Sometimes people say that water is removed from clothes in a spin dryer b 6 adoewxz3xdi,/2 k xoi.9c0yy centrifugal force throwing 2.i xde/ xa0d oykczx3wi9,6othe water outward. What is wrong with this statement?

Will the acceleration of a car be the same when the car travel;orz h4;hfa,y s around a sharp curve at a constant 60 km/h as when it4rzh y,fo;ah; travels around a gentle curve at the same speed? Explain.

Suppose a car moves at constant speed along a hz9.fyb/5 o psuilly road. Where does the car exert the greatesp.fu bz5y9 o/st and least forces on the road: (a) at the top of a hill, (b) at a dip between two hills, (c) on a level stretch near the bottom of a hill?

Describe all the forces acting on a child. dtk0+ pwvo;b riding a horse on a merry-go-round. Which of these forces provideswt.dv +;0k obp the centripetal acceleration of the child?

A bucket of water can be whi8n pg2zvg yha3 u2sf26rled in a vertical circle without the water spilling out, even at the top of the circle when ypg f g23hvu2n26z8s athe bucket is upside down. Explain.

How many “accelerators” do you h b *164zxp sinr3i/raaave in your car? There are at least three controls in the car which can be used to cause the car to accelerate. Whrp4*axrsia 1n6 b z/i3at are they? What accelerations do they produce?

A child on a sled comes flying over the crest:g(bc: ,droqe of a small hill, as shown in Fig. 5–31. His sled does not leave the ground (he does not achieve “air”), but he feels the normal force between his chest and the sled decrease as he goes over the hill. Explain this decrease using Newton’s secooc(e: ,gdr:b qnd law.

Why do bicycle riders lean inward when roh3dxb8*uubn(i/3 5z y zvnh8xunding a curve at high speed?

Why do airplanes bank when they tuoj pu* 31uen/k 2+zu/ swexej)rn? How would you compute the banking angle given its speed and rao nuszj)pw 2/j/e3ee*1kxu+u dius of the turn?

A girl is whirling a ball on qo-x8s v xpj95l.3fof a string around her head in a horizontal plane. She wants to let go at precisely the right time so that the ball will hit a target on the other side of the yard. When should she let go of the ss f3-f5lxvq o8 j9x.optring?

Does an apple exert a gravitational forcewcbgk (qv)i: 9 on the Earth? If so, how large a force? Con:ibw( )9kqvcgsider an apple
(a) attached to a tree, and (b) falling.

If the Earth’s mass were double what it is, in what ways wob8swuq9tf3hfd/zk: 3 ok ba4 8jwg9op+*-yc iuld the Moon’s orbit be different?/ o 8ck49ujqhgo +3zbf -p*8f:ytbsk9daw3i w

Which pulls harder gravitationally, the ;0gx -l q+avz-ni zdt:5bv v1cEarth on the Moon, or the Moon on the Earth? Which accelerates1 v:-q d-g;5v+0bixanz ztcv l more?

The Sun's gravitational pull on the Earth is much larger than the Moon's. iqn u(tjv qz4 r9wej0b.*,qu6 Yet the Moon's is mainly re6ti4wqv*qj n0.u r u 9bz,j(qesponsible for the tides. Explain. [Hint: Consider the difference in gravitational pull from one side of the Earth to the other.]

Will an object weigh more at the equator or at the poles? What two effects aksaut0r7:g )c re at work? Do they oppua t csr:kg0)7ose each other?

The gravitational force on the Moon due to the Ea9c8pfim2 f,a brth is only about half the force on the Moon92cp,af fimb8 due to the Sun. Why isn’t the Moon pulled away from the Earth?

Is the centripetal acceleratione/ry 7u -pr .p-tpomg; of Mars in its orbit around the Sun larger or smaller than the centripetal acceleration of the Ear-ppu.r;g- op etm 7/ryth?

Would it require less speed to launch a satellite (a) tow,nxg;ky0n k 1oard the east or (b) toward the west?n;x kk ,yng10o Consider the Earth’s rotation direction.

