# Mechanical Engineering (Polski) — Podstawowy (A1/A2) 1: Classical Mechanics: Kinematics, Dynamics, Energy & Momentum

> [Polski] Mechanical Engineering (Polski): Foundational classical mechanics covering one- and two-dimensional kinematics, Newton's laws of motion, work-energy principles, impulse, momentum conservation, and circular dynamics.

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- **Level:** basic
- **Languages:** pl → pl
- **Total Cards:** 32

## Flashcards (32 Cards)

| # | Front (Term / Prompt) | Back (Definition / Answer) | Example | Multiple-Choice Options |
| :--- | :--- | :--- | :--- | :--- |
| 1 | What is the fundamental difference between an elastic collision and an inelastic collision? | • Elastic collision: Both total linear momentum and total kinetic energy are conserved (Σp_initial = Σp_final and ΣK_initial = ΣK_final; coefficient of restitution e = 1). • Inelastic collision: Total linear momentum is conserved, but total kinetic energy is NOT conserved (some kinetic energy is converted into thermal energy, sound, or plastic deformation; 0 <= e < 1). |  |  |
| 2 | What is the difference between a real centripetal force and the fictitious centrifugal force? | • Centripetal force: A real net physical force (originating from tension, gravity, friction, etc.) observed in an inertial reference frame that accelerates an object toward the center of curvature. • Centrifugal force: An apparent, fictitious inertial force experienced only within a non-inertial (rotating) reference frame, directed radially outward to account for an object's inertia in that accelerated frame. |  |  |
| 3 | What is Kepler's Third Law for circular planetary orbits derived from Newton's laws? | Equating gravitational force to centripetal force: G·M·m / r² = m·(4π²·r / T²), yielding: T² / r³ = 4π² / (G · M) where T is orbital period, r is orbital radius, and M is the central mass (e.g., Sun). The ratio T²/r³ is constant for all bodies orbiting the same central mass. |  |  |
| 4 | What do the slope and area under the curve represent on position-time, velocity-time, and acceleration-time graphs? | • Position-time graph: Slope = Instantaneous velocity (dx/dt). • Velocity-time graph: Slope = Instantaneous acceleration (dv/dt); Area under curve = Net displacement (Δx = ∫v dt). • Acceleration-time graph: Area under curve = Change in velocity (Δv = ∫a dt). |  |  |
| 5 | How does Tsiolkovsky's Rocket Equation explain rocket propulsion in a vacuum? | Δv = v_e · ln(m0 / mf) • Δv = Maximum change in rocket velocity • v_e = Effective exhaust gas ejection speed • m0 = Initial wet mass (rocket structure + propellant) • mf = Final dry mass (structural mass after fuel burnout) Thrust arises directly from conservation of linear momentum as high-velocity propellant mass is expelled backward. |  |  |
| 6 | How do distance and displacement differ, and how do speed and velocity differ? | • Distance: Total scalar length of the actual path traveled (always >= 0). • Displacement (Δx): Vector representing the straight-line change in position from initial to final point (Δx = x_final - x_initial). • Average speed: Total distance divided by time elapsed (scalar). • Average velocity: Displacement divided by time elapsed (vector: v_avg = Δx / Δt). |  |  |
| 7 | What is linear momentum (p = mv) and under what condition is the total linear momentum of a system conserved? | Linear momentum is the product of an object's mass and its velocity: p = m · v (a vector pointing in the direction of velocity). Total linear momentum of a multi-body system is conserved (Σp_initial = Σp_final) if and only if the net external force acting on the system is zero (ΣF_ext = 0). |  |  |
| 8 | What is the difference between inertial mass and gravitational mass, and what does the Weak Equivalence Principle state? | • Inertial mass (m_i): Measures an object's resistance to acceleration when subjected to any force (F = m_i · a). • Gravitational mass (m_g): Measures the strength of gravitational attraction experienced or exerted by the object (F_g = m_g · g). • Weak Equivalence Principle: m_i equals m_g identically for all bodies, causing all objects to fall with the exact same acceleration in a given gravitational field in vacuum. |  |  |
| 9 | What is uniform circular motion and why is an object moving in a circle at constant speed accelerating? | Uniform circular motion is motion in a circular path at constant tangential speed. Even though speed is constant, the direction of the velocity vector is continuously changing. This change in direction constitutes an inward acceleration called centripetal acceleration: a_c = v² / r = ω² · r always directed radially toward the center of curvature. |  |  |
