Unit 1: Forces and Motion Specification Checklist

Units and Measurement

• Fundamental and Derived Core Units (Specification 1.1):

  • Mass: Measured in kilograms ($\text{kg}$).
  • Length / Distance / Displacement: Measured in metres ($\text{m}$).
  • Speed / Velocity: Measured in metres per second ($\text{m/s}$).
  • Acceleration: Measured in metres per second squared ($\text{m/s}^2$).
  • Force / Weight: Measured in newtons ($\text{N}$).
  • Time: Measured in seconds ($\text{s}$).
  • Gravitational Field Strength: Measured in newtons per kilogram ($\text{N/kg}$).

• Specialist Units for Paper 2 Only (Specification 1.2P):

  • Moment of a Force: Measured in newton metres ($\text{Nm}$).
  • Momentum: Measured in kilogram metres per second ($\text{kg}\,\text{m/s}$).

Movement and Position

• Distance–Time Graphs (Specification 1.3):

  • Plotting: Time is positioned on the horizontal x-axis, and distance moved is positioned on the vertical y-axis.
  • Gradient Interpretation: The gradient (slope) of a distance–time graph represents the speed of the object.
  • Horizontal Line: Represents a stationary object (speed is zero).
  • Straight Sloped Line: Represents motion with a constant (steady) speed.
  • Curving Line (Increasing Gradient): Indicates acceleration (speed is increasing over time).
  • Curving Line (Decreasing Gradient): Indicates deceleration (speed is decreasing over time).

• Average Speed Relationship (Specification 1.4):

  • Defined by the formula:     $\text{average speed} = \frac{\text{distance moved}}{\text{time taken}}$
  • The distance moved is measured in metres ($\text{m}$), time taken in seconds ($\text{s}$), and average speed in metres per second ($\text{m/s}$).

• Practical Investigation of Motion (Specification 1.5):

  • Objective: Investigate the motion of everyday objects (e.g., toy cars or tennis balls) along a ramp or flat surface.
  • Apparatus: Ramp/track, toy car or ball, stopwatches, metre rule, and optionally light gates connected to a data logger for higher precision and reduced human reaction error.
  • Procedure:
  • Measure known distances along the track using a metre rule and mark them with chalk or tape.
  • Release the object from rest at a fixed start point at the top of the ramp.
  • Measure the time taken for the object to traverse each designated interval using a stopwatch or by allowing the object to interrupt light gate beams.
  • Repeat the timing procedure three times for each distance and calculate a mean time to minimize random experimental errors.
  • Calculate speed using the average speed formula ($\text{average speed} = \frac{\text{distance moved}}{\text{time taken}}$).

• Acceleration Relationship (Specification 1.6):

  • Acceleration is defined as the rate of change of velocity with respect to time:     $\text{acceleration} = \frac{\text{change in velocity}}{\text{time taken}}$
  • Symbolic equation:     $a = \frac{v - u}{t}$
  • Where $a$ is acceleration ($\text{m/s}^2$).
  • Where $v$ is final velocity ($\text{m/s}$).
  • Where $u$ is initial velocity ($\text{m/s}$).
  • Where $t$ is time taken ($\text{s}$).

• Velocity–Time Graphs (Specification 1.7, 1.8, 1.9):

  • Plotting (1.7): Time is plotted on the horizontal x-axis; velocity is plotted on the vertical y-axis.
  • Features of Motion:
  • Horizontal line at non-zero velocity: Constant velocity (zero acceleration).
  • Horizontal line on the time axis: Stationary ($v = 0\,\text{m/s}$).
  • Straight line sloping upwards: Constant (uniform) acceleration.
  • Straight line sloping downwards: Constant (uniform) deceleration.
  • Curved line: Non-uniform (changing) acceleration.
  • Determining Acceleration (1.8): Acceleration is evaluated directly from the gradient of the velocity–time graph:     $\text{gradient} = \frac{\Delta y}{\Delta x} = \frac{v - u}{t} = a$
  • Determining Distance Travelled (1.9): The total distance travelled is equal to the area between the velocity–time graph line and the time axis:
  • For geometric shapes, partition the area under the trace into right-angled triangles ($\text{Area} = \frac{1}{2} \times \text{base} \times \text{height}$) and rectangles ($\text{Area} = \text{base} \times \text{height}$).

• Uniform Acceleration Equation (Specification 1.10):

  • Relates final speed, initial speed, acceleration, and distance moved without requiring explicit time values:     $(\text{final speed})^2 = (\text{initial speed})^2 + (2 \times \text{acceleration} \times \text{distance moved})$
  • Standard algebraic formulation:     $v^2 = u^2 + 2as$
  • Where $v$ is final speed ($\text{m/s}$).
  • Where $u$ is initial speed ($\text{m/s}$).
  • Where $a$ is acceleration ($\text{m/s}^2$).
  • Where $s$ is distance moved ($\text{m}$).

