Net Force and Balanced Forces
You'll be able to calculate net force for parallel forces (qualitative).
At the 2022 Sydney to Hobart Yacht Race, Wild Oats XI experienced 35-knot winds pushing it forward while 120 kN of water drag pushed back, balanced forces kept it from flying apart.
Printable Worksheets
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Q1 · Two people push a box from opposite sides with equal force. Does it move?
Q2 · A skydiver falls at constant speed, they're not accelerating. Does that mean no forces act on them?
● Know
- Net force = sum of all forces on an object (considering direction)
- Balanced forces → no change in motion
- Unbalanced forces → change in motion
● Understand
- How to add forces in the same direction and subtract forces in opposite directions
- Why an object can be moving at constant speed with balanced forces
- How a free-body diagram represents all forces on one object
● Can do
- Calculate net force for parallel forces (qualitative)
- Draw a labelled free-body diagram for a given situation
- Predict motion from a given set of forces
When forces act in directions, you them to find the net force. When forces act in the direction, you them. If net force = zero, the forces are .
Ten people pushing on a door from both sides cancel each other out, net force = zero. But if 11 people push from one side and 10 from the other, the door moves. Net force is what's LEFT over after you add all forces up with direction.
There look like three rules for combining forces, and there is really only one. Forces are vectors, so a direction is part of the quantity, and combining them means asking how much is left over once the opposing directions have cancelled each other out.
When two forces point the same way nothing cancels, so the sizes simply add: 30 N east together with 20 N east is 50 N east. When they point in opposite directions they eat into each other, so you take the smaller from the larger and the answer keeps the direction of whichever was bigger: 30 N east together with 20 N west leaves 10 N east. When they are opposite and the same size, the cancelling is complete and nothing is left over, so 30 N east together with 30 N west gives a net force of 0 N and we call the forces balanced. Notice that "balanced" is not a fourth case; it is the second case with a leftover of zero.
| Situation | Forces | Net force | What happens |
|---|---|---|---|
| Tug of war, equal teams | 500 N left, 500 N right | 0 N | Rope stays still |
| Tug of war, one side stronger | 600 N left, 500 N right | 100 N left | Rope moves left |
| Two kids pushing a trolley forward | 30 N + 40 N forward | 70 N forward | Trolley accelerates forward |
Text description
- 1. Balanced: a rope pulled with 50 N each way. Net = 0 N; no change in velocity.
- 2. Unbalanced: a box pulled 20 N left and 25 N right. Net = 5 N right; it accelerates right.
- 3. Single force: a block pulled 10 N right. Net = 10 N right; it accelerates right.
- Net force is the sum of all forces, including their directions. All arrows use the same force scale.
- Zero net force means constant velocity, which can include being at rest. A non-zero net force changes velocity. An object can accelerate right while still moving left and slowing down.
A 50 N force acts north and a 30 N force acts south on a box. The net force is to the . The box will northward because the forces are .
When the net force on an object is zero, its forces are balanced, and the single thing that follows is that its motion does not change. That phrase is doing careful work, and the most common mistake in this whole topic is reading it as "it does not move". An object with balanced forces keeps doing exactly whatever it was already doing. If it was still, it stays still. If it was moving north at 20 km/h, it keeps moving north at 20 km/h. Scientists call this state equilibrium, and it covers both cases at once.
Three examples show the same zero producing two very different-looking outcomes. A book on a table has gravity pulling down and the normal force pushing up in equal measure, net force zero, and it stays still. A plane at cruising altitude has thrust matching drag and lift matching weight, net force zero, and it holds a steady speed at a steady height, which is anything but motionless. A skydiver at terminal velocity has gravity down matched by air resistance up, net force zero, and is falling extremely fast at a constant speed. If you find yourself wanting to say the skydiver must be slowing down, check which quantity the zero applies to: zero net force means zero change in motion, not zero motion.
When something is left over after the cancelling, the forces are unbalanced and the object's motion changes. Which of the four possible changes you see, starting to move, speeding up, slowing down or turning, depends on how the leftover force is pointing compared with the way the object is already going.