When will your apparent weight be the greatest, as measured by a us7o )sot.g4uy,7v qqscale in a moving elevator: when the elevator (a) accelerates downward, (b) accelerates upward, (c) is in free fall, (d) moves upward at constant speed? In which case would your ws o7 vuo7yt,)g4qsu.qeight be the least? When would it be the same as when you are on the ground?

What keeps a satellite up in its orbit around theEarth?

Astronauts who spend long periods in out 1 o;fniy, 07 is vd04elym5:pgb+tqdfer space could be adversely affected by weightlessness. One way to simulate gravity is to shape the spaceship like a cylindrical shell that rotates, with the astronauts walking on the inside surface (Fig. 5–32). Explain how this simulates gravity. Consider (a) how objects fall, (b) the force we feel on our feet, and (c) any other aspects of gravity you can think01 7;efifyl 0st+p dvqnm ,yi5gd:ob4 of.

Explain how a runner experiences “free fall” or “apparent weightlessness” bet.pfu56x l/rir a mk-6sween step ua-lpx6smi 6rk5 f/r.s.

The Earth moves faster i2 5ov0;u ckn hzvcn1h3n its orbit around the Sun in January than in July. Is the Earth closer to the Sun in January, or in July? Explain. [Note: Thvc12 k ;nzhcv5 o03unhis is not much of a factor in producing the seasons — the main factor is the tilt of the Earth’s axis relative to the plane of its orbit.]

The mass of Pluto was not known un l5j,b(lfw6s e7g2 jkotil it was discovered to have a moon. Explain how this discovery enabled an 5so,( wkljb6 l ej27fgestimate of Pluto’s mass.

  The Sun's gravitational pull on a2pb 1bipu.p8the Earth is much larger than the Moon's. Yet the Moon's is mainly responsible pbb2pu8a1p i.for the tides. Explain. [Hint: Consider the difference in gravitational pull from one side of the Earth to the other.]A child sitting 1.10 m from the center of a merry-go-round moves with a speed of 1.25 $\mathrm{~m} / \mathrm{s}$ . Calculate (a) the centripetal acceleration of the child,   
(b) the net horizontal force exerted on the child ( mass =25.0 $\mathrm{~kg}$)   

  A jet plane traveling 8/k x-)pe8;h* 2l4opp mf.xmnsvo2e9mv k mb n 1980 $\mathrm{~km} / \mathrm{h}(525 \mathrm{~m} / \mathrm{s})$ pulls out of a dive by moving in an arc of radius 6.00 km . What is the plane's acceleration in $g^{\prime}$ 's?    g's

  Calculate the centripetal acceleration of the Earth in its o78nc)owkwu,h rbit around the Sun, and the net force exerted on the Earth. What exerts this force on then , u)w8kow7hc Earth? Assume that the Earth's orbit is a circle of radius 1.50$ \times 10^{11} \mathrm{~m}$ . [Hint: see the Tables inside the front cover of this book.]    $\times10^{22}$

  A horizontal force ofvp0n ;:ac5xjcv-lsnro , w +z1 210 N is exerted on a 2.0-kg discus as it rotates uniforml : lcrnaspo x;cv5j1 z+wn-v,0y in a horizontal circle (at arm’s length) of radius 0.90 m. Calculate the speed of the discus.   

  Suppose the space shuttle is in orbit 400 km from the E;- ph(b1gco xue(u*wm arth's surface, and circles the Earth about once every 90 minutes. Find the centripetal acceleration of the space shuttle in its orbit. Express your answer in terwocp1m;*u(-egh(bx u ms of g , the gravitational acceleration at the Earth's surface. $\approx$    g

  What is the magnitude of the acceleration of a speck of clay on the vtyk-ll)ac ;( edge of a potter’s wheel turning at 45 rpm (revolutions per minute) if the wheel’s diametvkytlal;(-c )er is 32 cm?   

  A ball on the end of a string is revolved at a uniform rate in a vertical circl poi,9y vg kj*+hx4mm(( rcoi6e of radius 72.0 cm , as shown in Fig. 5-33. If its spee ,+y j6*rp4xkoo v (mi9(hgimcd is 4.00 $\mathrm{~m} / \mathrm{s}$ and its mass is 0.300 kg , calculate the tension in the string when the ball is (a) at the top of its path   
(b) at the bottom of its path.   

