Some Basic Concepts: Work, Energy, and Force
To do well on Mechanical Comprehension questions, you'll need to understand just a few basic concepts. For starters, you should know that in mechanics, work refers to a specific force applied over a specific distance. For example, your arm does work when it uses force to pick up a book. A lever does work when it uses force to lift a heavy object.
The ability to do work is called energy. Energy comes in several forms:
- Kinetic energy: Energy in a moving object.
- Potential energy: Energy that can be released under certain conditions. For example, potential energy is stored in objects when they are lifted off the ground. It is released when if the objects fall.
- Chemical energy: Energy stored in chemicals, such as in a flashlight battery. Chemical energy is potential until it is released in a chemical reaction.
- Electric energy: Energy in moving electrons in an electric current.
- Nuclear energy: Energy released by reactions in the nucleus of an atom.
- Solar energy: Energy in the heat and light from the sun.
On the ASVAB, you may be asked to tell which kind of energy is present in a given situation. For example, when a child's swing reaches its highest point and pauses momentarily before swinging back down, the swing has only potential energy and no kinetic energy. When it swings through its lowest point, the opposite is true: The swing has no potential energy (because it cannot fall any further) and all kinetic energy. As it swings back up the other side, the kinetic energy is converted back into potential energy.
Similarly, a battery stores electric energy as chemical energy. When the flashlight is turned on, electric energy passes through the filament in the flashlight bulb, where it is converted into heat and light.
Forces are powers that push or pull objects. A force has a magnitude (strength) that you can measure, and it has a direction. Some forces are obvious—when a bat hits a baseball, you can even hear the force being applied. Other forces, like gravity and air pressure, are much less obvious, but they are still real.
One kind of force is gravity. Gravity is an attractive force between objects. All objects create a gravitational attraction for each other. On Earth, gravity causes objects to fall toward the center of the Earth. Falling objects accelerate (fall faster) as they fall. (Acceleration is defined as the change in velocity, or speed in a particular direction.) If you discount air resistance, all objects fall at the same rate—a fact proved centuries ago by the Italian scientist Galileo. In real life, however, air resistance often disguises the fact that objects fall at the same rate.
Air resistance is a kind of friction. Friction is a force that results from the interaction between two surfaces that are touching each other. Friction acts as a resistance to the movement of an object. For example, friction makes it harder to push a heavy crate up a ramp. Friction also helps to keep the crate from sliding back down the ramp. Without friction, a car would slide all over the place because the tires could not get a grip on the pavement. Tables would slide all over the room, and billiard balls would never stop rolling! In machinery, friction can often be a problem. It can prevent machines from running smoothly and efficiently. That's why lubricants are used to reduce friction.
Two other forces are compression and tension. Compression is a force that pushes materials together. Tension is a force that pulls materials apart. Air pressure and water pressure are forms of compression. The force exerted by the cable in a pulley is a kind of tension. In a bridge, some parts are in compression and others in tension. The weight of the structure squeezes (compresses) the top and puts tension on the bottom. Steel reinforcing is strong in tension, so it is placed at the bottom of a bridge, where its tensile strength can support the load.
Principles of Mechanical Devices
Machines are devices that multiply force or motion. Some machines are simple devices that involve only a single force. A lever is an example. Other machines involve combinations of devices working together. A bicycle is an example. The essential thing about all machines is that in order to make them multiply your force, you must exert that force over a longer distance. You'll see how this works in the following section, which describes the main simple machines one by one. First, however, you need to learn how to calculate how much a machine multiplies your force.
Mechanical Advantage
The amount your force is multiplied by a machine is called the mechanical advantage, or MA. There are two ways to calculate MA.
- Divide the output force (called the load or sometimes the resistance) by the input force (called the effort): Load/effort = MA.
Example
With a lever, you use a 50-lb force (the effort) to lift a 200-lb weight (the load). What is the mechanical advantage of the lever? 200/50 = 4. MA = 4.
