Discover the answer to this question in this chapter.

Transcription

1 What are the apparent eight (agnitude and direction) and the nuber of g s eperienced by a 70 kg fighter pilot hen his aircraft is catapulted fro an aircraft carrier knoing that the plane accelerates up to a speed of 77 /s (150 knots) over a distance of 94.5 (on the USS Niitz)? coons.ikiedia.org/iki/file:us_navy_ n-4166b-033_an_f-a- 18_Hornet_attached_to_the_Warhaks_of_Strike_Fighter_Squadron_(VFA)_97_conducts_a_touch_and_go_landing_and_takeof f_aboard_the_niitz-class_aircraft_carrier_uss_abraha_lincoln_(cvn_72).jpg Discover the anser to this question in this chapter.

2 The starting point of Einstein s general relativity is the equivalence principle. To illustrate this principle, consider the to situations shon in the folloing figure. In the figure to the left, Joe is enclosed in a bo placed on the surface of the Earth. In the figure to the right, Bob is enclosed in a bo in space, far fro any large asses. This bo accelerates in the direction indicated in the figure ith an acceleration of 9.8 /s². thinkingscifi.ordpress.co/2012/07/21/intelligence-and-iagination/ The equivalence principle says that everything that happens in the boes ust be absolutely identical for Bob and Joe. For eaple, consider hat happens if Bob and Joe both drop a ball. When Joe drops his ball, the gravitational force akes the ball fall to the ground ith an acceleration of 9.8 /s². When Bob drops his ball, there is no longer any force acting on the ball, and it stops accelerating hile the Bob bo s continues to accelerate upards. To siplify, suppose that the speed of the bo is zero hen Bob drops his ball. The resulting otion of the ball and the bo is shon in the folloing figure version 7 Apparent Weight 2

3 The ball stays in place since no force acts on it hile Bob s bo accelerates upards. Fro inside the bo, Bob has the ipression that the ball is oving donards ith an acceleration of 9.8 /s². In fact, the otion of the ball observed by Bob is identical to the otion of the ball seen by Joe. The equivalence principle also eans that if you are locked inside a bo and observe objects accelerating toards to the botto of the bo, it is ipossible to kno if this happens because there is a gravitational force or because you are inside an accelerating bo. No eperient can help you deterine if you are on Earth or accelerating at 9.8 /s². If everything is eactly the sae for Bob and Joe, then Bob ust feel a eight sensation eactly identical to the eight sensation felt by Joe due to attraction of the Earth. As Joe feels a force directed toards the floor, Bob ust also feel a force directed toards the floor, so in direction opposite to the acceleration. Also, if the gravitational force is proportional to the ass, then the effect on Bob ust also be proportional to Bob s ass. Thus, the agnitude of this eight sensation on Bob ust be a version 7 Apparent Weight 3

4 If a person accelerates hile a gravitational force acts on hi, then the eight sensation is just the su of these to effects. This su is the apparent eight. Apparent Weight g + a app ( ) To understand the eaning of this equation, let s look at hat happens hen a person (e ll call hi Tony) take an elevator to go up a fe floors. When the elevator begins its otion, it accelerates upards, Then, a eight sensation directed donards is added to the donards sensation ade by the gravitational force, and Tony feels heavier..u1.eiu.edu/~cfadd/1150/05ucmgrav/wt.htl When the elevator reaches its destination, it slos don and accelerates donards. Then, a eight sensation directed upards is added to the donards sensation ade by the gravitational force, and Tony then feels lighter. To calculate the apparent eight, the and y-coponents of this equation ill be used. The coponents of this equation are (ith a horizontal -ais and a y-ais directed upards) Apparent Weight (in Coponents) app app y a g a y ith a horizontal -ais and a y-ais directed upards 2018 version 7 Apparent Weight 4

