Balanced and Unbalanced Forces: Who Wins the Tug of War?
Hi there, young scientist! In a tug of war on sports day, sometimes the rope hardly moves, and sometimes one team suddenly drags the other across the line. Why? It depends on whether the forces are balanced or unbalanced. You will draw forces as arrows, add them up to find the net force, and use it to predict whether an object stays still, cruises steadily, speeds up, slows down or turns. These ideas explain everything from a book on your desk to a skydiver on a parachute!
1. Showing Forces with Arrows
Quick recap: a force is a push or a pull, measured in newtons (N) (types of force are covered in the chapter Force). Every force has:
1. Size (magnitude) – how strong it is, e.g. 20 N.
2. Direction – which way it acts, e.g. to the left or upwards.
How to draw a force arrow
Length shows the size: a longer arrow means a bigger force.
Arrowhead shows the direction.
Tail starts on the object, where the force acts.
Label gives the name and size, e.g. "friction 10 N".
A force diagram described in words
Imagine a box drawn as a square. A 3 cm arrow points right from the box, labelled "push 30 N". A 1 cm arrow points left, labelled "friction 10 N". With the same scale for every arrow, 1 cm represents 10 N, so the push arrow is three times as long.
Key takeaway: A force arrow shows size (length) and direction (arrowhead). Label it with the force's name and its value in newtons.
2. Net Force: Adding Up the Forces
Objects often have several forces acting at once. The net force (also called the resultant force) is the single overall force that has the same effect as all the forces together. Here we only look at forces along one straight line (left–right or up–down).
Rule 1: Same direction – ADD
Forces in the same direction add up, and the net force acts in that direction.
Example: Two friends push a trolley to the right with 30 N and 20 N.
\(\text{net force} = 30\ \text{N} + 20\ \text{N} = 50\ \text{N}\) to the right.
Rule 2: Opposite directions – SUBTRACT
For forces in opposite directions, take the bigger minus the smaller. The net force acts in the direction of the bigger force.
Example: A trolley is pushed with 50 N to the right, and friction acts with 30 N to the left.
\(\text{net force} = 50\ \text{N} - 30\ \text{N} = 20\ \text{N}\) to the right.
Rule 3: Equal and opposite – ZERO
Two opposite forces of the same size cancel out: \(40\ \text{N} - 40\ \text{N} = 0\ \text{N}\). The net force is zero.
Three or more forces
Group the forces by direction, add up each group, then subtract the smaller total from the bigger total.
Worked example – tug of war: Team Red pulls left with 200 N, 150 N and 250 N. Team Blue pulls right with 180 N, 220 N and 160 N.
Left: \(200 + 150 + 250 = 600\ \text{N}\)
Right: \(180 + 220 + 160 = 560\ \text{N}\)
Net force: \(600\ \text{N} - 560\ \text{N} = 40\ \text{N}\) to the left. Team Red is winning!
Memory aid: "Same way, add away; opposite way, take away."
Key takeaway: The net force is the overall force on an object. Add forces in the same direction, subtract opposite ones, and always give both size and direction.
3. Balanced Forces: Net Force Is Zero
Forces are balanced when they cancel out, so the net force is zero. Balanced forces do not change an object's motion:
1. An object at rest stays at rest.
2. A moving object keeps moving at a constant speed in a straight line.
So balanced forces do not mean "not moving". They mean "no change in motion".
Example 1: A book on a table
Two forces act on a book resting on your desk:
Its weight (force of gravity), 5 N downwards.
The normal force from the table, 5 N upwards.
The force diagram shows a down arrow and an up arrow of equal length. \(5\ \text{N} - 5\ \text{N} = 0\ \text{N}\), so the forces are balanced and the book stays at rest.
Example 2: An evenly matched tug of war
Both teams pull with 500 N in opposite directions. The net force on the rope is zero, so it stays still, however hard everyone pulls!
Example 3: A car cruising at a steady speed
A car travels along a straight, level road at a steady 80 km/h. The driving force acts forwards; friction and air resistance act backwards. When they are equal, the forces are balanced, so the car keeps moving at a constant speed in a straight line. It is moving, but its motion is not changing.
Did you know? On an MTR train running straight at a steady speed, you can hardly feel yourself moving, because the forces on you are balanced. You only sway when the train speeds up, slows down or turns, as the forces become unbalanced!
Key takeaway: Balanced forces give zero net force, so the motion stays exactly the same.
4. Unbalanced Forces: Net Force Is Not Zero
Forces are unbalanced when they do not cancel out, so the net force is not zero. Unbalanced forces change an object's motion. The object may:
1. Start moving or speed up – net force in the same direction as the motion.
2. Slow down (or stop) – net force opposite to the motion.
3. Change direction – net force acting from the side.
Speeding up: a car pulling away
The light turns green. The driving force is 3000 N forwards; friction and air resistance total 1000 N backwards.