- Divide the length of the effort (called the effort distance) by how far the load moves (called the load distance): Effort distance/load distance = MA.
Example
With a pulley, you use 5 feet of rope (the effort distance) to lift a load 1 foot (the load distance). What is the mechanical advantage of the pulley? 5/1 = 5. MA = 5
Simple Machines
The simple machines are a group of very common, basic devices that have all been in use for a very long time. They are called simple because each one is used to multiply just one single force. The simple machines include the lever, the pulley, the inclined plane, the gear, the wedge, the wheel and axle, and the screw. You can count on the ASVAB to test your knowledge of simple machines.
Levers The first kind of simple machine is the lever, a device that helps you apply force to lift a heavy object. To understand levers, you'll need to know the following terms:
- Fulcrum: The stationary element that holds the lever but still allows it to rotate.
- Load: The object to be lifted or squeezed.
- Load arm (load distance): The part of the lever from load to fulcrum.
- Effort: The force applied to lift or squeeze.
- Effort arm (effort distance): The part of the lever from force to fulcrum.
There are three classes of levers. Let's examine them one at a time and see how to calculate MA for each.
Class 1 Lever In a class 1 lever, the fulcrum is between the load and the effort. If the fulcrum is closer to the load than to the effort (as it usually is), the lever has a mechanical advantage.
Mechanical advantage = effort distance/load distance = load/effort
Example
The figure shows a class 1 lever. What force (effort) is needed to lift the load? Since you know that MA = 3, use this formula to find the effort.
Class 2 Lever In a class 2 lever, the load is between the effort and the fulcrum. The effort arm is as long as the whole lever, but the load arm is shorter. So a class 2 lever always has a mechanical advantage.
Example
The wheelbarrow shown is a class 2 lever. What is its mechanical advantage?
MA = effort distance/load distance = 3/1.5 = 2
Class 3 Lever In a class 3 lever, the effort is between the load and the fulcrum. Tweezers and tongs are good examples of class 3 levers. The length of the effort arm and the load arm are calculated from the fulcrum, as with the class 2 lever.
Example
The figure shows a class 3 lever. What is the mechanical advantage?
MA = load/effort = 1/2 = 0.5
In other words, 2 pounds of effort would produce 1 pound of "squeeze" on the orange. We could call this a fractional mechanical advantage, or a mechanical disadvantage. But in return for reducing the squeezing force, each inch of effort movement produces 2 inches of load movement.
Balancing a Lever Some ASVAB problems may show you a diagram of a lever with various parts marked and ask you what force or weight is needed to balance the lever. To answer this kind of question, keep in mind that the moments of force (effort or load = distance) on either side of the fulcrum must be equal. Here is an example.
Example
What is the force F, in kilograms, needed to balance the lever? Add up the moments of force on either side of the fulcrum:
(2 kg × 8 ft) + (4 kg × 6 ft) = (8 ft × F)
Pulleys Another kind of simple machine that helps you lift a heavy object is the pulley, also called a block and tackle. In pulleys, the mechanical advantage is found in either of the following two ways:
- MA = effort distance/load distance.
- MA = number of supporting strands. Supporting strands of rope or cable get shorter when you hoist the load. We'll return to this, but don't just count strands—some do not shorten as you hoist.
Example
The figure shows a pulley attached to a beam that is used to hoist a heavy crate. Each foot of pull on the rope lifts the crate 1 foot. Effort distance = load distance, so MA = 1. Although this pulley allows you to pull down instead of up, it gives no mechanical advantage.
Example
The figure shows two pulleys. When you hoist, two strands of the rope must be shortened. So for every 2 feet of pull (effort distance), you get 1 foot of lift (load distance).
MA = effort distance/load distance = 2/1
The simplest way to find the pulley MA is to count the strands of rope on the movable pulley (in this case, the one attached to the load). MA = number of supporting strands.
Until now, we have ignored friction and the weight of the movable pulley and extra rope. As MA increases, these factors also increase, so there is a practical limit to the mechanical advantage of pulleys.
