Balanced and unbalanced forces

Push a stalled car and nothing happens if a friend pushes back equally hard from the other side — yet the same push sends the car rolling the moment that opposing push weakens. The difference between "nothing changes" and "it starts moving" is entirely about whether the forces on the car are balanced or unbalanced. This idea opens the CBSE Class 9 chapter Force and Laws of Motion, right after the "Motion" chapter described how things move without ever asking why. Here you learn that a force can change an object's speed, its direction, or its shape, and that what actually decides an object's fate is not any single force but the net force — the combined, left-over effect once all the forces acting on it are added along a line. Get this right and Newton's First Law, which comes next, will feel like common sense rather than a rule to memorise.

The core insight

Forces on a body are balanced when they add to a net force of zero, leaving its state of rest or motion unchanged, and unbalanced when a net force remains, which changes its speed or direction.

The core idea

A force is a push or a pull, and it can do up to three things to the object it acts on: change its speed, change its direction, or change its shape (squeezing a rubber ball, stretching a spring). When more than one force acts on the same body at once, none of them decides its fate alone — only their combined, net (resultant) effect matters. Class 9 keeps this strictly to forces acting along one straight line (collinear forces), so "combining" forces is simple sign arithmetic: forces pointing the same way add, forces pointing opposite ways subtract.

F_{net} = F_1 + F_2 + \cdots

where: $F_{net}$ is the net (resultant) force on the body, and each $F_i$ is one of the individual forces acting along the same line, taken as positive in a chosen direction and negative in the opposite direction.

Balanced forces are a set of collinear forces whose net is zero, $F_{net} = 0$ . A body at rest under balanced forces stays at rest; a body already moving continues at the same speed along the same straight line. Balanced forces can still change an object's shape even though they cannot start, stop, speed up, slow down, or turn it — two equal and opposite pulls on a spring stretch it without moving it anywhere.

Unbalanced forces are a set whose net is not zero, $F_{net} \neq 0$ . This leftover force is what changes the body's speed, its direction, or both — in short, it changes the body's state of rest or motion. A classic illustration is a tug of war: while both teams pull equally hard, the rope stays put (balanced); the instant one team pulls harder, a net force appears and the rope moves toward the stronger side. There is no separate formula for "how fast" an unbalanced force changes motion at this stage — that step needs Newton's Second Law, $F = ma$ , which builds directly on the idea introduced here.

Figure

A wooden block on a table with two equal opposing arrows on the left showing balanced forces and the same block on the right with a longer arrow overpowering a shorter one showing an unbalanced net force to the right

Derivation AFinding the net force on a body from collinear pushes and pulls

The goal is to show, starting only from the idea that forces along the same line add with sign, exactly how to combine any number of collinear forces into a single net force and read off from that number alone whether the body's motion will change — the reasoning every balanced-versus-unbalanced question in this chapter reduces to.

Step 1. Fix a positive direction. Before combining anything, choose one direction along the line of action as positive (commonly "the direction the body is pushed or already moving") and treat every force in that direction as positive, every force opposing it as negative. This choice is arbitrary but must stay fixed for the whole problem.

Step 2. List every force acting on the body along that line, with its correct sign. A push of $15\ \text{N}$ to the right and a friction force of $15\ \text{N}$ to the left become $+15\ \text{N}$ and $-15\ \text{N}$ once the rightward direction is chosen as positive.

Step 3. Add the signed forces to get the net force, $F_{net} = F_1 + F_2 + \cdots$ . Because the signs already encode direction, this single sum captures both the size and the direction of the combined effect — no separate direction bookkeeping is needed once Step 1 is fixed.

Step 4. Interpret the sign and size of $F_{net}$ . If $F_{net} = 0$ , the forces are balanced and the body's state of rest or motion is unchanged. If $F_{net} \neq 0$ , the forces are unbalanced, and the body's speed or direction changes in the direction of $F_{net}$ — the larger $|F_{net}|$ , the more forcefully that change occurs (exactly how much is the job of Newton's Second Law, not this chapter).

Worked example

A crate is being dragged along rough ground. Two workers pull it to the right with forces of $18\ \text{N}$ and $10\ \text{N}$ , while friction from the ground acts on it to the left with a force of $22\ \text{N}$ . Find the net force on the crate, state whether the forces are balanced or unbalanced, and describe what happens to its motion.

Step 1 — choose the positive direction and list the forces. Take rightward as positive. Pull 1 $= +18\ \text{N}$ , pull 2 $= +10\ \text{N}$ , friction $= -22\ \text{N}$ .

Step 2 — add the pulling forces first. The two workers pull in the same direction, so their forces add: $18\ \text{N} + 10\ \text{N} = 28\ \text{N}$ to the right.

Step 3 — combine with friction to get the net force. $F_{net} = 28\ \text{N} - 22\ \text{N} = 6\ \text{N}$ , directed to the right.

Step 4 — interpret. Since $F_{net} = 6\ \text{N} \neq 0$ , the forces are unbalanced. If the crate was at rest, it will start moving to the right; if it was already moving right, it will speed up in that direction. The net force on the crate is 6 N to the right, so the forces are unbalanced and the crate accelerates rightward.

Competitive stretch

If a third worker joins in and pulls with $6\ \text{N}$ to the left (opposing the other two), the net force becomes $28\ \text{N} - 22\ \text{N} - 6\ \text{N} = 0\ \text{N}$ : the forces are now exactly balanced, and the crate — however it was moving before this new pull was added — continues in that same state, at rest if it was at rest, or at the same rightward speed if it was already moving.

Common traps

Thinking "no motion" always means "no forces act" — a crate sitting still on the ground has weight pulling down and a support force pushing up; these are balanced, not absent.
Believing balanced forces can never do anything — they cannot change speed or direction, but two equal, opposite pulls can still stretch or squeeze an object's shape.
Assuming a moving body needs a constant unbalanced force just to keep moving at the same speed — with the net force zero, a moving body simply keeps going at that same speed in a straight line, no extra push required.
Confusing "equal forces" with "balanced forces" — forces are balanced only when equal-magnitude forces act along the same line in opposite directions; equal forces pointing the same way simply add together into a larger net force.

Ask the tutor: Unsure whether a specific everyday situation — like a lift moving at constant speed, or a ball slowing to a stop — counts as balanced or unbalanced forces? Ask the AI tutor to work through it force by force.

If a book on a table is not moving, does that mean no forces are acting on it?

No — two forces act on it at all times: its weight pulling down and the table's support force pushing up. These are equal in size and opposite in direction, so they are balanced and their net force is zero. Balanced does not mean absent; it means the forces cancel out so the state of motion (here, staying at rest) does not change. If you removed the table, the weight alone would be unbalanced and the book would fall.

Why doesn't a car moving at a constant speed on a straight, flat road need a net force to keep going?

Because "constant speed in a straight line" is exactly the condition Newton's First Law describes when the net force is zero. The engine's driving force is balanced by resistive forces like friction and air resistance, so the two cancel and the car's state of motion (steady speed, straight line) does not change. If the driver presses the accelerator harder, the driving force becomes larger than the resistive forces, the net force becomes unbalanced, and the car speeds up.

How do I know which direction to call positive when adding several forces?

It does not matter which direction you pick, as long as you pick one direction as positive, stay consistent for every force in that problem, and give every force pointing the opposite way a negative sign. The net force you calculate will come out with the correct sign either way — if you chose rightward as positive and the true net force points left, your answer will simply appear as a negative number, which you then read back as "net force to the left."

Balanced and unbalanced forces

The core idea

Worked example

Competitive stretch

Common traps

Before this

Where this leads