CHAPTER 12 Forces 3 SECTION KEY IDEAS Newton s Third Law As you read this section keep these questions in mind: What happens when one object exerts a force on another object? How can you calculate the momentum of an object? How does momentum change after a collision? What Is Newton s Third Law of Motion? Imagine kicking a soccer ball. The ball would move in a different direction. From Newton s first law, you know that the ball s motion could not have changed unless a force acted on it. Therefore, there must be a force acting on the ball. This force came from your foot. However, if you kicked a soccer ball, you would probably also feel a force on your foot. Where did this force come from? When you kick a soccer ball, your foot exerts a force on the ball. This force is called an action force. Atthe same time, the ball exerts a force on your foot. That force is called a reaction force. Sir Isaac Newton described the relationship between action forces and reaction forces in his third law of motion. Newton s third law of motion states that action forces always produce reaction forces. It also states that action forces and reaction forces are always equal in size, but act in opposite directions. The figure below shows the sizes and directions of action and reaction forces when a person kicks a soccer ball. READING TOOLBOX Organize After you read this section, create a Concept Map for momentum. Include the words momentum, mass, velocity, and direction in your map. According to Newton s third law, the foot and the soccer ball exert equal and opposite forces on each other. 1. Identify On the figure, label the action force and the reaction force. Interactive Reader 263 Forces
2. Apply Concepts A student has a weight of 534 N. The student sits in a chair. When the student sits in a chair, how much force does the chair apply to the student? FORCE PAIRS An action force and the reaction force that results are called a force pair. Newton s third law states that the forces in a force pair are equal in size, but opposite in direction. You may wonder why these forces do not cancel each other out, since they happen at the same time. The answer is that the forces act on different objects. For example, in the figure below, the action force acts on the water. The reaction force acts on the swimmer. The action force is the swimmer pushing the water backward. 3. Explain Why don t the action and reaction forces in the figure cancel each other out? The reaction force is the water pushing the swimmer forward. READING CHECK 4. Explain Why don t we notice Earth moving upward when an object falls toward the ground? EQUAL FORCES, UNEQUAL EFFECTS Imagine dropping a soccer ball. Earth s gravitational force pulls the soccer ball toward the ground. This is the action force. At the same time, the soccer ball exerts an equal gravitational force on Earth. This is the reaction force. The action force and the reaction force are the same size, but opposite in direction. It is easy to see the effect of the action force the ball falls to the ground. Why don t you notice the effect of the reaction force Earth being pulled upward? The answer is that these two equal forces act on objects with very different masses. Recall Newton s second law of motion: A large mass will accelerate less than a small mass when you apply the same amount of force. For example, the same amount of force acts on the soccer ball and Earth, but Earth s mass is much greater than the soccer ball s. Therefore, Earth s acceleration is much smaller than that of the soccer ball. Earth does move upward, but this acceleration is so small it is almost impossible to measure. Interactive Reader 264 Forces
SUMMARY OF NEWTON S THIRD LAW OF MOTION To summarize, there are four main ideas in Newton s third law of motion: Forces occur in pairs made up of an action force and a reaction force. Action and reaction forces are equal in size, but opposite in direction. Action and reaction forces act on different objects. Equal forces acting on different objects may have different effects. DETERMINING THE EFFECTS OF FORCES You can use Newton s third law of motion to determine how an object will move. For example, think again about the falling soccer ball. You can measure its weight, which is equal to the gravitational force on it the action force. Once you know the weight of the soccer ball, you know the size of the reaction force acting on Earth. If you know Earth s mass, you can calculate Earth s acceleration using Newton s second law of motion. What if you do not know the size of the force acting on an object? You may still be able to predict the object s motion using a quantity called momentum. Brainstorm Think of 10 examples of force pairs. Describe each action force with a partner. Ask your partner to try to think of the reaction force. Then, have your partner share his or her list of action forces with you. Try to think of the reaction force for each of your partner s action forces. What Is Momentum? Momentum is a property of all moving objects. The momentum of an object moving in a straight line is equal to its mass multiplied by its velocity. Momentum is represented by the variable p. Momentum Equation momentum = mass velocity p = mv The SI unit of momentum is kilograms times meters per second (kg m/s). Like velocity, momentum has both size and direction. An object s velocity and momentum are in the same direction. READING CHECK 5. Apply Concepts An object has a velocity of 10 m/s south. In what direction is its momentum? Interactive Reader 265 Forces
