Simple Machines: Screw

FIELDS OF STUDY: Classical Mechanics

ABSTRACT: A screw is an inclined plane with a spiraling groove wrapped around a cylinder. Screws are typically used to secure objects tightly together. They can also be used to clamp or crush objects, to excavate holes, or to move air.

PRINCIPAL TERMS

• actual mechanical advantage: the ratio comparing the input force of a machine to its output force, taking into account friction and other factors that limit the efficiency of real-world machines.
• ideal mechanical advantage: the ratio comparing the input force of a machine to its output force, ignoring friction and other factors that limit the efficiency of real-world machines.
• joule: abbreviated J, the International System of Units unit of work and energy.
• net force: the overall force acting on an object, determined by adding up all of the forces acting on that object.
• newton: abbreviated N, the International System of Units unit of force.
• power: amount of energy transferred over time; measured in watts, or joules per second.
• simple machine: the simplest devices capable of generating a mechanical advantage.
• work: the successful exertion of force on an object, or the successful transfer of energy; measured in joules.

Screws and Simple Machines

A screw is an inclined plane with a spiraling groove wrapped around a cylinder, typically with a pointed edge. Screws are generally used to secure objects tightly together, as in common household construction projects. Other uses for screws include clamping or crushing objects (as in a vice), excavating holes (a drill), and even moving air (a fan). Screws work by using the inclined plane to redirect and increase a turning force (torque) applied to the cylinder into a vertical force parallel to the cylinder.

Simple machines amplify and direct an input force. Generally, simple machines are distinguished from more complex machines by being the simplest possible systems that generate mechanical advantage. The classical simple machines are the lever, wheel and axle, pulley, wedge, and screw. (Gears are sometimes included as well.)

Complex machines, or "compound machines," can often be thought of as an assembly of several simple machines. Complicated assembly lines that factories use to move products can be broken into a series of ramps, gear trains, pulleys, and wheels and axles.

Trading Force for Distance

A force is said to do work if it moves an object. An object will move if the net force on it results in a positive force in any direction. Therefore, a screw held in place against a piece of wood has a net force of zero. Once the person holding the screw inserts a screwdriver and applies a rotational force to the screw, the threads begin to catch against the wood and push against it. In turn, the screw begins to bury itself into the wood. Once the screw is in motion, it has a positive net force.

Mathematically, work (W) is the product of the strength of the force (F) applied, the displacement of the object from its original position (s), and the cosine of the angle between the force and the displacement (θ):

W = Fs cosθ

Work and energy are both measured in joules (J). One joule is equal to the work performed (or energy transferred) when a force of one newton (N) moves something a distance of one meter. (One newton equals the force required to accelerate a one-kilogram mass at one meter per second per second.) Power is simply a measure of work over time, given in watts (W). One watt of power equals one joule of work per second.

The formula for work is useful for understanding the force-distance trade-off inherent to how screws (and all other simple machines) work. For the same reasons that energy can only be transformed—not created or destroyed—the total work performed at either end of a simple machine must remain constant. For this value to remain constant, a simple machine that amplifies force via mechanical advantage must also reduce the displacement (total distance moved) caused by that force.

Friction and Imperfect Machines

In the real world, no machine transfers force perfectly. Some is always lost to friction. Thus, a distinction is made between ideal mechanical advantage and actual mechanical advantage. The former assumes a perfect machine, unimpeded by friction or design flaws, that transmits a force perfectly. The latter is based on actual measurements of the ratio of input to output forces. The difference between an ideal machine and its real-world counterpart is referred to as "efficiency." Efficiency is the ratio of the actual, measured performance of a machine to its theoretically perfect performance.

Calculating a Screw’s Mechanical Advantage

The theoretical mechanical advantage of a screw (MA_screw) is dependent on the length of the lever (L) and the distance between threads (the pitch, P):

MA_screw = 2πL/P

The 2π value represents the fact that the circumference of one complete circle is 2π radians. The formula compares one complete turn of the lever to the perpendicular distance moved by the threads. The longer the lever is relative to the pitch of the screw, the greater the mechanical advantage.

Sample Problem

A carpenter needs to glue two boards together to create a stronger plank. The wood needs to be held tightly together for a long time in order for the glue to set, so the carpenter places the wood into a large vice. He turns the handle on the vice, screwing it tighter and tighter. The handle is a lever 20 centimeters long, and the threads of the screw are 2 centimeters apart. Using this information, calculate the mechanical advantage of this screw-vice system.

Answer:

Calculate the mechanical advantage using the standard equation for the mechanical advantage of a screw:

MA_screw = 2πL/P

The units used for the length of the lever and the length of the pitch are not important, so long as they are the same. Mechanical advantage is a simple proportion with no units. Plug in the given values from the sample problem:

MA_screw = 2π(20 cm) / 2 cm

MA_screw = 20π

MA_screw ≈ 62.83

The screw-vice amplifies any force the carpenter applies to the lever by nearly 63 times. This demonstrates that even a relatively small vice can offer a dramatic amplification of force across a very small distance.

The Many Uses of Screws

One of the first uses of the screw was to transfer water. According to legend, the Archimedes’ screw was developed by famed Greek inventor Archimedes (ca. 287–212 BCE) on a visit to Egypt as a method of lifting water into irrigation ditches. Also called a "screw pump," the device is a large screw with a broad thread fitted tightly inside a pipe. As the screw is turned, the threads pull water upward. Similar devices are still used to move water, grain, and other substances.

The "pulling" action of a screw can also be seen in the propellers of ships and propeller planes. These spin blades act like the threads on a screw. Indeed, Leonardo da Vinci (1452–1519) designed a helicopter-like device that used a large, broad-threaded screw to be spun by hand using a lever and to "pull" the device upward into the air. (Unfortunately, it did not work.) In the modern world, screws are common components of everyday items.

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