\(\text{net force} = 3000\ \text{N} - 1000\ \text{N} = 2000\ \text{N}\) forwards.
The net force is in the direction of motion, so the car speeds up (accelerates).
Slowing down: a car braking
The driver brakes at a red light. The engine stops pushing, and the brakes add a large backward friction force, say 4000 N in total.
The net force is 4000 N backwards, opposite to the motion, so the car slows down (decelerates) until it stops.
Changing direction
A football rolls towards the goal and a player kicks it from the side. The sideways net force makes it change direction. Likewise, a sideways force between the tyres and the road turns a bus at a corner. Even at the same speed, a change of direction is a change in motion.
Bigger net force, bigger change: a strong kick changes a ball's motion more quickly than a gentle tap.
Memory aid: "Zero net force, zero change. Some net force, some change!"
Key takeaway: Unbalanced forces give a non-zero net force that changes the motion: speeding up, slowing down or changing direction, in the direction of the net force.
5. The Skydiver: Balanced and Unbalanced Forces in One Jump
Two forces act on a skydiver: weight downwards and air resistance upwards. Weight stays the same, but air resistance gets bigger as the skydiver moves faster (see the chapter Friction and air resistance).
Stage 1: Just after jumping
The skydiver is slow, so air resistance is small. Weight is bigger, so the net force is downwards and the skydiver speeds up.
Stage 2: Falling faster
Air resistance grows with speed, so the downward net force gets smaller. The skydiver still speeds up, but more and more slowly.
Stage 3: A steady speed
Air resistance becomes equal to weight. The net force is zero, the forces are balanced, and the skydiver falls at a constant speed, called the terminal velocity.
Stage 4: The parachute opens
The parachute's huge surface area makes air resistance much bigger than weight. The net force is now upwards. The skydiver is still moving down, but slows down.
Stage 5: A new, slower steady speed
As the skydiver slows, air resistance falls until it equals weight again. The forces are balanced once more, giving a new, much lower constant speed for a safe landing.
Worked example: A skydiver's weight is 700 N. Just after the parachute opens, air resistance is 1200 N.
\(\text{net force} = 1200\ \text{N} - 700\ \text{N} = 500\ \text{N}\) upwards, so the skydiver slows down. Later, air resistance drops to 700 N: \(700\ \text{N} - 700\ \text{N} = 0\ \text{N}\), so the speed is steady.
Did you know? A skydiver falling belly-down reaches a steady speed of roughly 200 km/h. With the parachute open, the downward speed drops to roughly 20 km/h!
Key takeaway: When the parachute opens, the net force points upwards, but the skydiver does not fly up; they just slow down. A steady speed always means balanced forces.
6. Predicting Motion: A Step-by-Step Method
Use these three steps for any forces-and-motion question:
Step 1 – List every force on the object and its direction.
Step 2 – Calculate the net force (add same direction, subtract opposite).
Step 3 – Decide: zero net force means no change in motion; otherwise the object speeds up, slows down or turns.
Worked example: Cycling along a cycle track
Mei cycles on a flat, straight track: pedalling gives 120 N forwards; friction and air resistance give 120 N backwards.
Part A: \(120\ \text{N} - 120\ \text{N} = 0\ \text{N}\). Balanced, so Mei moves at a constant speed in a straight line.
Part B: She pedals harder: 180 N forwards. \(180\ \text{N} - 120\ \text{N} = 60\ \text{N}\) forwards, so she speeds up.
Part C: She stops pedalling (0 N forwards). At first the backward force is still 120 N, so the net force is 120 N backwards and she slows down.
Key takeaway: Forces first, net force second, motion last!
7. Common Mistakes to Avoid
Common mistake 1: "A moving object needs an unbalanced force pushing it forwards." Wrong! Steady motion in a straight line means balanced forces. Unbalanced forces only change motion.
Common mistake 2: "Balanced forces mean the object is not moving." Wrong! They mean the motion does not change. The object may be at rest or moving steadily.
Common mistake 3: Writing a net force with no direction, e.g. just "20 N". Write "20 N to the right" or "20 N upwards".
Common mistake 4: Mixing up balanced forces with action and reaction pairs. Balanced forces act on the same object. An action and reaction pair acts on two different objects, so they never cancel out (see Action and reaction).
Quick Review
1. A force arrow shows size (length) and direction (arrowhead). Force is measured in newtons (N).
2. The net force is the overall force on an object.
3. Same direction: add. Opposite directions: subtract; the net force points the way of the bigger force.
4. Balanced forces (net force zero): at rest stays at rest; moving keeps a constant speed in a straight line.
5. Unbalanced forces (net force not zero): the object speeds up, slows down or changes direction.
6. A skydiver falls at a steady speed when air resistance equals weight; an open parachute gives an upward net force until a new, lower steady speed.
Well done! Next time you see a tug of war or a car stopping at the lights, spot whether the forces are balanced. You are thinking like a physicist!