Physics Constants Quick Reference

Temperature and Gravitational Concepts

• The SI base unit of temperature is the Kelvin (K).
• Gravitational acceleration on Earth is represented by the constant ( g = 9.81 , \text{m/s}^2 ).

Hydrostatics and Pressure

• Hydrostatic pressure is given by the formula ( P = \rho gh ), where ( P ) is pressure, ( \rho ) is fluid density, ( g ) is gravitational acceleration, and ( h ) is the height of the fluid column.

Thermodynamics and Constants

• The Boltzmann constant (( k )) relates to the average kinetic energy of particles in a gas.
• The Avogadro constant (( N_A )) represents the number of constituent particles, typically atoms or molecules, in one mole of a substance, approximately ( 6.022 \times 10^{23} ).

Forces and Equilibrium

• The two forces that form a couple have equal magnitudes but act in opposite directions, creating rotational motion about a point.
• In a uniformly hinged rod scenario, the force direction from the hinge can be indicated by an arrow towards the rod, opposing its weight.

Mechanics of Compression and Density

• A child weighing 40 kg causes extra compression in a spring when standing on a diving board, calculated using Hooke's law.
• The density of a granite rock on another planet with double the gravitational acceleration remains the same as on Earth due to dependence on mass and volume, not gravity.

Fluid Dynamics and Motion Effects

• When a U-shaped tube with a stationary liquid is rotated about its axis, the liquid level will rise on the outside of the tube due to centrifugal force.
• A ball dropped from the same height will fall faster on a planet with ( 30 , \text{m/s}^2 ) acceleration due to gravity than on Earth.

Acceleration in Equal Motion

• In the case of a child and a sledge, both moving with equal acceleration, tension and inertia allow for simultaneous movement towards the pole.

Terminal Velocity and Collision Dynamics

• Both the stone S and foam rubber ball R achieve terminal velocity, where the force of gravity is balanced by air resistance.
• In a non-elastic collision between balls X and Y, ball X may lose kinetic energy and be deformed, potentially changing its velocity after impact.

Interaction and Frictionless Dynamics

• The frictionless pole allows the child to accelerate without resistance in the presence of external forces.
• The interaction of balls X and Y during a head-on collision is determined by their mass and velocity.

Atomic Structure and Particle Interaction

• When a neutron decays into a proton by emitting a beta particle, the change in quark structure involves a down quark converting to an up quark.
• An atom of element E that absorbs a neutron and emits an alpha particle transforms into a different element, reducing its atomic number by two.

Alpha Particle Experiment Insights

• The deflection of alpha particles by small angles implies that most of the atom's mass is concentrated in a small nucleus, rather than being uniformly distributed.
• The mass distribution within an atom can be inferred from the level of deflection observed in alpha particle scattering experiments, indicating a dense center.

Cambridge Assessment Context

• The Cambridge Assessment International Education Copyright Acknowledgements Booklet aims to recognize copyrighted materials used in assessments.
• Cambridge Assessment and UCLES (University of Cambridge Local Examinations Syndicate) are closely related, as UCLES is part of Cambridge Assessment.
• If items requiring clearance are unintentionally included, the publisher may take corrective actions to resolve the issue.
• Candidates can access the Cambridge Assessment International Education Copyright Acknowledgements Booklet through the official Cambridge Assessment website.