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# Mechanical Comprehension Review for Armed Services Vocational Aptitude Battery (ASVAB) Study Guide (page 3)

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Updated on Jun 23, 2011

### Velocity

Velocity means the rate at which an object is moving in such units as miles per hour or feet per minute. Exam questions on velocity might ask you to use velocity and time to determine the distance traveled. For instance, if a car travels at a constant velocity of 60 miles per hour for two hours, how far does it travel? The answer is velocity multiplied by time, or 60 mph times 2 hours for a total of 120 miles. You might also be asked about relative velocity in a question in which two objects travel at different speeds for different lengths of time.

### Direction

If you want to travel quickly from Kansas City to Denver, your velocity is unimportant if you're not traveling in the right direction. When answering mechanical motion questions, always note the direction of travel of the object or objects, if this information is given. Again, drawing a sketch of the situation usually helps.

### Acceleration

Acceleration is the rate of change of velocity or, in other words, how much faster you are going from one minute to the next. This is simpler than it sounds. If you are sitting in your car at a stop sign and then you press hard on the gas pedal, you get pushed back into the seat a bit. If you are traveling along the highway at a constant 50 mph, you don't have this feeling. However, if you hit the gas and accelerate to 65 mph, you are again pushed back into your seat. You have the same sensation when your airplane takes off on the runway. This sensation is the result of acceleration, an increase in how fast an object is traveling. The opposite of acceleration is deceleration, slowing down. Exam questions on acceleration may involve a little simple math.

### Friction

Friction is the naturally occurring force that acts to hold back an object in motion. If you slide a block of wood across a floor, the friction between the floor and the block causes a drag on the movement of the block. There are two things you should remember if you encounter an exam question about friction:

• Friction always slows down movement.
• All movement experiences frictional force to some degree.

The drag force of friction varies depending on the materials involved. If you've ever tried to drag a piece of furniture from a room with a carpeted floor to another room with a wood floor, you found that the piece of furniture was much easier to drag on the wood floor than on the carpet. The carpet has a higher coefficient of friction than wood. Materials with a high coefficient of friction include such things as sandpaper and brick. Examples of materials with a low coefficient of friction include non-stick cooking surfaces and ice. The differing coefficients of fiction explain why it's more difficult to pull a wooden block across a rough surface such as sandpaper than across a slick surface such as ice.

### Fluid Statics and Dynamics

The Mechanical Comprehension subtest includes questions on the behavior of fluids, including questions on pressure, density, and buoyancy.

### Pressure

As a solid object is submerged below the surface of a fluid, the fluid exerts a pressure on it. Have you ever noticed that when diving in a swimming pool you feel more and more pressure on your ears as you go deeper? This is the effect of the pressure of the fluid, water in this case, on your body. The fluid has weight. As you go deeper, more of this weight presses on your body. All fluids behave this way. The deeper a solid object is submerged, the higher the pressure. This behavior of fluids affects the design of machines such as submarines.

The formula for pressure is:
pressure = density × depth.

### Density

Density is a proportion of weight to volume. If you are comparing two fluids, for example, a gallon of the one with the higher density weighs more than the same volume (a gallon) of another liquid. The density of a solid object or other fluid is usually compared to the density of water, 62.4 pounds per cubic foot. Density controls whether an a solid object or another fluid will sink or float in a given fluid. If a solid object sinks when placed in water, then its density is more than that of water. Conversely, if an object floats, then it is less dense than water. Some liquids, such as mercury, are more dense than water. If mercury and water are combined in a jar, the water will float on top of the mercury. Other fluids, such as gasoline or motor oil, are slightly less dense than water. That is why when an oil tanker has a spill, it leaves an oil slick—the oil is floating on the surface of the water.

Density influences the amount of pressure a fluid exerts on an object. The denser the fluid, the faster the pressure increases on an object as it is submerged. Exam questions on density may include simple mathematical calculations, such as computing pressure by multiplying density times depth. Or they may simply ask you to compare the effects of pressure at different depths and densities.

### Buoyancy

Buoyancy is the force that acts to push an object submerged in a fluid to the surface. When you force a beach ball under water and then let it go, it springs to the surface. That's the effect of buoyancy.

Here's an example that shows how buoyancy works for an object that is denser than water. Let's say you have a glass that is completely full of water, and the water in the glass weighs one pound. Now put in a eight-pound steel ball, which occupies half of the volume of the glass. When the ball sinks, what happens? Half of the water in the glass, a half-pound worth, spills over the edge of the glass because the ball occupies half the volume of the glass. Now, here's a definition: the uplifting buoyant force acting on this ball is equal to the weight of the water displaced out of the glass by the ball. By definition, therefore, this ball weighs half a pound less when submerged in water than it does just sitting on the table.

