Physical Sciences Paper 1: How to Solve NSC Mechanics Problems Step by Step

Mechanics is the biggest slice of NSC Physical Sciences Paper 1 — usually about 60 of the 150 marks. It also has the highest ceiling: the same learner who scores 50% on the paper as a whole can score 90% on mechanics if they follow a consistent problem-solving routine. The examiner rewards structure. Below is the exact five-step routine that maps to how the DBE marks these questions.

Step 1: Read the question twice and identify the topic

Mechanics is one of five topics, but every problem falls into one of these buckets: vertical projectile motion, Newton's laws (usually with connected bodies on inclines or with pulleys), momentum and impulse, or work-energy-power. Read the question once quickly to categorise it. Then read it again slowly to underline the given information and the unknowns.

Step 2: Draw the diagram and mark all forces

Never solve a mechanics problem without a free-body diagram. Draw the object as a dot or a box, label its mass, and draw an arrow for every force acting on it: weight ($W = mg$) pointing down, normal ($N$) perpendicular to the surface, applied force ($F$) in its stated direction, friction ($f$) opposing motion, and tension ($T$) in the rope. If the object is on an incline, redraw the axes along and perpendicular to the incline — do not fight the geometry.

The diagram earns marks. Even a rushed sketch with every force labelled is worth two marks in most Newton's laws questions.

Step 3: Choose a positive direction and stick to it

Momentum and Newton's laws problems require signed quantities. Choose a positive direction at the start of the problem — usually the direction of initial motion or the direction of the applied force — and stick to it for every equation. If an object is moving to the right and you have chosen right as positive, a velocity of $-3$ m·s$^{-1}$ means it is now moving to the left. Learners lose marks by dropping the negative sign in the answer.

Step 4: Apply the correct law

The equations you will need are short:

• Newton's second law: $F_{net} = ma$. Sum the forces along the direction of motion.
• Newton's third law: action-reaction pairs. The examiner loves to ask you to name the reaction force and its point of application.
• Conservation of momentum: $p_{before} = p_{after}$. Only true when the system is isolated (no external forces).
• Impulse-momentum theorem: $F\Delta t = \Delta p$. Use this when a force is applied over a short time — collisions, catches, kicks.
• Work-energy theorem: $W_{net} = \Delta E_k$. The net work done on an object equals its change in kinetic energy.
• Conservation of mechanical energy: $E_{mech,i} = E_{mech,f}$. Only true when non-conservative forces (friction, applied force) do no work.
• Equations of motion: $v = u + at$, $v^2 = u^2 + 2as$, $s = ut + \frac{1}{2}at^2$. Use only when acceleration is constant. In vertical projectile motion, $a = -9.8$ m·s$^{-2}$ if you choose up as positive.

Step 5: Answer the whole question, not just the calculation

Grade 12 mechanics questions almost always end with an explanation: "Explain, using the concept of impulse, why airbags reduce injury." Write two sentences using the correct terminology from the CAPS document. In this case: "The airbag increases the time of contact ($\Delta t$). Because $F\Delta t = \Delta p$ and the change in momentum is fixed, a larger $\Delta t$ gives a smaller force $F$, reducing injury." That earns you three marks and takes 30 seconds.

Worked example: connected bodies

Two blocks are connected by a light inextensible string over a frictionless pulley. Block A (5 kg) hangs vertically. Block B (3 kg) sits on a horizontal frictionless surface. Calculate the acceleration of the system and the tension in the string.

Step 1: identify — Newton's second law with connected bodies. Step 2: draw the free-body diagrams. Block A has weight $W_A = 5 \times 9.8 = 49$ N down and tension $T$ up. Block B has tension $T$ to the right and no friction. Step 3: positive direction — the direction the system will accelerate. Block A pulls down, so positive is down for A and to the right for B. Step 4: apply. For A: $F_{net,A} = m_A a \Rightarrow 49 - T = 5a$. For B: $F_{net,B} = m_B a \Rightarrow T = 3a$. Add the equations: $49 = 8a \Rightarrow a = 6.125$ m·s$^{-2}$. Substitute back: $T = 3 \times 6.125 = 18.4$ N. Step 5: answer with units — $a = 6.13$ m·s$^{-2}$ and $T = 18.4$ N. Round to three significant figures. Full marks.

Vertical projectile motion

Every vertical projectile question tests the same three skills: reading a position-time or velocity-time graph, calculating maximum height or time of flight, and describing the direction of the velocity and acceleration during flight. Two facts save marks: the acceleration is always $-9.8$ m·s$^{-2}$ (downward) throughout the motion, even at the highest point; and at the highest point the velocity is zero but the acceleration is not.

Practise sketching velocity-time and position-time graphs from a described motion. In the November papers, graph sketching accounts for about eight marks and can be picked up almost for free if you have practised.

Momentum and collisions

Two objects collide and stick together — this is an inelastic collision. Momentum is conserved but kinetic energy is not. Two objects collide and bounce off — momentum is conserved and you may or may not have to check kinetic energy. Two objects collide and both come to rest — momentum is only conserved if they were moving in opposite directions and the total momentum was zero.

Write the momentum equation with the correct signs first, then solve. If you get a negative velocity, the object moves in the opposite direction to your chosen positive.

Revision plan

Spend three sessions a week on mechanics for the month before the exam. Session 1: Newton's laws with inclines and connected bodies. Session 2: vertical projectile motion. Session 3: momentum and impulse plus work-energy. Do one full mechanics section from a past paper in each session and mark it with the memo. By the second week the routine above will feel automatic.