What is a lever?
A lever is a stiff bar that can turn about a fixed point. That fixed point is the fulcrum (also called the pivot).
Every lever has five parts:
- Fulcrum: the point the bar turns around.
- Load: the weight or force you want to move.
- Effort: the force you put in.
- Load arm: the distance from the fulcrum to the load.
- Effort arm: the distance from the fulcrum to the effort.
An "arm" is always measured from the fulcrum, straight across to where the force acts (at a right angle to the force).
The law of moments: when does a lever balance?
A force that makes something turn has a moment (turning effect). Moment = force × distance from the fulcrum. Its unit is the newton metre (N·m).
A lever is balanced when the turning effects on both sides are equal:
Load × load arm = Effort × effort arm
So a long effort arm needs only a small effort. This is why a door handle is far from the hinges, and why a long spanner opens a tight nut easily.
Mechanical advantage
Mechanical advantage (MA) = load ÷ effort = effort arm ÷ load arm. If MA is more than 1, the lever multiplies your force. If MA is less than 1, it costs more force but gives more speed and movement at the load.
A lever never gives free energy: when you push with less force, you must push through a longer distance.
The three classes of lever
We sort levers by what sits in the middle.
- Class 1: fulcrum in the middle. Effort and load are on opposite sides. MA can be more than, equal to or less than 1. Examples: see-saw, scissors, crowbar, pliers, beam balance.
- Class 2: load in the middle. The effort arm is always longer than the load arm, so MA is always more than 1. Examples: wheelbarrow, bottle opener, nutcracker.
- Class 3: effort in the middle. The effort arm is always shorter, so MA is always less than 1, but the load moves fast and far. Examples: tweezers, fishing rod, broom, tongs.
Levers in your body and in sport
Bones are the bars, joints are the fulcrums, muscles give the effort and the body part or object is the load.
- Class 1: nodding your head. The neck joint is the fulcrum between the weight of the face and the neck muscles at the back.
- Class 2: rising on your toes. The ball of the foot is the fulcrum, body weight is the load, the calf muscle pulls up at the heel.
- Class 3: bending your arm (biceps curl). The elbow is the fulcrum, the biceps pulls just in front of it, the hand holds the load. Most body levers are Class 3: they trade force for speed and range of movement, which helps in throwing, kicking and hitting.
In sport, a longer lever (a straight arm, a bat or racket) makes the end move faster, so the ball leaves faster.
Project: make a steelyard balance
A steelyard is an old weighing scale made from one lever. The thing to weigh hangs on a short arm near the fulcrum. A small sliding weight moves along the long arm until the bar balances.
By the law of moments, a heavy object needs the slider farther out. So the long arm can be marked with masses.
Try it at home
- Take a 30 cm ruler. Tie a thread at the 10 cm mark to hang it (the fulcrum).
- Hang a small bag at the 0 cm end (load arm 10 cm).
- Hang a 20 g coin bundle as the slider on the other side. Slide until level.
- Put known masses in the bag (20 g, 40 g, 60 g) and mark where the slider balances each time. This is calibration.
- Check: do the marks come at equal gaps? They should, because moment grows evenly with mass.
Try it: predict, then check
Open the last 3D step. Set a 6 kg load (60 N) at 1 m. Predict the effort needed at 3 m. (Answer: 60 × 1 ÷ 3 = 20 N.) Then set it and see the bar balance. Now move the effort to 1.5 m without changing it: which way does the bar tip?
Key formulas and definitions
- Moment = force × perpendicular distance from the fulcrum (N·m)
- Balance (law of moments): load × load arm = effort × effort arm
- Mechanical advantage MA = load ÷ effort
- MA = effort arm ÷ load arm (ideal lever)
- Weight = mass × g, with g ≈ 10 N/kg
Worked examples
1. A 300 N load is 0.5 m from the fulcrum. The effort is 1.5 m from the fulcrum on the other side. What effort balances it?
Effort × 1.5 = 300 × 0.5 = 150, so effort = 150 ÷ 1.5 = 100 N. MA = 300 ÷ 100 = 3.
2. A child of mass 30 kg sits 2 m from the middle of a see-saw. Where must a 40 kg adult sit to balance?
Weights: 300 N and 400 N. 300 × 2 = 400 × d, so d = 600 ÷ 400 = 1.5 m from the middle, on the other side.
3. A wheelbarrow carries 600 N of bricks 0.4 m from the wheel axle. You lift the handles 1.2 m from the axle. Find the effort and the class.
Effort × 1.2 = 600 × 0.4 = 240, so effort = 200 N. The load is between the fulcrum (wheel) and the effort, so it is Class 2. MA = 3.
4. In a biceps curl the muscle pulls 0.04 m from the elbow and the hand holds a 50 N weight 0.32 m from the elbow. What force must the biceps give?
Effort × 0.04 = 50 × 0.32 = 16, so effort = 400 N. MA = 50 ÷ 400 = 0.125. Class 3: big force, but the hand moves 8 times farther and faster than the muscle.
5. A steelyard has the load hook 5 cm from the fulcrum and a 100 g slider. Where does the slider sit to balance a 1 kg fish?
Masses work the same way as weights (g cancels): 1000 g × 5 cm = 100 g × d, so d = 50 cm from the fulcrum.
6. A crowbar 1.2 m long has its fulcrum 0.2 m from the end that lifts a 1500 N stone. What effort is needed at the other end?
Load arm = 0.2 m, effort arm = 1.2 − 0.2 = 1.0 m. Effort = 1500 × 0.2 ÷ 1.0 = 300 N. MA = 5.
Common mistakes
- Measuring arms from the end of the bar instead of from the fulcrum.
- Thinking Class 3 levers are "bad". They need more force but give more speed and range of movement.
- Mixing up kg and N: change mass to weight (× 10 N/kg) before using moments, or use the same unit on both sides.
- Thinking a lever saves work. It saves force, but you push through a longer distance.