Name Class Date CHAPTER 2 Forces and Motion 3 Momentum SECTION BEFORE YOU READ After you read this section, you should be able to answer these questions: What is momentum? How is momentum calculated? What is the law of conservation of momentum? What Is Momentum? Picture a compact car and a large truck moving at the same velocity. The drivers of both vehicles put on the brakes at the same time. Which vehicle will stop first? You most likely know that it will be the car. But why? The answer is momentum. The momentum of an object depends on the object s mass and velocity. Momentum is the product of the mass and velocity of an object. In the figure below, a car and a truck are shown moving at the same velocity. Because the truck has a larger mass, it has a larger momentum. A greater force will be needed to stop the truck. STUDY TIP Visualize As you read, try to picture in your head the events that are described. If you have trouble imagining, draw a sketch to illustrate the event. READING CHECK 1. Identify What is the momentum of an object? TAKE A LOOK 2. Predict How could the momentum of the car be increased? Object A train moving at 30 km/h A bird sitting on a branch high in a tree A truck moving at 30 km/h A rock sitting on a beach Momentum Critical Thinking 3. Apply Concepts Fill in the chart to the left to show which object has the most momentum, which object has a smaller amount of momentum, and which objects have no momentum. Interactive Textbook 37 Forces and Motion
Name SECTION 3 Class Date Momentum continued How Can You Calculate Momentum? READING CHECK 4. Identify What do you need to know in order to calculate an object s momentum? Math Focus 5. Calculate A 6 kg bowling ball is moving at 10 m/s down the alley toward the pins. What is the momentum of the bowling ball? Show your work. If you know what an object s mass is and how fast it is going, you can calculate its momentum. The equation for momentum is p m v In this equation, p is momentum (in kilograms multiplied by meters per second), m is the mass of the object (in kilograms), and v is the velocity of the object (in meters per second). Like velocity, momentum has direction. The direction of an object s momentum is always the same as the direction of the object s velocity. Use the following procedure to solve momentum problems: Step 1: Write the momentum equation. Step 2: Replace the letters in the equation with the values from the problem. Let s try a problem. A 120 kg ostrich is running with a velocity of 16 m/s north. What is the momentum of the ostrich? Step 1: The equation is p m v. Step 2: m is 120 kg and v is 16 m/s north. So, p (120 kg) (16 m/s north) 1,920 kg m/s north TAKE A LOOK 6. Describe Use a metric ruler to draw an arrow next to the rocket to show its momentum. The size of the rocket s momentum is 15 kg m/s. The scale for the arrow should be 1 cm 10 kg m/s. Interactive Textbook 38 Forces and Motion
Name Class Date SECTION 3 Momentum continued What Is the Law of Conservation of Momentum? When a moving object hits an object at rest, some or all of the momentum of the first object is transferred to the second object. This means that the object at rest gains all or some of the moving object s momentum. During a collision, the total momentum of the two objects remains the same. Total momentum doesn t change. This is called the law of conservation of momentum. The law of conservation of momentum is true for any colliding objects as long as there are no outside forces. For example, if someone holds down the darker ball in the collision shown above, it will not move. In that case, the momentum of the lighter ball would be transferred to the person holding the ball. The person is exerting an outside force. The law of conservation of momentum is true for objects that either stick together or bounce off each other during a collision. In both cases, the velocities of the objects will change so that their total momentum stays the same. TAKE A LOOK 7. Identify Draw an arrow showing the size and direction of the darker ball s momentum after its collision with the lighter ball. READING CHECK 8. Identify When is the law of conservation of momentum not true for two objects that are interacting? When football players tackle another player, they stick together. The velocity of each player changes after the collision because of conservation of momentum. Although the bowling ball and bowling pins bounce off each other and move in different directions after a collision, momentum is neither gained nor lost. Say It Explain Words In a group, discuss how the everyday use of the word momentum differs from its use in science. Interactive Textbook 39 Forces and Motion
Name Class Date Section 3 SECTION VOCABULARY momentum a quantity defined as the product of the mass and velocity of an object 1. Explain A car and a train are moving at the same velocity. Do the two objects have the same momentum? Explain your answer. 2. Show Relationships Put the following objects in order of increasing momentum: a parked car, a train moving at 50 km/h, a train moving at 80 km/h, a car moving at 50 km/h. 3. Calculate A 2.5 kg puppy is running with a velocity of 4.8 m/s south. What is the momentum of the puppy? Show your work. 4. Explain What is the law of conservation of momentum? 5. Calculate A ball has a momentum of 1 kg m/s north. It hits another ball of equal mass that is at rest. If the first ball stops, what is the momentum of the other ball after the collision? (Assume there are no outside forces.) Explain your answer. Interactive Textbook 40 Forces and Motion
