"1 O O O. -U -7 P fl> 1 3. jff. (t) o o 1-7- PAa s: A - o 0'»«-« "Tf O ") ftt Ti 0 -- CO -1 O. fa n. i,, I. -n F en 2.0»- 4 T2. -5 Ut.

Transcription

1 crv/ 3 P -U -7 P fl> 1 3 (t) jff?- "1 s P ~* PAa s: A - "C '»«-«in i,, I ftt Ti -- c 4 T2-5 Ut j 3 C -1 p fa n l> -n F en 2.»- "Tf ") r

2 . x 2 "Z * "! t :.!, 21,, V\ C fn <? C 3- fl f\ - f- iw x.si * ~ fil ^jcr, 3 c: -! * -* - -b -5 b & -» -K -4- ftj "i * P»' -V D" 3 a -h i, 6 ~\ ^> S- -'" -T * a. * -«u» -^ EL. rv i> c* ir* ^ _- «*. a - - <» ff- (T * ^ -^ f- ^5 n <* 3 * - -f- 5u ^' (5) Q " ci_ L - r 1 ^ -i~ n>' - " 3"" ^t < <*> "*,. f!» 3 f> <T» X 3' 1 - ^' ;> S X P H c In Q, 11. A 5' w rt -s: tf w (l) ' ID ^ -» n> tr 3 -i -!- -*- * n. CT \,, «> -V -h > <* -? D "** r» ^ 9 Q "* <rx n IA U> -T «- fu 5 C?' E J > p T P> "D i 3 I/) c: ]- \ C 1? t _5., 1 "-*'. -K'^ I J.! 5? * - P ST* 3 3 f «H i- 1 P

3 yhy des mud fly ff a rapidly turning wheel? 7 ' 133. Astrnauts flating arund inside the space shuttle -are nt actually in a zer-gravity envirnment. What is the real reasn astrnauts seem weightless? %4. A girl at a state fair swings a ball in a vertical circle at i - the end f a string. Is the frce applied by the string. greater than the weight f the ball at the bttm f the ball's path? >: -. ~ use. practice prblems HB^^^R 35. Tarzan (m = 85 kg) tries t crss a river by swinging frm a 1. m lng vine. His speed at the bttm f the swing, just as he clears the water, is 8. m/s. Tarzan desn't knw that the vine has a breaking strength f 1. X 1 N. Des he make it safely acrss the river? Justify yur answer. (See Sample Prblem 7H.) 36. Apprximate the gravitatinal frce f attractin between a 5. kg girl and a 6. kg by if they are sitting 2.5 m apart in physics class. (See Sample Prblem 71.) 37. What is the gravitatinal frce between the prtn n-27,-31 (1.67 X 1~ 4/ kg) and the electrn (9.11 x ICT* 1 kg) in a hydrgen atm if they are 1. X 1~ m apart? (See Sample Prblem 71.) 38. A 515 kg rller-caster car rlls dwn past pint A and then up past pint B, as shwn in Figure a. If the vehicle has a speed f 2. m/s at pint A, what is the frce f the track n the vehicle at this pint? b. What is the maximum speed the vehicle can have at B fr gravity t hld it n the track?, (SeeiSample Prblem 7H.) B 39. During a slar \se, the mn, Earth, and sun lie n the same line,,\ath the mn between Earth and the sun. What frce is exerted n a. the mn by the sun? b. the mn by Earth? c. Earth by the sun? (See Sample Prblem 71. See the table in the appendix fr data n the sun, mn, and Earth MIXED REVIEW PRBLEMS 4. An airplane is flying in a hrizntal circle at a speed f 15 m/s. The 8. kg pilt des nt want his centripetal acceleratin t. exceed 7. times free-fall acceleratin. a. What is the minimum radius f the circular path? b. At this radius, what is the net frce mat maintains circular mtin exerted n the pilt by the seat belts, the frictin between him and the seat, and s frth? 43. A 2. x 1 3 kg car runds a circular turn f radius 2. m. If the rad is flat and the cefficient f static frictin between the tires and the rad is.7, hw fast can the car g withut skidding? -i 32. The inertia f the pieces f mud exceeds the frictinal frce that maintains the mud's circular mtin. 33. The astrnauts and space shuttle bth have the same acceleratin, that f free-fall acceleratin. Because f this, the astrnauts see everything. at rest and believe there is n frce n them. 34. Yes, the string must exert a frce equal t the ball's weight and the circular frce that maintains circular mtin. 35. n, 1.37 x 1 3 N > 1. X 1 3,N xl~ 8 N xl~ 47 N 38. a. b m/s 39. a x 1 2 N b. 1.99xl 2 N c. 3.55xl 22 N 4. a. 161m b. 5.49xl 3 N rev m 43.,12 m/s 44. a..965 m/s 2 b. 1.33X1 3 N c..985 Figure A 135 N car traveling at.'5. km/h runds a curve f radius 2. X 1 m.?ind the fllwing: a. the centripetal acceleratin f the car b. the frce that maintajns centripetal acceleratin c. the minimum icient f static frictin -ihe c#- r!» l^^4_,, 4.1 j.1,.-',_1., 1,1, '

4 ; peta I in s 48. An air puck f rnass;.25 kg is tied t a string and allwed t revlve in a circle f radius 1. m n a frictinless hrizntal surface. The ther end f the string passes thrugh a -hle in the center f the surface, and a mass f 1. kg is tied t it, as shwn in Figure The suspended mass remains in equilibrium while the puck revlves n the surface. a. What is the magnitude f the frce that maintains circular mtin acting n the puck? b. What is the linear speed f the puck? 49. In a ppular amusement-park ride, a cylinder f radius 3. m is set in rtatin at an angular speed f 5. rad/s, as shwn in Figure 7-2. The flr then drps away, leaving the riders suspended against the wall in a vertical psitin. What minimum cefficient f frictin between a rider's clthing and the wall f the cylinder is needed t keep the rider frm slipping? (Hint: Recall that F s = JJ. s F n, where the nrmal frce is the frce that maintains circular mtin.) Nte = \s 48. a. 9.8 N b. 2.xl 1 m/s Figure 7-19 Figure (II) In a "Rtr-ride" at a carnival, riders are pressed against the inside f a vertical cylinder 2.8 m in radius rtating at a speed f 3.2 rad/s when the flr drps ut. What minimum cefficient f frictin is needed s a persn will nt slip dwn? 23 (II) If the static cefficient f frictin between tires and rad is.7, what is the minimum turning radius n a level rad fr a car traveling at (a) 3 km/h, and (6) 6 km/h? A 5 1 b) H3 ft Tar mre. 25 (III) A car runds a curve f radius 5 m banked at an angle f 16. If the car is traveling at 7 km/h, will a frictin frce be required? If s, hw much and in what directin? The car's mass is 12 kg. A" - VQ B 5 M tl u 27 (III) If a plant is allwed t grw frm seed n a rtating platfrm, it will grw at an angle, pinting inward. Calculate what this angle will be (put yurself in the rtating frame) in terms f g, r, and As. V'

