Kinematics and Nature of Forces
Kinematics describes object motion through scalar and vector quantities. Distance represents the total path length traveled, whereas displacement defines the straight-line vector from an object's initial position to its final position. Speed measures the rate at which distance is covered, while velocity incorporates direction. Acceleration quantifies the rate of change in velocity over time.
Average Velocity
Calculated using displacement and elapsed time:
Where vavg is average velocity, Δx is displacement, and Δt is the elapsed time interval.
Forces driving or altering motion are broadly categorized into contact and non-contact interactions. Contact forces require physical touch between surfaces or objects; these include applied forces exerted directly by an external agent, normal forces acting perpendicular to contacting surfaces, tension transmitted along taut cables or strings, and frictional resistance. Conversely, non-contact forces act across spatial fields without physical touch, encompassing gravitational forces pulling masses toward one another, electrostatic forces attracting or repelling charged particles, and magnetic forces exerted on moving charges or magnetic materials.
Frictional Dynamics and Fluid Mechanics
Friction is a contact force that opposes the relative or intended motion between two touching surfaces, operating under static and kinetic regimes. Static friction acts between stationary surfaces, preventing movement until an applied force exceeds a maximum threshold. Once sliding begins, kinetic friction takes over to oppose continuous motion. Maximum static friction universally exceeds kinetic friction because resting surfaces have time to settle deeply into microscopic irregularities and valleys, whereas moving surfaces rapidly brush across elevated peaks.
Fluids exert hydrostatic pressure on container walls and submerged objects due to the gravitational weight of fluid layers above. At any given depth, hydrostatic pressure acts equally in all directions, regardless of container shape or total fluid volume.
Hydrostatic Pressure
Calculated using fluid density, depth, and gravitational acceleration:
Where P is pressure (in pascals or N/m²), ρ is fluid density (kg/m³), g is gravitational acceleration (m/s²), and h is depth (meters).
Fluid behavior is further governed by Pascal’s principle—which states that pressure applied to an enclosed fluid transmits undiminished throughout the system—and Archimedes’ principle, which establishes that a submerged object experiences an upward buoyant force (FB) equal to the weight of the fluid it displaces.
Mechanical Work, Energy, and Power Dynamics
Mechanical work occurs when an applied external force displaces an object along a vector parallel to that force. Mechanical energy exists as potential energy (Ep), stored by virtue of an object's position or state, and kinetic energy (Ek), generated by motion as a function of mass and the square of velocity.
Mechanical Work
Calculated as the scalar product of force and displacement:
Where W is work done, F is the applied force, s is displacement, and θ is the angle between the force and displacement vectors.
Power measures the rate at which work is performed or energy is transferred, measured in watts or joules per second. For example, two lifters raising a 100 kg weight a distance of 2 meters execute identical total work, but the lifter completing the movement in less time produces higher power.
Mechanical Power
Calculated as work done over time or force times velocity:
Where P is power, W is work, t is time, F is applied force, and v is constant velocity.
Machines manipulate these principles using mechanical advantage—the factor by which a mechanism multiplies input force, such as a crowbar providing a mechanical advantage of 4 by requiring only one-fourth the effort to lift a heavy load. Finally, system performance is measured by efficiency, defined as the percentage ratio of useful work output to total energy input.