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Module 1: Basic Concepts - Systems of Units
Different Systems of UnitsConverting Between Mass and Force
in the American Engineering SystemPractice Problems
Objective
- Using the American Engineering System, convert from pounds mass to pounds force and vice versa.
There are a number of different systems of units. Most people become aware of these different systems while in elementary school when faced with the dreaded set of conversions from English units to metric units. Actually, there are more than two. Table 1 provides information on five systems of units.
The first three systems of units presented in Table 1 have three defined units (length, mass, and time) and one (force) which is based on the other three. However, the American Engineering System has four different defined units, length, mass, force, and time. The word "pound" is used for both mass and force even though these are clearly not the same concept. Accordingly, some caution is needed when performing calculations in the American Engineering System, which remains the dominant system in the United States despite attempts to change to the cgs or SI systems of units.
Converting Between Mass and Force
in the American Engineering System
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#1
- In the American Engineering System, how do you distinguish between a mass of 100 pounds and a weight (i.e. a force) of 100 pounds?
The following symbols are useful when including the units for mass and force in dimensional calculations in the American Engineering System:
- Pounds mass, lbm
- Pounds force, lbf
The disadvantage of this terminology is that some care is needed to prevent confusing mass with force. The advantage is that numerical units of force are in familiar terms. For example, in the American Engineering System, a person with a mass of 100 pounds weighs 100 pounds force.
The numerical familiarity and convenience of the American Engineering System comes with a small cost. When performing calculations concerning force or energy, it is necessary to include a conversion factor to ensure that the units will work out properly. This factor is called gc and it has the following units.
Note the difference between the value of the conversion factor gc and the value of g, the average acceleration due to gravity (i.e. 32.2 ft/sec2). The acceleration of gravity actually varies slightly from location to location. The value for gc, 32.174, is the acceleration of gravity at sea level at 45 degrees latitude.
To convert between mass and force in the American Engineering System, use the following equation:
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Where:
Example Problem 1.
Calculate the Force on the Bottom of a Tank Filled with Water
What is the force on the bottom of a two-foot by three-foot rectangular tank of water holding 2.5 ft of water? See Figure 1.
Hint: Click on the buttons at the bottom left part of the screen to help you find conversion factors and values for constants to use in solving problems.
Solution:
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Where:
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Calculate the mass of water given that its density is 62.4 lbm/ft3.
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Calculate the force on the bottom of the tank.
Practice Problems
Systems of Units
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Instructions:
- Complete the Practice Problems before proceeding to the next lesson. Click on the button below.