Key Concepts in Mechanics: Momentum, Collisions, and Circular Motion
Key Concepts in Mechanics
Momentum and Collisions
Coefficient of Restitution: The negative ratio of the relative velocity after impact to the relative velocity before collision.
Completely Elastic Collision: A collision where kinetic energy remains constant.
Completely Inelastic Collision: A collision where the colliding bodies stick together and move off as a unit afterward.
Conservation of Momentum: The total momentum of colliding bodies before impact is equal to their total momentum after impact.
Elasticity:
Thermal Radiation, Black Bodies, Photoelectric Effect, and Photons
Thermal Radiation and Black Bodies
Electromagnetic energy emitted by a body due to its temperature is called thermal radiation. This thermal radiation varies with both temperature and the composition of the body. However, there is a set of bodies for which thermal radiation depends only on its temperature. They are called black bodies. The total power P emitted by a surface of temperature Ts satisfies the Stefan-Boltzmann law. The wavelength for which the maximum power output occurs is inversely
Read MoreUnderstanding Key Concepts in Fluid Mechanics and Elasticity
Hooke’s Law: Elasticity
When an object is subjected to external forces, it undergoes changes in size or shape, or both. These changes depend on the arrangement of atoms and their bonds in the material. When a weight pulls and stretches another, and when released, this weight returns to its normal size, we say it is an elastic body.
- Elasticity: The property to change shape when a force acts on an object, causing deformation, and the object returns to its original shape when the deformation ceases.
- Inelastic
Cosmic Composition: From Elements to Solar Systems
The Universe: Composition and Organization
The universe is composed of approximately 75% hydrogen, 20% helium, and 5% other elements. Dark matter, which we cannot see, makes up 90% of the universe, while visible matter (galaxies, stars, and planets) accounts for only 10%.
Organization of the Universe
- Universe: A vast collection of billions of galaxies.
- Super-Virgo Cluster: A group of millions of galaxies.
- Local Group of Galaxies: A group of about 30 galaxies.
- Milky Way: Our galaxy, containing approximately
Vector Calculus: Velocity, Acceleration, and Fields
Example 1: Ferris Wheel Motion
A child is sitting on a Ferris wheel with a diameter of 10 meters, making one revolution every 2 minutes. Find the speed of the child and draw velocity vectors at two different times.
Solution: The child moves at a constant speed around a circle of radius 5 meters, completing one revolution every 2 minutes. One revolution around a circle of radius 5 is a distance of 10π, so the child’s speed is 10π/2 = 5π ≈ 15.7 m/min. Hence, the magnitude of the velocity vector
Read MoreUnderstanding Motion, Force, and Energy in Physics
Item 5
Force is an interaction between two objects. There are four types of forces:
- The gravitational force
- The electromagnetic force, which causes chemical reactions
- Strong nuclear forces, which are responsible for the stability of atomic nuclei
- Weak nuclear forces, which are responsible for the instability of atomic nuclei
Weight (P) = Mass (M) * Gravity (G)
Item 6
Movement is a physical phenomenon defined as any change of position in space experienced by bodies in a system with respect to themselves
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