Physics

Physics is the science dealing with the properties, changes, and interactions of matter and energy. There are many branches of physics, including mechanics, thermodynamics, magnetism, optics, and electricity. This review will cover only the physics that might appear on the General Science section of the ASVAB.

Motion

Velocity is the rate at which an object changes position. Change in position is called displacement and velocity is defined as the total displacement per unit time. It can be calculated as velocity = displacement of an object ÷ time.

In physics, velocity is called a vector quantity, meaning it is fully described by both a magnitude and a direction. For example, a car traveling west that covers fifteen meters in two seconds would be described as having a velocity of 7.5 m/s (that is, miles per second) west. Displacement is also a vector, and both symbols often have a little arrow above them to signify this. Time is not a vector.

Momentum is a measure of the quantity of motion of an object. It corresponds to how difficult it is for a moving object to stop. The formula definition of momentum is Momentum = mass × velocity. In the symbolic version, momentum is represented by the letter p, since m is already in use for mass.

This relationship means, for example, that a semitrailer truck moving at 5 km/h has more momentum than a person walking at the same speed, and also that you have more momentum when running than when walking. Momentum is also a vector quantity, so that two objects moving towards each other have opposite directions of momentum which will partially or completely cancel out if they collide.

Acceleration is the rate of change of velocity. Acceleration = change in velocity ÷ change in time. The Δ (delta) symbol represents change.

You can see acceleration in a stopped vehicle when the light turns green and the driver depresses the gas pedal. The movement of the speedometer needle shows acceleration, as the car’s velocity is increasing moment by moment until it plateaus at cruising speed. Acceleration is also a vector quantity.

Question Analysis
A sports car hits the brakes and changes its velocity from 65 m/s to 40 m/s in five seconds. What is its average rate of acceleration? Step 1: The question asks for the acceleration of the car. The change in velocity and time of acceleration are required.
Step 2: Change in velocity is the difference between the final and initial velocity. This goes into the acceleration formula. Velocity has decreased, so acceleration should be negative.
Step 3: The acceleration is −5 m/s2, or the car decelerates at a rate of 5 m/s2. The prediction has a negative value to denote a direction opposite motion.
(A) −5 m/s
(B) 5 m/s
(C) 8 m/s
(D) 13 m/s		 Step 4: Select choice (A).

Now try one on your own.

  1. A bicycle initially at rest at the top of a hill accelerates as its rider coasts down. An accelerometer (which measures acceleration) records a fairly constant acceleration of 6.5 m/s2. If the rider reaches the halfway point 5.2 s into the trip, what was the velocity of the bicycle and rider at this time?
    1. 33.8 m/s, uphill
    2. 1.25 m/s, uphill
    3. 33.8 m/s, downhill
    4. 1.25 m/s, downhill

Explanation

Answer choice (C) is correct. The change in velocity can be calculated by rearranging the acceleration equation, then written as Δv = at. Since the bicycle and rider are initially at rest, the change in velocity is equivalent to the final velocity (after 5.2 s). This also means that both acceleration and the velocity any time after movement has begun are in the downhill direction. Thus, v2 = (6.5 m/s2)(5.2 s) = 33.8 m/s, downhill.

Forces and Energy

Force is the push or pull that causes an object to change its speed or direction of motion.

Weight is just one example of a force; in this case, the force is due to gravity. A unit of force is called a newton (N), which is the force required to impart an acceleration of one meter per second squared to a mass of one kilogram.

Work is performed on an object when there is an applied force that is along the same line of movement. Work = force × displacement, where the directions of force and movement are parallel.

A unit of work is called a newton-meter or joule (J). Performing work uses up energy, also measured in joules, which is equal to the amount of work performed. The reason we have to regularly consume food is that we are constantly using up energy: when we move, when our heart pumps blood, when our lungs inhale and exhale, when we generate warmth to maintain our body temperature, and so on. The nutritional information on food packages sometimes lists the food energy per serving in kilojoules (kJ) in addition to the traditional British unit of kilocalories (usually referred to, confusingly, as “calories” in everyday speech).

