4f. The Third Law: Forces in Pairs [Beyond Books - Introduction to Physics Concepts]

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4f. The Third Law: Forces in Pairs

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Earth and skydiver pull on one another (down arrow) to overcome air resistance (up arrow).

The third and final law of Newtonian mechanics is as intuitive and enchanting as the statement "You cannot touch without being touched." Yet the law (shown below) is often misunderstood and misapplied.

Newton's third lawIf one object exerts a force on another object, the other object exerts an equal force back on the first object.

According to legend, the Russian mystic Nostradamus's horse once refused to pull a cart after being hit on the head by an apple. The horse reasoned that, according to Newton's third law, any force that he exerted would be balanced by an equal and opposite force. The cart would thus never move, no matter how hard the horse tried.

A horse harnessed to a cart exerts an equal and opposite force to the cart as it exerts a force against the ground.

Perhaps awed by the horse's remarkable ability to apply scientific laws from the future (Newton developed his laws about a century after Nostradamus died), Nostradamus failed to find the flaw in this argument. The mystic was forced to get himself a less educated horse, which somehow did pull the cart.

The flaw in the first horse's argument is also a common misconception among beginning physics students. Fortunately, it is easily remedied. The key is understanding that action-reaction forces always act on different objects.

In the example here, the cart feels the unbalanced force applied by the horse and therefore accelerates if this force is greater than the frictional force of the ground on the cart. On the other hand, the horse feels an equal and opposite force applied by the cart but is able to accelerate forward if the frictional force of the ground on the horse is greater.

The two forces in an action-reaction force pair always act on two different objects. Consequently, the two forces can never cancel each other out. Acceleration of a particular object is caused by a net (unbalanced) force acting on that object.

Try It Out!

The space shuttle's rocket boosters propel the orbiter into space by exerting an equal and opposite force to the exhaust gasses.

A medium-sized apple has a mass of about 100 grams. What force does the apple exert on the Earth as the apple falls toward the ground? Why doesn't the Earth accelerate?
Suppose a bug is splattered all over the windshield of a car. Which one experienced the greater impact, the bug or the windshield? Which is stronger, the Earth's pull on an orbiting space shuttle or the space shuttle's pull on the Earth?

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