Gears Gears are a simple machine used to multiply rotating forces. Finding the MA of a gear is simplicity itself. Identify the driving gear (the one that supplies the force) and count the teeth. Count the teeth on the driven gear. Then use this formula:
Number of teeth on driven gear/number of teeth on driving gear = MA
Example
The figure shows a driving gear with 9 teeth and a driven gear with 36 teeth.
You will learn more about systems of driving and driven gears later in this chapter.
Sheaves Sheaves (often also called pulleys) and belts are a simple machine closely related to gears. To calculate the MA of a sheave system, divide the diameter of the driven sheave by the diameter of the drive sheave:
MA = driven diameter/drive diameter
Whenever the driven sheave is larger than the drive sheave, you get a mechanical advantage.
Example
The figure shows a sheave system. What is the MA?
You will learn more about systems of sheaves (pulleys) later in this chapter.
Inclined Plane Inclined plane is a fancy term for "ramp." An inclined plane is another simple machine that is used to lift heavy objects. The formula for finding the mechanical advantage of an inclined plane is as follows:
MA = length of the slope/vertical rise
To find the mechanical advantage, measure vertically and diagonally along the ramp.
Example
The figure shows an inclined plane. What is the mechanical advantage?
If the load weighs 400 lb, how much force is needed to push it up the ramp?
In real life, friction can play a huge role in ramps if the load is not on wheels. Most ASVAB problems will allow you to ignore friction in dealing with all simple machines.
Wedge The wedge is a type of inclined plane. It is one of the rarer simple machines. As always, MA = effort distance/load distance. The wedge is essentially two inclined planes, and the MA calculation also requires you to measure perpendicular to the long axis of the wedge.
Example
The figure shows a wedge. What is the MA?
Every time the wedge moves 5 inches, the load will move 2 inches. MA = 5/2 = 2.5. In reality, friction plays a major role in wedges.
Screw Screws are some of the handiest simple machines, although we usually think of a screw as a fastener rather than as a way to multiply force. Finding mechanical advantage can be complicated because it comes from two sources: the threads and the wrench you use to tighten the screw. But if you consider effort distance and load distance, the calculation is simple.
MA = effort distance/load distance
Example
The figure shows an 8-inch wrench turning a screw with 8 threads per inch. This screw has a pitch (movement per turn of the screw) of 1/8 inch. The effort distance is π × diameter = 3.14 × 16 inches = about 50 inches. The load distance per turn of the wrench is 1/8 inch, so MA = 50/1/8 = 400. In reality, the MA is much less, because of friction and because you don't push on the absolute end of the wrench. But this still demonstrates the power of screws as simple machines!
Most ASVAB questions will not require this much calculation, but it never hurts to be prepared!
Wheel and Axle Wheels are a common and essential part of daily life, but most of these wheels are not simple machines. Instead, they are a way to reduce friction by the use of bearings. A wheel and axle is a simple machine only when the wheel and axle are fixed and rotate together.
A typical wheel-and-axle simple machine is the screwdriver. The screwdriver's handle is the wheel, and the screwdriver's blade is the axle. For wheel-and-axle machines, mechanical advantage is calculated as follows:
MA = effort distance (radius of the wheel)/load distance (radius of the axle)
So for a screwdriver, MA = radius of the handle/ radius of the blade.
Example
The figure shows a brace and bit, a kind of heavy-duty screwdriver that is an example of a wheel and axle as a simple machine. What is the MA?
Effort distance/load distance = MA
A wheel and axle can also give a mechanical disadvantage. In a car or a bicycle, where the axle drives the wheel instead of the wheel driving the axle, a small motion at the axle creates a large motion at the circumference of the rim. In these cases, you need a larger force, but you get more motion in return.
Compound Machines
A compound machine is one in which two or more simple machines work together. For example, a screwdriver (wheel and axle) driving a screw is a compound machine. To find the mechanical advantage of a compound machine, multiply the MA of the simple machines together.
