Force and mass

In physics, we build on our intuitive understanding of force as either a push or a pull. Although forces are not visible, we do see and experience their effects. Forces cause bodies to deform: They expand springs, compress balloons, and bend beams. Also, as Newton's first law implies, a net (unbalanced) force will cause a body to change its velocity. These two effects are often seen together. For example, a ball struck by a bat is both deformed and accelerated.

FIGURE 3.6

In order to measure and compare forces, we may use the expansion of a "standard" spring A, shown in Fig. 3.6 a. We might define a force of one unit as the action that extends the spring by one unit of length. To measure larger forces, spring A must be calibrated. We take springs В and С and apply the same force (one unit) to each. By the simple method depicted in Fig. 3.6 b, a force of two units is applied to A, and so a "2" can be marked on the scale. This procedure is easily repeated for larger forces.

Force is clearly a quantity that has both magnitude and direction. But before one can call it a vector, one must verify that it obeys the law of vector addition. Figure 3.6 c shows a force F₁ of 4 units directed due east and a force F₂ of 3 units directed due north. Experiment shows that the combined effect of these two forces is the same as that of a force of 5 units in the direction 37° N of E. This is simply the magnitude and direction of the vector sum of these two forces, which confirms the vector nature of force.

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