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Physics 221, February 23

Key Concepts: Definition of momentum and impulse Conservation of momentum The center of mass Rockets. Physics 221, February 23. Linear momentum. Momentum: p = m v ( vector ) Rate of change: ∆ p /∆t = m∆ v /∆t = m a = F F x = ∆ p x / ∆t, F y = ∆ p y / ∆t

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Physics 221, February 23

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  1. Key Concepts: • Definition of momentum and impulse • Conservation of momentum • The center of mass • Rockets Physics 221, February 23

  2. Linear momentum Momentum: p = mv (vector) Rate of change: ∆p /∆t = m∆v/∆t = ma = F Fx = ∆px/ ∆t, Fy = ∆py/ ∆t Impulse: I = ∆p = pf – pi = F∆t(vector) Kinetic energy: Ekin = ½mv2 = p2/(2m) p = (2m*Ekin)1/2

  3. Two objects have masses m1 and m2, respectively. If m2 = 4m1, and both have the same kinetic energy, which has more momentum? • Object 1 with mass m1 . • Object 2 with mass m2 . • Their momenta are the same. For example: or or …. 30

  4. Extra credit: A piece of clay with mass m = 0.01 kg collides with the floor at speed of 2 m/s and sticks. The collision takes 0.01 s. The force the piece of clay experiences during the collision is (assume a constant force during the collision): • 0 N • 1 N • 2 N • 4 N • 8 N 30

  5. A ball (mass 0.40 kg) is initially moving to the left at 30 m/s. After hitting the wall, the ball is moving to the right at 20 m/s. What is the impulse of the net force on the ball during its collision with the wall? • 20 kg m/s to the right • 20 kg m/s to the left • 4 kg m/s to the right • 4 kg m/s to the left • None of the above 30

  6. You have heard the tried and true phrase “it is like running in to a brick wall”. Now it is time to dig a little deeper and modify the phrase. Assume you are in a car driving and come in contact with this proverbial brick wall. Your car can do three things after the strike: it can go through, come to stop or bounce back. Select the option which will be the most dangerous to you from an impulse point of view. • Going through the wall. • Coming to a stop. • Bouncing back. • All options are equally dangerous. 30

  7. Conservation of momentum For a system of objects, a component of the momentum along a chosen direction is constant, if no net outside force with a component in this chosen direction acts on the system. In collisions between isolated objects momentum is always conserved.  m1v1i + m2v2i = m1v1f + m2v2f Kinetic energy is only conserved in elastic collisions. (1/2)m1v1i2 + (1/2)m2v2i2 = (1/2)m1v1f2 + (1/2)m2v2f2 I explosions or disintegrations momentum is conserved. (∑mivi)before = (∑mivi)after Kinetic energy is not conserved. Stored potential energy is converted into ordered or disordered kinetic energy.

  8. Extra credit: Two objects with different masses collide and stick to each other. Compared to before the collision, the system of two objects after the collision has • the same total momentum and the same total kinetic energy. • the same total momentum but less total kinetic energy. • less total momentum but the same total kinetic energy. • less total momentum and less total kinetic energy. • not enough information given to decide. 30

  9. Block A has mass 1.00 kg and block B has mass 3.00 kg. The blocks collide and stick together on a level, frictionless surface. After the collision, the kinetic energy (KE) of block A is • 1/9 the KE of block B. • 1/3 the KE of block B. • 3 times the KE of block B. • 9 times the KE of block B. • the same as the KE of block B. 30

  10. You have a mass of 60 kg. You are standing on an icy pond, when your “friend” throws a 10 kg ball at you with speed 7 m/s.If you catch the ball, how fast will you be moving? • 0 m/s • 1 m/s • 2 m/s • 3.5 m/s • 7 m/s 30

  11. A 1 kg block slides along a horizontal frictionless surface with speed v =1 m/s. It collides with another 1 kg stationary block. After the collision the two blocks stick together and slide into a Hooke's-law spring with spring constant k = 100 N/m. What is the maximum compression (in m) of the spring? • 0.5 m • 25 cm • 7 cm • 5 mm 30

  12. Momentum conservation in the collision: m*v = 2m*v’, 1kg*1m/s = 2kg*v’, v’ = 0.5 m/s. The 2 block combination has kinetic energy: ½ mv2 = ½*2kg*(0.5 m/s)2 = 0.25 J This kinetic energy is converted into elastic potential energy. 0.25 J = ½ k(∆x)2= ½ 100 N/m (∆x)2 (∆x)2= (0.25/50) m2, ∆x = 7 cm

  13. Demonstrations Collisions and conservation of momentum Newton’s cradle http://www.youtube.com/watch?v=mFNe_pFZrsA Astroblaster http://www.youtube.com/watch?v=cloY0R5mj2s&feature=related

  14. Center of mass • The center of mass (CM) of a system moves as if the total mass of the system were concentrated at this special point.  • It responds to external forces as if the total mass of the system were concentrated at this point. • The total momentum of the system only changes, if external forces are acting on the system.  • The center of mass of the system only accelerates, if external forces are acting on the system. • Coordinates of the center of mass (CM):

  15. Extra credit:Two particles of masses 2 g and 6 g are separated by a distance of 6 cm. The distance of their center of mass from the heavier particle is • 1.5 cm • 2 cm • 3 cm • 4 cm • 4.5 cm 30

  16. A radioactive nucleus of mass M moving along the positive x-direction with speed v emits an α-particle of mass m. If the α-particle proceeds along the positive y-direction, the centre of mass of the system (made of the daughter nucleus and the α-particle) will • remain at rest . • move along the positive x-direction with speed less than v. • move along the positive x-direction with speed greater than v. • move in a direction inclined to the positive x-direction . • move along the positive x-direction with speed equal to v. 30

  17. The rocket principle System consisting of many parts: no external force  no acceleration of the CM But different parts of the system can accelerate with respect to the CM, as long as the total momentum of the system is constant. Examples: http://www.youtube.com/watch?v=D-5TovPg4F4

  18. Extra Credit: A 55 kg physics student is at rest on a 5 kg sled that also holds a chunk of ice with a mass of 1.5 kg. The student throws the ice horizontally with a speed of 12 m/s relative to the ground. If the sled slides over a frozen pond without friction, how fast (in m/s) are the sled and student traveling with respect to the ground after throwing the chunk of ice? • 0.3 m/s • 0.327 m/s • 5 m/s • 0.2 m/s • 0.218 m/s 30

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