Balanced Forces and Net Force Direction

Welcome back! In the previous lesson, you identified forces by asking what acts on an object and where each force comes from. Now you can ask a second question: Do those forces cancel, or is there an overall push in some direction?

This lesson introduces the net force, also called the resultant force. You’ll use force arrows and simple comparisons to decide whether forces are balanced and to state the direction of any net force. That will set up the next lesson, where you’ll examine what a net force means for an object’s motion.

One object, several forces, one overall result

Imagine a box on a table. Earth pulls the box downward, while the table pushes it upward. Both forces act on the box, even though they come from different sources. To find their overall effect, you must consider their sizes and directions together.

The net force is the overall force obtained by combining all the forces on the chosen object. Forces pointing in the same direction add. Forces pointing in opposite directions work against one another. If equal forces oppose each other, their overall effect in that direction is zero: they are balanced.

Watch how the force arrows change as forces are added to an object in this short video.

An arrow points in the direction of a force; a longer arrow can represent a larger force. But a net-force arrow is a summary of the forces, not one more force to add to the diagram. Keep that distinction in mind when looking at the illustrations below.

Finding the net force along one line

Suppose two people push a wheeled box to the right, one with $20\mathrm{N}$ and the other with $10\mathrm{N}$. Their forces reinforce each other, giving a net force of $30\mathrm{N}$ to the right. If instead one pushes right with $20\mathrm{N}$ and the other pushes left with $10\mathrm{N}$, the net force is $10\mathrm{N}$ to the right. The larger opposing force determines the direction.

Read the short “Resultant forces” section for diagrams of both arrangements.

For forces along a single line, this gives you a reliable method:

1. Add forces pointing one way; do the same for forces pointing the opposite way.
2. Compare the two totals. Equal totals mean a zero net force in that direction.
3. If the totals differ, subtract the smaller from the larger and state the direction of the larger total.

For example, a $14\mathrm{N}$ push to the left and a $14\mathrm{N}$ push to the right are balanced: the net force is $0\mathrm{N}$, with no direction. A $14\mathrm{N}$ push left against $9\mathrm{N}$ right gives a net force of $5\mathrm{N}$ to the left. Saying only “$5\mathrm{N}$” leaves out part of the answer.

If the sizes are not given, you can still reason qualitatively when it is clear which force is larger. If you only know that there are opposing forces—not how they compare—you cannot yet tell whether they balance.

Balanced does not mean “no forces”

Return to the box on the table. Suppose its weight is $100\mathrm{N}$ downward and the table’s upward support force is $100\mathrm{N}$. These forces balance, so the net force on the box is zero. Neither force has disappeared.

A stationary box is a familiar example of balanced forces, but being stationary is not the definition of balanced. An object moving steadily in a straight line can also have a zero net force. Read the two examples in the next part of the BBC Bitesize article, paying particular attention to the moving car.

The car example helps guard against a common mistake: a force in the direction of travel does not automatically mean there is a net force in that direction. You must also account for opposing forces. Likewise, you cannot decide that forces are balanced merely because two arrows appear in a diagram; their magnitudes must match.

Check every direction acting on the object

Forces on an object need not all lie on the same line. Consider a box being pushed across a level floor. Earth pulls down and the floor pushes up; a person pushes right and friction acts left. You can compare the vertical forces with each other, then compare the horizontal forces with each other.

Suppose the floor pushes up with $30\mathrm{N}$ and Earth pulls down with $30\mathrm{N}$. Vertically, the forces balance. If the person pushes right with $12\mathrm{N}$ while friction acts left with $8\mathrm{N}$, there is a net force of $4\mathrm{N}$ to the right. The forces on the box are unbalanced overall, despite being balanced vertically.

An upward force does not cancel a rightward force: they point in different directions. For forces to be balanced overall, they must leave no net force in any direction. If an object has a remaining upward force as well as a remaining rightward force, its net force points up and to the right. You do not need to calculate that diagonal force’s size here.

A launching rocket provides a simpler case in which the opposing forces lie along one vertical line:

The upward thrust is larger than the downward weight, so the forces are unbalanced and the net force points upward. The subtraction tells you its size; comparing the directions tells you where it points. In a more complete description of a real rocket, other forces might also matter. Always use the forces specified for the situation you are analysing.

Key takeaways

To decide whether forces are balanced, choose one object and combine all the forces on it, accounting for both size and direction. A zero net force means the forces are balanced and the net force has no direction. If they do not balance, state the net force’s direction as well as its size when the size is known. Check horizontal and vertical forces separately before deciding whether the object’s forces are balanced overall.

You can now determine the direction of an overall force without assuming it matches the object’s current direction of travel. Next, you’ll use that distinction to predict how an object’s motion changes.