5 Grade 12 University Physics Practice QUIZ n centripetal frce and apparent weight ' t>* USE g = 1 N/kg 1. a) A 2.5 kg ball is being whirled in a vertical circle using a string f radius 1.6 m. If the ball is being whirled at a cnstant speed f 7. m/s, find the tensin frce f the string n the ball at... the tp f the circle the bttm f the circle Answers. when it is 6 degrees frm the 1.a)52N,12N,64N b) 4. m/s tp f the circle with respect t the 2. a) 2 N, frictin,.2 vertical. b)11 degrees, 1198 N m/s, 1.8s..54 Hz N, 21 N, TN N 6. 18Qbillabngs b) Fr the same radius vertical circle f 1.6 m, what is the minimum speed fr the 2.5 kg ball t just cmplete a circle. 2. A 1. kg car mves in a circular curve f radius 2 m at a cnstant speed f 72km/h. a) If the curve is nt banked, i) find the centripetal frce required ii) what real frce must supply the centripetal frce iii) find the cefficient f frictin between rad and car b) If the curve is frictinless but banked, i) find the banking, angle required ii) find the nrmal frce n the car 3. A cnical pendulum mves in a hrizntal circle f radius.5 m at an angle f 3 degrees t the vertical. Find the speed, perid" and frequency. 4. A 7 kg actress is in an elevatr. Find her apparent weight if the elevatr is... a) accelerating up at 7 m/s/s b) accelerating dwn at 7 m/s/s c) at cnstant velcity f 7 m/s [up] 5. A 2. kg mass rests n a Newtn spring scale in an elevatr accelerating dwn at 3 m/s/s. Find the reading n the spring scale. 6. A unifrm circular mtin with radius 8 feet and speed 1 feet/s will prduce a centripetal.frce f 5 Billabngs. (named after Fred Billabng) Fr the same mass,if the radius is decreased t 2 feet, and the speed increased t3 feet/s, hw many billabngs f centripetal frce will be required? 7. Be able t derive equatins fr banked curves and the cnical pendulum.

6 52. Yu have determined the fllwing results when ding an investigatin. Using prprtining techniques, find the new "Value fr the centripetal frce. "Befre mass = 1 ball radius =.75 m frequency = 1.5 Hz After mass = 3 balls - radius == m frequency = 3. Hz centripetal frce =? units centripetal frce = 8. units A 2 g ball n the. end f a string is rtated in a hrizntal' circle f radius 1. m. The ball cmpletes 1 rtatins in 5. s. What is the centripetal frce f the string n the ball? In the Bhr mdel f the hydrgen atm, the electrn revlves 1- m arund "the nucleus. If the radius f the rbit is 5.3 x and the electrn makes 6.6 x 1 15 r/s, find (a) the acceleratin f the electrn and (b) the centripetal frce acting n the electrn. (This frce is due t the attractin between the psitively charged nucleus and the negatively charged electrn?) The. mass f the electrn is 9.1 x 1Q- 31 kg. 55. A string pendulum 1.12 m lng has a bb with a mass f 2 g. (a) What is the tensin in the string when the pendulum is at rest?.. (b) What is the tensin at.the bttm f the swing, if the pendulum is mving at 1.2 m/s? 56. When yu whirl a ball n a crd in a vertical circle, yu find a critical speed at the tp fr which the tensin in the crd is zer. This is because the frce f gravity n the bject itself supplies the necessary centripetal frce. Hw slwly can yu swing a 2.5 kg ball like this s that it will just fllw a circle with a radius f 1.5 m? 57. An bject f mass 3. kg is whirled arund in a vertical circle f radius 1.3 m with a cnstant velcity f 6. m/s. Calculate the maximum and minimum tensin in the string. 58. Snpy is flying his vintage war plane in a "lp the lp" path chasing the Red Barn. His^ instruments tell him the plane is level (at the bttm f the lp) and travelling with a speed f 18 km/h. He is sitting n a set f bathrm scales, and ntes that they read fur times the nrmal frce f gravity. n him. What is, the radius f the lp? Answer in metres. (SIN '75) >9. An Australian bushman hunts kangars with the fllwing weapn, a heavy rck tied t ne end f a light vine f length 2 m. He hlds the ther end abve his head, at a pint 2 m abve grund level, and swings the rck in a hrizntal circle. The cunning kangar has bserved that the vine always breaks when the angle 9 (measured between the vine and the vertical) reaches 6. At what minimum distance frm the hunter can the kangar stand.with n"danger f,a-direct hit? (SIN '72) i. A pendulum f mass 1. kg is suspended frm the rf f a car travelling n a level rad. An bserver in the car ntices, that the pendulum string makes an angle f 1 with the vertical'. What is the acceleratin f the car? units X 1CP N 54. (a) 9.1 x 1 22 m/s 2 (b) 5S! (a) 1.96 N (b) 2.2 N m/s x I 2 N, 54 N m m. 6.., 1.8 m/s 2

7

8