## How Mass and ForceWork

Terms such as mass, force, torque, work, power, and energy are frequently encountered around the industrial plant. This month's column, along with the next two, will take a look at what these terms mean and "how they work." What is mass? Generally, mass is defined as the measure of how much matter an object or body contains — in other words, the total number of subatomic particles (elect...
By Marshall Brain July 1, 2001

Terms such as mass, force, torque, work, power, and energy are frequently encountered around the industrial plant. This month’s column, along with the next two, will take a look at what these terms mean and “how they work.”

## What is mass?

Generally, mass is defined as the measure of how much matter an object or body contains — in other words, the total number of subatomic particles (electrons, protons, and neutrons) in the object. If you multiply your body mass by the pull of the Earth’s gravity, you get your weight.

It is important to understand that mass is independent of your position in space. The body’s mass on the moon is the same as on the Earth because the number of atoms is the same. The earth’s gravitational pull, on the other hand, decreases as you move farther away. Therefore, you can lose weight by changing your elevation, but the mass remains the same.

Mass is important for calculating how fast objects accelerate when force is applied to them.

## What is force?

One type of force commonly recognized is weight, which is the amount of force the Earth exerts on you. There are two interesting facts about this force.

• It pulls you down, or more exactly, towards the center of the earth.

• It is proportional to mass. If you have more mass, the earth exerts a greater force on you.

• When stepping on the bathroom scale, a force is exerted on the scale. This force compresses a spring, which moves the needle. When you throw a baseball, force is applied to the ball, which makes it speed up. An airplane engine creates a force, which pushes it through the air.

Force causes acceleration. If force is applied to a toy car by pushing it by hand, it starts to move.

The movement of the car is governed by Isaac Newton’s Second Law, which forms the foundation for classical mechanics. Newton’s Second Law states that the acceleration (a) of an object is directly proportional to the force (F) applied, and inversely proportional to the object’s mass (m) . Therefore, the more force applied to an object, the greater the rate of acceleration; and the more mass the object has, the lower the rate of acceleration. Newton’s second law is usually summarized in equation form:

a = F/m or F = ma .

To honor Newton’s achievement, the standard unit of force in the SI system was named the newton. One newton (N) of force is enough to accelerate one kilogram (kg) of mass at a rate of one meter per second, per second (m/sec2).

In fact, this relationship is really how force and mass are defined. A kilogram is the amount of weight at which 1 N of force will accelerate at a rate of 1 m/sec2. In English units, a slug is the amount of mass that 1 lb of force will accelerate at 1 ft/sec2, and a pound mass is the amount of mass that 1 lb of force will accelerate at 32 ft/sec2.

The Earth exerts enough force to accelerate dropped objects at a rate of 9.8 m/sec2, or 32 ft/sec2. This gravity force is often referred to as g in equations. If you drop an object off a cliff, for each second it falls, it speeds up by 9.8 m/sec2. If the object falls for 5 sec, it reaches a speed of 49 m/sec. If a car accelerated at this same speed, it would reach 60 mph in less than 3 sec!

Usually, when talking about forces, there is more than one involved, and they are applied in different directions. Consider a car sitting still. Gravity exerts a downward force everywhere on the car, while the ground exerts an equal and opposite upward force on the tires. Therefore, the car does not move.

When the car begins to accelerate, some new forces come in to play. The drive wheels exert a force against the ground in a horizontal direction that makes the car start to accelerate. When moving slowly, almost all of the force goes into accelerating the car. The car resists acceleration with a force equal to its mass multiplied by its acceleration. Force starts out large because the car accelerates rapidly at first. As it begins to move, air exerts a force against the car, which grows larger as the car gains speed. Aerodynamic drag force acts in the opposite direction of the force of the tires, which is propelling the car, so it subtracts from that force, leaving less force available for acceleration.

## Common units of mass and force

1000 gram (g) = 1 kilogram (kg)

= 2.205 pounds mass (lbm)

1 lbm = 0.4536 kg

1 slug = 14.5939 kg = 32.17 lbm

1 lb force (lbf) = 4.448 Newton (N) = 4.448 joules/meter

1 N = 0.2248 lbf