MOMENTUM Objectives • Define Momentum
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MOMENTUM Objectives • Define momentum. (8.1) • Define impulse and describe how it affects changes in 8 MOMENTUM momentum. (8.2) • Explain why an impulse is Momentum is conserved greater when an object bounces than when the same object THE BIG for all collisions as long comes to a sudden stop. (8.3) IDEA as external forces don’t • State the law of conservation interfere. of momentum. (8.4) • Describe how the conservation of momentum applies to ave you ever wondered how a tae kwon do expert collisions. (8.5) can break a stack of cement bricks with the blow • Describe how the vector nature Hof a bare hand? Or why falling on a wooden floor of momentum affects the law hurts less than falling on a cement floor? Or why follow- of conservation of momentum. through is important in golf, baseball, and boxing? To (8.6) understand these things, you need to recall the concept of inertia introduced and developed when we discussed Newton’s laws of motion. Inertia was discussed both in discover! terms of objects at rest and objects in motion. In this chap- MATERIALS five marbles, ruler ter we are concerned only with the concept of inertia in EXPECTED OUTCOME When a motion—momentum. marble or marbles collide with the marbles at rest, the momentum is the same before and after the collision. As a result, the same number of marbles emerges at the same speed on the other side. discover! ANALYZE AND CONCLUDE How Does a Collision Affect the Motion Analyze and Conclude 1. When one marble collides of Marbles? with 5 marbles, the colliding 1. Observing How did the approximate speed marble stops and one 1. Place five marbles, all identical in size and of the marbles before each collision compare marble emerges at the same shape, in the center groove of a ruler. Launch to after each collision? speed on the other side. a sixth marble toward the five stationary 2. Drawing Conclusions What factors determine When 2 marbles collide marbles. Note any changes in the marbles’ how the speed of the marbles changes in a with 4 marbles, 2 marbles motion. collision? emerge at the same speed. 2. Now launch two marbles at four stationary 3. Predicting What do you think would hap- The pattern continues with marbles. Then launch three marbles at three more marbles. pen if three marbles rolling to the right and stationary marbles, and so on. Note any two marbles rolling to the left with the same 2. The initial speed and changes in the marbles’ motion. speed were to collide? direction 3. Remove all but two marbles from the groove. 3. Three marbles move to the Roll these two marbles at each other with right and two marbles move equal speeds. Note any changes in the to the left. marbles’ motion. 124 124 8.1 Momentum Key Term ᭣ FIGURE 8.1 momentum A truck rolling down a Teaching Tip State that just hill has more momentum as a large truck and a roller skate than a roller skate with have different masses, a moving the same speed. But if large truck and a moving roller the truck is at rest and skate have different momenta. the roller skate moves, Define and discuss momentum as then the skate has more moving mass—inertia in motion. momentum. Ask Will a large truck always have more momentum than a roller skate? No, a large truck at rest has no momentum. A moving 8.1 Momentum roller skate has momentum. We know that it’s harder to stop a large truck than a small car when think! CONCEPT A moving object both are moving at the same speed. We say the truck has more CHECK ...... can have a large momentum than the car. By momentum, we mean inertia in motion. Can you think of a case momentum if it has a large mass, More specifically, momentum is the mass of an object multiplied by where the roller skate and a high speed, or both. the truck shown in Figure its velocity. 