BULLSEYE Lab Name: ANSWER KEY Dae: Pre-AP Physics Lab Projecile Moion Weigh = 1 DIRECTIONS: Follow he insrucions below, build he ramp, ake your measuremens, and use your measuremens o make he calculaions following. 1. (10 poins) Using he maerials in he back (insulaion foam, siding, cardboard, pvc pipe, ape, books, marbles, bullseye sign), build a ramp like he one shown a righ. The mos imporan x r building aspec is ha he ball roll off he able horizonally afer coming down an incline of some sor (i shouldn arc upwards ino he air or face downwards as i rolls off).. Selec a disance away from he able & ape down your bullseye arge. The cener of he bullseye mus be a leas 50 cm away from he place where he ball rolls off he able. 3. Adjus he heigh of your ramp (or he locaion of he bullseye) unil you are able o roll he seel ball down and make a bullseye (he small cener circle no jus any par of he arge) a leas wice in a row. Call he eacher, show him/her ha your se up can hi he bullseye y o wice in a row, and have him/her iniial here when you do i. INITIALS (five poins) 4. (one poin) Measure he disance x r he ball rolls down he ramp (see Figure a righ). Pu your measuremen in he able below in he correc blank (answer in meers). EX: 0.45 m x 50 cm 5. (one poin) Measure he ime o roll down he ramp (hrough he disance x). Pu your measuremen for ime in he able below (answer in seconds). EX: = 0.5 sec 6. Calculae he acceleraion a of he ball as i goes down he ramp by doing he following seps. a. (one poin) Deermine which of he following moion formulas from Uni will allow us o find he acceleraion of he marble down he ramp if we know he disance ravelled x r by he marble, and he ime elapsed. Pu an in he righ box. v = d velociy = disance ime + a final velociy = iniial velociy + acceleraionime d = ½(v o + ) disance = ½ (iniial velociy + final velociy)ime + ad (final velociy) = (iniial velociy) + acceleraiondisance a = v acceleraion = velociy ime d + ½a disance = iniial velociyime+ ½acceleraionime This is he only formula ha has disance, ime,, and acceleraion, a b. zero_ (one poin) Wha is he iniial velociy v o of he marble as i jus begins is rip down he ramp a disance x? The ball is no moving a all a he beginning. 1
c. Based on your answer o Sep b., how does he moion formula you picked in Sep a. simplify? The formula d + ½a becomes d = ½a because he v o erm drops ou since v o is zero and anyhing imes zero is zero. Wrie he simplified formula here: d = ½a (one poin). d. Now solve he moion formula from Sep c. for he acceleraion, a. In oher words, leave a by iself and ge everyhing else on he oher side of he equal sign. d = ½a d = ½a d = a d Wrie your formula for a here. a = d (one poin) a d = e. (one poin) Find he acceleraion a of he marble as i moves down he ramp using he daa you obained for disance, x r, and ime,, in Seps 4 and 5 above. Record your value for acceleraion in he able below. Show your work here. Acceleraion is measured in m/s. a = d (0.45 m) = (0.5) = 14.4 m/s 7. (one poin) Now look a he moion formula able below. Deermine which of he following moion formulas from Uni will allow us o find he final velociy of he marble as i comes down he ramp and ono he able if we know he iniial velociy of he marble v o, he acceleraion of he marble a, and he ime elapsed. Pu an in he righ box. v = d d = ½(v o + ) velociy = disance ime disance = ½ (iniial velociy + final velociy)ime + a final velociy = iniial velociy + acceleraionime The only formula ha has v o, he iniial velociy, a, he acceleraion, and, he ime = a + ad (final velociy) = (iniial velociy) + acceleraiondisance a = v acceleraion = velociy ime d + ½a disance = iniial velociyime+ ½acceleraionime 8. (one poin) Using he moion formula you seleced in Sep 7, find he final velociy of he marble as i leaves he ramp and makes is way across he horizonal able surface. Show your work here and record your answer in he correc blank in he answer able below. + a = 0 + 14.4 m/s (0.5 s) = 3.6 m/s DIRECTIONS: Fill in he missing blanks here: a. (one poin) Noice we are calling he final velociy and no jus because we are indicaing he marble s velociy when i leaves he ramp is horizonal and no _verical. b. (wo poins) Also, since he able is horizonal, he velociy a which he marble leaves he ramp is he same as he velociy he marble moves a when i falls of he able. The marble has a consan_ velociy on he able, meaning i does no accelerae. 9. (one poin) Now in he able below record (in meers) in he correc blank how far he bullseye is horizonally from he base of your able, x (see Figure a righ on p. 1). Remember ha he horizonal disance had o be a leas 0.50 m away from he able. EX: 1.5 m