  A 0.45$-\mathrm{kg}$ ball, attached to the end of a horizontal cord, is rotated in a circle of radius 1.3 m on a frictionless horizontal surface. If the cord will break when the tension in it exceeds 75 N , what is the maximum speed the ball can have?   

  What is the maximum speed with which a 1g-y cxmjf:)m:050-kg car can round a turn of radius 77 m on a flat road if the coefficient of my:fx :m cg)-jstatic friction between tires and road is 0.80? Is this result independent of the mass of the car?   

  How large must the coeffi;vs am8oq, asqlo8y*kg 4tk;e 9v hv-.cient of static friction be between the tires and the road it9ao4vkys8kam sv;*e,. oh qg8-l v;qf a car is to round a level curve of radius 85 m at a speed of 95km/h ?   

  A device for training astronau ywid .+hfsy lbg qt-p/6cu+02ts and jet fighter pilots is designed to rotate a trainee in a horizontal circle of radius 12.0 m . If the force felt by the trainee on her back is 7.85 times herh6+0 ld-/yb.g fp+wiq u2ycst own weight, how fast is she rotating?    rev/s    m/s
Express your answer in both $ \mathrm{m} / \mathrm{s}$ and $\mathrm{rev} / \mathrm{s}$ .

  A coin is placed 11.0 cm from the axis of aq53u y y63qis-r0slnc rotating turntable of variable speed. When the speed of the turntable is slowly increased, the coin remains fixed on the turntable until a rate of 36 rpm is reached and the coin sl0cr6-i5sl u3q3yqys n ides off. What is the coefficient of static friction between the coin and the turntable?   

  At what minimum speed must a roller coaster be tracea*9l6d 2/lg tlovt;veling when upside down at the top of a circlg2t ; 6el*/9vtocaldle
(Fig. 5-34) so that the passengers will not fall out? Assume a radius of curvature of 7.4 m .   

  (II) A sports car of mass 950 kg (including the driver) cro.8:fj87n a;e( 2hq hvjfk jcilsses the rounded top of a hill (radc a.l(; 2k8jqnhf7j fe:v8 jhiius =95$ \mathrm{~m}$ ) at 22 $\mathrm{~m} / \mathrm{s}$ . Determine
(a) the normal force exerted by the road on the car,   
(b) the normal force exerted by the car on the 72-kg driver   
(c) the car speed at which the normal force on the driver equals zero.   

  How many revolutions per minute would a 15-m-diam38w x4ideh )bhs j9nn.eter Ferris wheel need to make for thed8s xehh9i)n3w4nb .j passengers to feel “weightless” at the topmost point?    rpm

  A bucket of mass 2.00 kg is whirled in a vertv+ m/ s wg74ml+wso2soja)d7z ical circle of radius 1.10 m. At the lowest point of its motion the tension in the rope supporting the bucket is 25.0 N. /+dovo+sa7z jgs 4w)2sw l 7mm
(a) Find the speed of the bucket. $\approx$   
(b) How fast must the bucket move at the top of the circle so that the rope does not go slack?   

  How fast (in rpm) must a centrifuge rotate if a p,9 jy-adak6u farticle 9.00 cm from the axis of rotation is to ,j96afud ya-kexperience an acceleration of 115,000 $\mathrm{~g} $'s?    rpm

  In a "Rotor-ride" at a carnival, peopdweqe,ljt ,o 6z j6; fiv.r4m)le are rotated in a cylindrically walled "room." (See Fig. 5-35.) ewlq .;)f ,d6orzj6ejvtmi 4,
The room radius is 4.6 m , and the rotation frequency is 0.50 revolutions per second when the floor drops out. What is the minimum coefficient of static friction so that the people will not slip down? People on this ride say they were "pressed against the wall." Is there really an outward force pressing them against the wall? If so, what is its source? If not, what is the proper description of their situation (besides "scary")? [Hint: First draw the free-body diagram for a person.]   

