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Newton’s 3rd Law of Motion: Action and Reaction

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Newton’s 3rd Law of Motion: Action and Reaction. Book M Section 2.4 Pages: 64-69. Newton realized that forces are not “one-sided.” Whenever one object exerts a force on a second object, the second object exerts a force back on the first object.

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### Newton’s 3rd Law of Motion:Action and Reaction

Book M

Section 2.4

Pages: 64-69

Newton realized that forces are not “one-sided.”

• Whenever one object exerts a force on a second object, the second object exerts a force back on the first object.
• The force exerted by the second object is equal in strength and opposite in direction to the first force.
• The first force is called the “action” and the other force the “reaction.”
• Newton’s third law of motion states that if one object exerts a force on another object, then the second object exerts a force of equal strength in the opposite direction on the first object.

You may already be familiar with examples of Newton’s third law of motion.

• Perhaps you have watched figure skaters and have seen one skater push on the other.
• As a result, both skaters move—not only the skater who was pushed.
• The skater who pushed is pushed back with an equal force, but in the opposite direction.
• If they have the same mass, they will move at the same speed.
• But if one skater has a greater mass than the other, she will move backward more slowly.
• Although the action and reaction forces will be equal and opposite – the same force acting on a greater mass results in a smaller acceleration.

Newton’s third law is in action all around you.

• When you walk, you push the ground with your feet.
• The ground pushes back on your feet with an equal and opposite force.
• You go forward when you walk because the ground is pushing you!
• The air pushes back on those wings with an equal force that propels the bird forward.

A squid applies Newton’s third law of motion to move itself through the water.

• The squid exerts a force on the water that it expels from its body cavity.
• At the same time, the water exerts an equal and opposite force on the squid, causing it to move.

You have already learned that balanced forces, which are equal and opposite, add up to zero.

• In other words, balanced forces cancel out.
• They produce no change in motion.
• Why then don’t the action and reaction forces in Newton’s third law of motion cancel out as well?
• After all, they are equal and opposite.

To answer this question, you have to consider the object on which the forces are acting.

• Look, for example, at the two volleyball players in the photo below.
• When they hit the ball from opposite directions, each of their hands exerts a force on the ball.
• If the forces are equal in strength, but opposite in direction, the forces cancel out.
• The ball does not move either to the left or to the right.
• Red arrows show action
• forces. Blue arrows show
• reaction forces.

Newton’s third law, however, refers to forces on two different objects.

• If only one player hits the ball, as shown in the photo here, the player exerts an upward action force on the ball.
• In return, the ball exerts an equal but opposite downward reaction force back on her wrists.
• One force is on the ball, and the other is on the player.

The action and reaction forces cannot be added together because they are acting on different objects.

• Forces can be added together only if they are acting on the same object.
• The player's wrists exert the action force.
• The ball exerts the reaction force.

Newton also wrote about something that he called the “quantity of motion.”

• What is this quantity of motion? --Today we call it momentum.
• The momentum(moh men tum) of an object is the product of its mass and its velocity.
• The more momentum an object has, the harder it is to stop.
• You can catch a baseball moving at 20 m/s, for example, but you cannot stop a car moving at the same speed.

Why does the car have more momentum than the ball?

• The car has more momentum because it has a greater mass.
• A high velocity also can produce a large momentum, even when mass is small.
• A bullet shot from a rifle, for example, has a large momentum.
• Even though it has a small mass, it travels at a high speed.

What is the unit of measurement for momentum?

• Since mass is measured in kilograms and velocity is measured in meters per second, the unit for momentum is kilogram-meters per second (kg · m/s).
• Like velocity and acceleration, momentum is described by its direction as well as its quantity.
• The momentum of an object is in the same direction as its velocity..

Momentum is useful for understanding what happens when an object collides with another object.

• When two objects collide in the absence of friction, momentum is not lost.
• This fact is called the law of conservation of momentum.
• The law of conservation of momentum states that the total momentum of the objects that interact does not change.
• The quantity of momentum is the same before and after they interact.
• The total momentum of any group of objects remains the same unless outside forces act on the objects.
• Friction is an example of an outside force.

However--the word conservation means something different in physical science than in everyday usage.

• In everyday usage, conservation means saving resources.
• You might conserve water or fossil fuels, for example.
• In physical science, the word conservation refers to conditions before and after some event.
• A quantity that is conserved is the same after an event as it was before the event.

Two Moving Objects

• Two train cars traveling in the same direction on a track shown in the figure below.
• Car X is traveling at 10 m/s and car Y is traveling at 5 m/s.
• Eventually, car X will catch up with car Y and bump into it.
• During this collision, the speed of each car changes.
• Car X slows down to 5 m/s, and car Y speeds up to 10 m/s.
• Momentum is conserved—the momentum of one train car decreases while the momentum of the other increases.

One Moving Object

• Suppose that car X moves down the track at 10 m/s and hits car Y, which is not moving.
• The figure below shows that after the collision, car X is no longer moving, but car Y is moving.
• Even though the situation has changed, momentum is still conserved.
• The total momentum is the same before and after the collision.
• This time, all of the momentum has been transferred from car X to car Y.

Two Connected Objects

• Now suppose that, instead of bouncing off each other, the two train cars couple together when they hit.
• Is momentum still conserved? --The answer is yes.
• You can see in the figure below that the total momentum before the collision is again 300,000 kg · m/s.

Two Connected Objects

• But after the collision, the coupled train cars make one object with a total mass of 60,000 kilograms (30,000 kilograms + 30,000 kilograms).
• The velocity of the coupled trains is 5 m/s—half the velocity of car X before the collision.
• Since the mass is doubled, the velocity must be divided in half in order for momentum to be conserved.