How to balance a seesaw with unequal weights

How to use this simulation

1. With “Class 1” selected, notice the defaults: 60 N at 2 m against 40 N at 3 m. The two moments match, so the beam sits level.
2. Move the effort-arm slider, or drag the effort arrow on the canvas. Two coloured bars show the moments; the beam tips towards the bigger one.
3. Change the effort force to restore balance, then compare your own calculation with the “Effort needed to balance” reading.
4. Switch to class 2 and class 3. Watch which one gives a mechanical advantage above 1 and which one gives less than 1 in the readings panel.

A playground secret

You have probably ridden a seesaw. You are heavy, your friend is light. When you sit down, your end hits the ground and your friend dangles in the air. So what can you do so both of you hover level? One answer: slide towards the pivot while your friend stays at the far end. A light person can then lift a heavy one.

The same trick shows up everywhere: a crowbar shifting a boulder, a bottle opener, a wheelbarrow. Nobody says, “push harder.” They say, “hold it further out.” Distance is the real key.

In this lesson we give that key a name: the moment of a force. The rule is a single line, M = F × d, yet inside it hide seesaws, scissors, wheelbarrows, nutcrackers and even the way your own arm is built.

Start from zero: when does a push turn something?

Try opening a door by pushing near the hinge. Hard work! Push the handle, as far from the hinge as possible, and one finger does it. The force is the same, the result is not. Turning power depends on the force and also on how far from the pivot the force is applied.

The pivot, or fulcrum, is the point that does not move: the hinge of a door, the post in the middle of a seesaw. The further the line of the force sits from that point, the more it turns the object. And if the line of the force passes right through the pivot, it turns nothing at all. Push straight at the hinge and the door stays shut.

Physicists package this joint power of force and distance into one quantity, the moment of a force (often called torque). It measures the tendency to rotate, just as force measures the tendency to accelerate.

A turn has two possible senses: clockwise and anticlockwise. To add several moments you must give each sense its own sign. In the simulation we skip that bookkeeping by showing the two senses as two separate bars so they are easy to compare.

Words you must know

Exam questions on levers use the same few terms again and again. Keep each meaning next to a familiar example.

Where the formula comes from: defining a moment

Pick a pivot O. A force F acts so that the perpendicular distance from O to its line of action is d. That d is the arm of the force. By definition, the moment of the force is the product of force and arm.

On a seesaw the beam is horizontal and the weights pull straight down, so the distance measured along the beam is the perpendicular distance. If the beam tilts, the line of force stays vertical but the perpendicular distance shrinks by a factor of cosθ. The tilt in the simulation is small, so the simple formula is enough here.

The unit drops straight out of the formula: newton times metre, N·m. It looks like the joule, yet the two are different things. A joule measures energy and work. A moment measures the tendency to turn, so write N·m.

The principle of moments: one condition for balance

When several forces act on a body, each one tries to turn it its own way, some clockwise, some anticlockwise. If the efforts cancel out to zero, the body does not turn. That is the principle of moments: for a body in rotational balance, the sum of the anticlockwise moments about any point equals the sum of the clockwise moments about that point.

In the simulation’s starting state, 60 N acts 2 m from the fulcrum on one side and 40 N acts 3 m away on the other. The first moment is 60 × 2 = 120 N·m, the second 40 × 3 = 120 N·m. They are equal, so the beam is level.

Notice that the principle does not mention the beam’s own weight. That is because we assume the bar is light enough to ignore. A uniform heavy bar has its weight acting at its centre of gravity, the exact middle, and you add that as one more force. A worked example below does exactly that.

One more thing. When the bar is balanced the fulcrum pushes up with a force equal to all the downward forces together. That force has zero arm, so it never enters the moment equation. This is why choosing the fulcrum as your turning point makes the sums simplest.

Mechanical advantage: more load for less effort

Rearranging the balance condition gives load ÷ effort = effort arm ÷ load arm. The left side is the mechanical advantage. It tells you how many times the lever multiplies your effort. The right side is pure geometry, the two arm lengths.