| 10 | In standard projectile motion (neglecting air resistance), what are the horizontal and vertical components of velocity and acceleration? | • Horizontal (x): Acceleration ax = 0; velocity vx remains constant throughout flight (vx = v0·cos(θ)). • Vertical (y): Acceleration ay = -g (constant downward gravitational acceleration, ~9.8 m/s²); velocity vy changes linearly with time (vy = v0·sin(θ) - g·t). |  |  |
| 11 | What forces act on a block of mass m resting on an inclined plane of angle θ, and what are their component equations? | • Gravitational force (mg) acting straight downward, resolved into:   - Perpendicular to incline: F_perp = m·g·cos(θ)   - Parallel down incline: F_parallel = m·g·sin(θ) • Normal force (N) acting perpendicular to incline surface: N = m·g·cos(θ) • Static/Kinetic friction (f) acting parallel to incline opposing motion: f <= μ·N = μ·m·g·cos(θ) |  |  |
| 12 | What is the physical difference between a scalar quantity and a vector quantity in kinematics? | • Scalar: A physical quantity completely specified by magnitude and physical units alone (e.g., mass, time, speed, temperature, distance, kinetic energy). • Vector: A physical quantity requiring both magnitude and spatial direction for complete description (e.g., displacement, velocity, acceleration, force, linear momentum). |  |  |
| 13 | What is elastic potential energy stored in an ideal compressed or stretched spring? | U_s = (1/2) · k · x² where k is the spring stiffness constant (N/m) and x is displacement from equilibrium. It equals the area under the linear force-displacement graph (W = ∫k·x dx = (1/2)kx²). |  |  |
| 14 | How is instantaneous mechanical power defined and how is it calculated from force and velocity? | Power (P) is the time rate at which work is performed or energy is transformed: P = dW / dt When a force F acts on an object moving with instantaneous velocity v: P = F · v = F · v · cos(θ) Measured in Watts (1 W = 1 J/s = 1 N·m/s). |  |  |
| 15 | What is terminal velocity and under what force equilibrium condition is it reached by a falling object? | Terminal velocity is the maximum constant downward speed reached by an object falling through a fluid (such as air). It is attained when the upward aerodynamic drag force (Fd = 0.5·ρ·v²·Cd·A) equals the downward gravitational force (mg). Net force becomes zero, resulting in zero acceleration (dv/dt = 0). |  |  |
| 16 | What is mechanical impulse (J) and how does the Impulse-Momentum Theorem relate impulse to force and momentum? | Impulse (J) is the integral of force over the time interval of application: J = ∫[t1 to t2] F dt = F_avg · Δt The Impulse-Momentum Theorem states that the net impulse imparted to an object equals its change in linear momentum: J = Δp = p_final - p_initial = m·v_final - m·v_initial |  |  |
| 17 | What is the center of mass of a system of particles and how does it move under external forces? | The center of mass position vector is: R_cm = (Σ m_i · r_i) / (Σ m_i). According to Newton's Second Law for systems, the center of mass moves as if the entire system mass M were concentrated at that point and acted upon by the vector sum of all external forces: ΣF_ext = M · a_cm Internal forces between particles cancel in pairs by Newton's Third Law. |  |  |
| 18 | What is the Principle of Conservation of Mechanical Energy and when does it strictly hold? | The total mechanical energy (E = K + U) of an isolated system remains constant over time: K_initial + U_initial = K_final + U_final This conservation holds strictly when all forces performing work on the system are conservative forces (W_nc = 0). |  |  |
| 19 | What does Hooke's Law state for an ideal linear spring, and what is the physical meaning of the minus sign? | Hooke's Law: F_s = -k · x • F_s = Restoring force exerted by the spring (N) • k = Spring stiffness constant (N/m) • x = Displacement of the spring from its unstretched equilibrium position (m) The negative sign indicates the restoring force is always directed opposite to the displacement vector, acting to return the spring to equilibrium. |  |  |
| 20 | How does apparent weight (normal force N) change for a person of mass m standing on a scale in an elevator accelerating upward, downward, and in free fall? | • Accelerating upward (+a): N = m·(g + a) (feels heavier). • Accelerating downward (-a): N = m·(g - a) (feels lighter). • Moving at constant velocity (a = 0): N = m·g (true weight). • Free fall (a = -g downward): N = m·(g - g) = 0 (apparent weightlessness). |  |  |
