1 Lecture #2 of 25 Questions on Assignment #1? Homework Expectations /Office hours/Reserve (REA Mechanics Problem Solver, ISBN $25) Impulse and momentum conservation Rocket propulsion Worked problems Cross-product problem Saturn V launch I-4 :10

2 Homework Bliss :17

3 Definition of Impulse Impulse is a useful concept in the study of collisions. (e.g. Balls and bats, automobiles, comets and planets) Impulse is the average force acting over a time period multiplied by the time period. It may also be written as an integral Note the difference between impulse and work W. :22

4 Impulse and momentum change Impulse is useful because it directly allows expression of momentum change. :27

5 Impulse I -- Problem #L2-2 “A car crash” James and Joan were drinking straight tequila while driving two cars of mass 1000 kg and 2000 kg with velocity vectors and We may look at their collision in terms of impulse. Joan’s car applied an impulse to James’ car as follows: What is the final momentum of James’ car only? What is his final velocity? Calculate :32

6 Rocket Science I  Not the whole story  More general – get used to it  Case where m not constant  Instantaneous acceleration, but rocket keeps getting lighter!! :40

7 Rocket Science II  In absence of other forces  Separable ODE. Integrate both sides  Rocket velocity in terms of lost mass and exhaust velocity :45

8 Rocket Science III  If a rocket is 60% fuel, then it limits at v e  If a rocket is 90% fuel, then limit at 2.3 v e  At 99% fuel, limit is 4.6 v e :50

9 Specific Impulse  In practice of rocketry, the “specific impulse” is often quoted :45 :55

10 XIPS  Xenon Ion Propulsion System  Thrusts are milliNewtons  Used for “station-keeping” and deep- space missions :45 :55

11 Problem T3.7 :65 The first couple of minutes after a space shuttle launch can be described as follows: The initial mass is 2x10E6 kg, the final mass (after 2 minutes) is about 1x10E6 kg, the average exhaust speed is about 3000 m/s. If all this were taking place in outer space, with negligible gravity, what would be the shuttle’s speed at the end of this stage? What is the thrust during this same period and how does it compare with the total initial weight of the shuttle (on earth)?

12 Impulse II -- Problem #L2-3 “Another car crash” James and Joan are partly recovered from their previous injuries, and haven’t learned from their experience. They are drinking Jack Daniels and not wearing seat- belts. James’ vehicle has velocity vector Joan’s vehicle has Both vehicles’ mass=M. Both people’s mass=70 kg. Solve for case of inelastic and elastic collisions of vehicles. Joan has an airbag in her vehicle. It takes her 100 millisec to reduce her velocity relative to her vehicle to zero. James stops 5 millisec after impacting the steering wheel. What impulse does each person experience? What is average force for each? How many “g’s” do they feel. :75

13 Cross product – Problem #L2-1 Calculate A) Use the determinant method where B) Use the Levi-Civita density where  For any two indices equal  I,j,k even permutation of 1,2,3  I,j,k odd permutation of 1,2,3 :Bonus

14 Lecture #2 Wind-up. Got on WebCT? / Got Books? Office hours Friday 5-6 Homework problems in Taylor, Handout, Galileo problem – check the web. Second homework due in class Thursday 9/5 (Includes introducing gravity into rocket equation) :72