Force, Work and Energy

Forces, Mass, and Newton's Laws of Motion

A clear grasp of mechanics begins with the distinction between mass and weight. Mass is the actual amount of matter contained in an object and remains constant regardless of where that object is located in the universe. In metric units, mass is measured in grams or kilograms, while in U.S. customary engineering units, it can be measured in slugs. Weight, on the other hand, is a force caused by the gravitational pull acting on an object's mass. Because weight depends entirely on local gravity, an object's weight changes if gravity changes. Weight is measured in newtons within the metric system and in pounds-force within U.S. customary units.

A force is simply an interaction that pushes or pulls an object, carrying the potential to alter its speed, its direction of travel, or its physical shape. Objects inherently possess inertia, which is the natural tendency to resist any change in their state of rest or motion. This property forms the core of Newton's first law of motion: an object at rest stays at rest, and an object in motion continues moving at a constant velocity, unless acted upon by a net external force. When the forces acting on an object are balanced, the net force is zero, meaning the object either stays completely stationary or maintains a constant velocity. When unbalanced forces act on an object, a non-zero net force is created, causing the object to accelerate in the direction of that net force.

Newton's second law defines the mathematical relationship between net force, mass, and acceleration: net force equals mass times acceleration. Because calculators are not permitted on the ASVAB, whether you take the computer-adaptive CAT-ASVAB at a Military Entrance Processing Station (MEPS) or a Mobile Examining Team (MET) site, the internet-based PiCAT, or a paper student ASVAB, test questions focus on clean mental math and proportional reasoning. If an object's mass stays the same, doubling the net force acting on it will double its acceleration. Conversely, if the net force remains constant while the object's mass is doubled, its acceleration is cut in half.

Newton's third law of motion explains that for every action force, there is an equal and opposite reaction force. A crucial principle to remember is that action and reaction forces act on two different objects simultaneously. Because they act on different objects, action and reaction forces do not cancel when calculating the net force on either object; they do cancel as internal forces when both objects are treated as one system.

Work and Power in Mechanical Systems

In physical science, work has a very specific definition that differs from everyday conversation. A force does work on an object only when that object moves at least partly along the line of the applied force. If the motion occurs in the exact same direction as the force, the work done is positive. If the motion opposes the force, the work done is negative. Furthermore, if you apply a strong force to an object but no movement occurs, the work done on that object is exactly zero. Work is also zero if an object moves entirely perpendicular to the direction of the applied force, because that specific force performs no work along the path of motion.

When force and motion line up in the same direction, work is calculated using a straightforward formula: work equals force multiplied by distance. If the force acts at an angle relative to the path of movement, you only use the part of the force that acts along the line of motion. In the metric system, the standard unit of work and energy is the joule, which is equivalent to one newton-meter. In U.S. customary units, work is commonly expressed in foot-pounds of force, often shortened simply to foot-pounds. For example, lifting a 10-pound load straight upward through a distance of 4 feet requires 10 pounds multiplied by 4 feet, performing 40 foot-pounds of work.

Power describes the rate at which work is performed, or the rate at which energy is transferred over time. You calculate power by dividing the total work done by the time taken to complete it (Power = Work / Time). The metric unit of power is the watt, where one watt equals one joule of work performed per second. In standard English units, power is frequently measured in horsepower. One horsepower is defined as the ability to perform 550 foot-pounds of work per second, which equals approximately 746 watts.

Exam questions frequently test the inverse relationship between power and time. Because power measures how quickly an amount of work is finished, performing a given amount of work in half the time requires twice the amount of power. Lifting the same crate through the same height in 5 seconds instead of 10 seconds requires twice the average useful power.

Forms of Energy and Conservation

Energy is closely tied to work and shares the exact same units: joules in metric measurements and foot-pounds in U.S. customary measurements. Potential energy represents stored energy resulting from an object's physical position or arrangement. Common examples include the mechanical energy stored in the stretch of a spring or the gravitational potential energy of an elevated object. Gravitational potential energy increases whenever an object's height above the ground increases or whenever its mass increases.