Power is the rate at which work is performed, or energy is converted. It’s defined as the amount of work done or energy converted per unit of time and can be calculated as Power = work ÷ time, or Power = (force × distance) ÷ time.

The main unit of power is the watt (W), where one watt is defined as one joule per second. Be sure not to mix up the symbol for the Watt unit with the symbol for work in the formula, nor the formula symbol for mass with the symbol for the meter unit. Units go with a number. The letter symbols in each formula stand for an unknown measurement value which will be replaced by a number during calculation.

Study this example of an expert approach to an ASVAB question about measurement in science.

Question Analysis
Once outside the Earth’s atmosphere, a space shuttle’s propulsion system effects a net force of 10,000 N over a distance of 50 m. The potential energy of the craft is unchanged during this time. What increase in kinetic energy will result? Step 1: The question asks for the increase in energy. Because energy and work are both measured in joules, the answer will be in joules.
Step 2: Since work performed results in a conversion of energy from one form to another, the amount of increased kinetic energy (energy of movement) has to be the same as the amount of work done.
The formula for work is known.
Step 3: The increase in kinetic energy will be equal to the amount of work done, or 500,000 J.
(A) 0 J
(B) 0.005 J
(C) 200 J
(D) 500,000 J		 Step 4: Select choice (D).

Now you try your hand at a question.

  1. A hydroelectric dam captures the energy of falling water in order to provide electrical power to the grid. The water turns a turbine a total distance of 2.5 m every 10 s. The average force the water applies to the turbine is 10,000 N. What is the average rate of hydroelectric power generation of that turbine?
    1. 25 W
    2. 2,500 W
    3. 25,000 W
    4. 250,000 W

Explanation

Choice (B) is correct. The work done by the falling water is equal to

W = 10,000 N × 2.5 m = 25,000 J

Power is the rate at which work is done, or at which energy is used, converted, or delivered.

P = 25,000 J /10 s = 2,500 W

Newton’s Laws

Sir Isaac Newton was an English mathematician and physicist. In the seventeenth century, he came up with some of our most important formulas for understanding the properties of motion and gravity.

Newton’s first law of motion. An object at rest tends to stay at rest, and an object in motion tends to stay in motion at a constant speed in a straight line (constant velocity), unless acted upon by an unbalanced force. An example of an unbalanced force—one that keeps objects in motion from staying in motion on Earth—is friction, the force that resists relative motion between two bodies in contact. This law is also known as the law of inertia, with inertia referring to the tendency of all matter to resist changes in its motion.

Newton’s second law of motion. When dealing with an object for which all existing forces are not balanced, the acceleration of that object, as produced by the net force, is in the same direction as the net force and directly proportional to the magnitude of the net force, and is inversely proportional to the object’s mass. Expressed mathematically, acceleration = net force ÷ mass. When using this formula, the units for each of these measures must be m/s2, N, and kg, respectively.

The greater the mass of an object, the greater the force needed to overcome its inertia. This law actually encompasses the first law, as the special case of zero net force results in zero acceleration, i.e., no change in motion. Sometimes this law is written in the equivalent form, net force = mass × acceleration.

Newton’s third law of motion. For every action, there is an equal and opposite reaction. In other words, when an object exerts a force on another object, the second object exerts a force of the same magnitude but in the opposite direction on the first object. For example, consider what happens when a gun is fired. A bullet fires and the gun recoils. The recoil is the result of action-reaction force pairs. As the gases from the gunpowder explosion expand, the gun pushes the bullet forward and the bullet pushes the gun backward. The acceleration of the recoiling gun is, however, smaller than the acceleration of the bullet, because acceleration is inversely proportional to mass, and the bullet, as a rule, has a smaller mass than the gun, and is more easily accelerated.

