PHY 121 Ch 8b Lecture

PHY 121 Ch 8b Lecture - Lecture 15 Thursday, March 6 1...

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1 Lecture 15 Thursday, March 6
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2 There is an elastic collision between a body A in motion and a body B at rest. The two bodies have the same mass. A. The moving body A stops dead. B. A reverses its direction of motion; B starts to move in the same direction as A was moving originally. C. Both bodies come to a stop. D. Both bodies continue moving in the original direction A was moving, but at half the speed.
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3 In an elastic collision between two objects A. the sum of velocities of the two objects is constant. B. the net force on any of the objects is zero. C. the object with the smaller mass always has a larger final kinetic energy. D. the relative velocity of the two objects doesn’t change.
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4 An object's center of mass A. is at the object's geometrical center. B. is always at rest. C. is the point of the object at which all forces are applied. D. is a mass-weighted average of the positions of all particles in the object.
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5 The center of mass velocity A. is always zero. B. can be zero even if all particles in the system are moving. C. is always faster than the velocity of the lightest particle. D. is always faster than the velocity of the heaviest particle.
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6 Center of mass When an extended object flies in free fall, the motion may be complicated, but there is a geometrical point that follows a nice parabolic path as if it was a point object. This point is the center of mass . The center of mass is often (but not always) a point inside the object.
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7 Mathematical definition of the center of mass r cm = m 1 ! r 1 + m 2 ! r 2 + m 3 ! r 3 + ... m 1 + m 2 + m 3 + ... = m 1 ! r 1 + m 2 ! r 2 + m 3 ! r 3 + ... M Center of mass is a mass-weighted average position
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8 Center of mass motion ! a cm ! a cm = d v cm dt ! v cm ! v cm ! v cm = d ! r cm dt We can describe the center of mass motion in exactly the same way we describe a point-particle motion.
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9 Center of mass property M ! a cm = ! F ext ! The center of mass moves as if it was a point particle with a mass equal to the total mass of the system, and being acted upon by the net external force. This is the formal justification of the point particle model!
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10 Energy in a system of particles Our energy equation is: ! K + ! U = W other Suppose that we have an extended object of mass M under a gravitational force. The point particle model suggests ! 1 2 Mv cm 2 ( ) + ! Mgy cm ( ) = W other Is this correct?
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11 Example I A 1000 kg car traveling at 5 m/s runs into a solid, unbending wall. The bumper and the front end of the car crumple upon impact, resulting in the car’s center of mass moving 0.5 m before stopping. Analyze and interpret the forces and energy transfers of this collision.
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12 Example II A student jumps straight into the air and reaches a height h . Analyze this problem from the point of view of energy conservation.
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13 Internal kinetic energy Our expression K = 1 2 Mv cm 2 cannot be entirely correct. It predicts that an object rotating in place has zero kinetic energy!
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14 Problem 8.89 Two asteroids with masses
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PHY 121 Ch 8b Lecture - Lecture 15 Thursday, March 6 1...

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