5 Coon Mistake: Using the Wrong Aes to Calculate the Coponents of the Apparent Weight. The coponent equations obtained ere ade for a y-ais pointing upards and a horizontal -ais. You cannot rotate these aes. Using Neton s second la, another forula can also be obtained to calculate the apparent eight. This leads to app g + ( a) app g + F ( ) Apparent Weight app F g ( ) This forula says that the apparent eight can be calculated ith the su of the forces acting on the object, ithout considering the gravitational force. The apparent eight is then equal to the su of these forces but in the opposite direction. This is hy soe physicist defines the apparent eight as the force that ust be eerted on the object to support it. In coponents, still using the sae aes, this last equation is Apparent Weight (in Coponents) app app y F F g y ith a horizontal -ais and a y-ais directed upards Coon Mistake: Putting Nubers in the g + a or ( ) Equations app ( F g) These equations are vector equations. Thus, the correct anser is rarely obtained by directly substituting the values of g, a and F into these equations. You ust ork ith the and y-coponents of these equations. app 2018 version 7 Apparent Weight 5

6 According to this last equation, the change of apparent eight can be easured by standing on a scale in an elevator. Then, there is only one force acting on the person if the eight is ecluded: the noral force directed upards. This eans that the noral force has the sae agnitude (but opposite direction) as the apparent eight in such a case since F g app y y ( ) g + F g F N As a scale easures the contact force beteen the person and the scale (hich is the noral force), the change of apparent eight can be seen on the scale. The value indicated by the scale change at the start and at the end of the elevator ride (so hen there is an acceleration), as shon in this clip. It is often useful to copare the apparent eight to the actual eight on Earth to give a better idea of the sensation of eight. With the ratio of the agnitude of the apparent eight of the actual eight, the nuber of g s eperienced is obtained. (This is usually called the g-force. This is a bad nae since it is not a force. The ter nuber of g s ill therefore be used here.) Nuber of g s (n g ) N n g app app actual on Earth 9.8 s ² Thus, if a person eperienced 1.2 g s, then the person feels 1.2 ties heavier than noral. Eaple What are the apparent eight and the nuber of g s eperienced by a 60 kg person in an elevator in the folloing situations? a) The elevator is oving upards at a constant speed. The only thing that can change the apparent eight is an acceleration. Since the acceleration is zero here, the apparent eight is equal to the eight version 7 Apparent Weight 6

7 g 60kg N app y s² Therefore, the apparent eight is 588 N directed donards. The nuber of g s eperienced is n g 588N 1 588N Thus, the person feels like its eight is the sae as its noral eight on Earth in an elevator oving at constant speed. b) The elevator is accelerating upards at 2 /s². The apparent eight is g a app y 60kg kg 2 s² s² 708N Therefore, the apparent eight is 708 N directed donards. The nuber of g s eperienced is y n g 708N N Therefore, the person in this elevator feels like its eight is ties its noral eight on Earth. It is this kind of feeling that e get in an elevator that begins its upards otion (hich, therefore, accelerates upards). c) The elevator is accelerating donards at 2 /s². The apparent eight is g a app y ( ) 60kg kg 2 s² s² 468N Therefore, the apparent eight is 468 N directed donards. The nuber of g s eperienced is 2018 version 7 Apparent Weight 7 y

8 n g 468N N The person in this elevator thus feels like its eight is equal to ties its noral eight on Earth. It is this kind of feeling that e get in an elevator that stops its upards otion (hich, therefore, accelerates donards). d) The elevator is accelerating donards at 9.8 /s². The apparent eight is g a app y ( ) 60kg kg 9.8 0N There is no apparent eight. The nuber of g s eperienced is y s² s² n g 0N 0 588N The person in this elevator thus feels like he has no eight. It is this kind of feeling that e ould get is in an elevator hose cable breaks and oves donards in free-fall. The person in this elevator has the ipression that there is no gravity and floats freely in the elevator (up to the oent the elevator arrives at the botto of the elevator shaft )..u1.eiu.edu/~cfadd/1150/05ucmgrav/wt.htl e) The elevator is accelerating donards at 15 /s². The apparent eight is g a app ( ) 60kg kg 15 s ² s ² 312N The apparent eight is therefore 312 N directed upards (since it is positive). The nuber of g s eperienced is y 2018 version 7 Apparent Weight 8

