(a) Calculate the apparent weight of the student in the first part of the journey while accelerating downwards at 2.35 m s 2.

Transcription

1 Chapte answes Heineann Physics 1 4e Section.1 Woked exaple: Ty youself.1.1 CALCULATING APPARENT WEIGHT A 79.0 kg student ides a lift down fo the top floo of an office block to the gound. Duing the jouney the lift acceleates downwads at.5 s, befoe tavelling at a constant velocity of 4.08 s 1 and then finally deceleating at 4.70 s. (a) Calculate the appaent weight of the student in the fist pat of the jouney while acceleating downwads at.5 s. Apply the sign and diection convention fo otion in one diension. Up is positive and down is negative. Apply the equation fo appaent weight (the noal foce) kg a.5 s down g 9.80 s down 79.0 kg a.5 s g 9.80 s F net F net F g a g (79.0.5) ( ) N (b) Calculate the appaent weight of the student in the second pat of the jouney while tavelling at a constant speed of 4.08 s 1. Apply the sign and diection convention fo otion in one diension. Up is positive and down is negative. Apply the equation fo appaent weight (the noal foce) kg a 0 s down g 9.80 s down 79.0 kg a 0 s g 9.80 s F net F net F g a g (79.0 0) ( ) N

2 (c) Calculate the appaent weight of the student in the last pat of the jouney while tavelling downwads and deceleating at 4.70 s. Also conside that deceleation is a negative acceleation. Apply the sign and diection convention fo otion in one diension. Up is positive and down is negative. Apply the equation fo appaent weight (the noal foce) kg a 4.70 s down g 9.80 s down 79.0 kg a 4.70 s g 9.80 s F net F net F g a g ( ) ( ) N Woked exaple: Ty youself.1. WORKING WITH KEPLER S LAWS Deteine the obital speed of a satellite, assuing it is in a cicula obit of adius of k aound the Eath. Take the ass of the Eath to be kg and use G N kg k Choose the appopiate elationship between the obital speed, v, and the data that has been povided. a g GM v Make v, the obital speed, the subject of the equation. Substitute in values and solve fo the obital speed, v. v v GM GM ( ) ( ) s 1

3 Woked exaple: Ty youself.1. SATELLITES IN ORBIT Callisto is the second lagest of Jupite s oons. It is about the sae size as the planet Mecuy. Callisto has a ass of kg, an obital adius of k and an obital peiod of s (16.7 days). (a) Use Keple s thid law to calculate the obital adius (in k) of Euopa, anothe oon of Jupite, which has an obital peiod of.55 days. Note down the values fo the known satellite. You can wok in days and k. T constant fo all satellites of a cental ass. Wok out this atio fo the known satellite. Use this constant value with the atio fo the satellite in question. Callisto: k T 16.7 days Euopa: T constant T ( ) constant Make the subject of the equation Solve fo k Euopa has a shote peiod than Callisto so you should expect Euopa to have a salle obit than Callisto. (b) Use the obital data fo Callisto to calculate the ass of Jupite. Note down the values fo the known satellite. You ust wok in SI units. Select the expessions fo the equation fo centipetal acceleation that best suit you data. a v 4 T GM g Callisto/Jupite: T s kg G N kg M? 4 GM T These two expessions use the given vaiables and T, and the constant G, so that a solution ay be found fo M. Tanspose to ake M the subject. M 4π GT Substitute values and solve. M ( ) ( ) 4π kg

4 (c) Calculate the obital speed of Callisto in k s 1. Note values you will need to use in the equation v π T. Callisto: k T s v? Substitute values and solve. The answe will be in k s 1 if is expessed in k. v π T π k s 1.1 eview 1 F g g N Noal foce weight foce fo an object at est 150 N F net F net F g a g (45.0.0) ( ) N 4 F net F net F g a g (45.0 0) ( ) N 5 B. It is the only object that is on a suface and so it can expeience an upwads noal foce due to that suface. 6 C. Satellites obit aound a cental ass. The Eath does not obit Mas. The Moon does not obit the Sun and the Sun does not obit the Eath. 7 B. In ode to be geostationay, the satellite ust be in a high obit. 8 D. Inceasing the ass of the satellite will not affect its obital popeties. 9 a a g 0. s b F g g N (o 510 N to significant figues)

5 10 T constant fo satellites of Satun, theefoe the obital peiod fo each oon can be calculated. Fo Atlas: T 5 ( ) ( 0.60) Fo Titan: T T ( ) 6 4 T days Section. Woked exaple: Ty youself..1 TORQUE ON A COIL A single squae wie coil, with a side length of 4.0 c, is fee to otate within a agnetic field, B, of stength T. A cuent of 1.0 A is flowing though the coil. What is the toque on the coil? 1 I I I 4 B I Confi that the coil will expeience a foce based on the agnetic field and cuent diections supplied. Calculate the agnetic foce on one side. Deteine the distance,, fo the point of otation that the agnetic foce is applied. Using the ight-hand ule, confi that a foce applies on side out of the page. A foce applies to side 4 into the page. The coil will tun clockwise as viewed fo in font of side. Sides 1 and lie paallel to the agnetic field and no foce will apply. F IlB N length of side 4.0 c distance between axis of otation and application of foce 1 side length.0 c 0.00 Calculate the toque applied by the agnetic foce on one side of the coil. Since two sides, and 4, expeience a agnetic foce and hence a toque, the toque on one side should be ultiplied by to find the total toque. State also the diection of otation. τ F N Total toque N The diection is clockwise as viewed fo side.

