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# Page 1 Mechanical Comprehension Study Guide for the ASVAB

## How to Prepare for the ASVAB Mechanical Comprehension Test

### General Information

The Mechanical Comprehension section of the ASVAB test is designed to measure your aptitude for understanding basic mechanics. This does not necessarily mean always knowing the technical terms, but you do need to know what happens in simple mechanics. This section may not be used as widely as sections such as Word Knowledge or Arithmetic, but understanding basic mechanics is essential for certain important jobs in the military.

This test has three subsections: the principles of mechanical devices, mechanical motion, and fluid dynamics.

### Principles of Mechanical Devices

The principles of mechanical devices may involve questions about mechanical advantage, simple machines, compound machines, structural support, and properties of materials.

#### Work

In physics, work is defined as a force acting on an object resulting in a displacement. Force, equal to mass times acceleration, is commonly measured in Newtons. Displacement, a movement from one location to another, is commonly measured in meters. Work is the product of force and displacement and is commonly measured in Joules (Newton meters).

Work = Force x Displacement

Work can be positive or negative depending on the relationship between the direction of the applied force and the direction of the displacement. Force applied in the same direction as the displacement results in positive work, and force applied in the opposite direction as the displacement results in negative work.

Example: A 10N force is applied to a table to move it 5 meters. How much work is performed on the table by the force?

W = Fd W = (10N)(5m) W = 50Nm = 50 J

#### Energy

Energy can be thought of as the capacity to perform work. Regardless of the type of energy in question, all energy can be used to perform work.

In cases where there are no nonconservative forces acting on an object, the total mechanical energy is equal to the sum of the potential energy and kinetic energy of the object:

In cases where there is a nonconservative force acting on the object, the total energy is equal to the sum of the potential energy, the kinetic energy, and the work performed by the nonconservative force during the movement of the object:

##### Kinetic

Kinetic energy is energy associated with the motion of an object. It is described by the formula:

where m is mass, and v is velocity. Kinetic energy, like work, is measured in Joules.

Work and kinetic energy are related via the work-energy theorem, which states that the change in kinetic energy of an object is equal to the amount of work done. That is:

##### Potential

Potential energy is energy associated with the position of an object or objects. Potential energy comes in many forms: gravitational potential energy, elastic potential energy, electrical potential energy, etc. Gravitational potential energy is described by the equation:

where m is the mass of the object, g is the acceleration due to gravity, and h is the height of the object relative to a defined “ground,” of y = 0. As the object is raised higher, it gains more potential energy; as the object is lowered, it loses potential energy.

In the case of gravitational potential energy [when ignoring the friction force of air (drag)], when an object is released from a particular height, the amount of kinetic energy associated with the object is equivalent to the loss of potential energy up to that point.

Stated another way, when the object is stationary at its apex, it possesses entirely potential energy. As it falls, its potential energy is transformed into kinetic energy (and the work done by air friction in opposition to the object’s fall) until the very last moment right before the object hits the ground, when the object no longer possesses only kinetic energy and no potential energy.

##### Other Types of Energy

Chemical—the energy associated with the bonds found in molecules (As bonds are formed and destroyed, energy is gained or released in the form of heat or light.)

Electric—the energy associated with electrons in motion, otherwise known as a current

Nuclear—the energy associated with the composition of the nucleus of an atom

Solar—the energy associated with the light and heat released by the sun

#### Power

Power is defined as the amount of work done during a period of time:

It is measured in joules per second, otherwise known as watts.

#### Force

Forces are responsible for the interactions between two or more objects. They are vector quantities, possessing both a magnitude and a direction.

Most forces can be thought of as “pushes” or “pulls” (think attraction or repulsion, as in the case of the force of gravity, or the electric force).

When an object experiences no acceleration (equivalent to undergoing constant velocity), the sum of the forces acting on the object sum to 0.

##### Gravity

Gravity is the force of attraction acting between two masses. This force is described in the equation:

where G is the universal gravitational constant, $m_1$ is the first mass, $m_2$ is the second mass, and r represents the distance between the centers of the masses. The force of gravity is only attractive.

Gravity is the reason that any dropped object falls to the ground.

##### Friction

Friction is the force that opposes an object in motion; it is always opposite to the direction of motion. It arises from the microscopic interactions between surfaces.

In a system involving work done by friction, as in the case of a block sliding down a ramp, or a table pushed across a floor, the total energy in the system can be found by summing the potential energy, the kinetic energy, and the work done by friction.

##### Compression

Compression is a force applied inward from opposite sides of an object. Compression can be thought of as a force that squeezes an object. It is a pushing force.

##### Tension

Tension is a type of force that is exerted when pulling. We typically use pounds or Newtons to measure tension. It can occur when an object is tied to a rope or cable or when two ends of a rope are pulled in opposite directions.