9 n g 312N N The person in this elevator, therefore, feels like its eight is equal to ties the eight he norally has on Earth but directed upards. Therefore, this person alk on the ceiling of the elevator. (Note there is a rope that pulls the elevator don, because its acceleration cannot eceed 9.8 /s² if only the gravitational force is pulling the elevator don.).u1.eiu.edu/~cfadd/1150/05ucmgrav/wt.htl Eaple What is the nuber of g s eperienced by a person in a rocket at takeoff if the acceleration of the rocket is 6 /s² directed upards? The apparent eight is ( ) g a g + a app y y y It is ipossible to calculate the apparent eight because the ass of the astronaut is not knon. Despite this, the nuber of g s can be found. n g app g ( ay ) g + g ( g ay ) + ( ) 1.61 g s² s² 9.8 s² 2018 version 7 Apparent Weight 9

10 Eaple What are the apparent eight (agnitude and direction) and the nuber of g s eperienced by a 70 kg fighter pilot hen his aircraft is catapulted fro an aircraft carrier knoing that the plane accelerates up at a speed of 77 /s (150 knots) over a distance of 94.5 (on the USS Niitz)? The to coponents of the apparent eight are app app y a.fas.org/progras/ssp/an/uspns/air/fighter/f18.htl g To calculate the -coponent, the acceleration ust be knon. As it is knon that the speed changes fro 0 to 77 /s over a distance of 94.5, the acceleration is 2 a ( ) v v ( ) 2 a ( ) 77 / s 0 a 31.4 Therefore, the coponents of the apparent eight are a 70kg N s² app s² g 70kg N app y s² 2 The agnitude of the apparent eight is N 2 2 app app app y The direction of the apparent eight is app y θ arctan app 2018 version 7 Apparent Weight 10

11 The folloing figure illustrates this direction. The pilot feels a eight directed toards the back of the plane and a bit donards. The nuber of g s eperienced by the pilot is n g app g 2302N N The pilot feels 3.36 ties heavier than noral. Pilots can eperience a large nuber of g s during high acceleration aneuvers such as very tight turns. Therefore, they ust be able to ithstand large g-forces, a rather difficult thing to do. For eaple, if a person eperiences 5 g s directed upards, the blood in his bodies accuulates in the legs, thereby depriving the brain of blood. This could result in loss of consciousness hich is not a good thing if this happens hile you are piloting a jet fighter. To ithstand a high nuber of g s and, therefore, be able to ake tighter turns, special pants that squeeze the legs hen there is a substantial acceleration ere developed. By squeezing the legs, these pants prevent the blood fro accuulating in the loer part of the body. The pilot can also ithstand even ore g s if he contracts his leg uscles at the sae tie to squeeze to blood out. Aspiring Aerican pilots ust pass a test before becoing actual fighter pilots. They ust ithstand 9 g s for 10 seconds. They have only to chances to pass the test, otherise, they are rejected. Here are soe of these pilots. To reach the high nuber of g s shon in previous clips, pilots are placed in a centrifuge. Essentially, they sit in a bo aking a circular otion at the end of a long bea. As there is an acceleration in a circular otion, the apparent eight increases. If the bo rotates 2018 version 7 Apparent Weight 11

12 faster, the acceleration is larger, and the apparent eight also gets larger. Here is a centrifuge of this type in action. Eaple A centrifuge ith a 5 radius rotates ith a 1.5 second period. What is the nuber of g s eperienced by the person in the centrifuge? Here, the acceleration is directed toards the negative -ais. The to coponents of the apparent eight are app app y a g The agnitude of the apparent eight is app ( ) ( ) 2 2 g + a The agnitude of the acceleration ust be found. In a unifor circular otion, it can be found ith a 2 4π r 2 T 2 4π 5 2 (1.5 s) s² Even if the ass of the person is not knon, the nuber of g s eperienced can be found version 7 Apparent Weight 12

