Impulse and momentum conservation Rocket propulsion Worked problems Class #5 Impulse and momentum conservation Rocket propulsion Space-ship 1 Worked problems Matlab All but 5 people are registered. Go over T 1.16 and T1.9 :10

Class #4 Recap . Linear Drag (Sphere) Quadratic Drag (Sphere) :72

Impulse is a useful concept in the study of collisions. 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. What’s different between Impulse and work? One is vector, other scalar. One is integral over a path in space, other over time. What should be the units for impulse? Nt-m. :22

Impulse is a useful concept in the study of collisions. Summary 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. What’s different between Impulse and work? One is vector, other scalar. One is integral over a path in space, other over time. What should be the units for impulse? Nt-m. :22

Impulse and momentum change Impulse is useful because it directly allows expression of momentum change. This is the function of an air-bag in a vehicle – to spread out the impulse and reduce the max. force. :27

Impulse I -- Problem #L5-1 “A car crash” Jack and Jill were doing things they shouldn’t while driving two cars of mass 1000 kg and 2000 kg with velocity vectors We may look at their collision in terms of impulse. Jill’s car applied an impulse to Jack’s car as follows: What is the final momentum of Jack’s car only? What is his final velocity? Calculate Work this on board yourself :32

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!! dP/dt … Tend to talk more about p instead of mv. In quantum mechanics, the basic quantities are momentum and energy not mv or 1/2mv2. Remember the product rule. Units for m dot? Please follow along. Take your pencil and write notes in the corner. :40

In absence of other forces Separable ODE. Integrate both sides Rocket Science II In absence of other forces Separable ODE. Integrate both sides Rocket velocity in terms of lost mass and exhaust velocity Because it’s a definite integral, we don’t have a constant of integration Show in log base 10 because easier to see :45

If a rocket is 60% fuel, then it limits at ve Rocket Science III If a rocket is 60% fuel, then it limits at ve If a rocket is 90% fuel, then limit at 2.3 ve At 99% fuel, limit is 4.6 ve This is why want highest possible exhaust velocity This is also why use multi-stage rockets. :50

Specific Impulse Specific impulse is measured in “seconds”. Can go to air-force academy web-site where they are taking the same physics course you are Ion propulsion is real, and so are the arguments for space catapults. :45 :55

XIPS Xenon Ion Propulsion System Thrusts are 60-200 milliNewtons Used for “station-keeping” and deep-space missions Specific impulse is measured in “seconds”. Can go to air-force academy web-site where they are taking the same physics course you are Problems from Roswell. My colleagues might think I’m nuts. Ion propulsion is real, and so are the arguments for space catapults, but everything else is pseudoscience. :45 :55

Problem L5.2 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? How does it compare with the total initial weight of the shuttle (on earth)? Using answers for c and d, how many “g’s” do the astronauts feel on take-off? This is why want highest possible exhaust velocity This is also why use multi-stage rockets. :65

Impulse II -- Problem #L5-3 “Another car crash” Jack and Jill are partly recovered from their previous injuries, and haven’t learned from their experience. They are drinking cokes with rum and not wearing seat-belts. Jack’s vehicle has velocity vector Jill’s vehicle has Both vehicles’ mass=M. Both people’s mass=70 kg. Find final velocity of each vehicle for case of totally inelastic and completely elastic collisions of vehicles. Jill has an airbag in her vehicle. It takes her 100 millisec to reduce her velocity relative to her vehicle to zero. Jack stops 5 millisec after impacting the steering wheel. What impulse is delivered to Jack’s body by the steering wheel? Jill? What is average force each experiences during their collision? How many “g’s” do they feel. An elastic collision conserves energy. Inelastic does not. Why do cars have “crush zones?” Why do they have padded dashboards and airbags? :75