Momentum and Collisions: Conservation, Types, and Rocket Propulsion

1. Chapter 6 Momentum and Collisions

2. Momentum • The linear momentum of an object of mass m moving with a velocity v is defined as the product of the mass and the velocity • p = m v • SI Units are kg m / s • Vector quantity, the direction of the momentum is the same as the velocity’s

3. Momentum components • Applies to two-dimensional motion

4. Impulse cont. • When a single, constant force acts on the object • FΔt is defined as the impulse • Vector quantity, the direction is the same as the direction of the force

5. Average Force in Impulse • The average force can be thought of as the constant force that would give the same impulse to the object in the time interval as the actual time-varying force gives in the interval

6. Air Bags • The air bag increases the time of the collision • It will also absorb some of the energy from the body • It will spread out the area of contact • decreases the pressure • helps prevent penetration wounds

7. Conservation of Momentum • The principle of conservation of momentum states when no external forces act on a system (i.e. two objects that collide with each other), the total momentum of the system before the collision is equal to the total momentum of the system after the collision.

8. Conservation of Momentum, cont. • Mathematically: • The system includes all the objects interacting with each other • Assumes only internal forces are acting during the collision • Can be generalized to any number of objects

9. Types of Collisions • Momentum is conserved in any collision • Inelastic collisions • Kinetic energy is not conserved • Perfectly inelastic collisions occur when the objects stick together • Elastic collision • both momentum and kinetic energy are conserved • Actual collisions • Most collisions fall between elastic and perfectly inelastic collisions

10. More About Perfectly Inelastic Collisions • When two objects stick together after the collision, they have undergone a perfectly inelastic collision • Conservation of momentum becomes

11. Fig 6.11a, p. 167 Slide 18

12. More About Elastic Collisions • Both momentum and kinetic energy are conserved • Typically have two unknowns • Solve the equations simultaneously • A simpler equation sometimes can be used in place of the KE equation

13. Fig GA6.3, p. 183 Slide 49

14. 1. A disk is rotating at a constant rate about a vertical axis through its center. Point Q is twice as far from the center of the disk as point P is. The angular velocity of Q at a given time is • 1. twice as big as P's2. the same as P's3. half as big as P's4. none of the above • 2. When a disk rotates counterclockwise at a constant rate about a vertical axis through its center, the tangential acceleration of a point on the rim is • 1. positive.2. zero.3. negative.4. impossible to determine without more information. • 3. What concept in Sections 7.1-7.3 are you having the most difficulty with?

15. Sketches for Collision Problems • Draw “before” and “after” sketches • Label each object • include the direction of velocity • keep track of subscripts

16. Glancing Collisions • For a general collision of two objects in three-dimensional space, conservation of momentum implies that the total momentum of the system in each direction is conserved • Use subscripts for identifying the object, initial and final, and components • For elastic collision still have 1 equation for conservation of mechanical energy

17. Glancing Collisions • The “after” velocities have x and y components • Momentum is conserved in the x direction and in the y direction • Apply separately to each direction

18. Fig 6.15, p. 172 Slide 27

19. Rocket Propulsion • The initial mass of the rocket is M + Δm • M is the mass of the rocket • m is the mass of the fuel • The initial velocity of the rocket is v

20. Rocket Propulsion • The rocket’s mass is M • The mass of the fuel, Δm, has been ejected • The rocket’s speed has increased to v + Δv

21. Fig P6.30, p. 179 Slide 36

22. Fig P6.61, p. 182 Slide 47