Example
The axe shown is a compound machine. The handle is a lever, and the head is two inclined planes. Find the combined MA by multiplying the individual MA of each simple machine.
Structural Support
Some Mechanical Comprehension questions ask about the load carried by support structures such as beams or bridges—or sometimes by people. You will be given a diagram showing support structures and asked which one is strongest or weakest, or which support in the diagram is bearing the lesser or greater part of the load. To answer this kind of question, keep this in mind: When a load of any kind is supported by two support beams, posts, or people, the load is perfectly balanced if it is exactly centered. In that case, each beam, post, or person is bearing exactly half the load. However, if the load is not centered, then the beam, post, or person nearer to the load is bearing the greater part of the weight.
Example
The figure shows two people carrying a load. The load is centered. Each person is bearing half the load, or 75 lb.
Example
The figure shows two people carrying a load. Which person is bearing the greater part of the load? Common sense tells you that it's the woman, because she is closer to the load.
Questions about structural support may also ask you to decide which of several support structures is the strongest (or weakest). For this kind of question, you can often use your common sense. If a diagram shows several different structures, look for the one with the most brackets or other support elements. Also look for the one that leaves the least horizontal area (for example, the front part of a flat bookshelf) unsupported. A bracket that runs the whole width of the shelf provides better support than one that does not.
Example
Which of these four shelves can bear the most weight?
Choice D can bear the most weight. Of the four shelves, it is the strongest because it has the largest brackets, and because it has the most brackets.
Shape can also make a difference in the strength of a support structure. For example, a structure in which the support beams form rectangular shapes is not as strong as one in which the beams form triangular shapes. The reason is that while rectangular supports can easily bend out of shape, a triangle keeps its shape unless it falls apart entirely. That's why triangular shapes are used in support structures such as shelf brackets. That is also why you often see triangular shapes in the support structures of bridges, towers, and other buildings.
Example
Which bridge is the strongest?
In the diagram, bridge C is the strongest because its framework is made of many triangles.
Properties of Materials
Tools, machines, and structures can be made of many different materials, such as wood, metal, plastic, and the like. Each material has its own properties, or characteristics. Some Mechanical Comprehension questions will ask you about those properties, or ask you to compare the properties of different materials. Most questions of this type can be answered with simple common sense, based on your everyday experience. For some, you may need to recall some of the basic ideas you learned in high school science.
One of the most important properties of materials is the ability to conduct heat. Here is an example of a question about this property.
Example
Three pots are cooking on a stove. Pot A has a wooden handle, pot B has a metal handle, and pot C has a plastic handle. Which handle will feel hottest to the touch?
- A
- B
- C
- All three will feel equally hot
To answer this question, think about your everyday experience. For which pot would you need a potholder? You might also remember from a high school science class that metal is a better conductor of heat than either wood or plastic. The correct answer is choice B.
Another important property of some materials is the ability to bend without breaking. This is called flexibility. The springs on a car can bend millions of times without breaking because they are made of spring steel. A ceramic cup, on other hand, cannot flex even once without breaking. Materials that are somewhat flexible include regular steel, copper, and wood. Some flexible materials will spring back to their original shape after bending. Others will stay in the new shape.
Example
Which object shown will resume its original shape after bending?
The spring (choice C) will resume its original shape. Nails, screws, and bolts are not made of spring steel, and while you can bend them, they will not spring back into their original shape.
Another important property of some materials is the ability to be formed into a new shape through repeated blows from a hammer. This property is called malleability. You will probably not need to be able to recall this term, but you should be able to identify substances that have this property. Metals like steel and copper are malleable and can thus be formed into the shapes of tools, containers, and other objects. Glass and ceramics, on the other hand, are not malleable.
Still another important property of some materials is the ability to stretch without breaking. Rubber can stretch in this way. Metal, glass, and plastic can stretch when heated. Wood and paper, on the other hand, will not stretch.
Practice problems for this study guide can be found at:
Mechanical Comprehension Practice Problems for McGraw-Hill's ASVAB
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