Author Capstone Axis

Pressure and Its Applications 1. What is Pressure? Think of pressure as the “push” a fluid gives per unit area. The average pressure on a flat surface is  \( P_{\text{av}} = \dfrac{F}{A} \). For an infinitesimally small area, we write  \( P = \displaystyle \lim_{\Delta A \to 0} \dfrac{\Delta F}{\Delta A} \). Pressure is a […]

Why Study Fluids? Fluids are everywhere. Air wraps around the planet and water covers most of its surface. Every living creature—plants and animals alike—relies on fluids for vital processes. Learning how fluids behave helps us understand nature and many real-life technologies. :contentReference[oaicite:0]{index=0} 1. What Makes Liquids and Gases “Fluids”? Ability to flow ⟶ Both liquids and gases

Elastic Behaviour of Materials – Student-Friendly Notes Elastic Behaviour of Materials 1. How Materials Compress and Stretch Solids hardly compress because neighbouring atoms are tightly linked. Liquids compress a little more; the atomic links are looser than in solids. Gases compress the most—about a million times more than solids—because molecules barely interact. 2. Worked Example

Elastic Moduli — Fast & Friendly Notes When you stretch, squeeze, or twist something, its shape or size changes. Inside the elastic limit, the change is proportional to the applied force. That neat proportionality lets us define three elastic moduli that characterise every material. 1. Young’s Modulus (Y) — stretching or squeezing along the length

Stress–Strain Curve: Quick Study Notes Picture a metal wire that you pull harder and harder. The graph that tracks how much the wire stretches (strain) against the pulling force per area (stress) tells you a lot about the metal’s behavior and strength. Use this roadmap to master every stage of that curve. Key Definitions Hydraulic

Hooke’s Law & the Stress–Strain Story 1 · Stress, Strain, and Volume Changes When a fluid squeezes an object from all sides, the object pushes back with an internal restoring force per unit area called hydraulic stress. This hydraulic stress has the same numerical value as the fluid’s pressure. :contentReference[oaicite:0]{index=0} The fluid also changes the object’s volume.

Stress & Strain – Quick, Friendly Notes 1 ‒ Stress: the “push-back” inside a solid When you squeeze, pull, or twist a body that stays in static equilibrium, it builds a restoring force that tries to undo the deformation. The restoring force per unit area is called stress and is given by \( \sigma \;=\;\dfrac{F}{A} \)

Mechanical Properties of Solids – Quick Student Notes 1 Elasticity vs. Plasticity • Elasticity is a material’s built-in “memory.” Stretch it, squeeze it, or bend it a little and, once the push stops, it snaps back to its original shape :contentReference[oaicite:0]{index=0}. • Plasticity means the opposite: after the force is removed, the new shape stays.

Energy of an Orbiting Satellite 1 · Kinetic Energy (K) A satellite of mass m moving in a circular orbit of radius \(R_E+h\) has $$K=\frac12\,m\,v^{2} =\frac{G\,M_E\,m}{2\,(R_E+h)}$$ :contentReference[oaicite:1]{index=1} 2 · Gravitational Potential Energy (U) Taking the zero of potential energy at infinity, the value at distance \(R_E+h\) is $$U=-\frac{G\,M_E\,m}{(R_E+h)}$$ :contentReference[oaicite:3]{index=3} 3 · Total Mechanical Energy (E) The satellite’s total energy combines K and U: $$E=K+U=-\frac{G\,M_E\,m}{2\,(R_E+h)}$$ :contentReference[oaicite:5]{index=5} You can spot two handy relations: \(K=-\tfrac12\,U\) \(U=2\,E\)

Earth Satellites at a Glance Earth satellites—natural (the Moon) or artificial—revolve around the planet in circular or elliptical paths, just like planets around the Sun. Because of that, the same three Kepler laws apply :contentReference[oaicite:0]{index=0}. Since 1957, artificial satellites have become key tools for telecommunication, geophysics, and weather monitoring :contentReference[oaicite:1]{index=1}. Circular-Orbit Mechanics Balancing forces. For a satellite