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Center of mass Momentum Momentum is conserved

Chapter 9: Linear Momentum & Collisions. Reading assignment: Chapter 9.5-9.7 Homework : (due Wednesday, Oct. 5, 2005): Problems: 32, 36, 43, 52, 69, 71. Center of mass Momentum Momentum is conserved. Center of mass. Center of mass for many particles:. Black board example 9.1.

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Center of mass Momentum Momentum is conserved

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  1. Chapter 9: Linear Momentum & Collisions Reading assignment: Chapter 9.5-9.7 Homework : (due Wednesday, Oct. 5, 2005): Problems: 32, 36, 43, 52, 69, 71 • Center of mass • Momentum • Momentum is conserved

  2. Center of mass Center of mass for many particles: Black board example 9.1 Where is the center of mass of the arrangement of particles below. (m3 = 2 kg and m1 = m2 = 1 kg)?

  3. A method for finding the center of mass of any object. • Hang object from two or more points. • Draw extension of suspension line. • Center of mass is at intercept of these lines.

  4. Center of mass of a solid body (uniform density)

  5. Black board example 9.2 A uniform square plate 6 m on a side has had a square piece 2 m on a side cut out of it. The center of that piece is at x = 2 m, y = 0. The center of the square plate is at x = y = 0. Find the coordinates of the center of mass of the remaining piece.

  6. Motion of a System of Particles. Newton’s second law for a System of Particles The ____________ of a system of particles (combined mass M) moves like one equivalent particle of mass M would move under the influence of an external force.

  7. A rocket is shot up in the air and explodes. Describe the motion of the center of mass before and after the explosion.

  8. Linear Momentum The linear momentum of a particle of mass m and velocity v is defined as The linear momentum is a vector quantity. It’s direction is along v. The components of the momentum of a particle:

  9. From Newton’s second law: The time rate of change in linear momentum is equal to the net forces acting on the particle. This is also true for a system of particles: Total momentum = Total mass ·velocity of center of mass And: Net external force = ____________ in momentum of the center of mass

  10. Conservation of _________ momentum Thus: If no _________________ is acting on a particle, it’s momentum is conserved. This is also true for a system of particles: If no external forces interact with a system of particles the total momentum of the system remains constant.

  11. Black board example 9.3 • You (100kg) and your skinny friend (50.0 kg) stand face-to-face on a frictionless, frozen pond. You push off each other. You move backwards with a speed of 5.00 m/s. • What is the total momentum of the you-and-your-friend system? • What is your momentum after you pushed off? • What is your friends speed after you pushed off?

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