FOR EVERY ACTION THERE IS A REACTION: NEWTON'S THIRD LAW OF MOTION

Vocabulary:

• law of conservation of momentum - the momentum of an object will not change unless its mass, velocity, or both change
• momentum - the property of an object that determines how hard it is to start or stop an object in motion
• Newton's third law of motion - for every action, there is an equal and opposite reaction

One of the latest crazes in water sports is the jetpack. A jetpack can thrust a rider three stories high into the air at a speed of around 22 mph. Jetpacks work by ejecting water at high velocity toward the water's surface. As a result of this strong downward force, the rider is pushed upwards, flying high into the air. In order for the jetpack to exert enough force to function, it must be connected to a pump. The pump for the jetpack is located on a floating watercraft, such as a jet ski. Because the pump is heavy (and has a large mass), it needs to remain stationary. Otherwise, the sheer weight of the pump would prevent the rider from elevating into the air. Once the rider makes his or her way into the air, variations in water pressure can create imbalances in the forces that act on the rider. These imbalanced forces, according to Newton's first law of motion, allow the rider to change motion, swaying from one side to the other. The way these jetpacks work follows Newton's third law of motion. In this Lesson, you will learn more about Newton's third law of motion, as well as the law of conservation of momentum.

Understanding Newton's Third Law

Have you ever watched people skate at an ice rink? What happens when a person bounces into a wall or barrier? How does running into somebody change the way a person moves on the rink? If an ice skater crashes into a wall, he or she may fall down, or with enough force, end up rolling backward.

In both scenarios, for each action there was a reaction that took place. This is a demonstration of Newton's third law of motion. This law states that for every action, there is an equal and opposite reaction. Another way to state the law is that when one object exerts a force on a second object, the second object will exert a force on the first object with equal strength and in the opposite direction.

The science behind gymnastics

Gymnasts can accomplish amazing feats on various objects, like a balance beam. Flipping oneself high in the air and balancing on a 2-inch beam is not an easy task. What forces are involved when a gymnast performs a routine on a balance beam? The gymnast on the beam is an example of Newton's third law of motion. Even though the beam is not moving, the gymnast is pushing down on the beam through the force of his or her body. In return, the beam pushes back on the gymnast with an equal force but in the opposite direction.

The Forces of Action and Reaction

With Newton's third law of motion, there are two distinct forces to consider: action and reaction. Newton's first two laws of motion explain how an object with a single motion can change. For example, with the first law, if the force acting on an object were unbalanced, then it would change the object's motion. The second law describes a way to calculate the acceleration of an object in motion.

What happens when there are paired forces? Newton's third law of motion states that forces act upon each other in pairs in a manner that is equal and opposite. Even though the action-reaction force pairs are opposites, they do not cancel. This is because each force acts on different objects. As shown in Figure 8.1, when the player shoots the basketball, there is a force from the hands of the person that pushes the ball. There is also a force from the ball as it pushes back on the person while accelerating into the air. The only way these forces can cancel out is if they act on the same object.

Fig. 8.1 Action and reaction forces when shooting a basketball

Sometimes, it's hard to tell whether or not there is an action-reaction force pair. This happens when the mass of one of the objects is very large. For example, when you walk, you exert a force on the ground. The ground is also exerting a force back on you. This force is not felt because the mass of the ground, or the earth, is massive. The earth does not move because of the force a person puts on it.

Let's look at different examples of action-reaction forces.

Why does it hurt if you stub your finger on a wall? The reaction force of the wall is the same that you use to hit the wall.

If one blows up a balloon and releases it without tying it, the air inside the balloon will force its way out. This air surrounding the balloon will push back with an equal reaction force, and the balloon will travel upward.

A paddler in a canoe has an action force of rowing the canoe with a paddle, pushing it against the water. The water pushes back against the paddle in a reaction force, causing the boat to move forward.

Did You Know?

When a bird flies, it uses Newton's third law of motion. The wings of a bird push the air in a downward and backward motion. The air then pushes back on the bird but in the opposite direction. It is this action-reaction force that keeps the bird in the air, flying to its next destination.

Gaining Momentum

Another concept important to motion is momentum. When a forensic scientist is investigating an accident, he or she often must determine an object's momentum. When you ride a bicycle, it can be hard to get going. But after a few pedals, the wheels of the bicycle gain momentum, allowing you to travel faster and farther. This momentum also makes it hard for you to stop. What exactly is momentum?

Momentum is the property of an object that determines how hard it is to start or stop an object in motion. Momentum depends on the object's mass and velocity. Its symbol is usually expressed as p. The equation for momentum is shown in Figure 8.2.