Kinetic energy is the energy an object possesses purely due to its motion. The amount of kinetic energy an object holds increases in direct proportion to its mass, but it increases in proportion to the square of its speed. This squared relationship is a favorite concept on mechanical exams. If an object keeps the same mass but its speed is doubled, it will possess four times the kinetic energy. Tripling its speed would cause its kinetic energy to jump by nine times.

The law of conservation of energy states that energy cannot be created or destroyed. Instead, energy is transferred between interacting objects or converted from one form to another. For example, a falling object continuously converts its gravitational potential energy into kinetic energy as it loses height and gains speed. However, mechanical systems are not entirely frictionless. Friction between moving mechanical parts regularly converts a portion of the system's useful mechanical energy into thermal energy, which dissipates into the surroundings and causes physical wear over time.

Friction and Wear Reduction

Friction between solid surfaces resists their sliding or tendency to slide; an object moving through a liquid or gas also experiences resistance called drag. Static and sliding friction between solid surfaces act along the contact surface and oppose sliding or attempted sliding; fluid drag does not always act parallel to an object's surface. In simple dry-friction situations, the magnitude of friction depends on the types of materials involved and their surface conditions. Friction generally increases as the normal force pressing the surfaces together increases, but it is approximately independent of the apparent contact area between them.

Frictional forces appear in multiple distinct forms across mechanical systems. Static friction acts to prevent stationary surfaces from beginning to slide across one another, up to a certain maximum force limit. Once that threshold is crossed and movement begins, sliding friction (also called kinetic friction) opposes the surfaces actively sliding past each other. For any two identical surfaces pressed together with the same force, the maximum static friction is generally greater than sliding friction. Rolling resistance opposes a wheel or ball rolling across a surface and is usually much smaller than sliding friction under comparable conditions. Fluid friction, often referred to as drag, is the resistance encountered by an object moving through a liquid or a gas.

Because sliding friction between moving parts often converts useful mechanical energy into heat and can cause wear, technicians use methods to manage it. Applying lubricants such as oil and grease reduces friction and wear by separating or coating moving surfaces. Another common design strategy involves installing ball bearings or cylindrical rollers inside machinery, which significantly reduces friction by replacing sliding contact with rolling contact.

Simple Machines, Mechanical Advantage, and Efficiency

A simple machine makes mechanical work easier to accomplish by reducing the necessary effort force, changing the direction of the force, or changing how far or how fast the load moves. However, simple machines cannot output more work than the total energy put into them, because machines cannot create energy. When evaluating machines, mechanical advantage describes the ratio of the output force exerted by the machine to the input effort force applied to it.

Mechanical advantage can be greater than one, equal to one, or less than one. A machine with a mechanical advantage greater than one allows a small effort force to move or lift a significantly heavier load over a shorter distance. A machine with an ideal mechanical advantage less than one trades a larger effort force for greater load speed or travel distance; an actual mechanical advantage below one can instead result from energy losses. When a machine has a mechanical advantage of exactly one, the input force and output force are equal; this type of machine may change the direction of the force, although changing direction is not strictly required.

Engineers analyze machines using two related values: Ideal Mechanical Advantage (IMA) and Actual Mechanical Advantage (AMA). Ideal Mechanical Advantage is calculated by dividing input distance by output distance, completely ignoring friction. Actual Mechanical Advantage is calculated by dividing output force by input force. Because friction in the real world always wastes some of the input energy, a machine's Actual Mechanical Advantage is always less than its Ideal Mechanical Advantage.

Mechanical efficiency measures how effectively a machine transfers energy without waste. It is defined as the ratio of useful work output to total work input, expressed as a percentage. Mechanical efficiency can also be determined by dividing Actual Mechanical Advantage by Ideal Mechanical Advantage and multiplying by 100 percent. Because all real machines dissipate some input energy, frequently as heat generated by friction, their mechanical efficiency is always strictly less than 100 percent.