# Page 2-Mechanical Comprehension Study Guide for the ASVAB

## 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 (MA) of a machine when given the force of the effort and the weight or force of the load, use the formula:

$MA = \frac{Load}{Effort}$

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

$MA = \frac{100}{10} = 10$

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:

$MA = \frac{Effort_{distance}}{Load_{distance}}$

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

$MA = \frac{20}{1} = 20$

### 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.

#### Gears

The MA of a two-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:

$MA = \frac{20}{5} = 4$

#### Inclined Plane

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:

$MA = \frac{25}{5} = 5$

#### Lever

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 (e.g., a seesaw). 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 $$1$$
$MA = \frac{E_{distance}}{L_{distance}} = \frac{L_{force}}{E_{force}}$

Class $$2$$ levers have the fulcrum at one end (e.g., a 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 $$2$$
$MA = \frac{E_{distance}}{L_{distance}}$

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 $$3$$
$MA = \frac{Load}{Effort}$

#### Pulley

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.

#### Screw

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 $$2 \cdot \pi \cdot l$$, $$l$$ 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.

#### Wedge

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

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 compute 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). 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 its 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 letting it set, clay (and other such materials) will no longer be malleable.

## 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”.