A flat puck (mass M ) is rotated in a circle on a fr gzjm;/m,wso7 oqxn*:ictionless air-hockey tabl7zwq:gjx nm,oo;s/*m etop, and is held in this orbit by a light cord connected to a dangling block (mass m ) through a central hole as shown in Fig. 5-
36. Show that the speed of the puck is given by

$v=\sqrt{\frac{m g R}{M}}$

  Redo Example 5-3 , precisely this time, by not ignoring the we1v7. ugfyd*y/hu.g g 9h 9t 56ykwnhceight of the ball which revolves on a string 0.600 m long. In particular, find the mfhgk n9/dy . 5hutyu g1w69ey. v7hc*gagnitude of $\overrightarrow{\mathbf{F}}_{\mathrm{T}}$ , and the angle it makes with the horizontal. [Hint: Set the horizontal component of $\overrightarrow{\mathrm{F}}_{\mathrm{T}}$ equal to m $a_{\mathrm{R}}$ ; also, since there is no vertical motion, what can you say about the vertical component of $\overrightarrow{\mathbf{F}}_{\mathrm{T}}$ ?] $\overrightarrow{\mathbf{F}}_{\mathrm{T}}$ =    the angle =   

  If a curve with a radiuv7.zpza0b;38egl5k u-xy 9x o gqw3jcs of 88 m is perfectly banked for a car traveling 75 $\mathrm{~km} / \mathrm{h}$ , what must be the coefficient of static friction for a car not to skid when traveling at 95 $\mathrm{~km} / \mathrm{h}$ ?   

  A 1200$-\mathrm{kg}$ car rounds a curve of radius 67 m banked at an angle of 12$^{\circ}$ . If the car is traveling at 95$ \mathrm{~km} / \mathrm{h}$ , will a friction force be required? If so, how much and in what direction? $\approx$    down the plane

Two blocks, of massesnb n+/uw7nt90*ds*l.zbuo,q0kdi fr $ m_{1}$ and $m_{2}$ , are connected to each other and to a central post by cords as shown in Fig. 5-37. They rotate about the post at a frequency f (revolutions per second) on a frictionless horizontal surface at distances $r_{1}$ and $r_{2}$ from the post. Derive an algebraic expression for the tension in each segment of the cord.

  A pilot performs an evasive maneuver by diving ve+ q5 2gp1xkirjrtically at 310 $\mathrm{~m} / \mathrm{s}$ . If he can withstand an acceleration of 9.0 g 's without blacking out, at what altitude must he begin to pull out of the dive to avoid crashing into the sea?   

  Determine the tangential and 4xpacxc 9zsmmy,j;;0 centripetal components of the net force exerted on the car (by the ground) in Example 5-8 when imsc4y 9xc,pxza; j0 ;mts speed is 15$ \mathrm{~m} / \mathrm{s}$ . The car's mass is 1100 kg . F$_{tan}$ =    F$_R$ =   

  A car at the Indianapolis 500 accelerates uniformly from the pit area, going hzjp*vhn dy7/ys6x+ 2from rest to 320km/h in a semicircular arc with a radius of 220 m. Determine the tangential and radial acceleration of the car when it is halfway through the turn, assuming constant tangential acceleration. If the curve were flat, what would the coefficient of static friction have to be between the tires and the road to provide this acceleration with no slipping or skidding?dzp2h xyv/7nhy +j 6*s $\approx$   

  A particle revolves in a horizontal circle of radius 2.90 m uk0i*n * dwaj,k*7hspeais2zsq 7,)k . At a particular in)e*siz70q,pwnks i hkj2 ku,d*s*a7a stant, its acceleration is 1.05 $\mathrm{~m} / \mathrm{s}^{2}$ , in a direction that makes an angle of 32.0$^{\circ}$ to its direction of motion. Determine its speed (a) at this moment   
(b) 2.00 s later, assuming constant tangential acceleration.   

  Calculate the force of Earth’s gr*. hqodnl) 7uzavity on a spacecraft 12,800 km (2 Earth radii) above the Earth’s surface if h l*q7odzu) n.its mass is 1350 kg.   

