## Weight and Force Mass

The U.S. Customary system (sometimes referred to as a gravitational system) is a force-based system and the SI is mass-based system. The key to understanding how to solve problems in these two systems is to understand the relationship between mass and force. The definition of mass was proposed by Sir Isaac Newton.

One useful definition of mass (Hibbler, R.C. Engineering Mechanics, 6th edition. Macmillan, New York) is "Mass is a property of matter by which we can compare the action of one body with that of another. This property manifests itself as a gravitational attraction between two bodies and provides a quantitative measure of the resistance of matter to a change in velocity." This implies several things. Gravity is a form of acceleration. Thus, mass is independent of gravity. This means that your mass is the same on the earth, moon, or in rocket ship leaving the earth. Your mass is also the same in space orbiting the earth.

Mass can be determined by comparing an object of known mass to your object whose mass is not known. One way to do this is to place the object with the unknown mass in one pan of a balance scale and add objects of known mass in the other pan until the scale is balanced. Gravity is the acceleration acting on both pans of the balance scale. The balance scale will give the same results in the rocket ship, on the earth or on the moon.

Force or weight changes with gravity or acceleration. You will weight about 1/6th as much on the moon as on the earth, because the force attracting you to the moon, gravity is about 1/6th that of the earth's gravity. In orbit about the earth, where the net gravitational force is zero, your weight is zero.

In this book we are primarily interested in force rather than mass. Sir Isaac Newton's second law defines the relationship among mass (m), acceleration (a), and force (F). This equation is F = ma.

The SI unit of force is the Newton (N), the unit of mass is the kilogram, and the unit of acceleration is meter/second2 (m/s2). In the SI system we specify the mass of the object and calculated the weight. Since gravity is a form of acceleration, we can rewrite Newton's second law as:

W = mg where W is the weight in Newtons (N) and g is the acceleration by gravity at the earth's surface, 9.81 m/s2.

In the customary system we measure the force in pounds and calculate the mass. The unit of mass in the customary systems is the slug. Mass is calculated by:

m = — where W is the weight in pounds (lb) and g = 32.3 ft/s2.

The relationship of mass and weight can be explained using an example of a class 1 lever. Note: class one levers are explained in chapter 4. You are using a class 1 lever to pry a large rock from the ground. You push down on the end of the lever with enough force to raise your feet off the ground and the rock doesn't move. You have recently "weighed" yourself on a metric scale and your mass is 81 kg. The force arm length is 1.5 m and the resultant arm length is 0.3 m. What is the weight of the rock?

The first step in determining the weight of the rock is to convert your body mass to weight.

s2 s2

The second step is to calculate the weight of the rock using the formula for a class 1 lever and solving for Fr.

The equation for a class 1 lever is written in terms of a force, but weight is a force so Fa = W

The weight of the rock is greater than 4,000 N or 4 kN.