What you'll learn
Mechanics forms the foundation of CXC CSEC Physics and accounts for approximately 30% of Paper 02. This topic examines how objects move, the forces that cause motion, energy transformations, and the conditions for equilibrium. Mastery of mechanics is essential because concepts learned here connect to every other physics topic and appear in both structured questions and multiple-choice items.
Key terms and definitions
Displacement — the straight-line distance from the starting point to the final position, measured in a specified direction (a vector quantity measured in metres).
Velocity — the rate of change of displacement; speed in a specified direction (vector quantity, measured in m/s).
Acceleration — the rate of change of velocity (vector quantity, measured in m/s²).
Momentum — the product of mass and velocity (p = mv), measured in kg m/s or N s.
Newton — the SI unit of force; one newton produces an acceleration of 1 m/s² when applied to a mass of 1 kg.
Work done — the energy transferred when a force moves an object through a distance (W = Fd cos θ), measured in joules.
Power — the rate of doing work or transferring energy (P = W/t), measured in watts.
Principle of Conservation of Momentum — in a closed system where no external forces act, the total momentum before a collision equals the total momentum after the collision.
Core concepts
Linear motion and equations of motion
CXC CSEC Physics tests your ability to distinguish between scalar and vector quantities. Scalars have magnitude only (distance, speed, mass, time, energy), while vectors have both magnitude and direction (displacement, velocity, acceleration, force, momentum).
The equations of motion apply to objects moving with constant acceleration:
- v = u + at
- s = ut + ½at²
- v² = u² + 2as
- s = (u + v)t / 2
Where: u = initial velocity, v = final velocity, a = acceleration, t = time, s = displacement.
When solving motion problems, always establish a positive direction. For objects moving under gravity near Earth's surface, use a = 9.8 m/s² or 10 m/s² (depending on question requirements). Objects thrown upward decelerate at 10 m/s² until reaching maximum height where v = 0, then accelerate downward at 10 m/s².
Distance-time graphs show position on the vertical axis and time on the horizontal axis. The gradient equals speed. Horizontal lines indicate the object is stationary. Curved lines indicate changing speed.
Velocity-time graphs show velocity on the vertical axis. The gradient equals acceleration. The area under the graph equals displacement. Horizontal lines indicate constant velocity (zero acceleration).
Force, mass and Newton's Laws
Newton's First Law states that an object remains at rest or moves with constant velocity unless acted upon by a resultant force. This property is called inertia. A moving bus in Kingston continues forward even when brakes are applied; passengers lurch forward because their bodies tend to maintain constant velocity.
Newton's Second Law: The resultant force equals the product of mass and acceleration (F = ma). This relationship is fundamental to CXC questions. When multiple forces act on an object, calculate the resultant force by vector addition. If forces act along the same line, add forces in one direction and subtract forces in the opposite direction.
Newton's Third Law: When object A exerts a force on object B, object B exerts an equal and opposite force on object A. These action-reaction pairs act on different objects. When a cricketer hits a ball at the Queen's Park Oval, the bat exerts a force on the ball (causing it to accelerate), and the ball exerts an equal force on the bat (felt by the batsman as impact).
Weight is the gravitational force acting on a mass (W = mg). On Earth's surface, g = 9.8 m/s² or 10 m/s². A 60 kg student has a weight of 600 N. Weight is a force (vector, measured in newtons); mass is a scalar measured in kilograms and remains constant regardless of location.
Friction opposes motion between surfaces. Static friction prevents motion initially; once motion begins, kinetic friction acts. Friction depends on surface roughness and the normal reaction force. Friction converts kinetic energy to thermal energy.
Momentum and collisions
Momentum (p = mv) is a vector quantity. Exam questions commonly test conservation of momentum in collisions and explosions. In a closed system with no external forces, total momentum before equals total momentum after.
For two objects colliding: m₁u₁ + m₂u₂ = m₁v₁ + m₂v₂
Elastic collisions conserve both momentum and kinetic energy. Inelastic collisions conserve momentum but kinetic energy decreases (converted to heat, sound, deformation). Perfectly inelastic collisions occur when objects stick together after impact.
Impulse equals the change in momentum (Impulse = Δp = FΔt). A larger time interval reduces the force required to produce the same momentum change. Vehicles in Trinidad use crumple zones that increase collision time, reducing forces on passengers. A cricketer pulls their hands back when catching to increase contact time and reduce impact force.
Work, energy and power
Work done occurs when a force moves an object in the direction of the force. W = Fd cos θ, where θ is the angle between force and displacement. When force and displacement are parallel, W = Fd. Work is measured in joules (J).
If a force acts perpendicular to motion (like centripetal force in circular motion), no work is done because cos 90° = 0.
Kinetic energy is the energy possessed by a moving object: KE = ½mv². Doubling speed quadruples kinetic energy. A loaded truck traveling at 30 m/s on the Solomon Hochoy Highway has significantly more kinetic energy than a car at the same speed due to greater mass.
Gravitational potential energy is the energy stored when an object is raised in a gravitational field: GPE = mgh, where h is the vertical height above a reference point.
Principle of Conservation of Energy: Energy cannot be created or destroyed, only transformed from one form to another. Total energy in a closed system remains constant.
In a falling object with no air resistance: GPE lost = KE gained mgh = ½mv²
Power measures the rate of energy transfer: P = W/t or P = Fv. A more powerful engine transfers energy more quickly. Power is measured in watts (W) or joules per second.
Equilibrium and moments
An object is in equilibrium when:
- The resultant force in any direction equals zero (no linear acceleration)
- The resultant moment about any point equals zero (no rotational acceleration)
A moment (or torque) is the turning effect of a force about a pivot point. Moment = Force × perpendicular distance from pivot (measured in N m).
Moment = Fd
The Principle of Moments states that for an object in equilibrium, the sum of clockwise moments equals the sum of anticlockwise moments about any point.
Σ(clockwise moments) = Σ(anticlockwise moments)
Centre of gravity is the point where the entire weight of an object appears to act. For uniform symmetrical objects, the centre of gravity is at the geometric centre. An object remains stable when a vertical line from its centre of gravity falls within its base. The bauxite cranes used in Jamaica have wide bases and low centres of gravity to prevent toppling when lifting heavy loads.
Circular motion and centripetal force
An object moving in a circle at constant speed is accelerating because velocity (a vector) constantly changes direction. Centripetal acceleration acts toward the centre of the circle.
Centripetal force is the resultant force directed toward the centre that keeps an object moving in a circular path. This force can be provided by tension (satellite on a string), friction (car turning), or gravity (planets orbiting).
For a car navigating a roundabout in Bridgetown, friction between tyres and road provides the centripetal force. If speed is too high or the road is wet (reducing friction), the car skids outward tangentially.
Worked examples
Example 1: Equations of motion
A minibus traveling through Port of Spain accelerates uniformly from rest to 15 m/s in 6.0 seconds. Calculate: (a) the acceleration (b) the distance traveled during this time
Solution:
(a) Using v = u + at
- u = 0 m/s (from rest)
- v = 15 m/s
- t = 6.0 s
- 15 = 0 + a(6.0)
- a = 15 ÷ 6.0 = 2.5 m/s² [1 mark for substitution, 1 mark for answer with unit]
(b) Using s = ut + ½at²
- s = 0(6.0) + ½(2.5)(6.0)²
- s = 0 + 0.5 × 2.5 × 36
- s = 45 m [1 mark for correct equation, 1 mark for answer with unit]
Alternative method using v² = u² + 2as:
- 15² = 0² + 2(2.5)s
- 225 = 5s
- s = 45 m
Example 2: Conservation of momentum
A 0.50 kg coconut falls from a tree and strikes a stationary 2.0 kg bucket on the ground at 8.0 m/s. The coconut remains in the bucket. Calculate the velocity of the bucket and coconut immediately after impact.
