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Objective: To identify whether positive, negative, or zero work is being done, to identify the force that is doing the work, and to describe the energy transformation associated with such work.

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Linear Expansion of Materials

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Make sense of the equation that relates the amount of expansion of an object to the variables that affect the expansion.

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Use information from a table graph to compare the linear expansion of various material under varying conditions.

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Combine information from a table or equation with information from a graph to predict the amount of expansion of a material under varying conditions.

Making Comparisons

Make sense of the graph that shows how temperature affects the length of beams of different materials.

The Equation

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Combining Models

The Graph

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Linear Expansion of Materials As the temperature of a material increases, it begins to expand. For instance, a metal rod or beam will increase its length by an amount ΔL. The value of ΔL depends on the original length (Lo) at the original temperature (To), the temperature to which it is heated (T) and the coefficient of linear expansion (α). The equation relating these variables is shown in Figure 1. The amount of expansion depends upon the material; each material has its own unique coefficient of linear expansion. Coefficients for a variety of materials are shown in Table 1. Note that the left column includes metals and metal alloys and the right column includes non-metals. The expansion of a rod or beam in one dimension as described by Figure 1 is known as linear expansion. Linear expansion causes the length of a rod or beam to change with temperature. Figure 2 shows how the length of a beam varies as a function of temperature for four different materials.

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Physics-Interactives/Static-Electricity/

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1,1,2,1,1,1,1,1,2,1,1,1,1,1,1,1,1

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The Equation,The Graph,Making Comparisons,Combining Models

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