0.12 Phy1090: force -- introduction to statics, equilibrium, and  (Page 3/5)

How much do you weigh?

When you are standing on the scale, the gravitational force exerted on your body is being supported by the top surface of the scale. The top surface of the scale ispushing up with a force that is equal and opposite to the gravitational force that is trying to pull you toward the center of the earth.

The scale also has a weight

A gravitational force is also being exerted on the scale trying to pull it into the center ofthe earth. The floor underneath the scale is exerting an upward force on the scale equal to the combined gravitational force of you and the scale, causingyou, the scale, and the floor to be in equilibrium.

Compression

These two forces, one pushing down on the top of the scale and the other pushing up on the bottom of the scale causes the scale to experience something commonly called compression. In other words, the opposing forces aretrying to squeeze the scale into a puddle but the material from which the scale was constructed won'tallow that to happen.

Tension versus compression

As an aside, the state that we call tension is the opposite of the state that we call compression. If you sit with all of your weight on a stool, the legs of thatstool will be in a state of compression. If you sit with all of your weight in a porch swing supported by chains attached to the ceiling, those chains will be in tension.

A readout in pounds

The bathroom scale contains a mechanism that is capable of measuring the amount of compression that it is experiencing. It also contains a display mechanism that displays the amount ofcompression. Typically in the U.S., that compression value is converted to force and displayed in units of pounds.

The objective of the bathroom scale

The objective of the bathroom scale, therefore, is to measure the gravitational force exerted on your body (your weight) and to display that value foryour pleasure or displeasure as the case may be.

Units

In the so-called English system of units that is commonly used in the U.S., the word pound is used to indicate mass and the words pound force are used to indicate force. That can be confusing.

In the International System of Units, abbreviated SI, the standard unit of mass is the kilogram, abbreviated kg, and the standard unit of force is thenewton, abbreviated N.

A derived unit

As you learned in an earlier module, the SI units consist of base units and units that are derived from base units. The newton is a derived unit, which when expressed in SI base units is:

1 N = 1 kg *m/s^2

where

• N is the symbol for newton
• kg is the symbol for mass in kilograms
• m is the symbol for length in meters
• s is the symbol for time in seconds
• ^2 means "raised to the second power" or squared

Knowing the relationship between the newton and its base units is important when you are evaluating an equation and need to cause the units to cancel out so as to end up with only the correct units for theresult.

Conversion factor

The force that is trying to pull you into the center of the earth (your weight) can be expressed in any of the following units: