Physic 231 Lecture 14

Transcription

1 Physc 3 Lecture 4 Man ponts o last lecture: Ipulses: orces that last only a short te Moentu p Ipulse-Moentu theore F t p ( ) Ipulse-Moentu theore ptot, p, p, p, p, ptot, Moentu and external orces F p ext t tot, ptot, Man ponts o today s lecture: Rocket propulson. Totally nelastc collsons Elastc collsons n one denson: ( ) ( )

2 Conceptual queston Consder two carts, o asses and, at rest on an ar track. I you push rst one cart or 3 s and then the other or the sae length o te, exertng equal orce on each, the oentu o the lght cart s a) our tes b) twce c) equal to d) one-hal e) one-quarter the oentu o the heay cart.

3 Conceptual queston Whch o these systes are solated (.e. no external orces)? a) Whle slppng on a patch o ce (µ k 0), a car colldes totally nelastcally wth another car. Syste: both cars b) Sae stuaton as n a). Syste: the slppng car c) A sngle car slps on a patch o ce. Syste: car d) A car akes an eergency stop on a road. Syste: car e) A ball drops to Earth. Syste: ball ) A bllard ball colldes elastcally wth another bllard ball on a pool table. Syste: both balls

4 Exaple An astronaut s otonless n outer space. Upon coand, hs propulson unt strapped to hs back ejects soe gas wth a elocty o 4 /s, and the astronaut recols wth a elocty o -0.5/s. Ater the gas s ejected, the ass o the astronaut s 60kg. What s the ass o the ejected gas? p p p ast,0 ast, gas gas p0 0 p past, ; p, x ast ast ast, ast ast,, x, x ast, ast,, x p gas take oton to be along x axs 0.5 / s 60kg 4 / s 5.7kg

5 Rocket propulson The thrust orce on a rocket can be coputed usng the pulse oentu theore knowng the rate o ass esson / t o propellant and ts esson elocty and the elocty o the rocket 0. F propellant t Fpropellant t Thrust t ( ) ( ) Thrust

6 Prncples o collsons I there are no external orces, the total oentu s always consered durng a collson: p p p p p tot,,,,, ptot, In such collsons, howeer, the echancal energy ay or ay not be consered. We hae two useul lts: Totally nelastc collsons where the two objects stck together ater the collson. Here, largest energy loss possble or an solated syste occurs. Totally elastc collsons where the two objects bounce o each other and the echancal energy s the sae ater the collsons as t s beore the collson. Inelastc collsons can occur n whch the objects do not stck together. The energy loss n such collsons s less than what occurs n totally nelastc collsons where the object do stck together.

7 Totally nelastc collsons In solated systes (systes wthout external orces) oentu s consered. In totally nelastc collsons, the partcles stck together ater the collson. ptot,,0,0 ( ),0,0 Exaple: A 40 kg skater, sldng to the rght wthout rcton wth a elocty o.5 /s, suers a head on collsons wth a 30 kg skater who s ntally at rest. a) 0.7 /s b) 0.3 /s 0 c) 0.4 /s d) 0.86 /s 40kg (.5 / s ) 0.86 / 40kg 30kg s

8 Conceptual queston Suppose ran alls ertcally nto an open cart rollng along a straght horzontal track wth neglgble rcton. As a result o the accuulatng water, the speed o the cart a) ncreases. b) does not change. c) decreases.

9 Quz A 40 kg skater, sldng to the rght wthout rcton wth a elocty o.5 /s, suers a head on collsons wth another skater, ong to the let wth a elocty o /s. Ater the collson, the two skaters coe to rest. The ass o the second skater s: a) 0 kg b) 30 kg c) 3.3 kg d) 53.3 kg 0 40kg.5 / s / s 30kg

10 Conceptual queston I all three collsons n the gure shown here are totally nelastc, whch brng(s) the car on the let to a halt? a) I b) II c) III d) I, II e) I, III ) II, III g) all three

11 Totally elastc collsons To calculate the result o an elastc collson n one denson, we consdered the constrants o total oentu and energy conseraton: Eq. : Eq. : tot p tot,0,0,, E,0 We rearrange both equatons to get object on the let and object on the rght:,0 Eq.: (,0, ) (,,0) Eq. : (,0, ) (,,0) (,0, )(,0, ) (,,0)(,,0) New Eq. : ( ) ( ) Rearranged Rearranged,,0,, Cobnng the last equaton and the rearranged Equaton, we hae two equatons and unknowns whch we can sole to get, and, :,,,0,0,0,0,0,