### Mechanical Motion

The mechanical motion questions may include topics like systems of pulleys, systems of gears, rotating wheels and disks, cam and cam followers, and cranks and pistons.

Mechanical advantage is the amplification of a force by way of a machine. Utilizing mechanical advantage enables the output force to be larger than the input force.

To calculate the mechanical advantage of a machine when given the force of the effort and the weight or force of the load, use the formula:

For example, a 100 N object is lifted with a 10 N force, the mechanical advantage of this system is:

Other situations may involve not the magnitude of the forces, but the distances of the forces from a particular point. In these cases, the mechanical advantage can be computed using the formula:

where:
the $Load_{distance}$ is the distance the load travels or the distance from the fulcrum to the load
and
the $Effort_{distance}$ is the distance the effort travels or the distance from the fulcrum to the effort force

For example, a box is 20 m from a fulcrum and a force is applied at a location 1 m on the opposite side of the fulcrum, the mechanical advantage can be found by solving the equation:

#### Simple Machines

Simple machines are those used to amplify only one force. Gears, inclined planes, levers, pulleys, screws, wedges, and wheels and axles are all examples of simple machines. Each of these simple machines involves the usage of mechanical advantage to perform work.

The MA of a 2 gear system can be found by computing the ratio of the number of teeth of the gear being acted on to the number of teeth of the gear providing the driving.

For example, a gear with 20 teeth is being driven by a gear with 5 teeth, the MA can be found using:

Inclined planes make it easier to move an object by distributing the work required over a longer distance. The MA of an inclined plane can be found by computing the ratio of the length of the slope over the vertical rise of the slope.

For example, an inclined plane has a slope length of 25 m and a vertical rise of 5 m, its MA is:

There are three simple machine lever classes with which to be familiar:

Class 1 levers have a fulcrum between the load and the effort force (for example: see-saw). The MA of a class 1 lever is equal to the distance from the fulcrum to the effort force divided by the distance from the fulcrum to the load. This is also equivalent to the load force divided by the effort force:

Lever 1

Class 2 levers have the fulcrum at one end (for example: wheelbarrow) with the load closer to the fulcrum. The MA of a class 2 lever is calculated in the same manner as the class 1 lever:

Lever 2

where the load distance is calculated from the center of the load.

Class 3 levers have the fulcrum at one end with the force effort closer to the fulcrum. The MA of a class 3 lever is found by computing the ratio of the load force to the effort force:

Lever 3

The MA of pulleys can be found by taking the ratio of the effort distance with the load distance, where the effort distance is the distance from the effort force to the pulley and the load distance is the distance from the pulley to the load. In cases where there are multiple ropes attached to a load, the MA is equivalent to the number of attached ropes.

As you may have noticed, every MA problem entails first finding the effort force or distance and the load force or distance then calculating the ratio. Finding the MA for screws is no different. The MA of a screw is the ratio of the effort distance to the load distance, where the effort distance is $2 \cdot \pi \cdot l$, where $l$ is the length of the tool used to rotate the screw and the load distance is the distance the screw travels in one full turn.

An axe is an example of a wedge. Its MA can be computed by taking the ratio of the length of the wedge with the width or height of the wedge.

Wheel and axle machines, like a screwdriver, have an MA equivalent to the effort distance divided by the load distance, where the effort distance is equal to the radius of the screwdriver’s handle and the load distance is equal to the radius of its blade.

#### Compound Machines

Compound machines are those made up of more than one simple machine. To calculate the mechanical advantage of a compound machine, find the mechanical advantage of each of the simple machines of which it is composed and computing their product.

For example, if a compound machine is made up of three simple machines, one with an MA of 5, one with an MA of 2, and the last one with an MA of 1, the MA of the compound machine is $5 \cdot 2 \cdot 1 = 10$.

#### Structural Support

Structural support concerns the strength or weakness of the columns or frameworks upholding a structure. This can also involve objects being upheld between two or more people.

When analyzing a structural diagram presenting support(s), consider the location and/or distribution of the structure in relation to the quantity and type of support. For example, if a group of four people is carrying a weight and the weight is equidistant from each person, then each person is bearing the same portion of the weight. However, if the weight is closer to one of the people in the group, then that person is bearing a larger portion of the weight.

This concept can also apply to structures (like bridges for example). When comparing the strengths of these support structures, consider the number and type of the framework.

#### Properties of Materials

As a result of the inherent composition of materials (something beyond the scope of this test), different objects possess different properties. Three such properties of materials are heat conduction, flexibility, and malleability.

Heat conduction is the ease with which an object can conduct heat. From your experience, you may have noticed that some objects readily become hot when near a heat source, whereas other objects take a longer time to become hot. Those objects that quickly heat are said to conduct heat well. Metals are strong heat conductors. Plastic is not as good at conducting heat as metal.

