Simple Machines: Inclined Plane
An inclined plane is a basic type of simple machine that consists of a flat surface raised at an angle, allowing objects to be lifted or lowered more easily than by lifting them directly against gravity. This ramp-like structure transforms a horizontal push into a more effective diagonal force, making it easier to move heavy loads. The mechanical advantage (MA) of an inclined plane is calculated by the ratio of the length of the plane to its height, enabling users to exert less force over a longer distance.
Inclined planes are integral to various applications, from everyday tasks like moving furniture to industrial processes. They help illustrate fundamental concepts in physics, such as work, energy, and efficiency, which are crucial for understanding how machines operate. Despite their utility, real-world inclined planes face challenges like friction, which affects their efficiency—highlighting the difference between ideal and actual mechanical advantage. Overall, inclined planes are prevalent in daily life, underlying many structures and devices, including ramps, stairs, and slides.
Simple Machines: Inclined Plane
FIELDS OF STUDY: Classical Mechanics
ABSTRACT: An inclined plane, or ramp, is a simple machine consisting of a flat, rigid surface raised at an angle. The ramp that extends behind some moving trucks is a classic example of an inclined plane. A ramp directs and amplifies a forward push into the lifting or lowering of heavy objects, but it reduces distance.
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 an Inclined Plane?
An inclined plane is simply a ramp. It is a flat, rigid surface that is raised at one end to form a slope. Inclined planes can also be formed from solid, triangular objects laid on one side. They are typically used to lift or lower objects. Ramps amplify and redirect a horizontal input force (a push) into a stronger diagonal force parallel to the plane. They are among the oldest and simplest of the simple machines.
A simple machine is a device that makes a task—typically, moving some target object—easier by amplifying and directing an input force. Inclined planes transform a horizontal push into a stronger force upward or downward along a diagonal. This allows people to lift heavy objects by pushing forward instead of lifting upward directly against gravity.
Simple Machines and Mechanical Advantage
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. The mechanical advantage (MA) of an inclined plane is calculated as the ratio of the length (l) of the plane to the height (h) to which it is raised at one end:
A mechanical advantage of more than 1 indicates an amplification of force.
Simple machines often act as the building blocks for more complex machines, sometimes called compound machines. Factory assembly lines can be broken down into a series of ramps, gear trains, pulleys, and wheels and axles. Even the wedge, typically classified as a simple machine itself, can be considered two inclined planes fused together along the bottom.
Trading Force for 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. A heavy box sitting on a ramp experiences a net force of zero. However, if somebody applies a horizontal force to the box, sliding it upward and away, the net force will be positive in the diagonal direction of movement, because an object moving up or down a ramp always experiences a net force parallel to the incline. Note that forces with equal magnitude but opposite direction negate each other.
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 over a distance of one meter. Power is simply a measure of work over time. It is measured in watts (W), with one watt of power being equal to one joule of work done or energy transferred per second.
The formula for work, above, helps one understand the force-distance trade-off inherent in inclined planes. 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 reduce the displacement caused by that force. (The angle between the force and displacement determines whether that force caused the displacement.) Pushing a box up a ramp, for example, will not move the box as far as the same push would along flat ground, but the push will carry greater force.
Friction and Imperfect Machines
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. The smoother the ramp, the easier an object would move on it, as less energy would be wasted overcoming the friction between them. Unfortunately, less friction would also mean that the load could slide down the ramp more easily, negating the work.
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.
Sample Problem
A student has rented a moving truck to help her carry her things to her college apartment, where she is due to move in. One of the items she is trying to load into the truck is a massive heirloom dresser. The bed of the truck sits 1 meter (m) off the ground, the truck does not have a built-in ramp, and the student cannot lift the dresser even an inch. However, she sees several wide, sturdy planks of wood nearby. One plank is about 2 m long, and the other is about 4 m. The student knows she can use one of the planks to build a simple ramp. What is the mechanical advantage offered by each? Which would make moving the dresser easier?
Answer:
Use the formula for mechanical advantage (MA), where l is the length of the inclined plane and h is the height to which it is raised at one end:
First, plug in the given values for the shorter (2 m) plank:
Do the same for the longer (4 m) plank:
The longer plank, with a mechanical advantage of 4, would be twice as effective as the shorter plank at amplifying the force the student applies. This illustrates the force-distance trade-off: although the student must move the dresser a longer distance—across four meters instead of two—she can do so with less force. Doubling the length of the ramp while keeping the height the same doubles the mechanical advantage.
Inclined Planes Are Everywhere
Simple machines such as inclined planes permeate every aspect of daily life. Every staircase is like an unevenly built ramp, designed to let people ascend without tiring by moving diagonally instead of straight upward against gravity. Ramps have been used since antiquity to help move large loads and are common in construction and shipping.
More importantly, the principles of power, work, force, and mechanical advantage that govern the inclined plane, 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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