Mass vs. Weight and the Normal Force

Professor Dave here, let's learn the difference between mass and weight.

Most people are familiar with the terms mass and weight, and might assume that mass is simply a fancy word for weight. In actuality this is not the case, and the two terms have rather different meanings. To put it simply, mass is a scalar and weight is a vector. This means that mass has only magnitude, since it is a measure of an object's inertia, or essentially how much matter is present within the object. Weight, on the other hand has magnitude but also direction because

it is a force, specifically the force that is exerted on an object by virtue of its position in a gravitational field. We will learn more about gravity later, but for now we can just operate under the common understanding that gravity is a force that pulls things towards Earth. Mass and weight are related in that they are proportional and objects with more mass will weigh more than objects with less mass, but they are not the same thing, and when we discuss our weight in

common parlance we are actually referring to our mass. Weight can be calculated using Newton's second law or F = ma. Take an object like a 100 kilogram person. This value represents the mass of the person, which is more or less constant barring any huge changes in diet, as it is a measure of the amount of matter in the person. But the weight of the person will depend on their location. On the surface of the earth the acceleration due to gravity is 9.8 meters per second squared, so their

weight will be 980 Newtons. On the moon acceleration due to gravity is about one-sixth of that of earth, because the moon is much less massive, so the person will weigh considerably less as well. In vacuum of space far away from any massive object, the person will be essentially weightless, since there will be no appreciable acceleration due to gravity. In all of these cases the mass of the person does not change, but their weight will vary depending on the

presence and strength of a gravitational field. Since weight is a force, we will have to include weight in any free body diagram representing objects on earth. This will be a vector with magnitude equal to m times g pointing straight down towards the center of the earth where g represents the local acceleration due to gravity. We learned from Newton's third law that any force has an equal and opposite force and so we will often encounter something called the normal force. The normal force is

exerted by whatever surface the object sits on, and it points in the direction that is perpendicular to the surface. If this is a flat horizontal surface, the normal force will be straight up opposite in direction to the object's weight. The more mass an object contains the greater its weight and the greater the opposing normal force. If these are the only two forces acting on the object they will be equal, and the object will remain at rest. Now that we understand

the distinction between mass and weight as well as the way that weight will be depicted in free body diagrams, we are ready to look at other forces that can act upon objects. Let's check comprehension.

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