Levers and the Three Lever Classes
A lever is a rigid bar that turns about a fixed point called the fulcrum; it is balanced when the moment (torque) of the effort equals that of the load, Fede = Fldl, and the ideal mechanical advantage is the effort arm divided by the load arm. In brief: there are three classes of lever, depending on the order of the fulcrum, load and effort. First class: fulcrum in the middle (seesaw, scissors). Second class: load in the middle (wheelbarrow, nutcracker). Third class: effort in the middle (tweezers, fishing rod).
A crowbar lifts a heavy rock, and a pair of tweezers grips a splinter. Both are levers, although they work in different ways. This guide explains the principle of moments and the mechanical advantage of levers, describes the three classes, compares them in a table, works through a balance problem and a crowbar problem, and corrects common mistakes.
How does a lever work?
The turning effect of a force about a point is its moment (torque): moment = force × perpendicular distance from the pivot. A lever is balanced (in rotational equilibrium) when the clockwise moments equal the anticlockwise moments: Fe × de = Fl × dl, where de is the effort arm and dl the load arm (measured from the fulcrum). The ideal mechanical advantage is IMA = de ÷ dl. A long effort arm and a short load arm give a large force multiplication, but the effort must move through a greater distance than the load: the effort moves de/dl times as far.
What are the three classes?
- First class: the fulcrum lies between the effort and the load. It can have an MA larger, equal to, or smaller than 1, depending on the position of the fulcrum, and it reverses the direction of force. Examples: seesaw, crowbar, scissors, pliers, a claw hammer.
- Second class: the load lies between the fulcrum and the effort. The effort arm is always longer than the load arm, so MA > 1. The effort and the load act in the same direction. Examples: wheelbarrow, nutcracker, bottle opener, a door (hinge as the fulcrum).
- Third class: the effort lies between the fulcrum and the load. The effort arm is shorter than the load arm, so MA < 1: it needs a larger force but gives a larger distance and speed at the load. Examples: tweezers, fishing rod, a spade when digging, the human forearm (the elbow is the fulcrum, the biceps muscle applies the effort between the elbow and the hand).
Lever classes compared
| Class | Order | Mechanical advantage | Examples |
|---|---|---|---|
| First | Effort – fulcrum – load | Any value | Seesaw, scissors |
| Second | Fulcrum – load – effort | Greater than 1 | Wheelbarrow, nutcracker |
| Third | Fulcrum – effort – load | Less than 1 | Tweezers, fishing rod |
Worked example: balancing and prying
- Seesaw. A child of mass 40 kg sits 1.5 m from the pivot. Where must a child of mass 30 kg sit to balance? Moments: 40 × 9.8 × 1.5 = 30 × 9.8 × d, so d = 40 × 1.5 ÷ 30 = 2.0 m on the opposite side.
- Crowbar (first class). The effort arm is 1.2 m and the load arm is 0.20 m. IMA = 1.2 ÷ 0.20 = 6. To lift a load of 600 N, the ideal effort is 600 ÷ 6 = 100 N. When the effort end moves down 0.30 m, the load rises 0.30 ÷ 6 = 0.050 m.
- Wheelbarrow (second class). The load of 450 N acts 0.50 m from the wheel axle (fulcrum), and the handles are 1.5 m from the axle. The effort F satisfies F × 1.5 = 450 × 0.50, so F = 150 N.
- Forearm (third class). A 3.0 kg load held in the hand 0.35 m from the elbow, with the biceps attached 0.040 m from the elbow. The load force is 29.4 N. The biceps force: F × 0.040 = 29.4 × 0.35, so F = 257 N, about 8.75 times larger than the load.
Who explained the lever?
Archimedes derived the law of the lever in his work On the Equilibrium of Planes (third century BCE), and is credited with the statement, “Give me a place to stand, and I shall move the Earth.” Levers have been used since prehistoric times, for example in the shaduf, an irrigation device in ancient Egypt and Mesopotamia. Leonardo da Vinci analyzed levers and moments in the late 1400s.
Which mistakes are common?
Mistake 1: Measuring distances to the load or effort from the wrong place
Arms are measured from the fulcrum to the line of action of each force.
Mistake 2: Using the slant distance for a force at an angle
Use the perpendicular distance from the pivot to the line of the force.
Mistake 3: Thinking that all levers multiply force
Third-class levers have MA below 1 and are used to gain speed and range of motion.
Mistake 4: Forgetting that the force advantage costs distance
The effort end moves farther than the load end by the same ratio.