13 n g app g 9.01 ( g) + ( a ) g 2 2 g + a g ( + ) g a g g + a 2 2 g ( 9.8 ) + ( ) 2 2 s² s² 9.8 s² As soon as there is a circular otion, the apparent eight is different fro the actual eight, because there is an acceleration. This is indeed happening to us right no: our apparent eight is not g because of the rotation of the Earth. Eaple What is the nuber of g s eperienced by a person at the equator? The agnitude of the apparent eight is g a app y y spaceplace.nasa.gov/geo-orbits/en/ The acceleration of the person ust be found to deterine the nuber of g s. As the person akes on rotation ith a radius of 6380 k in 24 h (actually a little less), the centripetal acceleration toards the centre of the Earth is a y ( ) π 4π r T ( 86, 400s) s² The nuber of g s eperienced is therefore 2018 version 7 Apparent Weight 13

14 n g app g g a g g a g ( ) y y s² s² 9.8 s² Thus at the equator, a person feels like its eight is only 99.65% of hat it ould be if he ere at the pole (here there is no acceleration due to the Earth s rotation). It can be noted that it is possible that the eight sensation due to the acceleration copletely cancels the eight sensation due to gravity, as it as the case ith the freefalling elevator. Then the apparent eight becoes zero and the people then float as if there ere no gravity. These people are in a state of eightlessness. In fact, as soon as a person accelerates donards ith the sae acceleration as the acceleration due to gravity, the apparent eight becoes zero. Of course, this includes all free-fall otion. This is hat is happening to the astronauts in the space station. Since the space station in orbit around the Earth, it is endlessly free-falling toards Earth. Thus, the acceleration of the space station is the sae as the acceleration due to gravity, and the apparent eight of the astronauts is zero. Coon Mistake: Thinking that the Force of Gravity Acting on Astronauts in Orbit is Zero. It is not the eight (the force of gravity) that is zero; it is the apparent eight. Actually, the eight of the astronauts in orbit is barely less than hat it is on Earth. Moreover, if the eight ere zero, there ould be no force acting on the astronauts, and they could not ake a circular otion around the Earth because there ould be no centripetal force. There is no need to be in the space station to be in a state of eightlessness; you just have to accelerate donards ith an acceleration of 9.8 /s². Obviously, you can lock yourself in a free-falling bo, but there are a fe probles: the drag force that ill reduce the 2018 version 7 Apparent Weight 14

15 acceleration and, obviously, the ipact ith the ground. It is safer to do this free-falling otion in a plane folloing a parabolic path. en.ikipedia.org/iki/reduced_gravity_aircraft The top curved part of the trajectory is a parabola, the sae parabola that ould follo a free-falling object. This eans that for about 25 seconds, the plane has a 9.8 /s² donards acceleration and the apparent eight becoes zero during this part of the trajectory. Here is a video shoing the occupants of an aircraft aking such a trajectory. You can even do it as a tourist or in your on private plane. The direction of the apparent eight is iportant because it indicates in hat direction a person feels attracted. It can also be noted that: 1 Hanging objects align theselves ith the direction of the apparent eight. 2 Liquid surfaces are perpendicular to the direction of the apparent eight version 7 Apparent Weight 15

16 This latter effect can be seen in this video shoing ho the orientation of the surface of a liquid changes in a car in a curve. Proof for the Pendulu The deonstration that the pendulu ust be in the direction of the apparent eight at equilibriu can easily be ade. If the apparent eight forula ( ) app F g is applied for the pendulu, the result is quite siple. Without the eight, the only force that reains is the tension of the string. Therefore app T As the tension is in the sae direction as the string, the string ust be in the opposite direction to the apparent eight, as stated. Proof for Liquid Surfaces In a Non-Accelerating Liquid Assue that an object is in equilibriu in a liquid. This eans that the eight is equal to the buoyant force. (It could be a very thin balloon filled ith ater.) 2018 version 7 Apparent Weight 16