6 . eview 1 A. Recall the equation τ F. The axiu toque exists when the foce is applied at ight angles to the axis of otation. F nilb N into the page F nilb N out of the page 4 The foce will be 0 N. Side PQ is paallel to the agnetic field. 5 Consideing the diection of the foces acting on sides PS and QR, the coil would otate in an anticlockwise diection. 6 D. The diection of the cuent does not affect the agnitude of the toque. This is the only option that doesn t affect eithe the distance to the axis of otation o the agnetic foce fo the options available. 7 τ F sides F N 8 F nilb N 9 Cuent flows into bush P and aound the coil fo V to X to Y to W. So foce on side VX is down, foce on side YW is up, so otation is anticlockwise. 10 D. As F nilb, the coil will expeience oe foce, and otate faste, if the cuent and field stength ae inceased. Theefoe, A and B ae coect. Whethe C is coect will depend on how the aea is inceased. But if the length in the field is inceased, you would expect it to tun faste. If widened, it will expeience oe toque but that ay not ake it tun faste. Section. Woked exaple: Ty youself..1 CALCULATING THE SPEED OF ACCELERATED CHARGED PARTICLES Deteine the final speed of a single electon, with a chage of agnitude C and a ass of kg when acceleating acoss a potential diffeence of 1. kv. Establish what quantities ae known and what ae equied. Substitute values into the equation and e-aange to solve fo the speed. 1. kv V v? q C kg V V qv 1 v v v s 1

7 Woked exaple: Ty youself.. Heineann Physics 1 4e CALCULATING SPEED AND PATH RADIUS OF ACCELERATED CHARGED PARTICLES An electon gun eleases electons fo its cathode, which ae acceleated acoss a potential diffeence of 5 kv, ove a distance of 0 c between a pai of chaged paallel plates. Assue that the ass of an electon is kg and the agnitude of the chage on an electon is C. (a) Calculate the stength of the electic field acting on the electon bea. Apply the coect equation. Solve fo E. 5 kv V 0 c 0.0 E V d E V 1 (b) Calculate the speed of the electons as they exit the electon gun assebly. Apply the coect equation. 1 v qv Reaange the equation to ake v the subject. v qv Solve fo v. v s 1 (c) The electons then tavel though a unifo agnetic field pependicula to thei otion. Given that this field is of stength 0. T, calculate the expected adius of the path of the electon bea. Apply the coect equation. Solve fo. v eview 1 B. A chaged paticle oving in a agnetic field will expeience a foce. F qvb The electon will expeience a foce of N south. v qv (( ) (.5 10 )) s 1

8 4 a F qvb N b v v B v q Radius 1 diaete B v T v 0.06 ( ) ( ) s 1 7 A chaged paticle in a agnetic field will expeience a foce (F qvb). As foce velocity, the foce will incease as the velocity inceases. This will continue while the chage eains in the agnetic field, continuously acceleating the chage. 8 E k 1 v qv v qv ( ) (.0 10 ) s 1 Because the foces acting on the electon due to the electic and agnetic fields ae balanced, you can equate the. F E qe and F B qvb qe qvb E vb ( ) ( ) J V d so the plate sepaation, d V E d o 5.8 c

9 CHAPTER REVIEW 1 F net F net - F g a g ( ) ( ) N D. Objects in obit ae in fee fall. While still in obit aound the Eath, gavity is educed, but is still significant in agnitude. D. At this altitude, gavity is educed and so will be less than 9.8 N kg 1, hence, acceleation is less than 9.8 s. Note: B is not coect, because while the speed of the satellite would be constant, its velocity is not. 4 A. Appaent weightlessness is felt duing fee fall, when is zeo. 5 T constant fo satellites of Eath, theefoe the obital peiod fo each satellite can be calculated. Fo X: T constant k Fo Y: ( 5 ) k T Y ( 5 ) T Y T 15 T Y T Y T 15 T 15T T Y 11.T 6 a a GM ( ) s b a v v a s 1 c F g v 4 π GM g T 4π GM T T 4 π GM 4π ( ) T s 1 day s T days

10 7 a a GM g g GM b v ( ) 0.15 N kg 1 GM v GM s 1 8 a down the page b up the page 9 anticlockwise 10 a down the page b up the page c Zeo toque acts as the foces ae tying to pull the coil apat athe than tun it. The foce is paallel to the coil, athe than pependicula to it. 11 C. Revesing the diection of the cuent in the loop will ensue that the loop keeps tavelling in the sae diection. Use the ight-hand ule to veify this. 1 The coutato s function is to evese the cuent diection in the coil evey half tun to keep the coil otating in the sae diection. 1 Electons ae eleased fo a negative teinal o hot cathode of the evacuated tube and acceleate towads a positively chaged anode. They can be detected as they hit a fluoescent sceen at the ea of the tube. The electons ae acceleated by a high potential diffeence between the cathode and positively chaged anode. 14 v qv ( ) 19 ( ) s 1 15 v a The electon will expeience a foce at ight angles to its otion. This acts upwads in the initial oent and causes the electon to cuve in an upwads ac fo its stating position. b The adius of the electon path is dependent upon its velocity and the agnitude of the agnetic field that is acting. 17 a The stength of the electic field between the chaged plates is given by: E V d V 1 b Because the stength of the electic and agnetic fields is balanced, you can say that: F B F E qvb qe v E B s 1

11 18 v qv (( ) ( )) v s 1 B v q adius 1 diaete B T 0 a F qvb N b v