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Day 12 – June 4 – WBL Chapter 6 Linear Momentum and Collisions PC141 Intersession 2013Slide 1 In everyday language, the term “momentum” refers to a tendency to “keep moving”. The same is true in classical mechanics, where momentum (and the conservation thereof) is often used to analyze situations where two or more objects interact with each other. In the photo, a runaway train (with lots of momentum) interacted with the wall of the station, with a predictable outcome.

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Day 12 – June 4 – WBL Linear Momentum PC141 Intersession 2013Slide 2 the linear momentum of an object is the product of its mass and velocity

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Day 12 – June 4 – WBL Linear Momentum PC141 Intersession 2013Slide 3

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Day 12 – June 4 – WBL Linear Momentum PC141 Intersession 2013Slide 4

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Day 12 – June 4 – WBL Linear Momentum PC141 Intersession 2013Slide 5

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Day 12 – June 4 – WBL Force and Momentum The preceding equation tells us that the following statements are equivalent: 1.A non-zero net force results in a non-zero acceleration 2.A non-zero net force results in a change in momentum. 6.1 Linear Momentum PC141 Intersession 2013Slide 6 Projectile motion provides an example. As we know, the horizontal velocity is constant. Therefore, the horizontal linear momentum is constant, which is required, since there is no horizontal force in this case.

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Day 12 – June 4 – WBL Problem #1: Net Force PC141 Intersession 2013Slide 7 WBL LP 6.3 A net force on an object can cause… A …an acceleration B …a change in momentum C …a change in velocity D …all of the preceding

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Day 12 – June 4 – WBL Problem #2: Baseball PC141 Intersession 2013Slide 8 WBL Ex 6.5 A kg baseball traveling with a horizontal speed of 4.50 m/s is hit by a bat and then moves with a speed of 34.7 m/s in the opposite direction. What is the change in the ball’s momentum? Note: It’s always good to get a sense for “reasonable” numbers…if a baseball is traveling toward home plate at 4.50 m/s, it certainly wasn’t pitched…a pitched baseball would be traveling closer to 40 m/s. Perhaps this one was lobbed by a nearby coach. Solution: In class

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Day 12 – June 4 – WBL Problem #3: Bad Truck Driver PC141 Intersession 2013Slide 9 WBL Ex 6.13 A loaded tractor-trailer with a total mass of 5000 kg traveling at 3.0 km/h hits a loading dock and comes to a stop in 0.64 s. What is the magnitude of the average force exerted on the truck by the dock? Solution: In class

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Day 12 – June 4 – WBL Much of this chapter is concerned with collisions, in which two objects (at least one of which is initially in motion), are in contact for a period of time †. Examples are the contact between a baseball and bat, or between two balls on a snooker table. In most of these cases, the force is not constant as a function of time – it increases from zero to some maximum value, then decreases back to zero. The total time 6.2 Impulse PC141 Intersession 2013Slide 10 during which the force is non-zero is usually on the order of milliseconds. The figure shows one example of a force – vs – time graph. † technically speaking, a “collision” doesn’t have to actually involve physical contact between objects. As we know from chapter 4, there exist “non- contact” forces as well. The math is the same, but we’ll avoid these situations in PC141.

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Day 12 – June 4 – WBL Impulse PC141 Intersession 2013Slide 11

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Day 12 – June 4 – WBL Recall from chapter 5 that the area under a graph of force vs. position is equal to the net work done on an object (which, furthermore, is equal to the change in the object’s kinetic energy). Here, the area under a graph of force vs. time is seen to be equal to the impulse on the object, which is furthermore equal to the change in its linear momentum. 6.2 Impulse PC141 Intersession 2013Slide 12 Although in most cases the actual relation between force and time is complicated, using the average force facilitates finding the area under the curve.

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Day 12 – June 4 – WBL Problem #4: Astronaut PC141 Intersession 2013Slide 13 WBL Ex 6.25 An astronaut (mass of 100 kg, with equipment) is headed back to her space station at a speed of m/s but at the wrong angle. To correct her direction, she fires rockets from her backpack at right angles to her motion for a brief time. These directional rockets exert a constant force of N for only s. a)What is the magnitude of the impulse delivered to the astronaut? b)What is her new direction (relative to the initial direction)? c)What is her new speed? Solution: In class

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Day 12 – June 4 – WBL Problem #5: Pop Fly PC141 Intersession 2013Slide 14 WBL Ex 6.36 A baseball player pops a pitch straight up. The ball (mass 200 g) was traveling horizontally at 35.0 m/s just before contact with the bat, and 20.0 m/s just after contact. Determine the direction and magnitude of the impulse delivered to the ball by the bat. Solution: In class

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Day 12 – June 4 – WBL In chapter 5, we learned that energy is a conserved quantity (in that the total energy of the universe is constant). For systems smaller than the entire universe, there are conditions to this conservation – it only holds true for systems that are closed, and that contain no nonconservative forces. We also learned that when nonconservative forces are present, the total mechanical energy changes only by the extent that the nonconservative forces do net work on the system. Likewise, under certain conditions, the total linear momentum of a system is a conserved quantity. This fact allows us to analyze the dynamics of objects that undergo collisions. 6.3 Conservation of Linear Momentum PC141 Intersession 2013Slide 15

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Day 12 – June 4 – WBL Conservation of Linear Momentum PC141 Intersession 2013Slide 16

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Day 12 – June 4 – WBL Problem #6: Conserved Linear Momentum PC141 Intersession 2013Slide 17 WBL LP 6.9 The linear momentum of an object is conserved if A the force acting on the object is conservative B a single, unbalanced internal force is acting on the object C the mechanical energy is conserved D none of the preceding

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Day 12 – June 4 – WBL Problem #7: Really Bad Ice Skaters PC141 Intersession 2013Slide 18 WBL Ex 6.43 Two ice skaters not paying attention collide in a completely inelastic collision. Prior to the collision, skater 1, with a mass of 60 kg, has a velocity of 50 km/h eastward, and moves at a right angle to skater 2, who has a mass of 75 kg and a velocity of 7.5 km/h southward. What is the velocity of the skaters after the collision? Solution: In class

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Day 12 – June 4 – WBL Problem #8: Exploding Bomb PC141 Intersession 2013Slide 19 WBL Ex 6.47 An explosion of a 10.0-kg bomb releases only two separate pieces. The bomb was initially at rest and a 4.00-kg piece travels westward at 100 m/s immediately after the explosion. a)What are the speed and direction of the other piece immediately after the explosion? b)How much kinetic energy was released in this explosion? Solution: In class

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Day 12 – June 4 – WBL Problem #9: Ballistic Pendulum PC141 Intersession 2013Slide 20 WBL Ex 6.55

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