READING CHECK 6. Identify How does mass affect momentum? EFFECTS OF VELOCITY AND MASS ON MOMENTUM Look back at the equation for momentum. How does the velocity of an object affect its momentum? Mass and velocity are multiplied together to calculate momentum. Therefore, as an object s velocity increases, its momentum also increases. For example, a fast-moving car has more momentum than a slow-moving car of the same mass. How does mass affect momentum? If velocity stays the same, increasing mass also increases momentum. For example, a tractor-trailer truck has more momentum than a sports car moving at the same velocity. CALCULATING MOMENTUM Imagine a bowling ball rolling toward bowling pins. The ball has a mass of 6.00 kg. Its velocity is 10.0 m/s down the alley. What is the ball s momentum? Math Skills 7. Calculate An ostrich has a mass of 135 kg. It is running with a velocity of 16.2 m/s north. What is its momentum? Show your work. Step 1: List the given and unknown values. Step 2: Write the equation for momentum. Step 3: Insert the known values and solve for the unknown value. Given: mass, m = 6.00 kg velocity, v = 10.0 m/s down the alley p = mv Unknown: momentum, p p = (6.00 kg) (10.0 m/s down the alley) p = 60.0 kg m/s down the alley 8. Infer What is the momentum of a car that has stopped moving? FORCE AND MOMENTUM CHANGES Recall Newton s first law: an object s motion will not change until an unbalanced force acts on it. When you apply a force to a moving object, its motion changes. If its velocity changes, its momentum also changes. For example, a moving car has a certain velocity and momentum. When the driver applies the brakes, the car slows down. In other words, its velocity changes. Therefore, its momentum also changes. If you give an object more time to change its momentum, you will need to use less force to make that change. For example, if you move your arm back when you catch a baseball, the ball s momentum has more time to change. Your hand has to use less force to change the ball s momentum. This also means your hand feels less of a sting! Interactive Reader 266 Forces
What Happens to Momentum When Objects Collide? You can use the law of conservation of momentum to predict how objects will move after they collide, or hit. The law of conservation of momentum states that the total amount of momentum in an isolated system is conserved. Let s look at each part of this law to understand what it means. An isolated system is a group of objects that does not gain or lose mass or energy to its environment. Imagine a cue ball rolling across a table toward other billiard balls. The cue ball and the other balls are almost an isolated system. The balls do not gain or lose mass to the environment. They may lose a small amount of energy to friction, but the amount is generally small enough to ignore. Conserved means kept the same. The amount of momentum in an isolated system stays the same, no matter what happens within the system. Think again about the cue ball rolling across a table. When the cue ball hits the other balls, they move. Before the collision, the other balls are not moving; they have no momentum. Therefore, the total momentum in the system is equal to the momentum of the cue ball. When the cue ball hits another ball, it passes some of its momentum to the other ball. After the collision, all the balls have a different momentum. However, their total momentum is the same as it was before the collision. 9. Rephrase Write the law of conservation of momentum in your own words. 10. Explain Why does the cue ball slow down after it hits another ball? When a cue ball hits another ball on the table, the cue ball slows down. The other ball begins to move. The total momentum of the system stays the same. Interactive Reader 267 Forces
Section 3 Review SECTION VOCABULARY momentum a quantity defined as the product of the mass and velocity of an object 1. Explain How is velocity related to momentum? 2. Identify What is Newton s third law of motion? 3. Apply Concepts A skier pushes her ski poles against the ground. She begins to move across the snow. Earth does not seem to move. Identify the action and reaction forces in this example, and explain why the skier moves but Earth does not seem to. 4. Calculate A baby has a mass of 5.0 kg. The baby is on a train that is traveling east at 72 m/s. What is the baby s momentum? Show your work. 5. Calculate A kitten has a mass of 0.8 kg. It is moving forward with a momentum of 0.5 kg m/s. What is the kitten s velocity? Show your work. 6. Compare Describe the total momentum of billiard balls before and after the cue ball collides with another ball. Interactive Reader 268 Forces