Why pairs never cancel

The idea

The equal and opposite forces of the third law act on two different objects, so they never balance each other; equal and opposite forces acting on the same object do balance.

A puzzling thought

The water pushes the paddle forward and the paddle pushes the water backward, with equal forces. Yet the canoe moves forward.

How can the canoe move if the forces are equal and opposite?

• The two forces act on different objects
• The forces are not really equal
• The water pushes the canoe backward as well

Two situations

Look at both situations.

One object or two

In the pair, the water and the paddle each had only one of the forces on it, so the force on the paddle was not cancelled. On the rope both forces acted on the same object, so they balanced.

The equal and opposite forces of the third law act on two different objects, so they never balance each other; equal and opposite forces acting on the same object do balance.

Notes

Third-law pairs act on two different objects, so they never balance. Equal and opposite forces on the same object do balance.

Check yourself

Why do the two forces of a third-law pair not balance each other?

Two equal and opposite forces act on the same rope. What is the net force on it?

Which pair of forces balance each other?

The water pushes the paddle forward with a force of the same size as the paddle pushes the water backward. The paddle…

• They act on two different objects — correct. Yes!
• They are not equal in magnitude. The two forces of a pair are equal in magnitude. They act on different objects.
• They act in the same direction. The two forces of a pair are opposite in direction.
• Twice one force. Equal and opposite forces on the same object cancel out; they do not add.
• Zero, because they balance each other — correct. Yes!
• Equal to one of the forces. Equal and opposite forces on the same object balance, so the net force is zero.
• The push of the paddle on the water and the push of the water on the paddle. These two forces act on different objects, so they do not balance.
• The push of the foot on the ground and the push of the ground on the foot. These two forces act on different objects, so they do not balance.
• Two equal and opposite pulls on the same rope — correct. Yes!
• has a net force forward, because the backward force acts on the water — correct. Yes!
• has no net force, because the two forces cancel. The two forces act on different objects, so they do not cancel each other.
• has a net force backward. The force on the paddle is the forward push of the water.