Forces, Vectors, and Dynamics

• Effects and Types of Forces (Specification 1.11, 1.12):

  • Effects of Forces (1.11): Interactions between bodies can produce three fundamental mechanical changes:
  • Changes in speed (accelerating or decelerating an object).
  • Changes in direction of travel (turning or altering trajectory).
  • Changes in shape (stretching, compressing, twisting, or bending deformation).
  • Classification of Forces (1.12):
  • Gravitational force: Attractive pull between masses (e.g., downward pull toward Earth).
  • Electrostatic force: Attraction or repulsion between stationary electric charges.
  • Magnetic force: Interaction between magnetic poles or moving charges.
  • Friction: Contact force resisting sliding motion between adjacent surfaces.
  • Normal contact force (reaction force): Perpendicular force exerted by a surface supporting an object.
  • Tension: Pulling force exerted through a stretched string, cable, or spring.
  • Upthrust: Upward buoyant force exerted by a fluid on a submerged or floating body.
  • Drag / Air resistance: Frictional retarding force experienced by an object moving through a fluid.

• Scalar and Vector Quantities (Specification 1.13, 1.14):

  • Definitions:
  • Scalar Quantities: Quantities defined entirely by magnitude (numerical size) with no directional component (e.g., mass, distance, speed, time, energy, temperature).
  • Vector Quantities: Quantities defined by both a magnitude and a specific direction in space (e.g., displacement, velocity, acceleration, force, weight, momentum).
  • Vector Nature of Force (1.14): Force is a vector quantity because the outcome of applying a force depends strictly on the line and direction of action as well as its magnitude.

• Resultant Forces and Friction (Specification 1.15, 1.16):

  • Resultant Force Calculation (1.15): The resultant force is the single overall force that has the same physical effect as all individual forces acting upon an object combined.
  • For collinear forces acting in the same direction, add the magnitudes together ($F_{\text{res}} = F_1 + F_2$).
  • For collinear forces acting in opposite directions, assign a positive direction and subtract the opposing magnitude ($F_{\text{res}} = F_1 - F_2$).
  • Nature of Friction (1.16): Friction is an opposing contact force that acts antiparallel (directly opposite) to the relative direction of motion or intended motion of an object.

• Newton's Second Law of Motion (Specification 1.17):

  • The acceleration of an object is directly proportional to the unbalanced (resultant) force acting upon it and inversely proportional to its mass:     $\text{Force} = \text{mass} \times \text{acceleration}$$F = m \times a$
  • Where $F$ is unbalanced resultant force ($\text{N}$).
  • Where $m$ is mass ($\text{kg}$).
  • Where $a$ is acceleration ($\text{m/s}^2$).

• Weight and Gravitational Field Strength (Specification 1.18):

  • Weight is the gravitational force acting on an object's mass within a gravitational field:     $\text{Weight} = \text{mass} \times \text{gravitational field strength}$$W = m \times g$
  • Where $W$ is weight ($\text{N}$).
  • Where $m$ is mass ($\text{kg}$).
  • Where $g$ is gravitational field strength ($\text{N/kg}$).

Vehicle Stopping Distances

• Components of Vehicle Stopping Distance (Specification 1.19):

  • Total stopping distance consists of two independent consecutive segments:     $\text{stopping distance} = \text{thinking distance} + \text{braking distance}$
  • Thinking Distance: The distance travelled by the vehicle during the driver's reaction time (the period between seeing a hazard and applying the brakes):     $\text{thinking distance} = \text{speed} \times \text{reaction time}$
  • Braking Distance: The physical distance travelled by the vehicle while the braking system exerts a decelerating force to bring the vehicle to rest.

• Factors Affecting Stopping Distance (Specification 1.20):

  • Vehicle Speed:
  • Increases thinking distance linearly ($\text{thinking distance} \propto \text{speed}$).
  • Increases braking distance quadratically ($\text{braking distance} \propto \text{speed}^2$) because braking work must dissipate kinetic energy ($\frac{1}{2}mv^2$).
  • Vehicle Mass:
  • A greater mass increases braking distance because a larger force is required to achieve the same deceleration ($F = ma$).
  • Road and Environmental Conditions:
  • Wet, icy, oily, or loose gravel surfaces reduce friction between tyres and the road, drastically increasing braking distance.
  • Driver Reaction Time:
  • Factors such as tiredness/fatigue, alcohol consumption, illicit drugs, medication, and electronic or passenger distractions increase reaction time, which directly increases thinking distance.
  • Mechanical Maintenance Condition:
  • Worn tyre treads decrease grip and water dispersal, increasing braking distance.
  • Worn brake pads or failing hydraulic lines reduce maximum braking force, increasing braking distance.

