Lecture 16 (Momentum and Impulse, Collisions and Conservation of Momentum) Physics Spring 2017 Douglas Fields

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1 Lecure 16 (Momenum and Impulse, Collisions and Conservaion o Momenum) Physics Spring 2017 Douglas Fields

2 Newon s Laws & Energy The work-energy heorem is relaed o Newon s 2 nd Law W KE F d mv mvi F d 2 2 v v i m v v 2a x x 2 2 i i

3 Anoher Consequence o Newon s Laws Noice ha or Energy, we are alking abou a orce applied over a disance. In many cases, wha we know is no he disance over which a orce is applied, bu a ime during which a orce is applied. This will lead us o a new quaniy, called momenum, ha we will also ind very useul.

4 Momenum F ma This is no he way ha Newon wroe his amous equaion. He acually wroe i as: F d d Where p is he momenum p

5 Momenum p mv Then d d dm dv F p mv v m d d d d I he mass is consan, hen he irs erm is zero, and we ge back our version o Newon s 2 nd Law: 0 dm dv dv F v m m ma d d d

6 Ne Impulse d FNe F p d F d dp 2 2 Ne Ne p F d dp p p p J F d p p The impulse is deined as he inegral o he orce over ime, and is hereore equal o he change in momenum over ha same ime period.

7 How is his useul? Impulse There are many cases when he orce or he ime isn known, bu he change in momenum is 2 J F d p p 1 Ne 2 1

8 Car Crashes In an auomobile crash, he driver s momenum immediaely beore he acciden and immediaely aer are deermined, bu he orce acing on hem is no. I depends upon he amoun o ime he change in momenum occurs.

9 Impulse In many cases, we may know he ime period ha a orce acs, bu no he exac orm o he orce as a uncion o ime. In hese cases, we can examine he average orce ha aced. 2 2 Ne Avg Avg 1 1 J F d F d F p p

10 Example 1

11 Example 2

12 CPS Quesion 19-1 Two masses experience he same orce, F, over he same disance, x. Describe he dierence in he kineic energy beween he wo masses a he end o he pah. A) The heavier mass has more kineic energy. B) The ligher mass has more kineic energy. m=1kg F F C) They have he same kineic energy. D) No enough inormaion o solve. m=2kg x

13 Proo Le s use our equaions o moion 2 2 v vi 2ax xi 2ax 2 F v 2 x m bu, KE mv m 2 x F x Independen o mass! F m

14 CPS Quesion 19-2 Two masses experience he same orce, F, over he same disance, x. Describe he dierence in he momenum beween he wo masses a he end o he pah. A) The heavier mass has more momenum. B) The ligher mass has more momenum. m=1kg F F C) They have he same momenum. D) No enough inormaion o solve. m=2kg x

15 Proo Le s use our equaions o moion 2 2 v vi 2ax xi 2ax v 2 F 2 x m F v 2 x m bu, F p mv m 2 x 2mFx m NOT independen o mass!

16 Collisions Collisions are ineracions beween bodies. Generally, here is a large orce acing over a shor period o ime: Pool balls, or ba and ball. Bulle srikes a wooden arge. Meeor srikes he earh. Cosmic ray his an aom in he amosphere. Someimes collisions ake a longer period o ime: Space probe sling-shos around a plane or sun. Galaxies collide.

17

18 Collisions In many circumsances, collisions o a sysem o bodies (can be more han wo) has no NET orces acing on hem rom ouside o he sysem.

19 In ha case, since Collisions 1 Then p 2 = p 1, or beer saed, he momenum o he sysem remains consan. I does NOT mean ha he kineic energy o he sysem is consan 2 J F d p p Ne 2 1

20 Drag Force Series o collisions: or n paricles hiing in ime, p so, Avg nmv J nmv so, F nmv n mv bu, nm Av so, F Avg Av 2 v or each paricle, p i 0 p mv p mv

21 Collisions Two general caegories o collisions: Elasic Boh momenum and kineic energy are conserved. Inelasic Only momenum is conserved. In general a collision is somewhere beween hese (no all kineic energy is los in inelasic collisions).

22 CPS 20-1 Given one ball wih iniial velociy in he Newon s cradle, how many balls will have a non-zero inal velociy on he oher side? A) 1 B) 2 C) 3 D) 4 E) I depends

23 Problem 8.84 For mos sudens, he problem here is Where is momenum conserved and where is energy conserved? Momenum conserved v bi v B v b vb beore aer beore aer Energy conserved h

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