AP Physics Kinematic Wrap Up

Transcription

1 AP Physics Kinematic Wrap Up S what d yu need t knw abut this mtin in tw-dimensin stuff t get a gd scre n the ld AP Physics Test? First ff, here are the equatins that yu ll have t wrk with: v v at x x vt at v v a x x Nte: this is the same as: 0 0 v v ax v ax That s it. That s all yu get. Here s the stuff that yu have t be able t d r talk abut:. Yu shuld knw hw t deal with displacement and velcity vectrs s yu can: a. Relate velcity, displacement, and time fr mtin with cnstant velcity. Okay, this is easy stuff. We did us a bunch f prblems and stuff n this. Basically yu use the v d! It s the x t x x vt at ne. See, the acceleratin is zer because yu have a equatin. Nte that yu dn t seem t have it in the list abve. But yu cnstant velcity, s all the terms with acceleratin in them cancel ut. x x vt at becmes x x vt if the initial displacement is zer, then we x v t x vt kay? get b. Calculate the cmpnent f a vectr alng a specified axis, r reslve a vectr int cmpnents alng tw specified mutually perpendicular axes. We did a bunch f this. We learned hw t use the sine and csine functin t reslve a vectr int its cmpnents. c. Add vectrs in rder t find the net displacement f a particle that underges successive straight-line displacements. 53

2 This is anther skill that yu have wrked hard t develp. Reslve the vectrs int cmpnents, add up the x and y cmpnents and then slve fr the resultant vectr. Yu prbably gt sick f ding prblems like this. Usually, in the test, this will be part f a questin that is really dealing with smething else. Fr example, yu might have t find tw electric frce vectrs and then add them up t find the resultant. d. Subtract displacement vectrs in rder t find the lcatin f ne particle relative t anther, r calculate the average velcity f a particle. This sunds hrribly difficult, but it s just a simple business with adding vectrs.. Yu shuld understand the mtin f prjectiles s yu can: a. Write dwn expressins fr the hrizntal and vertical cmpnents f velcity and psitin as functins f time, and sketch r identify graphs f these cmpnents. N dubt yu came t lve ding the prjectile mtin prblems. The Physics Kahuna was prud t shw yu hw t d them. We did bunches f stuff n this. b. Use these expressins in analyzing the mtin f a prjectile that is prjected abve level grund with a specified initial velcity. This is a standard prjectile mtin prblem. Yu learned hw t d them in yur sleep. Or maybe it just seemed like that. N dubt, having wrked s hard t master them, yu dreamed f prjectile prblems. There aren t many free respnse questins that are just abut prjectile mtin r velcity r acceleratin. These cncepts are tested, but the questins are usually nested away in a questin n smething else. Typical kind f thing wuld be a questin abut cnservatin f mmentum r the energy in a spring where yu figure ut hw fast smething is mving after a cllisin r after it s been launched by a cmpressed spring. The thing is n a smth table that is a certain distance abve the deck and yu will be asked hw far it will land frm the edge f the table when it slides ff the table tp. That srt f deal. Here s an example. This is the first questin frm the 998 AP Physics test:. Tw small blcks, each f mass m, are cnnected by a string f cnstant length 4h and negligible mass. Blck A is placed n a smth tabletp as shwn belw, and blck B hangs ver the edge f the table. The tabletp is a distance h abve the flr. Blck B is then released frm rest at a distance h abve the flr at time t = 0. 54

3 a. Determine the acceleratin f blck B as it descends. b. Blck B strikes the flr and des nt bunce. Determine the time t at which blck B strikes the flr. c. Describe the mtin f blck A frm time t =0 t the time when blck B strikes the flr. d. Describe the mtin f blck A frm the time blck B strikes the flr t the time blck A leaves the table. e. Determine the distance between the landing pints f the tw blcks. The main thrust f the questin is t lk at Newtn s laws (which we will sn get int). Yu use Newtn s laws and frces t figure ut the acceleratin in part a. Part b des deal with the stuff yu ve learned. Yu use Part c is anther applicatin f Newtn s laws. Have t wait a bit fr this ne. Part d is yet anther Newtn s law deal. We ll learn t d this later. y at t figure ut the time. Part e yu can d, blck B falls straight dwn, blck A slides ff the table with sme hrizntal velcity. When it slides ff the table it is a prjectile and yu can easily figure ut the hrizntal distance. Here s hw we d part b: In part a the acceleratin was fund t be (yu ll learn hw t slve this part sn enugh): a g Using this acceleratin, we can easily find the time the blck takes t fall: y at g y h t t h g Nw let s take a sht at part e: e. Determine the distance between the landing pints f the tw blcks. We knw the acceleratin f the system, we knw that blck A gets accelerated a distance f 3 h, s we can find its speed when it reaches the end f the table: 55

4 g h v v at v 0 g v hg We knw that the blck will fall a distance f h, s we can figure ut hw lng it will take fr it t fall t the deck. y h 4h y at t t a g g 4h x vxt x hg h g The 994 AP test has a free respnse tw dimensinal mtin prblem. We basically did it in a quiz.. A ball f mass 0.5 kilgram, initially at rest, is kicked directly tward a fence frm a pint 3 meters away, as shwn belw. The velcity f the ball as it leaves the kicker's ft is 0 meters per secnd at an angle f 37 abve the hrizntal. The tp f the fence is.5 meters high. The kicker's ft is in cntact with the ball fr 0.05 secnd. The ball hits nthing while in flight and air resistance is negligible. a. Determine the magnitude f the average net frce exerted n the ball during the kick. This is stuff yu dn t knw hw t d yet (but yu will). b. Determine the time it takes fr the ball t reach the plane f the fence. This part we can d. We knw that the hrizntal velcity is cnstant. x 3 m x vxt t.0 s vx m 0 cs37 s c. Will the ball hit the fence? If s, hw far belw the tp f the fence will it hit? If nt, hw far abve the tp f the fence will it pass? 56

5 T determine if the ball will hit the fence, we need t find its vertical psitin after.0 secnds have elapsed, this is the time it takes t reach the plane f the fence frm part b abve: y v t at m m y 0 sin37.0 s s 4.4 m s s Since the ball has a height f 4.4 m and the fence is.5 m tall, clearly the ball will pass ver the fence. The height f the ball ver the fence is simply the height f the ball minus the height f the fence: 4.4 m.5 m.9 m ver the fence d. On the axes belw, sketch the hrizntal and vertical cmpnents f the velcity f the ball as functins f time until the ball reaches the plane f the fence. The idea here is that the hrizntal velcity is cnstant, but that the vertical velcity is changing. The lwer graph shws this, the velcity is a straight line. The pint where it crsses the x axis and becmes negative is, f curse, the highest pint n its path where its velcity is zer. 57