Defintions (Static Equilibrium)

UNITS

In science, we prefer to use the SI system of units. But the constuction world is still deeply entrenched in the British system. If you go to the lumber yard and ask for a treated 2.4 m by 5 cm by 10 cm piece of lumber. You will get a blank stare, not an 8 ft 2 by 4! Below is a table with both the SI and the British units for most quantities we will use this semester. The first three are the fundamental units of length, mass, and time. All other units for mechanical quantaties are derived from these three. Later in the semester you will study electricity, so those units are also given below.

Quantity SI British Fundamental SI unitsFundamental Brit units
Length meters (m) foot (ft) - -
Mass kilogram (kg) slug - -
Time second (s) second (s) - -
Force Newton (N) pound (lb) kg m/s2 slug ft/s2
Energy Joule (J) footpound (fp) N m ft lb
Heat Energy Joule (J) calorie (cal) N m2 -
Power Watt (W) footpound per second (fps) J/s 2 ft lb / s 2
Pressure Pascal (Pa) pounds per square inch (psi) N / m2 lb / in2
Charge Coulomb (C) Coulomb (C) - -
Current Ampere (A) Ampere (A) C / s C / s

And some useful conversions ...

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Weight

Weight is related to the mass of an object, but is not quite the same. Let's talk about mass first.

The mass of an object is a measure of its inertia, or resistance to change in motion. A large mass is more difficult to speed up or slow down than a smaller mass. The mass of an object remains the same no matter where it is. Newton's Second law defines mass (or perhaps it defines force, depending upon your point of view). For a mass m subjected to a single force F, the object will accelerate with an acceleration a. There are related by

F = m a

In the "metric" system of units, mass is measured in kilogram (kg), acceleration in m/s2, and force is in Newtons (N). In the British system, the units are slugs (yes, that's right, slugs!), ft/s2 and pounds (lb). And now weight is ...

The weight of an object is the force of gravity exerted on the object ... by the planet the object is on. That's why the weight of an object is different on the moon than on the earth. (But the mass is the same!) Here on the earth, all objects in freefall (that means only gravity is acting) accelerate at a = g, where g = 9.8 m/s2 = 32 ft/s2. So, from Newton's Second, F = ma becomes

W = mg

The weight of an object is mg, regardless of whether the object is in freefall. The earth's gravitational force does not turn off, just because you hit the ground. It is truly relentless.

A few convenient "equivalencies" to know are

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Center of Mass

The center of mass (COM) of an object is the point where we can imagine all the mass to be located for purposes of calculating sums of forces and moments. In a reasonably uniform gravitational field, like that found on the earth's surface, the COM is the same as the center of gravity (COG). This is the point at which gravity acts. We draw the weight force vector as if gravity were acting on this one point. We will consider the COM and COG as one and the same.

For geometrically symmetric objects, the COM is at the geometric center. For example, the COM of a sphere is at the center of a sphere. The COM of a uniform 2 by 4 is exactly half way from either end. The COM of a non-symmetric object can be found experimentally by hanging the object from a string. (OK, so this is not practical for something like a car. But there's is a clever method for doing that.) The COM will be directly below the the line of the string. Hang the object from a different point, and again the COM will lie along that line as well. Where two intersect, is the COM. Try it with an odd shaped piece of cardboard.

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Line of Action

The line of action of a force is simply the line through the force arrow. The perpendicular distance (d) to this line is just the shortest distance from the pivot point to the line. This is a straightline path that meets the line of action at a 90o angle. Take a look at the example below. Jamal's sign hangs from the side of his building. There are three forces acting on the sign; the weight (w), the support cable (T for tension), and the "wall force", the force the building wall exerts on the upper bar of the sign. Notice that this force is shown as two, one vertical and one horizontal. These are called the components of the force, but they add up to the one force the wall exerts. Engineers often break forces into components for convenience, but we'll not focus on that right now.

If we take the wall point as our pivot, the wall force will not appear in the moments equation. The blue lines show the line of action for the weight and tension. The green lines show the perpendicular distance, d for each force. Note that the weight will produce a positive (cw) moment and the tension will create a negative (ccw) moment. They must add to zero. If we know the weight, we can find the tension T in the cable. That could be crucial to Jamal's decision as to how strong a cable he needs to buy!

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