M Forces, Motion, and Energy Answer Key continued 9. A gravity arrow should be pointing down, and an air resistance arrow should be pointing up; arrows should be the same length. 10. the apple 11. Never; every object with mass has weight. 12. The shuttle and astronauts are falling at the same rate. 13. orbit farther from Earth 14. There should be a straight, horizontal line drawn from the shuttle s current position to the right-hand side of the figure. 15. an unbalanced force 16. The arrow should point from the moon to the Earth. 17. horizontal motion and vertical motion 18. above the bulls-eye 19. horizontal, gravity, curved 20. 9.8 m/s 2 ; gravity causes everything to accelerate by 9.8 m/s 2. 1. No, objects in free fall are affected only by gravity. Parachutists are affected by gravity and air resistance. 2. Cause Effect Gravity acts on a falling object. Air resistance equals gravity and acts in the opposite direction. The object accelerates toward Earth. The falling object reaches terminal velocity. 3. final g t final 9.8 m/s s 3.5 s 34.3 m/s 4. centripetal force 5. Gravity affects vertical motion. Gravity slows upward vertical motion of the projectile and increases downward vertical motion of the projectile. SECTION 2 NEWTON S LAWS OF MOTION 1. They are the same size. 2. It will not change speed or direction. 3. It will stay at rest. 4. It will continue to move at the same velocity. 5. The distances would be greater. 6. Apply an unbalanced force in the direction opposite to its motion. 7. Friction slows it down. 8. The groceries have no unbalanced force acting on them. So they continue moving in a straight line. 9. The golf ball has less mass or less inertia. 10. the pickup truck 11. Arrows should point from person to cart; arrows in left-hand and middle figures are the same length; arrow in right-hand figure is longer. 12. newtons (N), or kg m/s 2 13. 10 kg m/s 2, 10 kg m/s 2 1.02 kg, 9.8 m/s 2 14. F ma F (1,250 kg)(40 m/s 2 ) F 50,000 N 15. action force down arrow, reaction force up arrow 16. They are the same size. 17. The batter is exerting a force on the bat, which is greater than the force exerted by the ball. 18. The action force arrow should point from the ball toward the ground. The reaction force arrow should point from the ground toward the ball. 19. Earth is much bigger than the object, so its acceleration is very small. 1. Objects with large masses have large inertia. 2. The arrow should be the same size and direction as the arrow in the question. 3. An arrow should point left. Its length should be the difference in length of the arrows shown in the question. 4. Increase the force on the object; decrease the mass of the object. 5. The action force is the push by my foot on the ball. The reaction force is the push by the ball on my foot. 6. F ma, F 40 kg 4.5 m/s 2 180 N SECTION 3 MOMENTUM 1. the product of the object s mass and velocity 2. increase in its speed or its mass 3. Object Momentum A train moving at 30 km/h A bird sitting on a branch high in a tree A truck moving at 30 km/h A rock sitting on a beach most momentum no momentum less momentum no momentum Interactive Textbook Answer Key 83 Forces, Motion, and Energy
M Forces, Motion, and Energy Answer Key continued 4. its mass and its velocity 5. p m v p 6 kg 10 m/s at the pins p 60 kg m/s at the pins 6. The arrow should be 1.5 cm long and pointing up. 7. The arrow should point from the dark ball to the right-hand side of the figure. It should be the same size as the arrow in the top image. 8. when outside forces are present 1. No, the train has more momentum because it has a larger mass. Momentum is velocity times mass. Because both have the same velocity, the object with larger mass has more momentum. 2. parked car, car moving at 50 km/h, train moving at 50 km/h, train moving at 80 km/h 3. p m v p 2.5 kg 4.8 m/s south 12 kg m/s south 4. During a collision, momentum is neither lost nor gained (as long as no outside forces are acting). 5. 1 kg m/s north Chapter 3 Forces in Fluids SECTION 1 FLUIDS AND PRESSURE 1. any material that can flow and take the shape of its container 2. the force exerted on a given area 3. pressure force area pressure 3,000 N 2m 2 pressure 1,500 Pa 4. The arrows would still be the same length. The pressure inside still must equal atmospheric pressure. 5. It decreases. 6. about 1/2 7. The weight of the entire atmosphere is pushing down. 8. The weight of more and more fluid is pushing on the same area. 9. 201 kpa 10. When you suck on the straw, you suck air out of it. Since there is less air in the straw, the air pressure is lower. 11. The pressure inside the lungs is greater than the pressure outside. 1. The particles of the fluid hit the walls of the container. The force they exert causes pressure. 2. Density is the mass of a substance divided by its volume. Materials that are more dense will exert more pressure than materials that are less dense. 3. pressure force area pressure 2.5 N 0.012 m 2 pressure 208 Pa 4. A muscle in your chest contracts. The volume of your chest gets larger. Air pressure inside your chest is lower than atmospheric pressure. Air flows into your lungs. The muscle in your chest relaxes. The volume of your chest gets smaller. Air pressure inside your chest is higher than atmospheric pressure. Air flows out of your lungs. SECTION 2 BUOYANT FORCE 1. Fluid pressure increases with depth. 2. differences in pressure 3. 3.6 N 4. float 5. Its weight is equal to the buoyant force of the water it displaces. 6. more 7. The buoyant force is greater than the log s weight. 8. the mass of an object divided by its volume 9. If it is denser than water, it will sink. If it is less dense than water, it will float. 10. Greater; air is more dense than helium, so the same volume has a greater mass. 11. The volume of the ship is much larger than the volume of the steel used to make it. 12. If the shape increases the volume, the object s density decreases. 13. by letting water into its ballast tanks 14. by letting gases into, or releasing them from, the swim bladder Interactive Textbook Answer Key 84 Forces, Motion, and Energy