1.3 Newton's second law of motion  (Page 3/7)

One of the most important applications of Newton’s second law is to calculate weight    (also known as the gravitational force), which is usually represented mathematically as W . When people talk about gravity, they don’t always realize that it is an acceleration. When an object is dropped, it accelerates toward the center of Earth. Newton’s second law states that the net external force acting on an object is responsible for the acceleration of the object. If air resistance is negligible, the net external force on a falling object is only the gravitational force (i.e., the weight of the object).

Weight can be represented by a vector because it has a direction. Down is defined as the direction in which gravity pulls, so weight is normally considered a downward force. By using Newton’s second law, we can figure out the equation for weight.

Consider an object with mass m falling toward Earth. It experiences only the force of gravity (i.e. the gravitational force or weight), which is represented by W . Newton’s second law states that $F_{net}=ma$ . Since the only force acting on the object is the gravitational force, we have $F_{net}=W$ . We know that the acceleration of an object due to gravity is g , so we have $a=g$ . Substituting these two expressions into Newton’s second law gives

This is the equation for weight—the gravitational force on a mass m . On Earth, $g=9.80m/s^2$ , so the weight (disregarding for now the direction of the weight) of a 1.0 kg object on Earth is

Although most of the world uses newtons as the unit of force, in the United States the most familiar unit of force is the pound (lb), where 1 N = 0.225 lb.

Recall that, although gravity acts downward, it can be assigned a positive or negative value, depending on the positive direction in your chosen coordinate system. Be sure to take this into consideration when solving problems with weight. When the downward direction is taken to be negative, as is often the case, acceleration due to gravity becomes $g=-9.8 m/s^2$ .

When the net external force on an object is its weight, we say that it is in freefall    . In this case, the only force acting on the object is the force of gravity. On the surface of Earth, when objects fall downward toward Earth, they are never truly in freefall because there is always some upward force due to the air resistance that acts on the object (and there is also the buoyancy force of air, which is similar to the buoyancy force in water that keeps boats afloat).

Gravity varies slightly over the surface of Earth, so that the weight of an object depends very slightly on its location on Earth. Weight varies dramatically away from Earth’s surface. On the Moon, for example, the acceleration due to gravity is only $1.67 m/s^2$ . Because weight depends on the force of gravity, a 1.0 kg mass weighs 9.8 N on Earth and only about 1.7 N on the Moon. It is important to remember that weight and mass are very different, although they are closely related. Mass is the quantity of matter (how much “stuff”) in an object and does not vary, but weight is the gravitational force on an object and is proportional to the force of gravity. It is easy to confuse the two, because our experience is confined to Earth, and the weight of an object is essentially the same no matter where you are on Earth. Adding to the confusion, the terms mass and weight are often used interchangeably in everyday language; for example, our medical records often show our “weight” in kilograms, but never in the correct units of newtons.