Can a person keep 100 tons from falling? Can one crush a piece of iron with one’s hand? Can a child resist a strong man? Yes, they can.

Ask a strong man to turn a flywheel in the clockwise direction while holding a spoke near the axle. The torque will be small in this case: the force is great but the lever arm is short. If a child pulls the wheel in the opposite direction, holding a spoke near the rim, the torque may turn out to be large: the force is small but the lever arm is long. The condition for equilibrium will be \[M_{1} = M_{2}, \quad \textrm{or} \quad F_{1}d_{1} = F_{2}d_{2}\] Using the law of moments, a person can acquire fabulous strength.

The action of levers serves as the most striking example of this.

You want to lift an enormous stone with the aid of a crow-bar. This task will turn out to be possible for you to accomplish, even though the stone weighs several tons. The crow-bar is placed on a pivot and is the solid body of our problem. The pivot is the centre of rotation. Two torques act on the body: a hindering one from the weight of the stone, and a helping one from your hand. If the subscript 1 refers to the muscular force, and the subscript 2 to the weight of the stone, the possibility of lifting the stone can be expressed concisely: \(M_{1}\) must be greater than \(M_{2}\).

The stone can be supported above the ground provided that \[M_{1} = M_{2}, \quad \textrm{or} \quad F_{1}d_{1} = F_{2}d_{2}\]

If the short lever arm (from the pivot to the stone) is fifteen times smaller than the long one (from the pivot to the hand), then a person acting with his entire weight on the long end of the lever will support a one-ton stone in a raised position.

A crow-bar placed on a pivot is a rather widespread and the simplest example of a lever. A ten- to twenty-fold gain in force is usually achieved with the aid of a crow-bar. The length of a crow-bar is about \(1.5\,\mathrm{m}\), but it is usually difficult to place the pivot nearer than \(10\,\mathrm{cm}\) from its bottom. Therefore, one of the lever arms will be from fifteen to twenty times as long as the other, and so this will also be the gain in force.

A chauffeur will easily raise an automobile weighing several tons with the aid of a jack. A jack is a lever, of the same type as a crow-bar, placed on a pivot. The points of application of the forces (the hand, the weight of the car) lie on opposite sides of pivot of the jack. Here the gain in force is about forty- to fifty-fold, which makes it possible to easily lift an enormous weight.

A pair of scissors, a nutcracker, pliers, pincers, nippers and many other instruments are all levers. You can easily find the centres of rotation (pivots) of the solid bodies depicted in Figure 1, as well as the points of application of the two forces-active and hindering.

In cutting tin-plate with a pair of scissors, one tries to open them as wide as possible. What is accomplished by this? One succeeds in slipping the piece of metal closer to the centre of rotation. The lever arm of the torque one is overcoming becomes shorter, and so the gain in force is greater. When moving a pair of scissors, or nippers, an adult ordinarily acts with a force of 40-50kg f. One of the lever arms can be twenty times longer than the other. It turns out that we are able to cut into metal with a force of \(1000\,\mathrm{kg}\) f. And this with the aid of such simple instruments.

The windlass is a variety of lever. With the aid of a windlass (Figure 2), water is taken out of a well in many villages.