5.1.2 Combining Forces

FIGURE 5.2a shows a box being pulled by two ropes, each exerting a force on the box. How will the box respond? Experimentally, we find that when several forces $\vec{F}_{1}$ , $\vec{F}_{2}$ , $\vec{F}_{3}$ , . . . are exerted on an object, they combine to form a net force given by the vector sum of all the forces:

{\vec{F}}_{net} \equiv \sum_{i = 1}^{N} {\vec{F}}_{i} = {\vec{F}}_{1} + {\vec{F}}_{2} + \dots + {\vec{F}}_{N}

(5.1)

Recall that $\equiv$ is the symbol meaning “is defined as.” Mathematically, this summation is called a superposition of forces. FIGURE 5.2b shows the net force on the box.

The figure illustrates the top view of a box which is being pulled by a rope from two different directions.

The figure illustrates the free body diagram of two forces acting on a box.

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