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8 Conservation of Linear Momentum Conservation of Linear Momentum Kinetic Energy of a System Collisions Collisions in the Center of Mass Reference Frame Hk: 33, 39, 53, 59, 63, 81, 87.
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Linear Momentum
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Conservation of Linear Momentum
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Kinetic Energy of a System
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Impulse on a Particle
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Impulse on a System
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Average Force
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Impulse is Area under F(t)
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Types of Collisions: ●Complete Inelastic: K Thermal (v1f = v2f) ● Inelastic: K Thermal (v1f ≠ v2f) ● Elastic: Ki = Kf (v1f ≠ v2f)
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The Center-of-Mass Reference Frame
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Problems
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08-4. A bullet of 230 grains moves horizontally at 830 feet per second and strikes a 10lb wood block lying at rest on a horizontal surface. The bullet takes 1.0 millisecond to stop inside the block. a) Convert the data to SI units.
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08-4 b) Calculate the speed the block moves at just after the bullet stops in the block. System momentum conserved when external impulse is negligible.
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08-4 c) Calculate the kinetic energy of the bullet before the collision and of the moving block + bullet after the collision. What percent of the original kinetic energy is converted to other energies? What percent is retained as kinetic?
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08-4 d) Calculate the impulse received by the block. e) If the collision lasts 1.0 millisecond, calculate the average force exerted on each object.
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08-5. Two masses move on a frictionless horizontal surface. M1 = 1kg, v1i = 4m/s. M2 = 4kg, v2i = 1m/s in a laboratory. The masses collide elastically along a straight line. a) Show that in the center of mass frame that the initial velocities are +2m/s and -1m/s. (first calculate: vcm = +2) b) What are the final velocities in the lab frame?
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08-5 c) Calculate the system-momentum before and after the collision in the lab-frame. d) Calculate the initial and final kinetic energies of the system in the lab-frame. Are these energies consistent with the definition of an ‘elastic collision’? This is consistent with an elastic collision
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08-3. Two objects collide in two dimensions. No external forces act at any time. In SI units: p1i = (3, 4) p2i = (2, 1) b) Make a sketch of the momentum vectors before and after the collision. a) If p1f = (3, 2), then calculate p2f. a) Pi = (3, 4) + (2, 1) = (3, 2) + (px, py) = Pf (5, 5) = (3+px, 2+py) px = 2 py =3 p2f = (2, 3) Pi Pf b)
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c) Calculate the angle each momentum vector makes with the x-axis. b) d) Angle of final total momentum vector Pf = Pi = (5, 5): Pf
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08-2. Two masses move on a frictionless horizontal surface. M1 = 1kg, v1i = 4m/s. M2 = 2kg, v2i = 1m/s. a)Find the center of mass speed. b) The masses collide along a straight line. Find v1f if v2f = 2.3 m/s and no other external forces act.
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c) Calculate the initial and final kinetic energies. Is the collision energetically possible? It is possible for kinetic energy to decrease due to the production of thermal energy in a collision.
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