In addition to those three laws of motion, Newton also developed Newton’s law of universal gravitation. All objects in the universe attract each other with an equal force that varies directly as a product of their masses, and inversely as a square of their distance from each other. This force is known as gravity. Newton’s law of universal gravitation is expressed by the following equation (where G is a constant with a value of 6.67 × 10−11 and r is the distance between the two objects’ centers of mass):

Take, for example, the gravitational force between the Sun and the Earth. The following consequences follow from the law of universal gravitation:

At the surface of the Earth, the acceleration due to gravity is 9.8 m/s2. This bears remembering, and can be applied to the formula for Newton’s second law to determine the weight (gravitational force) of any object given its mass.

Question Analysis
A 600 g squid propels itself by firing a jet of water with a force of 21 N. The water jet is pointed in an easterly direction. What will be the acceleration of the squid? Step 1: The question asks for acceleration and provides mass and force, which means Newton’s laws are being used.
Step 2: The squid is firing a jet towards the east; however, the question asks about the acceleration of the squid, not the water jet. From Newton’s third law, the water being pushed out in a jet to the east is simultaneously pushing on the squid to the west with the same force, which means acceleration will be westward.
The mass of the squid must be converted to kg, and then, along with the given force, used to find magnitude of acceleration.
Force on squid (equal and opposite) = 21 N, west
Mass of squid = kg
a = = 35 m/s2, west
Step 3: Acceleration is 35 m/s2, west. Both the calculated magnitude and the reasoned direction must be included in the prediction.
(A) 0.035 m/s2, west
(B) 35 m/s2, east
(C) 35 m/s2, west
(D) 28.6 m/s2, east		 Step 4: Choice (C) matches the prediction.

Now try one on your own:

  1. A man pushes a 15 kg shopping cart across a rough surface, applying a force of 15 N in the direction of motion. A friction force resists the movement of the wheels across the surface with a magnitude of 15 N opposite to the direction of motion. What will be the effect on the motion of the shopping cart?
    1. The cart will slow down at a rate of 1 m/s2.
    2. The cart will continue its uniform velocity.
    3. The cart will speed up at a rate of 1 m/s2.
    4. The cart will speed up at a rate of 2 m/s2.

Explanation

The correct answer is (B). Since the two forces acting on the cart are equal in magnitude but opposite in sign (direction), the net force will be equal to zero. Net force = +15 N − 15 N = 0 N. By Newton’s second law, with no net force there can be no acceleration, which means, by definition, the velocity will not change.

Energy

As mentioned earlier in this chapter, energy can be defined as the capacity to do work. Many ASVAB energy questions deal with mechanical energy, which may be either kinetic or potential. Kinetic energy is the energy possessed by a moving object. Potential energy is the energy stored in an object as a result of its position, shape, or state.

According to the law of conservation of energy, energy can neither be created nor destroyed. Instead, it changes from one form to another. For example, if a rock is poised right at the edge of a cliff, the rock has potential energy relative to the ground at the bottom of the cliff. If the rock is dislodged and falls freely, that potential energy is converted completely to kinetic energy at the instant just before the rock hits the ground.

Sound and light energy travel in waves (although it gets complicated in the case of light). So let’s take a look at the properties of waves.

Sound Waves

Sound waves are produced when an object vibrates, disturbing the medium around it, creating an outward ripple in all directions. These ripples (waves) can travel through air, liquids, and solids, but they cannot be transmitted through a vacuum, or empty space. Sound waves transmitted through air do not travel as fast as those transmitted through water, and those transmitted through water do not travel as fast as those transmitted through metal or wood.

