Mechanical ComprehensionLesson 4 of 18
Levers
The three classes, fulcrum placement, and calculating advantage from arm lengths.
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Levers are the clearest of the simple machines and the most asked. The whole topic is one classification rule and one equation.
The three classes
Read the middle. It classifies every lever.
| Class | What is in the middle | Advantage | Examples |
|---|---|---|---|
| First | the fulcrum | can be more or less than 1 | seesaw, crowbar, scissors, pliers |
| Second | the load | always more than 1 | wheelbarrow, nutcracker, bottle opener |
| Third | the effort | always less than 1 | tweezers, fishing rod, shovel, human forearm |
The mnemonic that works is the order F-L-E for the middle element across the three classes: Fulcrum, Load, Effort, first, second, third.
Why second is always above 1 and third always below
In a second-class lever the load sits between the fulcrum and the effort, so the effort is always further from the fulcrum than the load is. A longer effort arm always means an advantage above 1.
In a third-class lever the effort sits between, so the effort arm is always the shorter one, and the advantage is always below 1.
That is not a flaw. A third-class lever multiplies speed and distance: your forearm's muscle pulls hard over an inch and your hand moves fast over a foot. A fishing rod and a shovel do the same.
Only first-class levers can go either way, depending on where the fulcrum sits.
The equation
Effort x effort arm = load x load arm.
The arms are measured from the fulcrum, which is the detail people get wrong.
A 300-pound load sits 2 feet from the fulcrum. The effort is applied 6 feet from the fulcrum. What effort is needed?
300 times 2 is 600. Divide by 6: 100 pounds.
A 50-pound effort is applied 8 feet from the fulcrum, lifting a load 2 feet from it. How heavy a load can it lift?
50 times 8 is 400. Divide by 2: 200 pounds.
Mechanical advantage = effort arm / load arm, which in the first example is 6 over 2, or 3 - and indeed 300 divided by 100 is 3.
Both routes agree, and checking one against the other catches arithmetic errors.
Moving the fulcrum toward the load increases the advantage, because it lengthens the effort arm and shortens the load arm at the same time. That is why you slide a pry bar's pivot as close to the object as you can, and it is a question: "to lift the load with less force, the fulcrum should be moved" - toward the load.
Reading a lever question
- Find the fulcrum. It is the pivot, and it may be an axle, an edge, or a hinge rather than a drawn triangle.
- Find the load and the effort.
- Whichever of the three is in the middle names the class.
- Measure both arms from the fulcrum.
- Apply effort times distance equals load times distance.
Step 4 is where the errors are. A question may give the total length of the bar rather than the two arms, in which case one arm is the total minus the other.
A 10-foot bar has its fulcrum 2 feet from the load end.
The load arm is 2 feet and the effort arm is 8 feet, not 10.
Balancing
A balanced lever has equal moments on both sides, a moment being force times distance from the fulcrum.
Two children sit on a seesaw. One weighs 80 pounds and sits 6 feet from the pivot. The other weighs 120 pounds. Where must they sit to balance?
80 times 6 is 480. Divide by 120: 4 feet.
The heavier one sits closer, which is the general result and a useful sanity check.
What you can skip
Across the 120 questions on this topic in our bank:
- Efficiency. No lever question involves efficiency; every one is ideal.
- The lever's own weight. No lever question gives the bar a weight to include (one mentions it in passing); treat the lever as weightless.
- Bell cranks never appear; compound levers come up four times, and the compounding rule in the mechanical advantage lesson covers them.
Where people lose points
Measuring an arm from the end of the bar rather than from the fulcrum.
Mixing up second and third class. Load in the middle is second; effort in the middle is third.
Thinking a third-class lever is badly designed. It buys speed.
Using the whole bar length as one arm when the fulcrum is inside it.
Moving the fulcrum the wrong way to increase advantage. Toward the load.
Forgetting that a first-class lever can have an advantage below 1, if the fulcrum is nearer the effort.
Work one in under a minute
A wheelbarrow carries 180 pounds. The load's center is 18 inches from the wheel, and the handles are 54 inches from it. What lift is needed at the handles, and what class of lever is this?
The wheel is the fulcrum, the load is in the middle and the effort is at the handles, so it is a second-class lever.
180 times 18 is 3,240. Divide by 54: 60 pounds.
Check: the advantage is 54 over 18, which is 3, and 180 over 3 is 60. Agreed, and above 1 as a second-class lever must be.
Where this leads
The arm-length ratio here is the same ratio as the radii in a wheel and axle, and the moment equation is what torque questions use.
Related lessonsReference
- Torque and Rotation - force times lever arm, generalized
- Wheel and Axle - a lever that goes all the way round
- Mechanical Advantage - the trade every lever makes
- Pulleys - the other classic machine, counted differently
Practice this topic
Check that this lesson stuck. Answer questions on levers only, and see the right answer and why after each one.
Practice Levers questions