17 In this case, the pressure increases ith depth in the liquid. The higher pressure belo the object creates the buoyant force directed upards. In this case, the buoyant force is F g B Lines indicating the locations here the pressure is the sae can be dran. Of course, these lines ust be perpendicular to the vector shoing the direction of the pressure increase. The surface of the liquid ust atch a constant pressure line (ith a pressure equal to the atospheric pressure). If the pressure as not constant along the surface, a force parallel to the surface ould force the ater to ove. The ater ould then ove until the pressure is the sae everyhere on the surface. Thus, the surface is horizontal hen the ater does not accelerate. In an Accelerating Liquid If the liquid and the object in the fluid accelerates toards the right, the situation shon in the figure is obtained. The only force that can accelerate the object toards the right is the buoyant force as the eight is alays vertical. This eans that the buoyant force ust no be in the direction indicated in the figure. Then, the su of forces is This eans that F g a B ( ) g + F a 2018 version 7 Apparent Weight 17 B

18 As the ters in parenthesis is the apparent eight, the folloing result is obtained F B First, this result shos that the direction of the buoyant force is no in a direction opposed to the apparent eight. In addition, hen the agnitude of the buoyant force is copared ith buoyant force hen there is no acceleration, the result is app F F B ith acceleration B ithout acceleration app n g This eans that the agnitude of the force is ultiplied by the nuber of g s. Thus, a ore general version of buoyant force can be given. Buoyant Force (F B ), Better Version 1) Magnitude of the force 2) Direction of the force F ρn 9.8 N V B g kg f here ρ is the density of the fluid n g is the nuber of g s eperienced by the object and V f is the volue occupied by the object in the fluid. In a direction opposed to the apparent eight..boundless.co/physics/fluids/density-and-pressure/pressure/ 3) Application point of the force Distributed all over the surface of the part of the object that is in the fluid. (Here, the point of application can be set at the centre of the part of the object that is in the fluid.) A buoyant force in this direction eans that the pressure is greater in the place shon in the figure. To have a higher pressure there, the pressure ust increase in the direction of the apparent eight version 7 Apparent Weight 18

19 As equal pressure surfaces are alays perpendicular to the direction of the pressure increase and the pressure increase is in the direction of the apparent eight, the surface of constant pressure ust be perpendicular to the apparent eight. As the surface of the liquid is a constant pressure surface, it follos that the surface of the liquid ust be perpendicular to the apparent eight. The to previous proofs sho that everything happens eactly as if there ere a gravitational force in the direction of the apparent eight. This is hat e are supposed to have since the effect of acceleration is indistinguishable fro the effect of gravity. Eaple A glass of ater is firly fied on a table in a plane taking off. If the ater surface is oriented as shon in the figure, hat is the acceleration of the plane? Let s start by finding the angle of the surface. According to the figure to the left, this angle is 2 θ arctan This angle is also the angle beteen the vertical and the apparent eight as can be seen in the figure to the right. The angle beteen the apparent eight and the positive -ais is thus ( ) The coponents of the apparent eight are app app y a g The acceleration can be found ith the vector direction forula version 7 Apparent Weight 19

20 tanθ g tanθ a s² ( ) tan a 6.53 app y app s² 9.8 a Eaple In hat direction is the apparent eight of this singing co if there is no drag? At first glance, it sees that the solution to this proble ill be quite coplicated if e try to solve it ith g + a app ( ).clipartof.co/portfolio/djart/illustration/co-elephantand-pig-singing-together-on-a-playground htl Since the acceleration coes fro a centripetal acceleration and a tangential acceleration, the total acceleration is not easy to find. Hoever, the solution is uch sipler if the forula ith the su of the forces is used. app F g ( ) This forula tells us that the apparent eight is in the opposite direction of the su of the forces, ithout considering the force of gravitation. As here there is only one force (the tension force) if the force of gravitation is ecluded, the apparent eight is in the opposite direction to the tension force. The direction of the apparent eight is then shon is the figure. If this co could hold a glass of ater (if it had fingers), the surface of the ater ould alays be perpendicular to the direction of the rope version 7 Apparent Weight 20

