Inertia forces

In the above example, of the accelerating glider, the force applied to one end of the rope by the aircraft is greater than the air resistance acting on the glider at the other end. As far as the rope is concerned, however, the force it must apply to the glider tow-hook must be equal to the air resistance force plus the force required to accelerate the glider. In other words, the forces on the two ends of the rope are in equilibrium (as long as we ignore the mass of the rope). The extra force that the rope has to apply to produce the acceleration is called an inertia force.

As far as the rope is concerned, it does not matter whether the force at its far end is caused by tying it to a wall to create a reaction or by attaching it to a glider which it is causing to accelerate, the effect is the same – it feels an equal and opposite pull at the two ends. From the point of view of the glider, however, the situation is very different; if there were a force equal and oppo­site to the pull from the rope, no acceleration would take place. The forces on the glider are not in equilibrium.

Great care has to be taken in applying the concept of an inertia force. When considering the stresses in the tow-rope it is acceptable to apply the pulling force at one end, and an equal and opposite force at the other end due to the air resistance plus the inertia of the object that it is causing to accelerate. When considering the motion of the aircraft and glider, however, no balancing inertia force should be included, or there would be no acceleration. A free-body diagram should be drawn as in Fig. 1.2.

This brings us to the much misunderstood third law of Newton: to every action there is an equal and opposite reaction. If a book rests on a table then the table produces a reaction force that is equal and opposite to the weight force. However, be careful; the force which is accelerating the glider produces a reaction, but the reaction is not a force, but an acceleration of the glider.

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