The pitch of sound is directly related to the frequency (rate of vibration) of the sound waves. Sound waves with a high frequency (high rate of vibration) produce a high pitch. Frequency is usually measured in hertz (Hz), defined as the number of repetitions per second. Sound waves with a very high pitch (high number of vibrations per second) are inaudible to humans, although they can be heard by dogs and other creatures. The typical audible hearing range for a human is from about 20 Hz to 20 kHz. Sometimes, a human (or a dog, for that matter) will perceive a sound as being a different frequency than the actual frequency of the sound. This is due to the Doppler effect. The Doppler effect occurs when either the source of the sound waves, the listener, or both, are moving closer together (pitch frequency sounds higher than it is) or farther apart (pitch frequency sounds lower than it is). A perfect example of the Doppler effect is the way the sound of a police or ambulance siren seems to change when it zooms by.

The Electromagnetic Spectrum

It’s important to realize that visible light makes up only one small part—the visible part—of the electromagnetic spectrum. The electromagnetic spectrum covers all the different wavelengths and frequencies of radiation. Visible light waves fall in the middle of the electromagnetic spectrum. Starting with lowest frequency (which corresponds to the longest wavelength), the electromagnetic spectrum goes from radio waves to microwaves to infrared waves to visible light to ultraviolet light to X-rays and finally to gamma rays, the most active radiant energy known to exist.

Visible light breaks down into different colors as well, based upon the frequency of the waves. Red has the lowest frequency, which is why wavelengths just below the frequency of visible light are called infrared; likewise, violet has the highest frequency, so wavelengths just above the frequency of visible light are called ultraviolet.

Optics

As noted above, light, as well as the entire
electromagnetic spectrum, possesses properties of waves. However, unlike sound waves, which are mechanical, light waves are electromagnetic and can travel through empty space. They also travel at much higher speeds than do sound waves. The speed of light in a vacuum is 299,792,458 meters per second (or roughly 300 million meters per second or 186,000 miles per second).

Refraction

It should be noted, however, that the effective speed of light can vary depending on the material the light waves are passing through; for example, light passes more slowly through water or glass than through a vacuum. The ratio by which light is slowed down is called the refractive index of that medium. For instance, the refractive index of a diamond is 2.4, which means that light travels 2.4 times faster when passing through a vacuum than when traveling through a diamond.

The change in speeds causes light to bend when passing from one medium to another (like a vehicle changing direction when hitting a slick patch of road). This bending is what’s called refraction, and light bends at a greater angle when the change in the index of refraction is greater.

Reflection

Any wave, including light, that bounces off a flat, smooth barrier follows the law of reflection, which states that the angle of incidence is equal to the angle of reflection as measured from a line normal (at a 90° angle) to the barrier. In the case of light, this barrier is often a mirror.

The Law of Reflection

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Concave and Convex Mirrors and Lenses

Mirrors and lenses either can be flat, or they can be concave (curved in, like a cave) or convex (curved out, like a swelling). Because of the law of reflection, a concave mirror is also called a converging mirror, because the angles of incidence of rays of light parallel to the normal all converge upon a point.

Converging Mirror

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If you draw the mirror away from the source of the image, the image falls out of focus as the image source nears the mirror’s focal point, the point where the mirror’s angles of incidence converge. As the image source keeps moving beyond the focal point, the image reappears in the mirror, only upside down.

A convex mirror, on the other hand, is known as a diverging mirror because it diverges the light waves that strike it.

Lenses, unlike mirrors, operate on the principle of refraction. A convex lens—one that is thicker in the middle than on the edges—is also called a converging lens because it converges parallel waves that pass through it. This type of lens is used in reading glasses to correct farsightedness, as well as in magnifying glasses, cameras, telescopes, and microscopes.

A concave lens—one that is thicker on the edges than it is in the middle—is also known as a diverging lens because it diverges the light waves that pass through it. In nearsightedness, light waves converge before they meet the retina. A nearsighted person sees objects close up but not far away. A concave lens placed before the eye bends light so that it converges further back in the eye, reaching the retina and correcting nearsightedness.

Converging Lens (a) and Diverging Lens (b)

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Study the approach an expert test taker would use on an ASVAB question about optics.

