Simple Machines: Wedge
A wedge is a type of simple machine characterized by its triangular shape, featuring a thick, flat end and two sloping sides that converge at a point. It functions by amplifying an input force applied to its flat end and redirecting that force perpendicularly outwards, making tasks like cutting or splitting more efficient. Common examples include axe heads, knives, and doorstops, which either cut through materials or secure objects in place. The mechanical advantage provided by a wedge can be calculated by comparing the lengths of its sloped sides to the width of its base, illustrating how narrower wedges amplify force more effectively than wider ones. However, wedges are affected by friction, which can reduce their efficiency in real-world applications. This efficiency is measured by comparing actual performance to an ideal, frictionless scenario. Wedges play a crucial role in countless everyday tools and machinery, serving as foundational elements that help explain the principles of work, force, and energy transfer in more complex systems. Understanding wedges enhances our grasp of how simple machines operate and their significance in mechanical design.
Simple Machines: Wedge
FIELDS OF STUDY: Classical Mechanics
ABSTRACT: A wedge is a simple machine consisting of a triangular object with one thick, flat end and two sloped sides that come to a point at the other end. Examples of wedges include axe heads, railroad spikes, and chisels. Wedges amplify and redirect an input force. Pushing on the wedge’s thick end produces an amplified force pushing out to either side of the sharp end, perpendicular to the input force. Wedges are often used to cut or pry things apart.
PRINCIPAL TERMS
- actual mechanical advantage: the ratio of the output force of a machine to the input force, taking into account friction and other factors that limit the efficiency of real-world machines.
- efficiency: the measure of how effective a machine is at transforming or transferring energy, quantified as the ratio of the actual performance of the machine to an idealized, theoretical version of it.
- ideal mechanical advantage: the ratio of the output force of a machine to the input force, ignoring friction and other factors that limit the efficiency of real-world machines.
- joule: the International System of Units (SI) unit of work and energy; one joule is equal to the work done by a force of one newton acting across a distance of one meter.
- net force: the sum of all of the forces acting on an object.
- newton: the International System of Units (SI) unit of force; one newton is equal to the force required to accelerate a one-kilogram mass at one meter per second per second.
- power: the rate of work or energy transfer over time.
- work: the use of force to successfully displace an object from its original position.
What Is a Wedge?
A wedge is a simple machine. It is a triangular object with one thick, flat end and two sloped sides that form a point at the other end. It works by amplifying a force applied to the flat end and redirecting it out to either side of the point, perpendicular to the input force. Axe heads, for instance, amplify the downward force of a swing and redirect it to either side as the sharp end of the head is driven into wood, forcing the wood apart and chopping it in two. Most cutting surfaces work the same way, but on different scales. Wedges may also be used to secure objects in place, as with railroad spikes or doorstops.
Simple machines such as wedges are devices that make tasks—typically, moving some target object—easier by redirecting or amplifying an input force. Generally, simple machines differ from other, more complex machines by virtue of being the simplest ways to multiply a force. The multiplication of a force by a tool or machine is called mechanical advantage.
The six classic simple machines are the lever, the wheel and axle, the pulley, the inclined plane, the wedge, and the screw. Simple machines often act as the building blocks for more complex machines, sometimes called compound machines. For instance, a hand-crank can opener consists of a wedge (the cutting edge), a wheel and axle (the crank), and levers (the grips).
Force vs. Distance
A force is said to do work if it displaces an object from its original position. If the net force acting on an object is positive in any direction, the object will move in that direction. An axe lying flat on a log experiences a net force of zero. If someone swings the axe straight down, the net force is positive in the direction of gravity, and the gravitational force of the earth is doing work on the axe.
In physics, work (W) is equal to 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 directions of force and displacement (θ):
W = F × s × cosθ
Work and energy are both measured in joules (J). One joule is equal to the work done or energy transferred when a force of one newton (N) moves something a distance of one meter. Power, measured in watts (W), is simply the rate of work over time. One watt of power is equivalent to one joule of work done or energy transferred per second (J/s).
The formula for work, above, helps one understand the force-distance trade-off inherent in how wedges and other simple machines work. For the same reasons that energy can only be transformed, not created or destroyed, the total work done at either end of a simple machine must remain constant. To keep the work value constant, a simple machine that amplifies force via mechanical advantage must also reduce the displacement caused by that force. (The angle between the force and displacement determines whether that force caused the displacement.)
The mechanical advantage (MA) of a wedge is calculated as the ratio of the length of one sloped side (l) to the width of its base (w):
A mechanical advantage of more than 1 indicates an amplification of force. A narrow wedge provides greater amplification of force in exchange for moving the target a shorter distance. Doubling the base width while keeping the side lengths the same would reduce the mechanical advantage by half. Correspondingly, doubling the side lengths while keeping the base width the same would doubles the mechanical advantage.
Friction Interferes
In the real world, there is no perfect machine. Even the simplest machines fail to transmit forces perfectly; some energy is always lost to friction. In the real world, a distinction is made between ideal mechanical advantage (assuming a perfect machine) and actual mechanical advantage (taking into account friction and other forces).
The difference between a theoretically perfect machine and its real-world counterpart is measured in terms of its efficiency. Efficiency is the ratio of the actual, measured performance of a machine to its theoretically perfect performance. A perfect machine would have an efficiency value of 1. In the real world, wedges lose efficiency due to friction between the sloping sides and the surfaces they move against.
Sample Problem
A camper has a big pile of wood she needs to chop into smaller pieces for a fire. She has one axe handle with two different axe-head attachments. One axe head is narrow, with a base 5 centimeters (cm) wide and sides 20 cm long. The other is the same length, but its base is twice as wide. Calculate the mechanical advantage of each axe head. Which would offer the camper the greater advantage?
Answer:
Use the formula for the mechanical advantage (MA) of a wedge, which is the length (l) of the sides divided by the width (w) of the base:
Plug in the given values for the first axe head, the narrow one, and calculate:
The second axe head is also 20 cm long, but its base is 10 cm. Calculate its mechanical advantage as well:
The narrower axe, with a mechanical advantage of 4, would be twice as effective at amplifying the applied force as the thicker axe, with a mechanical advantage of 2. This illustrates a basic principle of how wedges work.
The reason wedges in the real world are not always extremely narrow is due to a combination of the limits of materials—very narrow wedges can be fragile—and the fact that sometimes thicker, heavier wedges are useful. In the case of the axe, for example, the weight of the axe head is added to the force of the swing.
Wedges Are Everywhere
Simple machines such as wedges permeate every aspect of daily life. Almost every cutting tool, from a knife to a sword to a pair of scissors, uses a wedge to push apart the surface it is cutting. Wedges can also be used to pin things in place by being driven into a material; instead of splitting the material, the amplified force allows the wedge to be driven securely into place. Old iron railroad spikes are simple bars with a wedged end that were used to hold rail tracks in place.
More importantly, the principles of power, work, force, and mechanical advantage that govern wedges, along with the basic structures of classic simple machines, provide the foundation for a deeper understanding of the more complex machinery encountered in everyday life.
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