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Momentum and Collisions

Momentum and Collisions. Physics 2053 Lecture Notes. Momentum and Collisions. Momentum and Collisions. Topics. 6-01 Momentum and Impulse. 6-02 Conservation of Momentum. 6-03 Collisions. Momentum and Collisions. Momentum and Impulse. F. m. m. Momentum and Impulse.

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Momentum and Collisions

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  1. Momentum and Collisions Physics 2053 Lecture Notes Momentum and Collisions

  2. Momentum and Collisions Topics 6-01 Momentum and Impulse 6-02 Conservation of Momentum 6-03 Collisions Momentum and Collisions

  3. Momentum and Impulse F m m Momentum and Impulse A block moving with an initial velocity vi is acted on by a constant force F for a time Dt. Momentum is a vector Momentum and Collisions

  4. Momentum and Impulse Momentum and Impulse Newton’s 2nd Law p Momentum and Collisions

  5. Momentum and CollisionsProblem v A 12 kg hammer strikes a nail at a velocity of 8.5 m/s and comes to rest in a time interval of 8.0 ms. (a) What is the impulse given to the nail? m (b) What is the average force acting on the nail? Momentum and Collisions

  6. Momentum and Collisions 07-01 The area under the curve on a Force versus time (F vs. t) graph represents A) impulse. B) momentum. C) work. D) kinetic energy. Momentum and Collisions

  7. Conservation of Momentum u1 v1 Fm v = u FM M M M m m m u2 v2 Conservation of Momentum p(before) = p(after) Collision between to moving objects Fm = - FM FmDt = - FMDt Dpm = -DpM m(u2- u1) = -M(v2- v1) mu2- m u1 = - Mv2+ Mv1 Mv1 + m u1 = Mv2+ mu2 Momentum and Collisions

  8. Conservation of Momentum V = ? M M m before after Collision with a stationary block v m Momentum and Collisions

  9. Momentum and Collisions07-08 A 9,300 kg boxcar traveling at 15.0 m/s strikes a second boxcar at rest. The two stick together and move off with a speed of 6.0 m/s. What is the mass of the second car? . Momentum and Collisions

  10. Conservation of Momentum V after before Bullet fired into a block which is initially at rest. v M m mv (M + m)V Momentum and Collisions

  11. Momentum and Collisions 07-01 A freight car moves along a frictionless level railroad track at constant speed. The car is open on top. A large load of coal is suddenly dumped into the car. What happens to the velocity of the car? A) It increases. B) It remains the same. C) It decreases. D) cannot be determined from the information given Momentum and Collisions

  12. Collisions Elastic Collisions Momentum and Kinetic Energy are both conserved Inelastic Collisions Only Momentum is conserved Momentum and Collisions

  13. Collisions m1 m1 vf m2 before after An Inelastic Collision v1 v2 m2 Momentum and Collisions

  14. Momentum and Collisions 07-01 In an inelastic collision, if the momentum is conserved, then which of the following statements is true about kinetic energy? A) Kinetic energy is also conserved. B) Kinetic energy is gained. C) Kinetic energy is lost. D) none of the above Momentum and Collisions

  15. Momentum and Collisions 07-01 Two objects collide and stick together. Kinetic energy A) is definitely conserved. B) is definitely not conserved. C) is conserved only if the collision is elastic. D) is conserved only if the environment is frictionless. Momentum and Collisions

  16. Collisions vA1 vB1 mA mB mA mB vA2 vB2 Elastic Collision (General Equations) Momentum and Collisions

  17. Collisions mA mB vA2 vB2 Elastic Collision (vB1 = 0) Ball B is initially at rest. vA1 mB mA Momentum and Collisions

  18. Collisions vA1 m m m m VB2 Elastic Collision (vB1 = 0 and mA= mB) Momentum and Collisions

  19. Momentum and Collisions 07-01 In an elastic collision, if the momentum is conserved, then which of the following statements is true about kinetic energy? A) Kinetic energy is also conserved. B) Kinetic energy is gained. C) Kinetic energy is lost. D) none of the above Momentum and Collisions

