Physics 3 Lecture 3 Mi Main points it o td today s lecture: Elastic collisions in one diension: ( ) v = v0 + v0 + + ( ) v = v0 + v0 + + Multiple ipulses and rocket propulsion. F Δ t = Δ v Δ v propellant 0 Δ Fpropellant = ( v v0 ) = Thrust Δt Δ Thrust = ( v0 v ) Δt Center o Mass MtotXc = ixi MtotYc = iyi i i M V P v = = tot c tot i i i
st Midter Exa Exa is Wednesday October 5 th. I you will be away on a University sponsored trip, you need to ake alternative testing arrangeents with e by the end o today (Friday). Probles will be siilar to Lon-Capa, but soewhat sipler on the average. Answers will be Multiple Choice. You should prepare one 8.5 by sheet o orulae. You can use both sides o the sheet. We will have a review on Monday. There are a set o practice probles on course web site. I have also distributed by eail soe suggestions about how you can prepare or the exa. You should review the hoework, lectures, book and then prepare your orula sheet. You should then attept the practice probles with only the orula sheet as a reerence. Hoework is not due next week. Instead, you should the do the corrections set, which will be available on LONCAPA as a regular hoework assignent on Thursday evening next week. The corrections set will consist o the sae probles as on the idter exa. I have already sent an eail about how the corrections set can iprove your idter score.
Conceptual quiz A copact car and a large truck collide head on and stick together. th Which undergoes a larger change in the agnitude o the oentu? Assue this syste o car plus truck to be isolated a) car b) truck c) The agnitude o the oentu change is the sae or both vehicles. d) Can t tell without knowing the inal velocity o cobined ass. The syste o car and truck is isolated. P car, + P truck, = P car,i + P truck,i P P = P P car, car,i truck,i truck, Δ P = Δ P car truck
Energy loss in totally inelastic collisions Exaple: A 40 kg skater, sliding to the right without t riction with a velocity o.5 /s, suers a head on collisions with a 30 kg skater who is initially at rest. How uch energy is lost in this collision? a) )9J b) J c) 5 J v 40kg.5 / s = = 0.86/s 70kg KE = v + v + v d) 8 J ( ) 40 kg v 0,0.5 /s loss v,0 0 KE loss? 30 kg loss KEloss = 40kg.5 / s 70kg 0.86 / s KE = 9.JJ ( ) ( )
Expressing Kinetic energy in ters o oentu p A car has oentu and ass. In ters o these two quantities, express the kinetic energy. KE K.E. = v p = v p v = p p K.E. = = p K.E. = = p
Review Conceptual Question In the deonstration, one car is heavier than the other, but both experience the sae orce and both start ro rest and run until they achieve the sae displaceent in the positive direction. Which car has the greater inal oentu? Hint: express oentu in ters o work A. The lighter car. B. The heavier car. C. They have the sae oentu. Force does the sae work on each car. By the work energy theore: p W = KE W = KE = KEi = KE p = W p = W Slide 9-33
Additional Questions In the deonstration, two cars start ro rest. One car is heavier than the other, but both experience the sae orce and both run or the sae tie. Which car has the greater inal oentu? A. The lighter car. B. The heavier car. C. They have the sae oentu. F ave ave Δ t = Δp p 0 = 0 F Δ t = p = p p 0 Slide 9-3
Totally elastic collisions Proo: To calculate the result o an elastic collision in one diension, we considered the constraints o total oentu and energy conservation: Eq. : Eq. : + p tot = v,0 + v,0 = v, v, tot = v,0 + v,0 = v, v, E + We rearrange both equations to get object on the let and object on the right: Eq. : ( v,0 v, ) = ( v, v,0) Eq. : ( v,0 v, ) = ( v, v,0) ( )( ) ( )( ) New Eq. : ( v + v ) = ( v v ) Rearranged Rearranged v v v + v = v v v + v,0,,0,,,0,,0,0,, + Cobining the last equation and the rearranged Equation, we have two equations and unknowns which we can solve to get v, and v, : In one diension the result or the collisions o two asses is: = + v, v,0 + + = + v, v,0 + + v v,0,0,0
Exaple A kg cart oves with a velocity o 3 /s to the right on a rictionless track. It collides elastically with a stationary kg cart. a) What are the inal velocities o the two carts? kg kg v a) v, = v,0 = 3/s= /s, = v,0 + v,0 + 3kg + + kg v v, = v,0 = 3 / s = 4 / s, = v,0 + v,0 + + + 3kg b) In a rae oving with the initial velocity o the irst cart, what are the initial and inal velocities o the two carts? kg b) v = v v kg i i v 0,0,0,0,0 v = v v = 0,0,0,0 v,0 0 3 /s v = v v = 0 3 / s = 3 / s,,,0 v,? v = v v = /s 3/s= /s v = v v = 4/s 3/s= /s,,,0 v,?
v 0,0 =0 Conceptual question A gol ball (ass ) is ired at a bowling ball (ass ) initially iti at rest and bounces back elastically. Copared to the bowling ball, the gol ball ater the collision has a) ore oentu but less kinetic energy. b) ore oentu and ore kinetic energy. c) less oentu and less kinetic energy. d) less oentu but ore kinetic energy. e) none o the above p, = v, v,0 v, = v,0 + p = v v v v = v,,0 0 KE = ( v ) ( v ) KE + v, v,0 v,0 ( ) KE, = v, v,0 v, v,0 4 = KE,0 I >>,,,0,0,,,0 0,0 0
Exaple A 3 kg cart (cart ) oving with a velocity o + /s collides with a 3 kg cart (cart ) oving with a velocity o -3 /s. What are the inal velocities o cart and cart? a) v = /s, v = -3 /s b) v = -3 /s, v = /s v, = v,0 + v,0 c) v = /s, v = -.5 /s + + d) v = -.5 /s, v = /s v,0 v,0 v,? v,? 3 kg v, = v,0 = 3/s v = v + v + + 3k kg,,0,0 /s -3 /s v = v = / s,,0 The two carts exchange velocities i they have equal asses.
Conceptual proble Suppose you are on a cart, initially iti at rest on a track with very little riction.you throw balls at a partition that is rigidly ounted on the cart. I the balls bounce straight back as shown in the igure, is the cart put in otion? a) Yes, it oves to the right. b) Yes, it oves to the let. c) No, it reains in place. The syste o balls, an and car is isolated. Ptot, = Pballs + Pan + cart = Ptot,i = 0 P = P = nuber o balls thrown v an+ cart balls ball ball
X Center o Mass The center o ass o a syste is a ass weighted average over the positions o the various asses. = x Y i c = y i i i Zc = z i i i M M M c i i total total total X Exaple Three asses are lined up along the x axis, with y=0, and z=0 or all three asses. Mass has = kg is at x=. Mass has =0.5 kg and is at x=3. Mass 3 has 3 =.5 kg and is at x=4. Where is the center o ass? = x c i i i Mtotal Y = Z = 0 = ( kg + 0.5kg3 +.5kg4 ) 9.5 = ( + 0.5+.5).4 kg 4 c c
Properties o the center o ass The velocity o the center o ass is given by the total t oentu divided by the total ass. Thereore, the center o ass velocity o an isolated syste is constant. Movie V = P = v tot c i i i Mtotal Mtotal I an external orce acts on a syste o particles, the center o ass ollows a trajectory that this the sae as would be ollowed by a single particle with ass M total. Movie total