A.2.4—Resultant force from diagrams

Add force components

The resultant force is the vector sum of all forces on the chosen body:

$\vec F_{net}=\sum\vec F$

Resolve angled forces into perpendicular components before adding.

Connect to acceleration

For constant mass, apply Newton’s second law along each axis:

$\sum F_x=ma_x,\qquad \sum F_y=ma_y$

Use equilibrium correctly

If the resultant force is zero, acceleration is zero, but the object may still have constant non-zero velocity. A balanced vertical component does not imply every force is absent.

Common trap

Do not add force magnitudes without their directions. A component that balances another contributes zero only along the same axis.

How it is assessed

The evidence asks for the acceleration of a truck from a tension diagram, rewarding the correct component equation and trigonometric interpretation.

Command terms

Determine / Calculate

What earns marks

Resolve the angled tension or other force into components, identify the component that produces acceleration, and apply $F=ma$. Keep the component angle tied to the diagram; a complementary angle changes sine to cosine.

Watch for

Using the total tension rather than its horizontal component, or using sine/cosine for the wrong angle shown in the diagram.

Representative question

[Maximum number: 2]

Determine the acceleration of the truck.

$\begin{aligned} T \sin 30^{\circ}=m a \text { OR } T \cos 30^{\circ}=m g a=g \tan 30^{\circ}=5.66 \approx 5.7 \mathrm{~m} \mathrm{~s}^{-2} \end{aligned}$

Accept reversed trig functions if $60^{\circ}$ used.

Award [2] for CNA

[2]

Build the force model

Choose the system, draw a labelled free-body diagram, classify the interactions and resolve components. Apply Newton’s laws with the correct boundary: contact forces, field forces, friction, tension, buoyancy and restoring forces each have their own direction and conditions.

Track momentum

Use $ec p=m ec v$ , $ec J=\Delta ec p$ and momentum conservation only after checking external impulse. Distinguish elastic and inelastic collisions, explosions and energy transfer.

Track circular motion

The inward resultant provides $a_c=v^2/r=\omega^2r$ . It may come from tension, gravity, normal, friction or a field force. Angular and linear descriptions are linked by $v=\omega r=2\pi r/T$ .

Final checks

Ask: Which body is the system? Which forces are external? Is mass constant? Is acceleration uniform or radial? Is kinetic energy conserved, transferred or increased?

A.2.4—Resultant force from diagrams

Find the Resultant Force from a Diagram

A.2.4 Exam Analysis

Assessment in practice

Retrieve the A.2 Forces and Momentum Model

Question 1