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phys1111ch7solutions - CHAPTER 7 IMPULSE AND MOMENTUM...

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CHAPTER 7 IMPULSE AND MOMENTUM CONCEPTUAL QUESTIONS ___________________________________________________________________________________________ 1. REASONING AND SOLUTION The linear momentum p of an object is the product of its mass and its velocity. Since the automobiles are identical, they have the same mass; however, although the automobiles have the same speed, they have different velocities. One automobile is traveling east, while the other one is traveling west. Therefore, the automobiles do not have the same momentum. Note that both momenta have the same magnitude, however, one car has a momentum that points east, while the other car has a momentum that points west. ___________________________________________________________________________________________ 2. SSM REASONING AND SOLUTION Since linear momentum is a vector quantity, the total linear momentum of any system is the resultant of the linear momenta of the constituents. The people who are standing around have zero momentum. Those who move randomly carry momentum randomly in all directions. Since there is such a large number of people, there is, on average, just as much linear momentum in any one direction as in any other. On average, the resultant of this random distribution is zero. Therefore, the approximate linear momentum of the Times Square system is zero. ____________________________________________________________________________________________ 3. REASONING AND SOLUTION a. Yes. Momentum is a vector, and the two objects have the same momentum. This means that the direction of each object’s momentum is the same. Momentum is mass times velocity, and the direction of the momentum is the same as the direction of the velocity. Thus, the velocity directions must be the same. b. No. Momentum is mass times velocity. The fact that the objects have the same momentum means that the product of the mass and the magnitude of the velocity is the same for each. Thus, the magnitude of the velocity of one object can be smaller, for example, as long as the mass of that object is proportionally greater to keep the product of mass and velocity unchanged. ____________________________________________________________________________________________ 4. REASONING AND SOLUTION a. If a single object has kinetic energy, it must have a velocity; therefore, it must have linear momentum as well. b. In a system of two or more objects, the individual objects could have linear momenta that cancel each other. In this case, the linear momentum of the system would be zero. The kinetic energies of the objects, however, are scalar quantities that are always positive; thus, the total kinetic energy of the system of objects would necessarily be nonzero. Therefore, it is possible for a system of two or more objects to have a total kinetic energy that is not zero but a total momentum that is zero.
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79 IMPULSE AND MOMENTUM ____________________________________________________________________________________________ 5. REASONING AND SOLUTION The impulse-momentum theorem, Equation 7.4, states that ( 29 f 0 t m m Σ ∆ = - F v v . a. If an airplane is flying horizontally with a constant momentum during a time t , then from Equation 7.4, ( 29 t Σ F = 0. There is no net impulse ( 29 t Σ F on the plane during this time interval.
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