DIRECTIONS: Fill in he missing blanks here: a. (four poins) Afer he marble flies off he able horizonally, i will experience wo kinds of moion. I will coninue o move horizonally as i was before bu i will now also sar o _ move/fall verically due o he pull of he force of graviy on i. b. (hree poins) Bu as we saw in he Falling Monkey Firesarer/video and he Firesarer/Myhbusers video abou shooing a _bulle ou of a gun a he same ime as you dropped he bulle nex o he gun, horizonal movemen is independen of verical movemen. Graviy doesn _affec/impac horizonal movemen. 10. (one poin) Now look a he moion formula able below. Deermine which of he following moion formulas from Uni will allow us o find he ime i akes he marble o fly horizonally from he able hrough a horizonal disance x o hi he bullseye if i is moving a a horizonal velociy of. Remember: he acceleraion due o graviy does NOT affec horizonal moion. Pu an in he righ box. v = d velociy = disance ime This is he formula for consan velociy problems where here is no acceleraion. + a final velociy = iniial velociy + acceleraionime d = ½(v o + ) disance = ½ (iniial velociy + final velociy)ime + ad (final velociy) = (iniial velociy) + acceleraiondisance a = v acceleraion = velociy ime d + ½a disance = iniial velociyime+ ½acceleraionime 11. (one poin) Solve for ime in he formula you seleced in Sep 10. and find he ime i ook he marble o hi he bullseye. Record your answer in he correc blank in he able below. Show your work here. v = d = d 1.5 m = = 0.4 s 1.50 m was he horizonal disance from he able o he bullseye and 3.6 m/s was vxf, he horizonal v 3.6 m/s velociy of he marble. 1. Now le s verify if our ime ha we found in Sep 11. is reasonable by doing he following seps. a. (one poin) Measure he heigh y o of he able off he ground (See Figure a righ on p. 1) in meers. Record your answer in he correc blank in he able below. EX: 0.9 m DIRECTIONS: Fill in he missing blanks here: a. (one poin) The ime for he marble o move horizonally from he able o he arge is he same ime for he marble o _fall down o he ground as graviy pulls i down. b. (hree poins) Graviy pulls hings down o he ground a a rae of negaive _10 meers per second per second. Graviy is very predicable. So if we did our mah righ, we should be able o find ou how _far_ (in m) he marble fell in he ime 3
we found in Sep. 11 when pulled down by graviy. This disance fallen by he marble should mach up prey closely wih he _heigh_ of he able ha we measured in Sep. 1.a. c. (one poin) Look again a he moion formula able below. Deermine which of he following moion formulas from Uni will allow us o find he disance d he marble falls from he able afer seconds have passed if he marble has an iniial velociy of v o and is being acceleraed due o graviy. Pu an in he righ box. v = d d = ½(v o + ) velociy = disance ime disance = ½ (iniial velociy + final velociy)ime + a final velociy = iniial velociy + acceleraionime + ad (final velociy) = (iniial velociy) + acceleraiondisance a = v acceleraion = velociy ime d + ½a disance = iniial velociyime+ ½acceleraionime This is he only formula wih disance d, ime, and acceleraion, a. d. Wai a second! Le s hink abou he verical velociy of he marble as i leaves he able. DIRECTIONS: Fill in he missing blanks here: (one poin) Since he marble flew off he able horizonally, i s iniial verical velociy is _zero. Graviy sill hasn had ime o ac upon i. e. (one poin) So our formula from Sep. c. simplifies. Wrie down your simplified formula here: d = ½a NOTE: his formula is a LOT like he formula in Sep 6.c. above. f. (one poin) The verical acceleraion is due o graviy which has a value of _-10 meers per second per second. g. (one poin) Plug in your value for a from Sep f. above and he ime you found in Sep 11 ino your formula and solve for he disance fallen, y o. Pu your answer here: d = ½(10 m/s )(0.4) _= 0.87 m. h. (one poin) Is he answer for Sep g. above reasonably close o he answer you go for y o from Sep 1.a.? YES NO 0.9 m (our measured able heigh) is reasonably close o 0.87 m (our calculaed falling disance/able heigh) 13. Now le s find he final verical velociy of he marble righ before i his he ground. This is one of your menal mah ricks. DIRECTIONS: Fill in he missing blanks here: (wo poins) I ook he marble 0.4 s_ (Ans. o Sep. 11) seconds o fall o he ground. If graviy increases he velociy of a falling objec by 10 meers per second per second, hen he final verical velociy of he marble is 4. m/s. Pu your answer in he correc blank in he able below. This is he menal mah hing we praciced. Graviy (10 m/s/s), g, imes he ime, = verical velociy 14. Final sep. We said earlier ha he marble is moving horizonally and falling a he same ime once i leaves he able. vy 4
15. Righ before i lands, i is moving diagonally a a velociy of meers per second as shown in he illusraion a righ: a. (hree poins) DIRECTIONS: Fill in he missing blanks here. To find he final diagonal velociy of he marble righ before i his he ground we have o recognize he geomeric shape of a righ riangle above formed by he hree velociies pu ogeher. This les us use he _Pyhagorean_ Theorem o find he value of, he final diagonal velociy, which is he hypoenuse of he riangle. is he adjacen side of he riangle and is he opposie side. b. (one poin) Find he final velociy, of he marble from Sep 15.a. and pu he answer in he correc blank in he able below. Lengh of ramp, x r (in m) ha he marble rolls down Heigh of able, y f (in m) above ground Y o Horizonal disance, x, from able o arge (in m), where he marble falls x Time, r (in s) o roll down he ramp o edge of able Time, f (in s) marble is in he air afer rolling off he able Acceleraion, a, of marble down he ramp (in m/s/s) a Horizonal velociy, v x, of he marble when i flies off he able Final verical velociy,, of he marble when i lands. Final diagonal velociy,, of he marble when i lands. x r 0.45 m 0.9 m 1.5 m 0.5 sec 0.4 s 14.4 m/s 3.6 m/s 4. m/s 5.5 m/s Final diagonal velociy from Pyhagorean Theorem: c = a + b = + = v y + = (4. m/s) + (3. 6 m/s) = 17. 36 + 1. 96 = 30. 3 = 5.5 m/s 5