Question Analysis
Through which medium will light travel the fastest? Step 1: The question asks for the fastest medium for light to travel through.
Step 2: Light is slowed down by different materials. Materials with high indices of refraction tend to be denser, and slow down light the most. The least dense material should provide light the greatest speed.
Step 3: The answer choice with the least dense material will be correct.
(A) a vacuum
(B) air
(C) diamond
(D) pure hydrogen		 Step 4: Of the available choices, empty space, or (A) a vacuum, is the least dense material (or lack of material) possible. Light should travel fastest through a vacuum. In fact, the “speed of light” is defined for a vacuum.

Try your hand at the question below.

  1. “Waves” of heat can be seen above a hot stove element or flame, as the background appears to be distorted or out of focus just at that spot. This is an example of
    1. diffraction
    2. refraction
    3. reflection
    4. convergence

Explanation

Choice (B) is correct. The background can only appear distorted if the light rays are following a different path through the heated area than other light rays moving through the room. Since the light is still traveling through the space, rather than being bounced away, this is refraction, not reflection. It occurs because the air near the heat source is of a different density, resulting in different indices of refraction in different patches of air.

Heat

There are three means by which heat energy may be transferred from one object to another: conduction, convection, and radiation. Heat energy is always transferred from warmer to cooler environments.

Conduction is the simplest method of heat transfer. It is accomplished by direct contact, such as placing your finger on a hot iron, which we recommend that you not try at home. Metals are generally good conductors of heat. Other materials, such as wood, Styrofoam, and plastic, are poor conductors of heat, which makes them good insulators.

Convection transfers heat by the actual movement of hot particles of a fluid. The hot air rising from a bonfire is an example of convection. Ocean currents and wind are caused by convection movements caused by temperature differences.

Radiation occurs when electromagnetic waves transmit heat. The heat we get from the Sun travels through space as radiation.

Magnetism

Simple magnets have two poles: a north pole and a south pole. Much as it happens in a Hollywood romance, opposites attract. If you try to bring together two north poles of a magnet—or two south poles, for that matter—they will repel one another, and you can feel their repulsive force. If, on the other hand, you move the north pole of one magnet toward the south pole of another magnet, they will attract each other.

Because the Earth itself is magnetized and has a North Pole and a South Pole, a magnetic compass, which contains a small, lightweight magnet balanced on a nearly frictionless, nonmagnetic surface, can be used to tell direction. The magnet, which is generally called a needle, has one end marked with an arrow and often the letter “N.” This end of the needle is the magnet’s south pole, which constantly orients itself to point toward the Earth’s North Pole, allowing the person reading the compass to gain bearings from that direction.

Study the example below.

Question Analysis
The arrival of a warm front, a mass of hot air moving into an area, is an example of Step 1: The question asks for a phenomenon to be identified as one of three methods of heat transfer or as a magnetic effect.
Step 2: The methods of heat transfer are identified by how heat energy physically travels. If actual hot physical molecules bring heat with them, it’s convection.
Step 3: The question stem specifies that the warm air itself is moving into the area. By definition, that makes this an example of convection.
(A) conduction
(B) convection
(C) radiation
(D) the Earth’s magnetic field at work		 Step 4: Choice (B) matches the prediction.

Now you try one:

  1. Wooden spoons are sometimes used in kitchens instead of metal ones when stirring hot pots of soup. What’s a reasonable explanation for this?
    1. Wood does not conduct heat as well as metal, so the person stirring won’t get burned.
    2. Wood draws in convection heat so that it does not flow into the pot.
    3. Wood is magnetic, and diverts heat.
    4. Wood is a good conductor of radiation.

Explanation

Choice (A) is correct. Of the methods of heat transfer, only conduction would allow heat to move from a hot liquid into a solid spoon. It makes sense that a less conductive material would be purposely chosen to minimize the amount of heat that is able to travel from the soup, through the spoon, to the cook’s fingers. The other choices, on the other hand, suggest a misunderstanding of how the methods of heat transfer work.