube that had undergone a partial vacuum and contained two electrodes, one positive and one negative, connected to a source of high-voltage continuous current.

J.J. Thomson: Discovering the Electron

In 1897, J.J. Thomson proved that the cathode ray consisted of minute particles of negative electric charge that are attracted by the positive electrode. He achieved determining the relationship between charge and mass for these particles. He carefully measured how magnetic and electric fields deviated the electrons' trajectory. Independently of their origin, they... Continue reading "Key Discoveries in Atomic Theory and Radioactivity" »

Wave Motion

Wave motion refers to the transmission of a disturbance from one point to another without the net transport of matter.

Wave Classification

Based on Direction of Propagation

• One-dimensional waves: Propagate in a single direction.
• Two-dimensional waves: Propagate in two directions.
• Three-dimensional waves: Propagate in three directions.

Based on Medium of Propagation

• Mechanical waves: Require a material medium for propagation. Their speed depends on the characteristics of the medium.
• Electromagnetic waves: Do not require a material medium and can propagate in a vacuum (e.g., visible light).

Based on Direction of Disturbance

• Transverse waves: The direction of propagation is perpendicular to the direction of the disturbance.
• Longitudinal waves:

Geocentric Theory

Aristotle proposed the following:

• The Earth is round and immobile at the center of a celestial sphere, which houses the stars.
• The planets and stars rotate in a celestial sphere with uniform circular motion around the Earth.

Ptolemy improved Aristotle's theory. The Ptolemaic theory was based on circular orbits but later included eccentric orbits and epicycles to describe the movement of the planets. He maintained that the Earth was the center of the universe.

Heliocentric Theory

Copernicus and Galileo, who demonstrated this theory with a microscope he had built, proposed the heliocentric theory. However, Copernicus did not reveal his theory until the 16th century. It affirmed the following points:

• The Sun is at the center of the

Force is a physical quantity that can cause a body to deform or change its state of motion (start moving, stop, or change direction). As a vector quantity, force has both magnitude and direction. Its magnitude is measured in Newtons (N) within the International System of Units (SI).

Characteristics of a Force

Since force is a vector quantity, to fully define its characteristics, we need to know:

• Application Point: This is the specific point on the body where the force is applied. It represents the origin of the force vector.
• Magnitude (or Intensity): This is the numerical value indicating the strength of the force, measured in Newtons. It corresponds to the length of the force vector.
• Sense: This indicates the specific direction along the line of

Wave Reflection Study

Purpose

To study the reflection of a plane wave, generated by a wave source, off different obstacles.

Planning

1. Position the right triangle reflector in the form of a right angle.
2. Generate plane waves incident upon the reflector.
3. Affix paper to the table. Use a ruler to draw one or more lines to show the front of the incident wave and the reflected wave front. Ensure the ruler is parallel to the corresponding disturbance.
4. Trace the position of the reflective barrier.
5. Repeat steps for two other positions of the triangle.

Part 2: Reflection in a Curved Obstacle

1. Trace the circular barrier on a new sheet of paper.
2. Mark the position where the reflected waves converge.
3. Turn off the generator. Use your fingertip to produce a circular pulse

Photomultiplier Characteristics

What is dark current?

The dark current is a small amount of current flowing in the photomultiplier even when it is not illuminated. This current should be minimized for accurate measurements. The region between 800 V and 1300 V is often ideal for operating the photomultiplier.

The primary source of dark current is the thermionic emission rate from the photocathode and dynodes. Other sources include:

• Leakage current
• Incandescent lighting phenomena
• Field emission
• Current from residual gas ionization
• Radioactive contamination within the device materials

What is the photomultiplier gain?

The gain (G) of a photomultiplier is the ratio between the number of electrons at the output and the number of photons incident on the photocathode.... Continue reading "Photomultiplier Dark Current, Gain & Lifetime Measurements" »

Concept of Slope and Gradient

The closeness of curves indicates a steep slope, while a large separation indicates a slight incline. This equidistance, whenever we have to compare the two cases, is the same. The equidistance of curves in a plane is unique.

• A series of concentric curves, where the heights rise to the center, indicates a rise or hill.
• A series of concentric curves, in which the dimensions decrease toward the center, indicates a depression or hollow.

We define slope as the ratio between the horizontal and vertical displacement, always looking from the top down. The gradient is defined as the ratio between the vertical and horizontal displacement.

Alignment

• Natural Distance (Dn): Dn is the distance traveled on the ground, following the