Moentu, Ipulse and Collisions Moentu eeyday connotations? physical eaning the tue easue of otion (what changes in esponse to applied foces) d d ΣF ( ) dt dt Moentu (specifically Linea Moentu) defined p to be genealized late so dp Σ F dt note: oentu is a ecto p x x, p y y, p z z PhysC8 p
Ipulse Duing a constant foce ΣF t ΣF t p define Ipulse J J ΣF t J p fo a foce which is not constant : J t ΣFdt p t so J F t p ΣF x (F a ) x a t t ΣFdt t t t d dt t dt adt p t Integal is aea unde the cue! PhysC8 p
PhysC8 p3 Fo a paticle initially at est the paticle s oentu equals the ipulse that acceleated the paticle fo est to its cuent state of otion. (analogous to K wok to acceleate paticle fo est ) Kinetic enegy can be witten in tes of oentu and ass J p p so 0 p K K ) (
Ex: 0.40 kg ball ipacts a wall hoizontally with a speed of 30 /s and ebounds hoizontally with a speed of 0 /s. The ball is in contact with the wall fo.0s. Deteine the ipulse and aeage foce on the ball. Ex: 0.40 kg socce ball taeling hoizontally to the left at 0 /s is kicked up and to the ight at a 45 degee angle with a speed of 30 /s. The ball is in contact with the foot of the kicke fo.0s. Deteine the ipulse and aeage foce on the ball. PhysC8 p4
Conseation of Moentu: an application of action-eaction inteacting objects, no extenal foces dp dp Fon, Fon dt dt Fon Fon P p p dp d dp dp ( p p ) dt dt dt dt Fon Fon 0 P is constant! Genealize and conside extenal foces: If the ecto su of extenal foces on a syste is zeo, the total oentu of the syste is constant. PhysC8 p5
Using conseation of oentu in pobles: deteine if oentu is conseed select a coodinate syste (oentu is a ecto!) sketch befoe and afte diagas elate total initial oentu to total final oentu, coponent by coponent! sole equations (use additional equations as appopiate such as conseation of enegy) PhysC8 p6
Exaple: Rifle ecoil: 3 kg ifle is used to fie a 5 g bullet. The elocity of the bullet elatie to the gound is 300 /s afte being fied. What is the oentu and enegy of the bullet? What is the oentu and enegy of the ifle? What is the ecoil speed of the ifle? Exaple: -D collision: cats collide head-on on a fictionless tack. The fist cat has a ass of.5 kg and appoaches the collision with a speed of /s. The second cat has a ass of.3 kg and appoaches the collision with a speed of /s. fte the collision, the second cat ebounds fo the collision at a speed of /s. Deteine the initial kinetic enegies and final elocities and kinetic enegies of both asses. How uch enegy is lost in this collision? PhysC8 p7
Exaple: -D collision. 5.00 kg ass initially oes in the positie x-diection with a speed of.00 /s, and then collides with a 3.00 kg ass which is initially at est. fte the collision, the fist ass is found to be oing at.00 /s 30º fo the positie x-axis. What is the final elocity of the second ass? What is the total initial and final kinetic enegy of the syste? PhysC8 p8
Elastic and Inelastic Collisions Elastic Collisions inteaction is conseatie foce echanical enegy is conseed no stickiness Inelastic Collisions inteaction is not conseatie foce soe echanical enegy is lost soe stickiness Copletely Inelastic Collisions inteaction is not conseatie foce axiu loss of echanical enegy collides stick togethe afte the collision In all collisions, oentu is conseed; in elastic collisions, enegy is conseed as well. PhysC8 p9
PhysC8 p0 Copletely inelastic collisions so ( ) take object initially at est (can conside as -d poble) K K so K K so ) ( ) ( ) ( enegy is always lost in a copletely inelastic collision
Exaple: -D collision: cats collide head-on on a fictionless tack. The fist cat has a ass of.5 kg and appoaches the collision with a speed of /s. The second cat has a ass of.3 kg and appoaches the collision with a speed of /s. fte the collision, the the cats stick togethe. Deteine the initial kinetic enegies and final elocity and kinetic enegy of both asses. How uch enegy is lost in this collision? PhysC8 p
Exaple: allistic Pendulu. bullet of ass is fied into a block of wood of ass M, whee it eains ebedded The block is suspended like a pendulu, and swings up to a axiu height y. Relate M, and y to the bullets initial elocity. Exaple: 000 kg ca taeling east at 0 /s collides (copletely inelastically) with a 000 kg ca taeling noth at 5 /s. Find the elocity of the weckage just afte the collision, and the enegy lost in the collision. PhysC8 p
PhysC8 p3 Elastic Collisions exaine -d elastic collision, with at est befoe collision, ) ( ) ( 0 ) ( 0 elatie elocity o enegy oentu
Exaple: -D collision: cats collide elastically head-on on a fictionless tack. The fist cat has a ass of.5 kg and appoaches the collision with a speed of /s. The second cat has a ass of. 3 kg and appoaches the collision with a speed of /s. Deteine the initial kinetic enegies and final elocities and kinetic enegies of both asses. Exaple: neuton (ass u.66e-7 kg) taeling at.6e7 /s stikes a cabon nucleus (ass u). What ae the elocities afte the collision? by what facto is the neuton s kinetic enegy educed by the collision? PhysC8 p4
Exaple: spacecaft of ass 85 kg appoaches Satun head on with an initial speed of 9.6 k/s while Satun (ass 5.69E6 kg) oes along its obit at 0.4 k/s. The gaitational foce of Satun on the spacecaft swings the spacecaft back in the opposite diection. What is the final speed of the spacecaft. PhysC8 p5
Exaple: n elastic (-d) collision of two pucks on a fictionless ai table occus with the fist ass ( 0.500 kg) appoaching at 4.00 /s in the positie x-diection and the second ass (0.300 kg) initially at est. fte the collision, the fist puck oes off at a speed of.00 /s in an unknown diection. What is the diection of the fist pucks elocity afte the collision, and what is the speed and diection of the second puck afte the collision/ PhysC8 p6
PhysC8 p7 Cente of Mass aka Cente of Inetia aeage location of ass on a syste of paticles i i i c c c i i i c z y siilaly x x x x Σ Σ Σ Σ L L L L ), ( otion of cente of ass ) ( oentu total M c i i i c P L L L Σ Σ
exaple: Jaes (ass 90.0 kg) and Raon (ass 60.0 kg) ae 0.0 apat on a fozen pond. Midway between the is a ug of thei faoite beeage. They pull on opposite ends of a light ope stetched between the. When Jaes has oed 6.00 towads the ug, how fa and in what diection has Raon oed? PhysC8 p8
Extenal foces and the otion of cente of ass Mac a a L ΣF ΣFext ΣFint action eaction ΣFint 0 dp Mac ΣFext dt dc d( Mc) since Mac M dt dt PhysC8 p9
exaple: Jaes (ass 90.0 kg) and Raon (ass 60.0 kg) ae 0.0 apat on a fozen pond. Midway between the is a ug of thei faoite beeage. They pull on opposite ends of a light ope stetched between the. When Jaes has oed 6.00 towads the ug, how fa and in what diection has Raon oed? PhysC8 p0