Motion with resistive forces
Section: Dynamics | Syllabus: Cambridge AS Level Physics 9702
Friction Friction is a resistive force that acts where surfaces contact each other. It always acts in the opposite direction to the motion or the intended motion. Translational Equilibrium: According to Newton's First Law, an object in motion will continue with uniform velocity unless a resultant force acts.
On a solid surface, friction is usually that force. Work Done: Friction converts kinetic energy into thermal energy (heat). Resultant Force with Friction If a driving force exceeds the friction force, the object accelerates.
The friction reduces the net acceleration: a = F_driving - F_frictionm. Drag and Viscosity Objects moving through fluids (liquids or gases) experience a resistive force called drag (or viscous drag). Factors Affecting Drag: Speed: Greater speed leads to greater drag.
For many objects, drag is proportional to v^2. Cross-sectional Area: A larger area presented to the fluid increases drag because more fluid must be pushed aside. Shape (Streamlining): Streamlined shapes allow smooth, non-turbulent flow, significantly reducing drag compared to blunt shapes.
Viscosity: This is the "thickness" or resistance of a fluid to flow. Air has low viscosity; water has higher viscosity; oil or honey is very viscous. Important Tip Two objects of the same size and shape moving at the same speed through the same fluid experience the same drag force , regardless of their mass.
Terminal Velocity When an object falls under gravity, it eventually reaches a constant speed called terminal velocity (v_t), where the upward drag equals the downward weight. The Process of Reaching v_t: Release (t=0): v=0, so Drag (D) = 0.
Resultant force = W. Acceleration = g. Falling (v increasing): D increases. Net force (W - D) decreases. Acceleration decreases. Equilibrium (D = W): Net force = 0. Acceleration = 0. The object continues at a constant terminal velocity .
Diagram: Stages of Falling Show a sequence of three free-body diagrams for a falling ball: (1) At t=0, only weight arrow. (2) Mid-fall, weight arrow and small drag arrow. (3) Terminal velocity, weight and drag arrows are equal length.
The Role of Mass (Table Tennis vs. Golf Ball) A golf ball and a table tennis ball have equal diameters but different masses (m_golf approx 20 imes m_tt). Explanation At the same speed, both experience the same drag force .
However, because a = racW - Dm, the lighter table tennis ball experiences a much larger deceleration effect from the resistance. It reaches terminal velocity sooner and at a lower speed. The heavier golf ball continues accelerating for longer.
Worked Example: Falling in Different Fluids Three identical steel balls are dropped: A (vacuum), B (air), C (water). Analysis Ball A (Vacuum): No resistance. v increases uniformly (a = g). The v-t graph is a straight line through the origin.
Ball B (Air): Low resistance. Acceleration decreases slightly over 1m. Graph curves slightly. Ball C (Water): High resistance (viscosity). Acceleration decreases significantly. v increases much less rapidly than in air.
Graph: v-t Graphs for Different Fluids Plot velocity vs time for a vacuum (diagonal straight line), air (curve leveling off at high speed), and water (curve leveling off quickly at low speed). Horizontal Motion and Maximum Speed Vehicles reach a maximum speed when the resistive forces (air resistance + friction) become equal to the maximum driving force provided by the engine.
Worked Example: Thrust SSC Land Speed Record Why must a land speed record involve two passes in opposite directions within one hour? Solution This accounts for wind speed and ground slope . Running in both directions ensures that any advantage from a tailwind or downhill slope is cancelled out when results are averaged.
Projectile Motion with Air Resistance In real-world conditions, air resistance acts in the direction opposite to the velocity vector at every instant. Effects of Air Resistance: Reduced Range: The horizontal component of velocity decreases over time.
Reduced Height: The vertical upward motion is opposed by both gravity and air resistance. Asymmetry: The path is no longer a perfect parabola. It is "steeper" on the way down than on the way up. Diagram: Projectile Path with Air Resistance Overlay two projectile paths: a dashed symmetrical parabola (no air resistance) and a solid asymmetrical path (with air resistance) that has a lower peak and shorter range.
Key Definitions Terminal Velocity: Constant speed reached when Drag = Weight. Viscosity: Resistance of a fluid to flow. Streamlining: Designing shapes to minimize turbulent flow and drag.
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