Fig. 8.2 Mathematical expression for momentum

Recall that velocity has a magnitude and direction; it is a vector. Because velocity is part of the momentum equation, momentum also has a magnitude and direction. Let's use this equation to solve a problem in Figure 8.3.

Fig. 8.3 Momentum depends on mass and velocity.

What is the momentum of the bowling ball?

What you know:

• mass 7.72 kg
• velocity 4.47 m/s

Solve for momentum:

• p
• p (7.72 kg)(4.7 m/s)
• p 34.5 kg*m/s

By solving the equation, you now know that the bowling ball needs a momentum of 34.5 in order to travel at a velocity of 4.47 to hit the bowling pins.

Momentum depends on mass and velocity. Something very massive, like a semitruck, has great momentum, even at a slow velocity. Something very small, like a bullet, can have the same momentum as a semitruck or even greater, because the bullet travels at an extremely high velocity.

Law of Conservation of Momentum

There is a law that governs momentum: the momentum of an object will not change unless its mass, velocity, or both change. This law is referred to as the law of conservation of momentum. Even though an object's momentum cannot change, it can be transferred from one object to another. This is observed when you play a game of pool and use the cue ball to hit a group of balls.

At first, the group of balls is motionless. The cue ball (white ball) is moving at a fast velocity due to force exerted from the pool stick. Once the cue ball collides with the group of balls, it slows down while the rest of the balls begin to move. At this collision, there was a transfer of momentum between the objects. The momentum gained by the balls is equal to the momentum lost by the cue ball. Not considering the action of any other forces on the balls, their total momentum is conserved.

What happens to the momentum of objects that collide? Regardless of the collision, momentum will remain conserved. You can use the law of conservation of momentum to find the velocity of an object after a collision.

Take Figure 8.4 for example. There are two carts, each with a different mass and velocity. Total momentum can be calculated using the equation in Figure 8.5.

Fig. 8.4 Conservation of momentum

Fig. 8.5 Mathematical equation used to determine the total momentum of objects

This equation can be applied to determine the initial momentum that occurs at the moment the two carts collide.

What you know:

Solve for total momentum:

What happens to momentum after the collision? The total momentum remains the same, but the velocities of the carts have changed. The mass of the carts is now equal to the sum of the masses from both carts. Using this information, you can determine the velocity of the carts.

Did you notice something while calculating the momentum of both carts? Momentum was never destroyedit just transferred from one object to another. Although the momentum of the carts remained the same for this example, keep in mind that there can be cases where momentum will change because the mass and/or velocity of an object changes. This should make perfect sense given the mathematical expression used to describe the relationship between mass, velocity, and momentum (Fig. 8.2).

1) Select the best answer. What does Newton's third law of motion state?

	For every action, there is an unequal and same direction reaction.
	For every action, there is an equal and opposite reaction.
	For every action, there is an equal and same direction reaction.
	For every action, there is an unequal and opposite reaction.

2)Select the best answer. What does the law of conservation of momentum state?

	The momentum of an object will not change unless its mass changes.
	The momentum of an object will not change unless its mass, velocity, or both change.
	The momentum of an object will not change unless its direction changes.
	The momentum of an object will not change unless its velocity changes.

3)Select the best answer. Why can't we feel all the action-reaction forces around us?

	This happens when the gravity of one of the objects is very large and does not move.
	This happens when the gravity of one of the objects is very small and does not move.
	This happens when the mass of one of the objects is very small and does not move.
	This happens when the mass of one of the objects is very large and does not move.

4)Select the best answer. Why can a bullet with a tiny mass have the same momentum as a slow-moving semitruck?

	The bullet has a very small speed.
	The bullet has a very large acceleration.
	The bullet has a very large speed.
	The bullet has a very small acceleration.

5)Select the best answer. What will happen to the momentum of a ball when it hits another ball?

	The momentum will decrease.
	The momentum will be transferred to the other ball and stay the same.
	The momentum will increase.

6)Select the best answer. In the case of all collisions, momentum is _____.

	lost
	gained
	conserved

7) Selectall that apply. To increase momentum, what should change?

	increase mass
	decrease velocity
	increase velocity
	decrease mass

8) Label the action and reaction forces in the picture.

Choices

action

reaction

9)Label the action and reaction forces in the picture.

Choices

reaction

action

10)Label the action and reaction forces in the picture.

Choices

reaction

action

11)Solve for momentum using the information in the table.

Object	Mass (kg)	Velocity (m/s)	Momentum
bird	0.05	22
high school student	100	15
bullet	0.006	700
satellite	4,000	7,000