21 Without training, 3 or 4 g s can quickly becoe uncofortable. The displaceents of fluids in the body that deprive the brain of blood, and the uscle effort required to stay in place can quickly ehaust soeone. As racing drivers can eperience up to 5 g s in very fast curves, they ust do a lot of training to be able to ithstand these high nubers of g s. You already kno that fighter pilots can ithstand 9 g s for 10 seconds ith a lot of efforts. But can a huan body ithstand ore than that? During the 40 s and 50 s, John Stapp sought to anser this question ith a series of tests in hich he eperienced an increasingly large nuber of g s. Here is one of these tests. Stapp survived a 46.2 g s test. Since he had his head forard in this test, blood accuulated in his head. This shattered the capillaries in his eyes, thereby filling his eyes ith blood and aking hi blind for a fe days. If the acceleration lasts for a very short period, fluids do not have tie to ove and no uscular effort is required to stay in place. Then, it is possible to ithstand uch larger g-forces. It is not uncoon for people to survive car crashes hile eperiencing up to 50 g s. Over 50 g s, serious injury ay occur but is it possible to survive a 100 g s crash. Kenny Bräck even survived this accident in hich he eperienced, during a very short tie, 214 g s! (We kno this because there are acceleroeters in race cars.) Bräck returned to racing 2 years later but he as not quite the sae pilot. Apparent Weight app g + ( a ) app F g ( ) Apparent Weight (in Coponents), First Forula app app y a g a y ith a horizontal -ais and a y-ais directed upards 2018 version 7 Apparent Weight 21

22 Apparent Weight (in Coponents), Second Forula app app y F F g y ith a horizontal -ais and a y-ais directed upards Nuber of g s (n g ) n g app app actual on Earth 9.8 s ² Buoyant Force (F B ), Better Version 1) Magnitude of the force 2) Direction of the force F ρn 9.8 N V B g kg f here ρ is the density of the fluid n g is the nuber of g s eperienced by the object and V f is the volue occupied by the object in the fluid. In a direction opposed to the apparent eight. 3) Application point of the force.boundless.co/physics/fluids/density-and-pressure/pressure/ Distributed all over the surface of the part of the object that is in the fluid. (Here, the point of application can be set at the centre of the part of the object that is in the fluid.) 2018 version 7 Apparent Weight 22

23 7.2 Apparent Weight ith Rectilinear Accelerations 1. Karl, hose ass is 70 kg, is in a rocket. At takeoff, the rocket has a 6 /s² acceleration directed upards. a) What is Karl s eight (agnitude and direction)? b) What is Karl s apparent eight (agnitude and direction)? c) What is the nuber of g s eperienced by Karl?.einstein-online.info/spotlights/geoetry_force 2. Karl, hose ass is 70 kg, is in a rocket. This tie, the rocket takes off vertically fro the surface of the Moon (here g is only 1.6 N/kg). At takeoff, the rocket has a 6 /s² acceleration directed upards. a) What is Karl s eight (agnitude and direction)? b) What is Karl s apparent eight (agnitude and direction)? c) What is the nuber of g s eperienced by Karl?.einstein-online.info/spotlights/geoetry_force 3. White Zobie is a odest-looking electric car, but it is capable of soe etraordinary perforances. theelectricautorevie.co/2010/03/25/electric-drag-racing-hite-zobie/ It can reach a speed of 100 k/h in only 1.8 s, leaving cars such as Ferraris far behind. Assuing that the acceleration is constant, hat is the nuber of g s eperienced by the driver during this acceleration? 2018 version 7 Apparent Weight 23

24 4. Karl, hose ass is 70 kg, is in a rocket. Shortly after liftoff fro Earth, the rocket has an acceleration of 6 /s² in a direction at 30 ith the vertical. a) What is Karl s apparent eight (agnitude and direction)? b) What is the nuber of g s eperienced by Karl?.einstein-online.info/spotlights/geoetry_force 7.3 Apparent Weight in Circular Motion 5. Odette, hose ass is 120 kg, is in a roller-coaster cart folloing the track shon in this figure..chegg.co/hoeork-help/questions-and-ansers/physics-archive-2011-noveber-02 a) What are the apparent eight and the nuber of g s eperienced by Odette hen the carriage is at point A if the speed of the carriage is 25 /s at this location? b) What are the apparent eight and the nuber of g s eperienced by Odette hen the carriage is at point B if the speed of the carriage is 10 /s at this location? 6. What should be the period of rotation of the Earth so that the apparent eight of a person vanishes at the equator? (Use 6378 k for the radius of the Earth.) 2018 version 7 Apparent Weight 24