| 21 | How do angular velocity (ω) and angular acceleration (α) relate to linear tangential velocity (v) and tangential acceleration (a_t)? | For circular motion of radius r: • Tangential velocity: v = r · ω (where ω is angular velocity in rad/s: ω = dθ/dt). • Tangential acceleration: a_t = r · α (where α is angular acceleration in rad/s²: α = dω/dt). • Total linear acceleration is the vector sum: a_total = sqrt(a_t² + a_c²). |  |  |
| 22 | What is the difference between a conservative force and a non-conservative force? | • Conservative force: Work done moving an object between two points is strictly path-independent, and net work around any closed path is zero (∮F·dr = 0). It has an associated potential energy function (F = -∇U). Examples: gravity, electrostatic force, ideal spring force. • Non-conservative force: Work done depends on the specific path taken, dissipating mechanical energy as thermal energy. Examples: friction, fluid viscosity, air drag. |  |  |
| 23 | In an ideal Atwood machine with two masses m1 and m2 (m1 > m2) connected by a massless string over a frictionless pulley, what is the system acceleration? | a = ((m1 - m2) / (m1 + m2)) · g The tension in the string is: T = (2 · m1 · m2 / (m1 + m2)) · g Derived by applying Newton's Second Law to both masses simultaneously. |  |  |
| 24 | What is the formula for gravitational potential energy near Earth's surface compared to universal gravitational potential energy? | • Near Earth's surface (uniform field approximation): U = m·g·h (relative to reference height h = 0). • Universal gravitational potential energy (between masses M and m separated by distance r): U(r) = -G·M·m / r (where zero potential energy is set at infinite separation r -> ∞). |  |  |
| 25 | What is Newton's Law of Universal Gravitation and what is the gravitational field strength (g) at a distance r from a spherical mass M? | • Force: F_g = G · (M1 · M2) / r²   where G is the gravitational constant (6.674 x 10⁻¹¹ N·m²/kg²). • Field strength: g(r) = F_g / m = G · M / r²   directed radially toward the center of mass M. At Earth's surface (r = R_earth), g ≈ 9.81 m/s². |  |  |
| 26 | What is the Work-Energy Theorem and what is its mathematical relationship to kinetic energy? | The Work-Energy Theorem states that the net work (W_net) done on a particle by all external forces equals the change in its translational kinetic energy (ΔK): W_net = ΔK = (1/2)·m·v_final² - (1/2)·m·v_initial² Derived directly from integrating Newton's Second Law over a spatial displacement (W = ∫F dx = ∫m(vdv/dx)dx = ∫m v dv). |  |  |
| 27 | At what launch angle above horizontal ground is the range of a projectile maximized, and why do complementary angles yield equal ranges? | • Maximum range occurs at 45° (in vacuum on level ground), because range R = (v0² / g) · sin(2θ), and sin(2θ) reaches its maximum value of 1 at 2θ = 90° (θ = 45°). • Complementary angles (θ and 90° - θ) yield identical ranges because sin(2(90° - θ)) = sin(180° - 2θ) = sin(2θ). |  |  |
| 28 | What is a completely (perfectly) inelastic collision and what is the formula for the final velocity of two colliding masses that stick together? | A completely inelastic collision occurs when colliding bodies adhere and move together with a common final velocity (v_f), resulting in maximum possible kinetic energy loss consistent with momentum conservation: v_f = (m1·v1 + m2·v2) / (m1 + m2) |  |  |
| 29 | What is the calculus definition of instantaneous velocity and instantaneous acceleration? | • Instantaneous velocity: The first time derivative of the position vector: v(t) = dx / dt = lim(Δt -> 0) [Δx / Δt] • Instantaneous acceleration: The first time derivative of velocity, or second time derivative of position: a(t) = dv / dt = d²x / dt² |  |  |
| 30 | What is the formula for the escape velocity from a spherical celestial body of mass M and radius R? | v_esc = sqrt(2 · G · M / R) Derived by setting total mechanical energy equal to zero (K + U = 0): (1/2)·m·v_esc² - (G·M·m / R) = 0 Escape velocity is independent of the mass m of the escaping object. |  |  |
| 31 | What are the four kinematic equations for linear motion under constant acceleration? | 1. v = v0 + a·t 2. Δx = v0·t + (1/2)·a·t² 3. v² = v0² + 2·a·Δx 4. Δx = ((v0 + v) / 2) · t where v0 is initial velocity, v is final velocity, a is constant acceleration, t is time elapsed, and Δx is displacement. |  |  |
| 32 | What physical force provides the necessary centripetal force for: 1) a car rounding an unbanked curve, 2) a satellite in orbit, and 3) a tetherball on a string? | 1. Car rounding flat curve: Static friction between tires and pavement (f_s = m·v² / r). 2. Satellite in orbit: Gravitational attraction between Earth and satellite (F_g = G·M·m / r² = m·v² / r). 3. Tetherball on a string: Radial component of string tension (T·sin(θ) = m·v² / r). |  |  |

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