Page 1. Physics 131: Lecture 14. Today s Agenda. Things that stay the same. Impulse and Momentum Non-constant forces

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1 Physcs 131: Lecture 14 Today s Agenda Imulse and Momentum Non-constant forces Imulse-momentum momentum thm Conservaton of Lnear momentum Eternal/Internal forces Eamles Physcs 201: Lecture 1, Pg 1 Physcs 201: Lecture 1, Pg 2 Thngs that stay the same So far we have focused on thngs that change Velocty Poston Now we wll elore some thngs that stay the same We say they are conserved Collsons! Physcs 201: Lecture 1, Pg 3 Page 1

2 Lnear Momentum Movng object has lnear momentum such that: mv Vector quantty n same drecton as velocty Unts: kg m/s mv y mv y Physcs 201: Lecture 1, Pg 4 Newton s Second law Newton s second law was orgnally wrtten n terms of momentum d F net dt d( mv) dv F net m dt dt ma (1) F net (2) ma Equaton (1) and (2) are equvalent f the mass s not allowed to change. Physcs 201: Lecture 1, Pg 5 Newton s Second law From ths way may defne Imulse F avg t t J F avg Physcs 201: Lecture 1, Pg 6 Page 2

3 Imulse-Momentum Theorem An mulse on an object leads to a change n the objects momentum. (Ths s a vector) J J f f J The momentum after an nteracton, lke a collson or eloson, equals the momentum before the nteracton lus the mulse that arses from the nteracton. Physcs 201: Lecture 1, Pg 7 You dro an egg onto A) the floor B) a thck ece of foam rubber. In both cases, the egg does not bounce (assume the egg hts each surface wth the same seed v). In whch case s the magntude of the mulse greater? A) Floor B) Foam C) It s the same Clcker Queston 1: Physcs 201: Lecture 1, Pg 8 Pre-Class Quz Why do cars have crumle zones? Same Area = Imulse F F t t Pre-class Quz: Ths s why cars have crumle zones, to ncrease t and decrease the force. Physcs 201: Lecture 1, Pg 9 Page 3

4 Clcker Queston 2: Two dentcal balls are droed from the same heght onto the floor. In case 1 the ball bounces back u, and n case 2 the ball stcks to the floor wthout bouncng. In whch case s the mulse gven to the ball by the floor the bggest? (a) Case 1 (b) Case 2 (c) Both are the same Physcs 201: Lecture 1, Pg 10 Clcker Queston 3: A lght lastc cart and a heavy steel cart are both ushed wth the same force for 1.0 s, startng from rest. After the force s removed, the momentum of the lght lastc cart s that of the heavy steel cart. Same force, same tme same mulse Same mulse same change of momentum A. greater than B. equal to C. less than D. Can t say. It deends on how bg the force s. Physcs 201: Lecture 1, Pg 11 Conservaton of Momentum Newton s second law for a system F et net d dt The total momentum of an solated system remans constant Physcs 201: Lecture 1, Pg 12 Page 4

5 Conservaton of Lnear Momentum The total momentum of an solated system remans constant object 1 object 2 object 1 object 2 f mv mv m + mv = mv f + mv f mv mv v f mv f mv f n -drecton In y-drecton Physcs 201: Lecture 1, Pg 13 Conservaton of Lnear Momentum Collsons Elosons v =?? 10 m/s 15 kg Physcs 201: Lecture 1, Pg 14 Clcker Queston 4: Two cars collde on the street. Durng the collson are the two cars techncally an solated system? A. No, the two cars are not techncally an solated system. B. Yes, the two cars are techncally an solated system. Physcs 201: Lecture 1, Pg 15 Page 5

6 Clcker Queston 5: Two blocks are sldng to the rght on a frctonless surface and collde as shown below. Before the collson, the block M on the left has a seed of 4 m/s, and block 3M has a seed of 1 m/s. After the collson the rght block (3M) s observed to travel to the rght wth seed 2 m/s. What s the velocty of the 1M-block after the collson? (a) 1 m/s to the left (b) 5 m/s to the left (c) 0 m/s (d) 1 m/s to the rght (e) 5 m/s to the rght v=2 m/s Physcs 201: Lecture 1, Pg 16 Clcker Queston 6: A small car and a large truck collde head-on and stck together. Whch one feels the larger mulse? a) the car b) the truck c) they both feel the same mulse d) can t tell wthout knowng the fnal veloctes Physcs 201: Lecture 1, Pg 17 Clcker Queston 7: You drve down a one-way street at 30 mh when you see an dentcal car headng straght toward you at 30 mh. You have two otons: ht the car head-on or swerve nto a massve concrete wall (also head-on). What should you do? (Assume the collson tme s aro. the same n both cases) a) ht the other car b) ht the wall c) makes no dfference d) call your hyscs rof!! e) get nsurance! Physcs 201: Lecture 1, Pg 18 Page 6

7 Clcker Queston 8: Two balls of equal mass are thrown horzontally wth the same ntal velocty. They ht dentcal statonary boes restng on a frctonless horzontal surface. The ball httng bo 1 bounces back, whle the ball httng bo 2 gets stuck. Whch h bo ends u movng faster? (a) Bo 1 (b) Bo 2 (c) same 1 2 Physcs 201: Lecture 1, Pg 19 Clcker Queston 9: Two dry ce ucks slde on a horzontal, frctonless surface. Puck A, whch s 2 kg, moves at seed 7 m/s n the ostve drecton and Puck B, whch s 1 kg, moves at seed 8 m/s n the negatve y drecton as shown n the fgure. The ucks collde near the star n the fgure. After the collson Puck B s movng n the ostve drecton, whle Puck A s movng n the drecton that makes 45 wth the ostve -as as llustrated. What s the seed of Puck A after the collson.? (a) 1 m/s (b) 2 m/s (c) 2 2 m/s (d) 4 m/s (e) 4 2 m/s Physcs 201: Lecture 1, Pg 20 Page 7