physics midterm 3

System

The chosen object or collection of objects under consideration, represented in isolation as a center-of-mass symbol. [1]

Free-Body Diagram (FBD)

A diagrammatic representation showing a system as a center-of-mass symbol, all external forces exerted ON the system (with tails at the center of mass), an acceleration vector next to it, and a reference axis. [1-3]

Translational Equilibrium

The physical state of an object at rest or moving with constant velocity, where acceleration is zero (a = 0) and the vector sum of external forces equals zero (\sum F = 0). [4, 5]

Net Force (\sum F)

The vector sum of all forces exerted on an object, equal to the time rate of change in the object's momentum (\sum F = dp/dt) or m*a for constant mass. [6-8]

Newton's First Law (Law of Inertia)

In an inertial reference frame, any isolated object at rest remains at rest, and any isolated object in motion continues moving at a constant velocity. [9]

Newton's Second Law

The vector sum of the forces exerted on an object equals the time rate of change in momentum (\sum F = dp/dt); when mass is constant, \sum F = m*a. [7, 8]

Newton's Third Law

Whenever two objects interact, they exert on each other forces that are equal in magnitude and opposite in direction (F_12 = -F_21). [8, 10, 11]

Interaction Pair

Two equal and opposite forces exerted between two interacting objects; both forces can NEVER appear on the same Free-Body Diagram. [10, 11]

Reciprocity Rule

To find the interaction partner of a force, swap the two nouns and reverse the direction (e.g., "Earth pulls down on me" -> "I pull up on Earth"). [12, 13]

Contact Force

A force that arises when interacting objects physically touch each other, such as pushing, pulling, or surface friction. [14]

Field Force

A force associated with action at a distance without physical touching, such as gravitational and electromagnetic forces. [14]

Gravitational Field Force (Near Earth)

The downward force exerted by Earth on an object of mass m, with vertical component F_x^G = -mg. [15, 16]

Elastic Force

The force exerted by a compressed or stretched material operating within its reversible elastic range. [17]

Hooke's Law

The elastic force exerted by a spring on a load: (F_by_spring_on_load)_x = -k(x - x0), where k is the spring constant and (x - x0) is displacement from relaxed length. [18]

Spring Constant (k)

A parameter measuring spring stiffness, equal to the inverse slope of the displacement vs. force line (k = F / \Delta x). [18, 19]

Tension (T)

The tensile stress transmitted undiminished from one end of a rope, thread, or spring to the other when gravity acting on the connector is negligible. [20]

Superposition of Forces

The property where multiple individual forces acting together cause the exact same acceleration as a single force equal to their vector sum. [7]

Impulse (J_x)

The momentum change delivered by a force, equal to the area under a force-versus-time curve: J_x = \Delta p_x = \int F_x dt. [21]

SI Unit of Force (Newton)

1 Newton (N) = 1 kg·m/s^2. [7]

Work (W)

The change in energy of a system caused by external forces (\Delta E = W), measured in Joules (J). [22-24]

Force Displacement (\Delta x_F)

The displacement of the exact point of application of a force; a force does work ONLY if its force displacement is nonzero. [25, 26]

Positive Work

Work done when force and force displacement point in the same direction, increasing system energy. [23, 27]

Negative Work

Work done when force and force displacement point in opposite directions, decreasing system energy. [23, 27]

Particle

An object with mass m and no internal structure (\Delta E_int = 0), whose only energy change is kinetic energy (\Delta E = \Delta K). [24]

Work Equation (Particle in 1D)

W = (\sum F_x) * \Delta x_F for constant force, or W = \int F_x dx for variable force. [28, 29]

Double Counting Gravitational Energy Rule

Use gravitational potential energy (\Delta U_G) when Earth is inside the system, or external work by Earth (W_Earth) when Earth is outside, but NEVER both in the same energy balance. [30]

FBD Subscript Notation Rule

Label forces as F_by,on^type (c = contact, G = gravitational); every force on a single FBD MUST share the exact same second subscript letter representing the system object. [31-33]

Center of Mass Acceleration

The center of mass of a system of objects accelerates as if all mass were concentrated at the center of mass and external forces were applied there (\sum F_ext = m_tot * a_cm). [22, 34]

Elevator Stool Formula

\sum F_x = F_floor^c - F_person^c - F_gravity^G = m * a_x. [7, 35, 36]

Tennis Ball Racquet Formula

F_racquet^c - mg = m(9g) => F_racquet^c = 10mg. [16]