Say the load is 600 N and its arm is 0.5 m. The longer you make the effort arm, the smaller the effort. The table below is computed in code, so you can check every row in the simulation.

But nothing is free. The longer the effort arm, the further your hand has to travel. Energy conservation says: smaller force, bigger distance. In an ideal lever the work put in equals the work got out.

Three classes of lever: who sits in the middle?

Every lever has three parts: fulcrum, load and effort. Which one sits between the other two decides the class. An easy memory aid: classes 1, 2, 3 have the fulcrum, the load and the effort in the middle, in that order.

Try it in the simulation

Each experiment takes a minute, but doing it once yourself means you will not forget the rule. Start from the defaults.

• Experiment 1: in class 1, double the load force. Which way does the beam tilt? Now double the effort arm to restore balance.
• Experiment 2: keep the load arm short and stretch the effort arm, then read “Effort needed to balance”. Effort falls while mechanical advantage rises.
• Experiment 3: drag the effort position along the canvas. At the instant the two bars match, the beam stops. Write down the distance in metres.
• Experiment 4: choose class 2 and try to put the effort closer than the load. The simulation keeps half a metre of gap, because otherwise it would no longer be a class 2 lever.
• Experiment 5: in class 3 note that the mechanical advantage is below 1. In your own words, explain why the effort force exceeds the load force at balance.
• Experiment 6: switch off “Show the arm lengths” and estimate the distances from the tick marks on the beam. Switch it on again to check.

Check a seesaw by arithmetic

The table below lists four pairs with their moments computed. Put each pair into the simulation and see whether it agrees.

Solved problems

Every number is computed in code. Write each step in your notebook before reading the next line.

Mistakes that cost marks

The same few errors turn up in answer scripts year after year. Read the list and spot your own.

• The distance is the perpendicular distance from the pivot to the line of the force, not just the straight-line distance to where it is applied. A slanted force shows the difference.
• The unit of a moment is N·m, not J. They look alike but mean different things.
• Measure every distance from the same pivot. Mixing two pivots in one problem is the most common slip.
• Mixing up class 2 and class 3. Find who sits in the middle: the load or the effort.
• Thinking a mechanical advantage below 1 means a bad lever. In class 3 it is normal, and you gain speed in return.
• Forgetting the weight of a uniform bar. Put it at the centre of gravity and include its moment.
• Adding moments without checking the sense. Clockwise and anticlockwise need opposite signs.

Levers hiding in daily life

Once you can spot them, levers are everywhere. A few samples:

• Scissors: two class 1 levers joined, with the screw as the fulcrum.
• Balance scale: a class 1 lever with equal arms, level when the two pan moments match.
• Bottle opener: the rim is the fulcrum, the cap is the load and your hand is the effort, class 2.
• Tweezers: class 3, ideal for gripping delicate things gently.
• Fishing rod: class 3, a small movement of the hand swings the tip a long way.
• Dhenki: an old village class 1 lever for husking rice, press with the foot and the other end rises.
• Your body: nodding the head is class 1, rising on tiptoe is class 2, bending the arm is class 3.

Exam corner: CBSE and NCERT style

Board papers ask for definitions, short derivations and numericals. Here is a typical set.

Quick revision

Skim these few lines the night before the exam.

• Moment M = F × d, in N·m, measures the tendency to rotate.
• In balance the sum of anticlockwise moments equals the sum of clockwise moments.
• For a lever, W × d₁ = F × d₂ and mechanical advantage = load ÷ effort = d₂ ÷ d₁.
• Class 1 has the fulcrum in the middle, class 2 the load, class 3 the effort.
• Class 2 always has an advantage above 1, class 3 always below 1, class 1 can be anything.
• More advantage means more distance moved by the effort. Energy is not saved.
• The weight of a uniform bar acts at its centre of gravity.

Frequently asked questions