2022 / 2023 ASVAB For Dummies

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Understanding Physics Forces for the ASVAB Test

You will want to have a basic understanding of the forces studied in physics for the ASVAB. By applying force (a push or pull), you can open the door or close it, speed it up (slam it) or slow it down (catch it before it slams), or make it change direction (push it shut when the wind blows it open).

In physics, applying force allows changes in the velocity (the speed and direction) of an object. A change in velocity is known as acceleration. Here’s the mathematical formula to determine force:

Force = Mass x Acceleration

Martial artists use this concept all the time. Although a larger fighter may have more size (mass), a smaller fighter can usually speed up more quickly (have more acceleration), possibly resulting in both fighters’ applying the same amount of force. This concept is why 110-pound martial artists can break boards and bricks just as well as 200-pound martial artists.

The basics of action and reaction

Sir Isaac Newton sure was one of the sharpest crayons in the box. His third law of motion states that for every action (force) in nature, there’s an equal and opposite reaction. In other words, if object A exerts a force on object B, then object B also exerts an equal and opposite force on object A. Notice that the forces are exerted on different objects. As you sit in your chair, your body exerts a downward force on the chair, and the chair exerts an upward force on your body. There are two forces resulting from this interaction: a force on the chair and a force on your body. These two forces are called action and reaction forces. This force can also be used to describe how a motorboat moves through the water. As the propellers turn, they push the water behind the boat (action). The water reacts by pushing the boat forward (reaction).

Equilibrium: Finding a balance

Forces are vector quantities. That means they have both a magnitude (size) and a direction associated with them. Forces applied in the same direction as other forces increase the total force, and forces that move in opposite directions reduce the total force. In general, an object can be acted on by several different forces at any one time.

A very basic concept when dealing with forces is the idea of equilibrium or balance. When two or more forces interact so that their combination cancels the other(s) out, a state of equilibrium occurs. In this state, the velocity of an object doesn’t change. The forces are considered to be balanced if the rightward forces are balanced by the leftward forces and the upward forces are balanced by the downward forces.

If an object is at rest and is in a state of equilibrium, then it’s at static equilibrium. Static means being stationary or at rest. For example, a glass of water sitting on a table is at static equilibrium. The table exerts an upward force on the glass to counteract the force of gravity.

Under pressure: Spreading out the force

Pressure is a measurement of force over an area. Pressure is usually measured in pounds per square inch (psi). The formula for deriving pressure is If 50 pounds of force is exerted on 10 square inches of surface, the amount of pressure is 5 pounds per square inch (5 = 50 / 10). Consider this: If you’re sleeping in bed, the amount of pressure being exerted per square inch is much less than when you’re standing on your feet. The surface area of the bottoms of your feet (supporting all that weight) is much less than the surface area of all your body parts that touch the mattress.

Ever wonder how a person can lie on a bed of nails? The answer involves elementary physics. His or her body rests evenly on hundreds of nails; therefore, no individual nail exerts a great amount of pressure against the skin. Have you ever seen someone stand on a bed of nails? It’s unlikely because more pressure is on the feet, and the nails would puncture the feet.

A barometer is a gauge that measures atmospheric pressure. Normal atmospheric pressure is 14.7 psi. A change in air pressure means the weather is about to change.

Kinds of forces

Here are some of the forces that act on objects:

• Friction: Resistance to the motion of two objects or surfaces that touch
• Gravity: The physical property that draws objects toward the center of Earth (and other objects that have mass)
• Magnetism: The property of attracting iron or steel
• Recoil: The property of kicking back when released
• Static electricity: The production of stationary electrical charges, often the result of friction

Friction: Resisting the urge to move

When one surface (such as a floor) resists the movement of another surface (the bottom of a piano), the result is frictional resistance. (This friction isn’t like resisting orders to cut the grass. That type of resistance may cause friction between you and your dad, but I’m talking about a different kind of resistance here.) In order to perform work — that is, to get an object to move in the direction you’re pushing or pulling — sometimes you have to overcome friction by applying more force. For example, when you’re moving a piano across a smooth, vinyl floor, little friction is produced, so the amount of force required to push the piano comes from the piano’s weight and the very minor friction produced by the smooth floor. But when you’re moving a piano across a carpeted floor, more friction is produced, so you have to push harder to move the same piano the same distance. Rolling friction (like the friction that occurs when you roll a wheel along the pavement) is always less than sliding friction (which occurs when you shove a piano along the floor). If you put wheels on a piano, it’s much easier to push! You can decrease friction by using a lubricant. Oil, grease, and similar materials reduce friction between two surfaces. So theoretically, if you oil the bottom of a piano, it’s easier to move! (Oiling the bottom of your piano isn’t recommended — for reasons involving the appearance of your floor and piano.)