Free Fall and Terminal Velocity

• Dynamics of Falling Objects (Specification 1.21):
  • Initial Release:
  • At the instant of release ($v = 0\,\text{m/s}$), the only force acting downward is weight ($W$). Air resistance (drag) is zero.
  • The unbalanced resultant force equals the object's weight, producing maximum initial acceleration downward ($a = g$).
  • Accelerating Phase:
  • As the falling speed increases, air resistance acting upward increases in direct opposition to motion.
  • The downward resultant force decreases ($F_{\text{res}} = W - \text{Drag}$), causing the acceleration of the object to decrease progressively according to $a = \frac{F_{\text{res}}}{m}$.
  • The object continues to gain speed, but at a decreasing rate.
  • Terminal Velocity State:
  • Air resistance continues to increase until it becomes equal in magnitude and opposite in direction to the downward weight ($\text{Drag} = W$).
  • The resultant force becomes zero ($F_{\text{res}} = 0\,\text{N}$).
  • Acceleration drops to zero ($a = 0\,\text{m/s}^2$).
  • The falling body continues to descend at a steady, maximum equilibrium velocity known as terminal velocity.

Deformation, Elasticity, and Hooke's Law

• Practical Investigation of Force and Extension (Specification 1.22):

  • Apparatus: Retort stand, boss and clamp, steel helical spring, metal wire, rubber band, meter rule, set of standard slotted masses with mass hanger, pointer (fiducial marker).
  • Procedure:
  • Set up the apparatus with the ruler clamped vertically adjacent to the spring or material.
  • Record the initial unloaded length of the specimen ($L_0$) using the attached pointer to avoid parallax error.
  • Add slotted masses in incremental steps (e.g., $100\,\text{g}$ or $1\,\text{N}$ increments).
  • Measure the new extended length ($L$) after each mass is added.
  • Compute the extension ($x$) for every load:       $x = L - L_0$
  • Unload the masses incrementally and re-measure to test whether permanent deformation occurred.
  • Plot a force–extension graph with load force ($\text{N}$) on the y-axis and extension ($\text{m}$ or $\text{mm}$) on the x-axis.
  • Material Comparisons:
  • Helical spring: Produces an initial linear force–extension line through the origin.
  • Metal wire: Shows an extremely steep linear region with minimal extension before plastic deformation or snapping.
  • Rubber band: Displays a non-linear S-shaped curve (hysteresis loop) during loading and unloading, not obeying a simple linear relation.

• Hooke's Law and Linear Region (Specification 1.23):

  • The initial straight-line region of a force–extension graph passing through the origin demonstrates Hooke's law.
  • Hooke's law states that the extension of an elastic body is directly proportional to the applied force, provided the elastic limit is not exceeded:     $F \propto x$
  • The end of this linear relationship on the graph is designated as the limit of proportionality.

• Elastic Behaviour (Specification 1.24):

  • Definition: Elastic behaviour is the ability of an object or material to recover its original shape and resting dimensions after the deforming forces causing tension or compression are removed.
  • Inelastic / Plastic Behaviour: If the applied force exceeds the elastic limit, the material undergoes permanent (plastic) deformation and does not return to its original shape once the load is released.

Momentum, Impulse, and Safety [Paper 2 Only]

• Relationship for Momentum (Specification 1.25P):

  • Momentum ($p$) is defined as the product of mass and velocity:     $\text{Momentum} = \text{mass} \times \text{velocity}$$p = m \times v$
  • Where $p$ is momentum ($\text{kg}\,\text{m/s}$).
  • Where $m$ is mass ($\text{kg}$).
  • Where $v$ is velocity ($\text{m/s}$).
  • Momentum is a vector quantity possessing both magnitude and the directional orientation of the velocity vector.

• Force and Rate of Change of Momentum (Specification 1.28P):

  • Force equals the rate of change of momentum over time:     $\text{Force} = \frac{\text{change in momentum}}{\text{time taken}}$$F = \frac{mv - mu}{t}$
  • Where $F$ is force ($\text{N}$).
  • Where $mv$ is final momentum ($\text{kg}\,\text{m/s}$).
  • Where $mu$ is initial momentum ($\text{kg}\,\text{m/s}$).
  • Where $mv - mu$ is the total change in momentum ($\Delta p$).
  • Where $t$ is the impact duration / contact time ($\text{s}$).