The ball weighs less underwater, but it still sinks. Why? Because the ball weighs more than the water it displaces. How, then, is it possible to make a ship that floats in water out of steel, when steel is more dense than water? Simple. Take a thin sheet of steel and form it into a kind of bowl shape. As this thin shell is lowered into the water, it will displace enough water to make it float.

### Properties of Materials

Mechanical components and systems can be fabricated using many different materials such as steel, wood, concrete, and plastic. All of these materials react differently to stress, temperature changes, and other external factors. You must understand the properties of materials—weight, strength, density, and thermal properties—in order to answer test questions about them.

### Weight

The weight of an object is simply a measure of its heaviness.

### Strength

The loads and stresses placed on a material must be less than the strength of the material in order to prevent failure. A material's strength can be measured in several ways. A concrete building foundation has lots of weight compressing on it and must have high compressive strength. A steel construction girder has a large pulling force acting on it and must therefore have a high tensile strength. The materials selected for a given project depend in part on the loads the structure will have to bear.

### Density

Think of a one-gallon bottle full of feathers and another full of steel. Which bottle would be heavier? Both bottles have the same volume, but the one full of steel would obviously weigh more, because steel has a higher density (weight per unit volume) than feathers. Feathers have a low density; it would take a large volume—a big stack of them—to amount to any significant weight. On the other hand, a small volume of steel, which has a fairly high density, is reasonably heavy. Just remember that a material with a higher density will hurt more if you drop it on your toe!

In the English system of units, density is typically measured in pounds per cubic foot or pounds per cubic inch.

### Thermal Properties

The thermal properties of materials—how they respond to changes in termperature—affect their suitability for various applications. Most materials expand slightly as the temperature increases and contract as the temperature decreases. This amount of expansion and contraction varies for each material but is typically very small; you could not see it with your eyes.

The effect of even this small amount of expansion or contraction can be significant on some mechanical systems. For instance, the internal combustion engine of a vehicle generates heat as it operates. All of the parts of the engine must be manufactured so that they fit together properly at both high and low temperatures. Likewise, an airplane experiences very low temperatures when flying at high altitudes, so that the metal of its body contracts a bit. The designers of the airplane must take this effect into account.

The strength of some materials is also affected by changes in temperature. Most materials get weaker as the temperature increases because the bonds between the individual molecules that make up the material get weaker as the molecules move more rapidly. This is why some building materials, such as steel, are coated with insulation during construction. If the building catches fire, the insulation will help maintain the strength of the steel girders.

### Choosing Materials for a Given Application

In deciding what materials to use for a given application, weight, strength, density, and thermal properties must all be taken into consideration. For instance, if you wanted to build an airplane wing, you might consider using either steel or aluminum. Steel is stronger than aluminum. However, aluminum has a lower density; that is, an aluminum wing would be lighter than a steel wing of the same size. Therefore, you could use more aluminum to provide adequate strength and still have a lighter total weight.

Other factors, such as cost and how easy the materials are to work with, are also taken into account when selecting materials for a project.

### Structural Support

Mechanical systems such as buildings and bridges require proper structural support in so they can hold up heavy loads. An object's center of gravity and its weight distribution affect the design of structural support.

### Center of Gravity

The center of gravity of an object is the point at which all of the object's weight appears to act. For instance, you can balance a pencil on your finger by placing your finger under the pencil at the middle of its length. The center of gravity of that pencil is halfway along its length. Likewise, a round ball has its center of gravity at its center. Other objects that are not so symmetrical also have a center of gravity, which can be located through calculations.

Exam questions on center of gravity usually involve symmetrical objects so that the math does not become complicated. Take your time, draw a sketch of the object, and use common sense.

### Weight Distribution

The distribution of weight on a structure such as on a bridge is also important to understand. If there are three trucks uniformly spaced across the length of a bridge that is supported only at its ends, then each support bears an equal amount of the load. However, if the trucks are all located close to one end of the bridge, then the support on that end will be holding up a higher load than the support on the opposite end.

Bridges and buildings have highly variable loads. The worst-case weight distribution must be accounted for—for instance, trucks standing nose to tail for the whole length of the bridge—even if that isn't very likely to happen

As with most Mechanical Comprehension questions, using the picture given, or drawing one if it's not provided, will help you see the location and distribution of the objects.