Gravity: What goes up must come down

Sir Isaac Newton invented gravity in 1687 when he failed to pay attention while sitting under a tree and got bonked on the noggin by an apple. Before that, gravity didn’t exist, and everyone just floated around. Okay, I’m kidding. Isaac Newton didn’t invent gravity. But the famous mathematician was the first to study gravity seriously, and he came up with the theory (now a scientific law) of how gravity works.

Newton’s law of universal gravitation states that every object in the universe attracts every other object in the universe. Earth produces gravity, and so do the sun, other planets, your car, your house, and your body. The amount (force) of the attraction depends on the following:

• Mass: The force of gravity depends on the mass of (amount of matter in) the object. If you’re sitting in front of your television, you may be surprised to know that the television set is attracting you. However, because the mass of the TV is so small compared to the mass of Earth, you don’t notice the physical “pull” toward the television set.

Note that the force of gravity acting on an object is equal to the weight of the object. Of course, other planets have lesser or greater masses than Earth, so the weight of objects on those planets will be different.

• Distance: Newton’s law also says that the greater the distance is between two objects, the less the objects will attract each other. In other words, the farther away an object is from Earth (or any large body), the less it will weigh. If you stand at the top of a high mountain, you will weigh less than you will at sea level. Don’t get too excited about this weight-loss technique. Gravitational pull isn’t the next big diet craze. The difference is incredibly small. Sorry!

For an object to really lose weight, it must be far away from Earth (or any other large body). When an object is far enough away from these bodies that it experiences practically no gravitational pull from them, it’s said to experience weightlessness — just like the astronauts you see on TV.

Gravity pulls objects downward toward the center of Earth, so the old saying “what goes up must come down” is appropriate when discussing gravity. If you fire a bullet straight up into the air, it will travel (overcoming the force of gravity) until it reaches its farthest or highest point, and then it will fall.

Applying force to two ends: Tension

Tension force is the force transmitted through a rope, string, or wire when force is applied to both ends. The force is the amount of tension directed along the rope, string, or wire and pulls equally on the objects at both ends. Tension force is usually measured in either pounds-force or newtons (N); 4.45 newtons equal 1 pound-force.

Elastic recoil: The trampoline of physics

Liquids and gases don’t have a specific shape, but solid matter does. Solids are perfectly happy with the way they look and resist changes in shape. If you exert a force on a solid shape, it responds by exerting a force in the opposite direction. This force is called elastic recoil. Take a look at the following figure. The cat is standing on a board suspended on two blocks. While the board bends, the cat can feel the force of the board trying to regain its original shape. If the cat steps off the board, the board will spring back to its normal state.

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Knowing about Kinetic Energy & Resistance for the ASVAB

On the Mechanical Comprehension subtest of the ASVAB test, you need to know the definition of work and understand the basics of potential and kinetic energy and resistance.

Mechanically speaking, work happens when a force (usually measured in pounds) moving over a measurable distance (usually measured in feet) overcomes a resistance. In the United States, the unit of measure for work is often called a foot-pound. (Note: The rest of the world uses the newton-meter, or joule.) One foot-pound of work occurs when a 1-pound weight is lifted to a height of 1 foot. You can represent this concept in equation form:

Work = Force × Distance

Work is different from effort; work is the result of effort. You can think of effort as being force and of work as being what you produce with that force.

Working out the difference between potential and kinetic energy

Energy is the capacity to do work. Every object in the universe has energy, and it’s either potential or kinetic. Potential energy is stored energy — energy that’s not doing anything at the moment but that’s in the object by virtue of its position in a field. If a book is resting in your hands, the book itself is holding potential energy. If you raise the book over your head, you’re increasing its potential energy (thanks to the Earth’s gravitational pull). When you accidentally drop it, all its potential energy becomes kinetic energy, or energy in motion. When the book hits the ground, its energy becomes potential again. Potential energy can’t be transferred between objects. The more massive an object is, the more potential and kinetic energy it has (so a bowling ball contains more energy than a basketball does). Both these forms of energy are measured in joules.

Overcoming resistance

The resistance that the work overcomes isn’t the same thing as the weight of the object. (If you’ve ever tried to put your freaked-out cat in a cat carrier to go to the vet, you know what I mean.) In other words, if you try to move a 1,200-pound piano, you’ll probably notice a measurable difference between the amount of work it takes to shove it along the floor and the amount of work it takes to carry it up the stairs. But don’t take my word for it — you can demonstrate this concept at home. First, find a 1,200-pound piano and push it across the floor. Next, put it on your back and carry it up the stairs. See the difference? (Really, don’t put the piano on your back. I’m just trying to make a point here.) When you move the piano across the floor, you’re really working (pushing) against the frictional resistance (the force that’s produced when two surfaces rub together) of the piano rather than its full weight. Under these circumstances, the frictional resistance of the piano offers less resistance than its full weight. There are times when an object’s full weight is less than its frictional resistance. Consider trying to push a textbook across a deep-pile carpet. Picking the book up and carrying it is easier.

