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Unformatted text preview: 509 Chapter 8 Systems of Particles and Conservation of Momentum Conceptual Problems 1 • Determine the Concept A doughnut. The definition of the center of mass of an object does not require that there be any matter at its location. Any hollow sphere (such as a basketball) or an empty container with any geometry are additional examples of three- dimensional objects that have no mass at their center of mass. *2 • Determine the Concept The center of mass is midway between the two balls and is in free-fall along with them (all forces can be thought to be concentrated at the center of mass.) The center of mass will initially rise, then fall. Because the initial velocity of the center of mass is half of the initial velocity of the ball thrown upwards, the mass thrown upwards will rise for twice the time that the center of mass rises. Also, the center of mass will rise until the velocities of the two balls are equal but opposite. correct. is ) ( b 3 • Determine the Concept The acceleration of the center of mass of a system of particles is described by , cm i ext i, ext net, a F F r r r M = = ∑ where M is the total mass of the system. Express the acceleration of the center of mass of the two pucks: 2 1 1 ext net, cm m m F M F a + = = and correct. is ) ( b 4 • Determine the Concept The acceleration of the center of mass of a system of particles is described by , cm i ext i, ext net, a F F r r r M = = ∑ where M is the total mass of the system. Express the acceleration of the center of mass of the two pucks: 2 1 1 ext net, cm m m F M F a + = = because the spring force is an internal force. correct. is ) ( b Chapter 8 510 *5 • Determine the Concept No. Consider a 1-kg block with a speed of 1 m/s and a 2- kg block with a speed of 0.707 m/s. The blocks have equal kinetic energies but momenta of magnitude 1 kg·m /s and 1.414 kg·m/s, respectively. 6 • ( a ) True. The momentum of an object is the product of its mass and velocity. Therefore, if we are considering just the magnitudes of the momenta, the momentum of a heavy object is greater than that of a light object moving at the same speed. ( b ) True. Consider the collision of two objects of equal mass traveling in opposite directions with the same speed. Assume that they collide inelastically. The mechanical energy of the system is not conserved (it is transformed into other forms of energy), but the momentum of the system is the same after the collision as before the collision, i.e., zero. Therefore, for any inelastic collision, the momentum of a system may be conserved even when mechanical energy is not. ( c ) True. This is a restatement of the expression for the total momentum of a system of particles....
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