1. Department of Physics and Applied Physics 95.141, F2010, Lecture 16 Physics I 95.141 LECTURE 16 11/03/10

2. Department of Physics and Applied Physics 95.141, F2010, Lecture 16 Outline Impulse Conservation of Momentum and Energy Elastic and Inelastic Collisions What do we know? –Units –Kinematic equations –Freely falling objects –Vectors –Kinematics + Vectors = Vector Kinematics –Relative motion –Projectile motion –Uniform circular motion –Newton’s Laws –Force of Gravity/Normal Force –Free Body Diagrams –Problem solving –Uniform Circular Motion –Newton’s Law of Universal Gravitation –Weightlessness –Laws –Work by Constant Force –Scalar Product of Vectors –Work done by varying Force –Work-Energy Theorem –Conservative, non-conservative Forces –Potential Energy –Mechanical Energy –Conservation of Energy –Dissipative Forces –Gravitational Potential Revisited –Power –Momentum and Force –Conservation of Momentum –Collisions –Impulse

3. Department of Physics and Applied Physics 95.141, F2010, Lecture 16 Collisions and Impulse Over the course of a collision, the inter-object Forces change very quickly. Example: a serve in tennis….. –We can think of this as a spring system, with the compression/extension of the ball/strings occurring over a small fraction of a second (~5ms)

4. Department of Physics and Applied Physics 95.141, F2010, Lecture 16 Collision and Impulse From Newton’s second law, we can write: This integral is known as the Impulse

5. Department of Physics and Applied Physics 95.141, F2010, Lecture 16 Collisions and Impulse The impulse of a Force is simply the integral of that Force over the time the Force acts.

6. Department of Physics and Applied Physics 95.141, F2010, Lecture 16 Example Imagine the force exerted by a tennis racket on the ball during a serve can be approximated by the F vs time plot below. What is the impulse acting on the.056 kg ball? What is the speed of the serve? Force (kN)

7. Department of Physics and Applied Physics 95.141, F2010, Lecture 16 Shaken, not stirred……

8. Department of Physics and Applied Physics 95.141, F2010, Lecture 16 Bond, James Bond Using Energy, can we explain why the window doesn’t break when they push off, but does when they come back to it?

9. Department of Physics and Applied Physics 95.141, F2010, Lecture 16 Bond, James Bond Using Impulse, can we why the window breaks? –Assume the push-off takes 0.5 seconds, so that Bond goes from 0m/s to v o in 0.5s. –On the return, however, Bond and Wai Lin brace their legs, and they are slowed to a stop in 0.05 seconds.

10. Department of Physics and Applied Physics 95.141, F2010, Lecture 16 Bond, James Bond Calculate average Force for each case (push-off and impact)

11. Department of Physics and Applied Physics 95.141, F2010, Lecture 16 Conservation of Momentum In the previous lecture we discussed the quantity of momentum The change of momentum of an object can be related to the net Force on the object In a collision, momentum is conserved, as long as no external forces act on the system Impulse

12. Department of Physics and Applied Physics 95.141, F2010, Lecture 16 What about Energy? In the case of the fender bender where the cars lock bumpers and travel on together, is kinetic energy conserved? Remember, Car1 (1000kg) traveling at 10m/s hits Car2 (1000kg), which is at rest, and their bumpers lock together.

13. Department of Physics and Applied Physics 95.141, F2010, Lecture 16 Conservation of Energy Total energy is always conserved. In collisions, sometimes we can say that not only is total energy conserved, but kinetic energy is conserved. –During a collision, for a split second, some or all energy is stored in elastic potential energy. –But this energy is quickly returned to either thermal or kinetic energy (or both) –Two hard elastic objects (billiard balls) usually end up with the same total kinetic energy When this happens, the collision is referred to as an elastic collision.

14. Department of Physics and Applied Physics 95.141, F2010, Lecture 16 1D Elastic Collisions We must now consider both conservation of energy and momentum. In the last section, we had to give the masses and 3 out of 4 velocities. If we know the collision is elastic, then we only need to know 2 out 4 of the velocities.

15. Department of Physics and Applied Physics 95.141, F2010, Lecture 16 1D Elastic Collisions Example Ball 1 is traveling with a velocity of 10 m/s and Ball 2 with a velocity of 3 m/s. What are the final velocities of the balls, if they have the same mass? 10m/s 3m/s

16. Department of Physics and Applied Physics 95.141, F2010, Lecture 16 In General Say you have two masses (mA and mB), each traveling with initial speeds (vA and vB).

17. Department of Physics and Applied Physics 95.141, F2010, Lecture 16 Interesting…. For any elastic collision in 1D, the relative speed of the two objects after the collision is the same as it was before the collision, but the direction opposite! This is a simpler way of writing conservation of Energy for 1D!

18. Department of Physics and Applied Physics 95.141, F2010, Lecture 16 Elastic Collision, Equal Masses If you start with two mass (m A = m B ).

19. Department of Physics and Applied Physics 95.141, F2010, Lecture 16 Unequal Masses, Target at Rest If you start with two mass (mA and mB) with mB at rest. What happens if mA is much more massive than the target? What if target is much more massive (mA << mB)

20. Department of Physics and Applied Physics 95.141, F2010, Lecture 16 Newton’s Cradle Given what you now know about elastic collisions, you should be able to explain this:

21. Department of Physics and Applied Physics 95.141, F2010, Lecture 16 Inelastic Collisions A collision where Kinetic Energy is not conserved is known as an inelastic collision. Technically, all collisions are inelastic, since there is always some energy that is converted to heat, even when we model these collisions as elastic. A collision/process is inelastic when… –Some of the mechanical energy is converted into thermal or potential energy or… –In the case of explosions, when potential energy (chemical or nuclear, for example) is converted into kinetic energy

22. Department of Physics and Applied Physics 95.141, F2010, Lecture 16 Newton’s Cradle, revisited Suppose the period of motion for this Newton’s cradle is 0.5 s, and the height the 100g ball swings to decreases by 1mm each swing. How much thermal energy is generated each period? What is the power is dissipated?

23. Department of Physics and Applied Physics 95.141, F2010, Lecture 16 Perfectly Inelastic Collisions If two object stick together after a collision, this is known as a perfectly inelastic collision. Let’s revisit our car crash again. –1000kg car, travelling 10m/s hits a car at rest and their bumpers lock (perfectly inelastic collision)

24. Department of Physics and Applied Physics 95.141, F2010, Lecture 16 Dirty Harry

25. Department of Physics and Applied Physics 95.141, F2010, Lecture 16 What is the final speed of the dead guy? mbullet=20g vbullet=405m/s mbadguy=70kg

26. Department of Physics and Applied Physics 95.141, F2010, Lecture 16 Ballistic Pendulum A device used to measure the speed of a projectile. vovo v1v1 h m M M+m

27. Department of Physics and Applied Physics 95.141, F2010, Lecture 16 Ballistic Pendulum vovo v1v1 m M M+m

28. Department of Physics and Applied Physics 95.141, F2010, Lecture 16 Ballistic Pendulum v1v1 h M+m

29. Department of Physics and Applied Physics 95.141, F2010, Lecture 16 Ballistic Pendulum If the projectile mass is 10g and the pendulum mass is 3kg, and the pendulum swings to a height of 5cm, what is the velocity of the projectile before the collision?

30. Department of Physics and Applied Physics 95.141, F2010, Lecture 16 Summary Previous Lecture: Conservation of Momentum Today’s Lecture: Cons. Of Momentum plus Energy –Elastic Collisions (1D) –Inelastic Collisions (1D) –Perfectly Inelastic Collisions