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Computer drawing of two systems; equilibrium of forces

A very basic concept when dealing with forces is the idea of equilibrium or balance. In general, an object can be acted on by several forces at the same time. A force is a vector quantity which means that it has both a magnitude (size) and a direction associated with it. If the size and direction of the forces acting on an object are exactly balanced, then there is no net force acting on the object and the object is said to be in equilibrium. Because there is no net force acting on an object in equilibrium, then from Newton's first law of motion, an object at rest will stay at rest, and an object in motion will stay in motion.

Let us start with the simplest example of two forces acting on an object. Then we will show examples of three forces acting on a glider, and four forces acting on a powered aircraft.

In Example 1 on the slide, we show a blue ball that is being pushed by two forces, labeled Force #1 F1 and Force #2 F2. Remember that forces are vector quantities and direction is important. Two forces with the same magnitude but different directions are not equal forces. In fact,

F1 = - F2

for the coordinate system shown with the letter X below the ball. If we sum up the forces acting on the ball, we obtain the force equation on the left:

F1 + F2 = F net = 0

where F net is the net force acting on the ball. Because the net force is equal to zero, the forces in Example 1 are acting in equilibrium.

There is no net force acting on the ball in Example 1. Since the ball is initially at rest (velocity equals zero), the ball will remain at rest according to Newton's first law of motion. If the ball was travelling with a uniform velocity, it would continue travelling at the same velocity.

In Example 2, we have increased the magnitude of Force #1 so that it is much greater than Force #2. The forces are no longer in equilibrium. The force equation remains the same, but the net force is not equal to zero. The magnitude of the net force is given by:

F1 > - F2

F1 + F2 = F net

|F net| = |F1| - |F2|

where the "| |" symbols indicate the magnitude of the quantity included between the ends. The direction of the net force would be in the positive X direction because F1 is greater then F2. According to Newton's second law of motion, the ball would begin to accelerate to the right. Because there is a net force in Example 2, the forces are not in equilibrium.


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Editor: Nancy Hall
NASA Official: Nancy Hall
Last Updated: May 13 2021

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