Linear Momentum and Collisions

Transcription

1 Lnear Momentum and Collsons Chater 9 Lnear Momentum [kg m/s] x y mv x mv y Newton s nd Law n terms o momentum:

2 Imulse I - [kg m/s] I t t Fdt I = area under curve bounded by t axs Imulse-Momentum Theorem Proo:

3 Queston Fnd the ollowng usng the estmated orce-tme curve shown below or an object subjected to a orce F over a tme nterval o 5.00 s.: o The mulse delvered by the orce. o The average orce F avg. Queston A tenns layer receves a shot wth the ball (0.060 kg) ntally travelng horzontally at 0.0 m/s and returns the ball horzontally at 40.0 m/s n the ooste drecton. I the racket s n contact wth the ball or 4.00 x 0-3 s, determne the ollowng: The mulse delvered by the tenns racket The magntude o the average orce on the ball? 3

4 Conservaton o Lnear Momentum and Collsons Momentum s conserved whenever a system o nteractng artcles s solated (.e., no net external orces act on the system and thereore there s no net mulse) When there are no external orces (F ext = 0) on a system, ts mulse I = 0, and ts momentum s conserved! 4

5 Momentum and Auto Collsons In any collson, the total o the system s always conserved Elastc Collson - no hyscal contact occurs Inelastc Collson - hyscal contact occurs 5

6 6 Elastc Collson (-D) conserves both the momentum and knetc energy o the system K K K K v = m - m m + m æ è ç ö ø v + m m + m æ è ç ö ø v v = m m + m æ è ç ö ø v + m - m m + m æ è ç ö ø v Inelastc collson (-D) conserves only the momentum o the system and not ts knetc energy v m m ( ) Perectly nelastc: Inelastc:

7 Queston 3 Two blocks are ree to slde along the rctonless wooden track below. The masses o the blocks are m =.00 kg and m = 4.0o kg. Both masses are released rom rest at a heght o h = 5.00 m. When they meet at the bottom, they undergo an elastc-head on collson (although they don t touch). Calculate: (a) The seed o m and m just beore the collson (b) The seed o m and m just ater the collson (c) The maxmum heght that m and m rse ater the collson. Queston 4 An m = 0.0 kg wad o clay s hurled horzontally at an m = 0.00 kg wooden block ntally at rest on a horzontal rough surace. Just beore the nelastc collson, the clay strkes the block wth v c and stcks to t. Just ater the collson they both move wth v cb. The clay-block system then slde a dstance Δr = 7.50 m beore comng to rest v cb = 0 due to the orce o rcton (μ k = 0.650). o What s the magntude o ther velocty v cb just ater the collson? o What was the magntude o the clay s velocty v c just beore the collson? v c m m + m m v cb 7

8 Inelastc Collsons (-D) x y x y x y x y Queston 5 A car m = 500 kg s travelng due east at v = 5.0 m/s. A van m = 500 kg s travelng due north at v = 0.0 j m/s. They collde and move together wth a common seed v at an angle θ, N o E (as shown). o Fnd θ and v 8

9 The Center o Mass ont where the total mass o a system s concentrated CM can move as mass dstrbuton changes athlete usng hyscs 9

10 cm o a system o ont artcles x cm xm xm... m m... x m m M x m tot In -D: Queston 6 Fnd the CM o the system shown below where m = m =.0 kg, and m 3 =.0 kg. 0

11 cm o an extended symmetrc object o unorm mass dstrbuton Queston 7 A unorm sheet o steel s shaed as shown. o Fnd the x and y coordnates o the center o mass o the sheet

12 cm o an extended object x cm M tot xdm and y cm M tot ydm where M tot dm I the mass s unorm, we relate dm to a constant mass densty. lnear mass densty area mass densty volume mass densty M dm L d M dm A da M dm V dv I the mass o the object s non-unorm then the mass densty wll have a satal deendence,.e., λ = ax, that must be ntegrated. Queston 8 Show that the CM o a unorm rod o total mass M and length L les mdway between ts ends. x cm L xdm M 0 L x dx M 0 L xdx M 0 M L xdx M L 0 L L L

13 Queston 9 Suose a rod o length L = 0.30 m has a non-unorm mass dstrbuton, so that ts mass er unt length vares as λ(x) = (50 + 0x) g/m. a) Determne ts mass: M. b) Fnd ts cm: x cm CM o a trangle o unorm mass x cm = (/3)a and y cm = (/3)b 3