Solution:
Total momentum before = Total momentum after [1 mark for stating principle]
m₁u₁ + m₂u₂ = (m₁ + m₂)v [1 mark for correct equation]
- m₁ = 0.50 kg, u₁ = 8.0 m/s (downward)
- m₂ = 2.0 kg, u₂ = 0 m/s (bucket initially at rest)
0.50(8.0) + 2.0(0) = (0.50 + 2.0)v
4.0 = 2.5v [1 mark for substitution]
v = 4.0 ÷ 2.5 = 1.6 m/s downward [1 mark for numerical answer, 1 mark for direction]
Example 3: Moments and equilibrium
A uniform plank of length 4.0 m and weight 80 N is supported at its centre. A load of 120 N is placed 1.2 m from one end. Calculate the distance from the pivot where a 60 N force must be applied on the opposite side to balance the plank.
Solution:
For equilibrium, clockwise moments = anticlockwise moments [1 mark]
The plank's weight acts at its centre (the pivot), so produces no moment.
Distance of 120 N load from pivot = 2.0 - 1.2 = 0.8 m [1 mark]
Let distance of 60 N force from pivot = d
Clockwise moment = 120 × 0.8 = 96 N m [1 mark]
Anticlockwise moment = 60 × d [1 mark]
96 = 60d
d = 96 ÷ 60 = 1.6 m [1 mark for answer with unit]
Common mistakes and how to avoid them
Confusing mass and weight — Mass is measured in kilograms and is constant everywhere. Weight is a force measured in newtons (W = mg) and varies with gravitational field strength. Always use W = mg to convert between them.
Neglecting direction in vector calculations — When using equations of motion or conservation of momentum, establish a positive direction and consistently apply signs. An object moving upward might have positive velocity; when moving downward, velocity is negative.
Using the wrong equation of motion — The four equations apply only to constant acceleration. Carefully identify which quantities are given and which you need to find. If time is not given and not required, use v² = u² + 2as.
Forgetting to convert units — CXC questions may give speeds in km/h or cm/s. Always convert to m/s before substituting into equations. Distance in centimetres must become metres. Mass in grams must become kilograms.
Calculating moments incorrectly — The distance used in moment calculations is the perpendicular distance from the line of action of the force to the pivot. If a force acts at an angle, resolve it into components or use the perpendicular distance.
Mixing up kinetic energy and momentum — Both depend on mass and velocity but have different relationships. KE = ½mv² (scalar, depends on v²). Momentum = mv (vector, depends on v). They have different units and conservation laws apply in different situations.
Exam technique for Mechanics
Command words matter — "Calculate" requires numerical work with units. "Explain" needs physics principles applied to the context. "State" needs brief factual recall. "Describe" requires a sequence of points without detailed explanation. Each command word signals specific marking requirements.
Show full working — Structured questions typically award method marks even if the final answer is incorrect. Write the equation, substitute values with units, then calculate. This approach secures partial credit. Equations given in the CXC formula sheet can be used directly; state the equation first.
Unit discipline earns marks — Final answers without correct SI units lose marks. Include units at each calculation stage to track dimensional consistency. Force is always in newtons, not kg m/s² (unless specifically required).
Multi-part questions build logically — Part (a) often provides values needed for part (b). If you cannot complete an earlier section, use given values or reasonable estimates to attempt later parts. Examiners award marks for correct method regardless of earlier errors (error carried forward marking).
Quick revision summary
Mechanics covers motion (equations: v = u + at, s = ut + ½at², v² = u² + 2as), forces (F = ma, W = mg), momentum (p = mv, conserved in closed systems), energy (KE = ½mv², GPE = mgh, conservation principle), work (W = Fd), power (P = W/t), and equilibrium (resultant force = 0, clockwise moments = anticlockwise moments). Distinguish vectors from scalars. Use graphs to analyze motion. Apply Newton's three laws. Calculate moments as force × perpendicular distance. Remember centripetal force acts toward the centre in circular motion. Always include units and show working for maximum marks.