  20. Momentum and Collisions 07-01 When is kinetic energy conserved? A) in inelastic collisions B) in any collision in which the objects do not stick together C) in all collisions D) in elastic collisions Momentum and Collisions

  21. Momentum and Collisions 07-01 When a light beach ball rolling with a speed of 6.0 m/s collides with a heavy exercise ball at rest, the beach ball's speed after the collision will be, approximately, A) 0. B) 3.0 m/s. C) 6.0 m/s. D) 12 m/s. Momentum and Collisions

  22. Momentum and CollisionsProblem Two billiard balls of equal mass undergo a perfectly elastic head-on collision. If one ball’s initial speed was 2.00 m/s and the other’s was 3.00 m/s in the opposite direction, what will be their speeds after the collision? Momentum and Collisions

  23. Collisions h v Cons. Energy Cons. Momentum Ballistic Pendulum vo M m Momentum and Collisions

  24. Collisions h Cons. Momentum V Ballistic Pendulum Find the speed of the bullet v M m Momentum and Collisions

  25. Collisions h Cons. Energy V Ballistic Pendulum M Momentum and Collisions

  26. Momentum and CollisionsProblem A 28 g rifle bullet traveling 230 m/s buries itself in a 3.6 kg pendulum hanging on a 2.8 m long string, which makes the pendulum swing upward in an arc. Determine the vertical and horizontal components of the pendulum’s displacement. Momentum and Collisions

  27. Momentum and CollisionsProblem A bullet is fired vertically into a 1.40 kg block of wood at rest directly above it. If the bullet has a mass of 29.0 g and a speed of 510 m/s how high will the block rise after the bullet becomes embedded in it? Momentum and Collisions

  28. Momentum and Collisions 07-01 Two objects collide and bounce off each other. Linear momentum A) is definitely conserved. B) is definitely not conserved. C) is conserved only if the collision is elastic. D) is conserved only if the environment is frictionless. Momentum and Collisions

  29. Momentum and Collisions 07-01 A 100 kg football linebacker moving at 2.0 m/s tackles head-on an 80 kg halfback running 3.0 m/s. Neglecting the effects due to digging in of cleats, A) the linebacker will drive the halfback backward. B) the halfback will drive the linebacker backward. C) neither player will drive the other backward. D) this is a simple example of an elastic collision. Momentum and Collisions

  30. Center of Mass (cm) xcm y m2 m1 x cm x1 x2 Momentum and Collisions

  31. Center of Mass (cm) xcm Rm Location of the cm of the Earth-Moon system mm me x Momentum and Collisions

  32. Momentum and CollisionsProblem y x Find the center of mass of the three-mass system shown in the diagram. Specify relative to the left-hand 1.00 kg mass. 1.0 kg 1.5 kg 1.1 kg 0.5 m 0.25 m Momentum and Collisions

  33. Momentum and Collisions 07-01 Consider two unequal masses, M and m. Which of the following statements is false? A) The center of mass lies on the line joining the centers of each mass. B) The center of mass is closer to the larger mass. C) It is possible for the center of mass to lie within one of the objects. D) If a uniform rod of mass m were to join the two masses, this would not alter the position of the center of mass of the system without the rod present. Momentum and Collisions

  34. Momentum and Collisions 07-01 Two cars collide head-on on a level friction-free road. The collision was completely inelastic and both cars quickly came to rest during the collision. What is true about the velocity of this system's center of mass? A) It was always zero. B) It was never zero. C) It was not zero, but ended up zero. D) none of the above Momentum and Collisions

  35. Chapter 7 Summary Momentum : Impules: Newton’s second law: Total momentum of an isolated system of objects is conserved. Momentum is conserved during collisions. Momentum and Collisions

  36. Chapter 7 Summary In an elastic collision, total kinetic energy is also conserved In an inelastic collision, some kinetic energy is lost. In a completely inelastic collision, the two objects stick together after the collision. The center of mass of a system is the point at which external forces can be considered to act. Momentum and Collisions

  37. END

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