A car pulling away from the lights has an engine force larger than the drag against it, so the leftover points forward, the same way the car is heading, and it speeds up. A rocket at launch has thrust larger than its weight plus air resistance, so the leftover points upward and it accelerates off the pad. A car braking still has a leftover, but now it points backward, against the direction of travel, and a leftover pointing against the motion slows the object rather than stopping it instantly. That last one is the case worth dwelling on: the braking car is still moving forward while the net force on it points backward, which shows that the direction of the net force and the direction of travel are two different things and do not have to agree.
A free-body diagram (FBD) shows all forces acting on a single object as labelled arrows. It lets scientists and engineers visualise all forces at once.
One rule decides everything about how an FBD is drawn: it shows only the forces acting on the object you have chosen, and nothing else. Forces the object exerts on other things are left out, other objects are left out, and the object's own motion is left out. That sounds restrictive, and it is exactly what makes the diagram useful, because once only the forces on one thing are on the page, the leftover after cancelling is that thing's net force and nothing has to be untangled first. The four steps below are all consequences of that one rule.
How to draw an FBD:
- Draw the object as a simple box or dot (in the centre of your space)
- Draw arrows starting FROM the centre of the object, pointing outward in each force's direction
- Make arrow lengths proportional to force magnitudes (longer = bigger force)
- Label each arrow with the force name and magnitude (e.g. "Weight 490 N")
Australian context, surfboard FBD:
Text description
- The surfboard is drawn as a box with four force arrows.
- Buoyancy acts up; weight acts down.
- The wave pushes it forward; drag acts backward.
In this FBD: weight (down) = buoyancy (up) → balanced vertically. Wave push (forward) > drag (backward) → net force forward → surfboard accelerates toward the beach.
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1Say out loud which object the diagram is aboutEvery arrow here is a force acting on the container.Do this first, every time, because it decides what counts. The container also pulls down on the cable, and the crane pushes down on the ground, and neither of those belongs on this diagram. Skipping this step is what produces diagrams with six arrows on them, and a diagram with a force that does not act on the chosen object cannot be added up correctly no matter how careful the arithmetic is afterwards.
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2Name each force and the direction it pointsWeight, 40,000 N downward. Tension, 40,000 N upward.Name them rather than just reading the numbers, because the name tells you what could change the force later. Weight comes from gravity acting on the container's mass, so it will not change while the container is being lifted. Tension comes from the cable being stretched, so the driver can change it. Knowing which is which is what lets you answer a follow-up question like "what does the driver do to start the container moving?"
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3Compare the sizes along each line of actionUp and down are opposite, and 40,000 N equals 40,000 N, so they cancel exactly. Net force = 0 N.Compare along one line at a time. Here everything is vertical so there is only one comparison to make, and nothing is left horizontally to worry about. Equal sizes in opposite directions is the one case where the leftover is exactly nothing, which is what "balanced" means.
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4Turn zero net force into a statement about motion, carefullyThe container's motion is not changing. It is either hanging still, or moving up or down at a steady speed.This is the step where most marks are lost. A balanced diagram does not tell you the container is stationary, because a container being winched up at a steady speed has exactly this same diagram. The diagram tells you about change, and change is the only thing a net force controls. An answer that says "it is not moving" has claimed more than the evidence allows; an answer that says "it is not speeding up or slowing down" has said precisely what is known.
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5Test the reading by changing one arrowIf tension rose to 45,000 N, net force would be 5,000 N upward and the container would speed up upward.Always finish by imagining one arrow changing, because it checks that you read the diagram rather than recognised it. It also answers the practical question the crane driver actually cares about: to start a hanging load moving upward, the tension must be made larger than the weight, not merely equal to it. Once the load is moving, dropping the tension back to 40,000 N keeps it going at that steady speed.
A boat is floating still on calm water. Two forces act vertically: weight (600 N down) and buoyancy (600 N up). A small motor then switches on, pushing the boat forward with 100 N. Water drag is 60 N backward. Predict: (a) Is the boat balanced vertically? (b) What is the net horizontal force and which direction does the boat move?
