StaticsStatics |
What kind of forces can you exert on an object? |
Hold a book in your two hands. What kind of forces can you exert on it? You could pull on the book to try to make it longer or you push it to try to make it shorter. The name for the force on the book that pulls on it is a tension force, while the name for the force that pushes on it is a compressive force.
You could also try to twist it, applying what is called a torsional force. Finally, place one hand on the front cover and the other hand on the back cover. Now push one hand to the right and the other to the left. This places a shear force on the book.
Tension forces are common. If you hang from a chin-up bar, your arms experience a tension force. Pulling on a rope, wire, or cable also exerts tension on them. Materials experiencing tension will stretch, some more and some less. Materials that stretch easily are called pliant; those that do not are called rigid.
Scientists have measured the response of materials to tension and compression. The ratio of the applied pressure (called stress) to the change in length divided by the original length (called strain) is called Young’s modulus. Its value varies from 10 GN/m^{2} (10 billion newtons per square meter) in wood to 200 GN/m^{2} in steel and cast iron. That means that for an equal force on it steel will stretch (or compress) 1/20 as much as wood. If you would hang a 120-kilogram (264 pound) ball from a 6-meter (19.7 feet) long steel cable 2.5 millimeters (0.9 inches) in diameter it would stretch 7 millimeters (0.3 inches).
In the case of the cable above when you remove the weight the cable will return to its original length. It is called an elastic material. If you exert a much larger force the cable won’t return to its original length. This is called the plastic region. At some point it will break. The force that breaks it is called the tensile strength. For steel the tensile strength is 1 GN/m^{2}. Thus for cable in the example above it would take a hanging mass of 500 kilograms (1,100 pounds) to break the cable.
Young’s modulus also describes the change in length of an object when a compressive force is exerted on it. When you stand you exert a compressive force on your leg bones and they will shrink somewhat in length. But a 70-kilogram (154 pound) person standing on one leg will compress it by only 0.01% of its length! The Young’s modulus for cartilage, the material between the bones in all parts of your body, is one ten-thousands as large as that of bone. So putting the weight of a 70-kilogram (154 pound) mass on a piece of cartilage with same area as the femur in your leg would compress it by 10% of its original thickness.
For compressive forces there is a compressive strength. But, many materials will buckle if too great a compressive force is placed on it. Brittle materials will, on the other hand, break. The compressive and tensile strength of bones is almost exactly the same.