Flexibility describes how well an object can bend without breaking and return to their original position. Springs are very flexible whereas glass is very inflexible.

Lastly, malleability describes how easily an object can be reformed into a new object. Something like clay or dough is extremely malleable; however, after applying heat and setting, something like clay will set and will no longer be malleable.

### Fluid Dynamics

The final subsection, fluid dynamics, usually involves questions about air pressure, water pressure, and filling and emptying tanks.

#### Air Pressure

Recall that the attractive force of gravity pulls everything with mass toward a central location. Because air is composed of millions of tiny molecules, air is also influenced by the gravitational force. This attractive force gives rise to the atmosphere surrounding earth. Additionally, because the force of gravity is stronger at the surface of the earth than it is 100 miles above the surface, there is more atmosphere closer to the surface. This increased atmospheric density is the underlying reason for a greater atmospheric pressure at the earth’s surface.

Air pressure can be thought of as the weight of the air acting on an area. This can be envisioned by imagining a portion of air trapped inside of a rectangle. The larger the imagined rectangle, the greater the air pressure (because there is more air, so more weight), and if the rectangle is kept the same size but more air is added (increasing the density) the air pressure also increases.

#### Water Pressure

Water, a fluid (like air), also exhibits pressure properties. Much like the atmospheric description, as one descends deeper into a body of water, the body of water exerts an increasing force per unit of area (because there is a larger amount of water weight above). There is another important concept related to fluid pressure that should be understood.

The hydraulic lift exploits fluid pressure to lift heavy objects with lighter objects and the aid of pressure. Hydraulic lifts utilize incompressible fluids (those that cannot be further condensed, like water) to transmit force through the fluid.

Consider two cylinders of different radii that are connected through a tank base and filled with a fluid. A force applied to one of the cylinders, because of the incompressibility of fluid, must be transferred to the other cylinder. This relationship can be quantified with the equation:

where $A_x$ represents the cross sectional area of the cylinder and $D_x$ represents the distance traveled by each of the cylinders/fluids. The MA of the system can be deduced from this relationship and expressed as:

#### Filling and Emptying Tanks

Occasionally a problem will arise that involves a tank that is being filled, emptied, or filled and emptied at a particular rate. These problems will often involve the conversion of a flow rate from seconds to minutes, or minutes to hours (etc.) and the combination of an inflow with an outflow. Recall that any inflow increases the amount of fluid in a tank and any outflow reduces the amount of fluid in a tank.

Consider a tank that is being filled at a rate of 1.5 gallons per hour. At the end of 4 hours, the tank will have a fluid volume of $1.5 \cdot 4 = 6$. If the tank is now emptied at a rate of 0.5 gallons per hour, how long will it take before it is empty?

If there are 6 gallons currently in the tank, and 0.5 gallons empty every hour, then 1 gallon empties every 2 hours. Multiplying this with the number of gallons will yield the amount of time required:

In cases where an inflow rate and an outflow rate are both provided, compute the total inflow volume after the amount of time specified, then compute the total outflow volume over the same period of time. The amount of fluid remaining after the time period will be the difference between the two volumes.

### The Physics Connection

To do well on this test, review your knowledge of fundamental physics. You don’t necessarily need to memorize all the terms you may have been forced to learn in high school, but you do need to understand how certain objects react to each other. For example, know how objects like levers, pulleys, gears, and pistons work. Note, however, that this test is not a judgment of how knowledgeable you are about physics; it is rather a judgment of how well you are able to comprehend the fundamentals of mechanical principles. It may gauge your ability to discern what will happen to a crane when its reach is extended (the center of gravity shifts), what direction friction acts on an ice skater, or how PSI (pressure per square inch) is calculated.

Some fundamentals of physics that should be reviewed include force (force = mass × acceleration), action/reaction, equilibrium, pressure, kinds of force (friction, gravity, magnetism, recoil, and static electricity), work, and energy. If you do not remember or understand these basic laws, review and learn them well. Though many questions do not require knowing formulas and can be solved in your head, some of the questions do require some calculation.

### Tips For Success

When taking the Mechanical Comprehension section of the ASVAB test, remember a few good tips:

First, bear in mind that the amount of force needed to move an object is never more than the weight of the object. This does not include resistance based on friction.

Second, when trying to decide between several answers, narrow it down to the answers that are mechanical. If an answer does not give a mechanical explanation to the problem, it is most likely wrong.

Third, a change in a mechanical operation will usually have pluses and minuses associated. For example, if a question asks what will occur when x changes, the answer is most likely one that involves both a “positive” and “negative,” “increase” and “decrease,” or “gain” and “loss.”