How close was your prediction?
Well done, you can handle forces in two directions independently.
Key idea: treat horizontal and vertical forces separately. Each pair must be checked independently.
For each scenario, find the net force and state whether the velocity is unchanged or the direction in which the object accelerates. Do not infer its current direction or speed from force alone.
| # | Forces | Net force | What happens? |
|---|---|---|---|
| 1 | 30 N east, 30 N west | ||
| 2 | 50 N north, 20 N south | ||
| 3 | 100 N forward, 100 N forward | ||
| 4 | 80 N right, 50 N left | ||
| 5 | 200 N up (thrust), 500 N down (weight) |
In your book, draw a free-body diagram for each of these three situations. Label every force with its name and direction. Then answer the question below.
Situation A: A stationary car parked on a flat road (forces: weight down, normal force up)
Situation B: A bike accelerating forward (forces: pedalling force forward, air resistance backward, pedalling force is larger)
Situation C: A skydiver at terminal velocity (forces: gravity down, air resistance up, both equal)
Q1. Two people push a shopping trolley: person A pushes with 30 N east, person B pushes with 20 N west. (a) What is the net force? (b) Which direction does the trolley move? (2 marks)
Q2. Draw a free-body diagram of a book sitting on a table. Label all forces and explain why the book stays still. (3 marks)
Q3. Explain the difference between balanced and unbalanced forces. For each, describe what happens to an object's motion. Give one example of each. (4 marks)
Answers
▾MCQ 1
C Equal and opposite forces cancel out: 10 N − 10 N = 0 N. Net force = 0, forces are balanced. Note: "−10 N" (D) is not a valid net force magnitude, net force is always zero or a positive value with a direction stated.
MCQ 2
B Forward acceleration means a forward change in velocity and therefore a net forward force. It speeds up a forward-moving car but slows a backward-moving car. Balanced forces (A/C) would mean no change in velocity.
MCQ 3
B Terminal velocity means constant falling speed (not zero!). That constant speed only occurs when forces are balanced, gravity down = air resistance up, net force = 0. If gravity were larger (A), the skydiver would still be accelerating downward.
MCQ 4
C Arrow length shows the magnitude (size) of the force. Arrow direction shows which way the force acts. A longer arrow means a bigger force, not higher speed or greater mass.
MCQ 5
C A floating, still boat is in equilibrium. Weight (gravity) pulls it down and buoyancy pushes it up with equal force. Net force = 0, so the boat does not move. Forces are definitely present (A is wrong); they are just balanced.
Short Answer 1
Model answer: (a) 30 N east − 20 N west = net force of 10 N east. (b) The trolley moves east (in the direction of person A's push).
Short Answer 2
Model answer: FBD: draw a rectangle labelled "book", with a downward arrow labelled "Weight (gravity)" and an upward arrow of equal length labelled "Normal force". The book stays still because the two forces are equal in magnitude and opposite in direction, giving a net force of zero. With no net force, there is no change in motion, the book remains stationary (Newton's First Law preview).
Short Answer 3
Model answer: Balanced forces: net force = 0. The object's motion does not change, it stays still if at rest, or continues at the same speed and direction if moving. Example: a book on a table (gravity down = normal force up, net = 0, book stays still). Unbalanced forces: net force ≠ 0. The object's motion changes, it speeds up, slows down, starts moving, or changes direction. Example: a rocket launching (thrust > gravity + drag, net force upward, rocket accelerates upward).
Remember the hook? A plane flies at constant speed and constant altitude with four forces acting on it, yet it's not accelerating or diving. That's exactly what balanced forces look like in real life!
Now explain how balanced forces keep that plane flying level. Then do the same for a skydiver falling at constant speed, why don't they keep accelerating? Use the terms net force, balanced, gravity, and air resistance.
- Net force = total force after adding all forces with direction. Same direction: add. Opposite: subtract.
- Balanced (net = 0): no change in motion. Unbalanced (net ≠ 0): motion changes, object accelerates.
- Free-body diagrams show all forces on one object as arrows, length = magnitude, direction = which way the force acts.