Gaining power by working more quickly

Power is the rate of work. If Mary Lou is able to lift more 50-pound sacks of potatoes onto the truck bed in 10 minutes than Joe is, Mary Lou is more powerful than Joe. Mathematically speaking, Power = Work / Time.

In this formula, work is usually measured in foot-pounds, time is measured in minutes, and power is measured in foot-pounds per minute. However, the unit of measure for power is commonly put in terms of horsepower (hp).

Horsepower is derived from the estimate that an average horse can do 33,000 foot-pounds of work in 1 minute (according to James Watt). Therefore, 1 horsepower = 33,000 foot-pounds per minute. One horsepower is also the same as 550 foot-pounds per second.

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Math Terminology You Should Know for the ASVAB

Yes, you must know math for the ASVAB. Math has its own vocabulary. In order to understand what each problem on the ASVAB Mathematical Knowledge subtest asks, you need to understand certain mathematical terms.

• Integer: An integer is any positive or negative whole number or zero. The ASVAB often requires you to work with integers, such as –6, 0, or 27.
• Numerical factors: Factors are integers (whole numbers) that can be divided evenly into another integer. To factor a number, you simply determine the numbers that you can divide into it. For example, 8 can be divided by the numbers 2 and 4 (in addition to 1 and 8), so 2 and 4 are factors of 8. The prime factorization of the number 30 is written 2 × 3 × 5.

Numbers may be either composite or prime, depending on how many factors they have:

• Composite number: A composite number is a whole number that can be divided evenly by itself and by 1, as well as by one or more other whole numbers; in other words, it has more than two factors. Examples of composite numbers are 6 (whose factors are 1, 2, 3, and 6), 9 (whose factors are 1, 3, and 9), and 12 (whose factors are 1, 2, 3, 4, 6, and 12).
• Prime number: A prime number is a whole number that can be divided evenly by itself and by 1 but not by any other number, which means that it has exactly two factors. The number 1 is not a prime number. Examples of prime numbers are 2 (whose factors are 1 and 2), 5 (whose factors are 1 and 5), and 11 (whose factors are 1 and 11).

• Base: A base is a number that’s used as a factor a specific number of times — it’s a number raised to an exponent. For instance, the term 4³ (which can be written 4 × 4 × 4, and in which 4 is a factor three times) has a base of 4.
• Exponent: An exponent is a shorthand method of indicating repeated multiplication. For example, 15 × 15 also can be expressed as 15², which is also known as “15 squared” or “15 to the second power.” The small number written slightly above and to the right of a number is the exponent, and it indicates the number of times you multiply the base by itself. Note that 15² (15 × 15), which equals 225, isn’t the same as 15 × 2 (which equals 30).

To express 15 × 15 × 15 using this shorthand method, simply write it as 15³, which is also called “15 cubed” or “15 to the third power.” Again, 15³ (which equals 3,375) isn’t the same as 15 × 3 (which equals 45).

• Square root: The square root of a number is the number that, when multiplied by itself (in other words, squared), equals the original number. For example, the square root of 36 is 6. If you square 6, or multiply it by itself, you produce 36.
• Factorial: A factorial is an operation represented by an exclamation point (!). You calculate a factorial by finding the product of (multiplying) a whole number and all the whole numbers less than it down to 1. That means 6 factorial (6!) is 6 × 5 × 4 × 3 × 2 × 1 = 720.

A factorial helps you determine permutations — all the different possible ways an event may turn out. For example, if you want to know how many different ways six runners could finish a race (permutation), you would solve for 6!: 6 × 5 × 4 × 3 × 2 × 1.

• Reciprocal: A reciprocal is the number by which another number can be multiplied to produce 1; if you have a fraction, its reciprocal is that fraction turned upside down. For example, the reciprocal of 3 is 1/3. If you multiply 3 times1/3, you get 1. The reciprocal of 1/6 is 6/1 (which is the same thing as 6)

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The reciprocal of 2/3 is 3/2. The number 0 doesn’t have a reciprocal. Get the idea?

• Rounding: Rounding is limiting a number to a certain number of significant digits (replacing some digits with zeroes). You perform rounding operations all the time — often without even thinking about it. If you have $1.97 in change in your pocket, you may say, “I have about two dollars.” The rounding process simplifies mathematical operations.

Often, numbers are rounded to the nearest tenth. The ASVAB may ask you to do this. If the number you’re eliminating is 5 or over, round up; for any number under 5, round down. For example, 1.55 rounded to the nearest tenth can be rounded up to 1.6, and 1.34 can be rounded down to 1.3.

Many math problems require rounding—especially when you’re doing all this without a calculator. For example, pi (π) represents a number approximately equal to 3.141592653589793238462643383 (and on and on and on). However, in mathematical operations and on the ASVAB, it’s common to round π to 3.14.