1. Physics 218: Mechanics Instructor: Dr. Tatiana Erukhimova Lectures 25-29

2. Center of Mass

3. Problem 5 from handout Find the position of the center of mass of the system of the sun and Jupiter. (Since Jupiter is more massive than the rest of the planets put together, this is essentially the position of the center of mass of the solar system.) Does the center of mass lie inside or outside the sun?

4. Motion of the Center of Mass

5. The center of mass of a system moves as if all of the mass of the system were concentrated at that point and as if all of the forces were acting at that point There is only the external forces that affect the motion of the center of mass ( ) Only external forces affect the motion of the center of mass

6. Momentum is a vector! Vector equation!

7. If

8. Conservation of Momentum If there is no external force on a system, then the total momentum of the system is a constant

9. True in X and Y directions separately!

10. Problem Solving For Conservation of Momentum problems: 1.BEFORE and AFTER 2.Do X and Y Separately

11. Before X Y

12. After Y X

13. Inelastic collision A collision in which the total kinetic energy after the collision is not equal to the kinetic energy before the collision is called an inelastic collision. A B BEFORE AFTER A B V after ?

14. Perfectly elastic collision A collision in which the total kinetic energy after the collision is the same than that before the collision is called an elastic collision. A B

15. A block of mass m is moving along x axis with a velocity of V 0. It collides with a block of mass M, initially at rest. 1) What is the change in kinetic energy of the system of two balls: a) if the collision is perfectly elastic; b) if the collision is perfectly inelastic (balls stick together after collision). 2) For m = M = m 0, find the velocity of each ball after a perfectly elastic collision.

16. Problem 4 p.200 In a nuclear collision an incoming proton has initial velocity of magnitude m/s. It collides with another proton, initially at rest. After the collision one proton goes off at 37 0 to the x axis. If the collision is perfectly elastic, find the velocities of the two protons after the collision.

17. The ballistic pendulum

18. “Famous Problem” from the book

19. A cannon is mounted on top of a narrow wall: There is no friction between the wall and the cannon. The cannon fires a cannon ball with a horizontal velocity v 0 =200 m/s. The cannon has mass 100 kg and the ball mass 10 kg. The height of the wall is 9.8 m. Find the final positions of the cannon and the cannon ball. Problem 5 p. 200

20. Quiz A block of mass m is sliding on a frictionless table with velocity v 0. It explodes into two pieces, one with mass m/3. The light piece flies off horizontally, perpendicular to the original direction of motion, with velocity 2v 0. Find as many equations as you need to find the velocity of the heavy piece.

21. You are standing on a frictionless surface. Some idiot throws a rock at you which you catch. In terms of your mass, the rock’s mass and the rock’s velocity find your position as a function of time after you catch the rock. Quiz

22. Impulse Changes in a particle’s momentum are due to impulse, which depends on the time over which the net force acts.

23. Impulse Suppose you throw a ball with a mass of 0.4 kg against a brick wall. It hits the wall moving horizontally to the left at 30 m/s and rebounds horizontally to the right at 20 m/s. a) Find the impulse of the net force on the ball during its collision with the wall. b) If the ball is in contact with the wall for 0.010 s, find the average horizontal force that the wall exerts on the ball during the impact.

24. Quiz A small car weighing m 1 is traveling due north when it collides with a pick-up truck weighting m 2 which was traveling due east. After the collision the two vehicles move off together at an angle θ north of east. The driver of the car claimed that the truck driver was at fault because he was exceeding the speed limit, going with a velocity v 1. If this were true, what was the car’s initial velocity?

25. Polar coordinates

26. Have a great day! Hw: Chapter 12 problems and exercises Reading: Chapters 12, 13