8.1 would have the same momentum mass velocity momentum? Teaching Resources Answer: 8.1 • Reading and Study or, in abbreviated notation, Workbook momentum mv • PresentationEXPRESS • Interactive Textbook When direction is not an important factor, we can say • Next-Time Question 8-1 momentum mass speed • Conceptual Physics Alive! DVDs Momentum which we still abbreviate mv. A moving object can have a large momentum if it has a large mass, a high speed, or both. A moving truck has more momentum than a car moving at the same speed because the truck has more 8.2 Impulse Changes mass. But a fast car can have more momentum than a slow truck. Momentum And a truck at rest has no momentum at all. Figure 8.1 compares the momentum of a truck to that of a roller skate. Key Term impulse CONCEPT What factors affect an object’s momentum? Common Misconceptions CHECK ...... Impulse equals momentum. FACT Impulse equals change in 8.2 Impulse Changes Momentum momentum. Teaching Tip Derive the If the momentum of an object changes, either the mass or the veloc- impulse–momentum relationship. ity or both change. If the mass remains unchanged, as is most often Equate the two definitions of the case, then the velocity changes and acceleration occurs. What pro- acceleration: F/m 5 Dv/t. A simple duces acceleration? We know the answer is force. The greater the force algebraic rearrangement yields acting on an object, the greater its change in velocity, and hence, the Ft 5 D(mv). greater its change in momentum. 125 CHAPTER 8 MOMENTUM 125 Teaching Tip Choose your examples of changing momentum in careful sequence. The derivation of Impulse The change in momentum depends on the force that First, describe those where Ft R(mv) is given in acts and the length of time it acts. As Figure 8.2 shows, apply a the objective is to increase Appendix G, Note 8.2. brief force to a stalled automobile, and you produce a change in its momentum (e.g., pulling a sling momentum. Apply the same force over an extended period of time shot or arrow in a bow all the way back, the effect of a long and you produce a greater change in the automobile’s momentum. A cannon for maximum range, force sustained for a long time produces more change in momentum and driving a golf ball). Second, than does the same force applied briefly. So both force and time are describe cases in which the important in changing an object’s momentum. objective is to minimize a force when decreasing momentum (e.g., pulling your hand backward FIGURE 8.2 ᭤ when catching a ball, driving into When you push with the a haystack vs. into a concrete same force for twice the wall, and falling on a spongy time, you impart twice surface rather than on a rigid the impulse and produce one). Last, describe examples twice the change in where the objective is to momentum. maximize forces when decreasing momentum (e.g., karate chops). The quantity force ϫ time interval is called impulse. In short- hand notation, impulse Ft The greater the impulse exerted on something, the greater will be the change in momentum. The exact relationship8.2 is impulse change in momentum or Ft (mv) The impulse–momentum relationship helps us to analyze a variety of situations where the momentum changes. Consider the familiar examples of impulse in the following cases of increasing and decreasing momentum. Increasing Momentum To increase the momentum of an object, it makes sense to apply the greatest force possible for as long as pos- sible. A golfer teeing off and a baseball player trying for a home run do both of these things when they swing as hard as possible and fol- low through with their swing. The forces involved in impulses usually vary from instant to instant. Look at Figure 8.3. A golf club that strikes a golf ball exerts Many interactions that are zero force on the ball until it comes in contact with it; then the force explainable by Newton’s third FIGURE 8.3 ᭡ in creases rapidly as the ball becomes distorted. The force then law can also be explained The force of impact on a diminishes as the ball comes up to speed and returns to its original by momentum conservation. golf ball varies throughout shape. So when we speak of such forces in this chapter, we mean the Newton’s laws flow nicely into the duration of impact. momentum and its conservation. average force. 126 126 ᭤ Teaching Tip Use the loose coupling between railroad cars as a very good example of the impulse–momentum relationship. The slack in the coupling of railroad cars is evident when a locomotive either brings a long train from rest into motion, or when it brings a moving train FIGURE 8.4 ᭡ to rest. If the change in momentum occurs over a long time, the force of impact is small. In both cases a cascade of clanks Decreasing Momentum If you were in a car that was out of think! is heard as each car in turn is control and had to choose between hitting a haystack, as in Figure engaged. Without the loose 8.4 or a concrete wall as in Figure 8.5, you wouldn’t have to call on When a dish falls, will the coupling, a locomotive might your knowledge of physics to make up your mind. Common sense impulse be less if it lands simply sit still and spin its wheels.