• Safety Features and Momentum Concepts (Specification 1.26P):

  • In a collision, a vehicle and its passengers undergo a defined change in momentum ($\Delta p = mv - mu$) from their initial speed to zero.
  • According to the relation $F = \frac{\Delta p}{t}$, the impact force experienced is inversely proportional to collision duration ($t$).
  • Increasing the collision or stopping time reduces the rate of change of momentum, significantly diminishing the peak impact force transmitted to the vehicle occupants.
  • Practical Safety Devices:
  • Crumple Zones: Structural zones in the front and rear of vehicles engineered to collapse predictably, extending the deceleration time of the cabin structure during an impact.
  • Seat Belts: Slightly stretchy webbing that elongates under violent deceleration, increasing the occupant's deceleration time and preventing hard collisions with the interior.
  • Airbags: Rapidly deployable cushions that soften head and chest deceleration, extending deceleration time and distributing the decelerating force over a broader surface area.

• Conservation of Momentum (Specification 1.27P):

  • Principle: In a closed system with no external resultant forces acting, the total momentum before a collision or explosion is strictly equal to the total momentum after the collision or explosion:     $\text{total momentum before} = \text{total momentum after}$
  • Formulation for a Two-Body Collision:$m_1 u_1 + m_2 u_2 = m_1 v_1 + m_2 v_2$
  • Where $m_1, m_2$ are the masses of the two interacting objects.
  • Where $u_1, u_2$ are initial velocities prior to interaction.
  • Where $v_1, v_2$ are final velocities following interaction.
  • Directional sign convention must be strictly assigned (e.g., motion to the right is positive; motion to the left is negative).

Newton's Third Law and Turning Effects [Paper 2 Only]

• Newton's Third Law of Motion (Specification 1.29P):

  • When body A exerts a force on body B, body B simultaneously exerts an equal and opposite force on body A.
  • Criteria for Newton's Third Law Force Pairs:
  • Must be identical in magnitude ($|F_A| = |F_B|$).
  • Must be exactly opposite in direction.
  • Must act along the same line of action.
  • Must act on two distinct, separate bodies.
  • Must be of the exact same physical type (e.g., both gravitational, both normal contact forces, or both friction).

• Moment of a Force (Specification 1.30P):

  • The moment of a force is a measure of its turning effect about a designated pivot point:     $\text{moment} = \text{force} \times \text{perpendicular distance from the pivot}$
  • Moment is measured in newton metres ($\text{Nm}$).
  • Force is measured in newtons ($\text{N}$).
  • Distance is the perpendicular distance from the line of action of the force to the pivot point, measured in metres ($\text{m}$).

• Centre of Gravity (Specification 1.31P):

  • The centre of gravity of an object is the single point through which the entire weight of the body may be considered to act.
  • For regular, uniform shapes of homogeneous density, the centre of gravity coincides with the geometric symmetry centre (centroid).

• Principle of Moments (Specification 1.32P):

  • For a system of parallel coplanar forces to be in rotational equilibrium, the sum of clockwise moments about any chosen pivot point must equal the sum of anticlockwise moments about that same pivot point:     $\sum \text{Clockwise Moments} = \sum \text{Anticlockwise Moments}$
  • For complete static equilibrium, the sum of upward forces must also equal the sum of downward forces ($\sum F_{\text{up}} = \sum F_{\text{down}}$).

• Support Forces on a Light Beam (Specification 1.33P):

  • Consider a light beam (a horizontal beam of negligible weight) supported at each end by support columns $A$ and $B$, with a heavy concentrated load of weight $W$ resting on the beam:
  • Upward equilibrium equation:       $F_A + F_B = W$
    • Where $F_A$ is the upward reaction force at support $A$.
    • Where $F_B$ is the upward reaction force at support $B$.
  • Taking moments about support $A$ for a beam of length $L$ with the load placed at distance $d$ from $A$:       $W \times d = F_B \times L$$F_B = \frac{W \times d}{L}$
  • Taking moments about support $B$:       $F_A = \frac{W \times (L - d)}{L}$
  • Behavior Under Moving Load:
  • When the load is placed directly at the midpoint ($d = \frac{L}{2}$), the upward forces share the weight equally ($F_A = F_B = \frac{W}{2}$).
  • As the heavy object shifts laterally toward support $A$ ($d \rightarrow 0$), the upward reaction force $F_A$ increases toward $W$, while the upward reaction force $F_B$ at the far support decreases toward zero.
  • As the object shifts laterally toward support $B$ ($d \rightarrow L$), the upward force $F_B$ increases toward $W$, while the upward force $F_A$ decreases toward zero.