Topic 2.2 Forces and Free-Body Diagrams: identify the forces acting on an object, represent them on a free-body diagram, and calculate the net force as the vector sum of all forces.

What this topic is asking

The College Board (Topic 2.2) wants you to identify every force acting on an object, draw a correct free-body diagram, and find the net force as the vector sum of those forces. The free-body diagram is the single most important problem-solving tool in mechanics: almost every dynamics question begins with one, and most lost marks trace back to a missing, extra, or mislabelled force.

What counts as a force

Every force has an agent, the thing exerting it. If you cannot name what is doing the pushing or pulling, it is not a real force and does not belong on a diagram. "Motion" and "inertia" are not forces; they are not exerted by anything.

Drawing a free-body diagram

The discipline of the free-body diagram is what makes it powerful: by isolating one object and drawing only the forces on it, you turn a confusing situation into a clean vector-addition problem. A good diagram labels weight ($mg$, always down), the normal force (perpendicular to the surface), friction (along the surface, opposing relative sliding), tension (along ropes), and any applied or spring force.

From forces to net force

Once the diagram is drawn, find the net force by adding the force vectors:

In practice you resolve each force into components, add the $x$-components to get $F_{net,x}$ and the $y$-components to get $F_{net,y}$, then recombine with $F_{net} = \sqrt{F_{net,x}^2 + F_{net,y}^2}$. The net force is what Newton's second law connects to acceleration: $\vec{F}_{net} = m\vec{a}$. If the net force is zero the object is in equilibrium (at rest or moving at constant velocity); if it is non-zero the object accelerates in the direction of the net force.

Why component analysis is the standard method

For forces along a single line you can add signed magnitudes directly, but as soon as a force acts at an angle (a rope pulled diagonally, a box on a ramp) you must resolve into components. The trick is to choose axes that make the problem simplest: for a flat surface use horizontal and vertical; for an inclined plane, tilt the axes so one runs along the slope and the other perpendicular to it, which lets you split gravity into a component down the slope ($mg\sin\theta$) and one into the slope ($mg\cos\theta$). Then you write one equation per axis. Keeping the two axes separate, exactly as in two-dimensional kinematics, means each becomes a manageable one-dimensional sum. The free-body diagram tells you which forces exist and which way they point; the component method turns that picture into the equations that give the acceleration. Mastering this two-step routine, diagram then components, is the backbone of every Newton's-second-law problem in the course.

Try this

Q1. A hanging lamp is held by a single vertical cord. State the two forces on the lamp and the net force if it hangs still. [2 points]

• Cue. Weight down and tension up; if still, they balance, so the net force is zero.

Q2. A $20$ N force acts right and a $12$ N force acts left on a block. Calculate the net force. [1 point]

• Cue. $20 - 12 = 8$ N to the right.