# Page 1 - Mechanical Comprehension Study Guide for the ASVAB

## 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 other sections**, such as *Word Knowledge* or *Arithmetic Reasoning*, but understanding basic mechanics is **essential for certain important jobs in the military**.

## Principles of Mechanical Devices

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

### Mass

To understand mass, you must first understand what matter is: anything that has mass and takes up space. Mass is considered **the amount of matter in any object** and it is *not* dependent on gravity.

### 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 zero.

#### 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 since all objects on Earth are impacted by the pull of Earth’s gravity.

#### 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.

### Newton’s Laws of Motion

In order to explain the motion of objects, Sir Isaac Newton developed what are known as the three laws of motion.

#### First Law

Newton’s first law of motion states that an object at rest will stay at rest and an object in motion will stay in motion unless acted on by an outside force. This law is also referred to as the **law of inertia**. Recall that *inertia* is the tendency of an object to resist a change in motion.

#### Second Law

Newton’s second law of motion describes the **relationship between mass, force, and acceleration**. The acceleration of an object will be directly proportional to the force exerted on an object, meaning if one goes up, so does the other. In addition, acceleration has an inverse relationship to an object’s mass, meaning that as one increases the other decreases.

#### Third Law

Newton’s third law of motion states that for every action there’s an **equal and opposite reaction**. For example, if you push on a wall, the wall is pushing against you with the same amount of force.

## Fluid Dynamics

Questions about fluid dynamics usually relate to 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 Earth’s surface 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 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:

\[A_1 \cdot D_1 = A_2 \cdot D_2\]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:

\[\frac{D_1}{D_2} = \frac{A_2}{A_1}\]### 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 (and so on), 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:

\[6\; gallons \cdot 2 \;hours = 12\]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.

## Torque

Torque refers to the twisting force being applied to an object.

## Work, Energy, and Power

Work, energy, and power are three important **scalar quantities** (those that can be described by numerical value alone, not with direction) in physics. Each is outlined below.

### Work

In physics, work is defined as **a force used to move an object a particular distance**. **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 Distance

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, at which point the object 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**.