25 7. Juliet, hose ass is 60 kg, is in a plane folloing this path at a constant speed..physics.fsu.edu/users/ng/courses/phy2053c/hw/ch05/ch05.ht a) What is Juliet s apparent eight (agnitude and direction)? b) What is the nuber of g s eperienced by Juliet? 8. Victor, hose ass is 50 kg, is on a roller-coaster ride. Soehere on the track, there is a loop as shon in this figure. cn.org/content/42086/latest/?collectioncol11406/latest At the top of the loop, the radius of curvature of the track is 10. What should be the speed of the carriage so that Victor has an apparent eight directed upards hose agnitude equals tice the agnitude of its eight? 2018 version 7 Apparent Weight 25

26 9. This forula 1 driver is eperiencing 4 g s in this curve hen the speed of the race car is 180 k/h. What is the radius of curvature of the track? digitalcatharsis.ordpress.co/tag/crone-plaza-hotel/ 10. To avoid ending up in eightless conditions in space, it as proposed to build a rotating space station ith this shape..rogersrocketships.co/page_vie.cf?id24 With the rotation of the station, astronauts ake a circular otion that gives the an acceleration and, therefore, an apparent eight. Astronauts ould alk on the outer all of the station as shon in this figure version 7 Apparent Weight 26

27 .batesville.k12.in.us/physics/phynet/mechanics/circular%20motion/ansers/assign_4_ansers.ht With the diensions shon in the figure, hat should be the period of rotation of the station so that peoples in the station have an apparent eight equal to their eight on Earth if this station is in space, far fro any planets or stars? 7.5 Direction of the Apparent Weight 11. What is the period of rotation of this ride that is rotating at constant speed?.chegg.co/hoeork-help/questions-and-ansers/popular-carnival-ride-consists-seats-attached-central-disk-cablespassengers-travel-unifor-q version 7 Apparent Weight 27

28 12. The surface of the ater in this glass is tilted at 20..foundalis.co/phy/Mach-bucket.ht What ould be the angle of inclination of the ater surface if the glass as 6 c fro the ais of rotation and the plate is still rotating ith the sae period? Challenges (Questions ore difficult than the ea questions.) 13. A 350 g block of cedar having a 400 c³ volue is tied to the botto of a container filled ith ater as shon in the figure. This container is in a car that accelerates to the right ith an acceleration of 2 /s²..chegg.co/hoeork-help/questions-and-ansers/physics-archive-2012-june-15 a) What is the buoyant force (agnitude and direction) on this block of cedar? (the density of ater is 1000 kg/³) b) What is the tension of the rope? c) What is the angle θ in this figure? 2018 version 7 Apparent Weight 28

29 14. There is soe ater in a spinning container. The period of rotation is T. What is the equation y f() of the shape traced by the surface of the ater? (In other ords, e re looking for a forula that gives the height of the ater as a function of the distance fro the ais of rotation.).eploratoriu.edu/snacks/ater-spinner 7.2 Apparent Weight ith Rectilinear Accelerations 1. a) 686 N donards b) 1106 N donards c) a) 112 N donards b) 532 N donards c) a) N at -101,3 b) Apparent Weight in Circular Motion 5. a) 8676 N donards, n g b) 376 N donards n g in 7. a) 162 N upards b) /s s 2018 version 7 Apparent Weight 29

30 7.5 Direction of the Apparent Weight s Challenges 13. a) 4 N at b) 0.5 N c) π 14. y + y 2 0 (It s a parabola) gt 2018 version 7 Apparent Weight 30