  At the surface of a certain planet, oj7vg( wyv:1 uc 1 )rk1chuwv/the gravitational acceleration g has a magnitr1 w)7y c(go vj:u cukwhvv1/1ude of 12 m/s$^2$ A 21.0-kg brass ball is transported to this planet. What is (a) the mass of the brass ball on the Earth and on the planet   
(b) the weight of the brass ball on the Earth and on the planet? $W_{Earth}$   $W_{planet}$  

  Calculate the acceleration due to gravity on the Moon. The Moon's radius,a i3ww-rm,i hlpv1e5 is 1.71 ,- 3amvhielp i,5rww4 $\times 10^{6} \mathrm{~m} $ and its mass is 7.35 $\times 10^{22} \mathrm{~kg}$ .   

  A hypothetical planet has a radiklcwy4wp8 )dp;4xkj9 us 1.5 times that of Earth, but has the same mass. What is the acceleration dul8x)dkj4 cy ;p4p9wk we to gravity near its surface?   

  A hypothetical planet has a mass 1.66 times that of Earth, but the same radius3z.,ikprx 3i3 k*01m.oqu1sszst h jv. What is g nearzi, o03 sr11.js isu.k*ktpm33v qhxz its surface?   

  Two objects attract each other gravitationally with a force of m7 ejul d*+ht82.5$ \times 10^{-10} \mathrm{~N}$ when they are 0.25 m apart.
Their total mass is 4.0 kg . Find their individual masses. m$_1$ =    m$_2$ =   

  Calculate the effective value of g , the acceleration of gravity, j 75 hmnm(5wjhat (a) 3200 m ( w575mmhjjhn   , and (b) 3200 km    , above the Earth's surface.

  What is thedistance from the Earth’s center to a point outsideb l,puf9)7ir)c hdas6 the Earth where thegravitational7a)6ip)fl, 9 cudbhs r acceleration due to the Earth is $\frac{1}{10}$ of its value atthe Earth’s surface?   $\times10^7$

  A certain neutron star has five times the mass of our Sun packed wmb 92i ,ct9hninto a sphere about 10 km in radius. Estimate the surface gravity o9 hw,2cntmb 9in this monster.    $\times10^12$

  A typical white-dwarf star, we 4nf;(qmt c/znag5+ zhich once was an average star like our Sun but is now in the last stage of its evolution, is the size of our Moon but has the mass of our Sun. What is the surface+g(/ mq;z5 nzntf4c ae gravity on this star?    $\times 10^7$

  You are explaining why astronauts feel weightless while orbiting in the m 8q;2ssrx ccq *)m 3mh7dd)lsspace shuttle. Your friends respond that they thought gravity was just a lot weaker up there. Convince them and yourself that it isn’t so by calculating the acceleration 3s8q d;m7)q ld sxmhrcs) *2cmof gravity 250 km above the Earth’s surface in terms of g.   

  Four 9.5-kg spheres are located at the corners of a square oy 6/2e+ +eyrf5ocueq5uvlgpns4 ) cq9 f side 0.60 m. Calculate the magnitude and direction of the total gravitational force exerted on one oncs5cequp/ +uqeey2 9yrf)v65l g4+ sphere by the other three.   $\times 10^{-1} \mathrm{~N} \text { at }$    $^{\circ}$

  Every few hundred years most of the planets g(6 vjf9qn-2(l k;6csta pyw9 xcgfp0line up on the same side of the Sun. Calculate the total force on the Earth due to Venus, Jupiter, and Saturn, assuming all x6sk 0fcj9ngclt-q 9;(vwpyp6f 2g(a four planets are in a line (Fig. 5-38). The masses are $M_{\mathrm{V}}=0.815 M_{\mathrm{E}}, M_{\mathrm{J}}=318 M_{\mathrm{E}}, \quad M_{\mathrm{S}}=95.1 M_{\mathrm{E}}$ , and their mean distances from the Sun are 108,150,778 , and 1430 million km , respectively. What fraction of the Sun's force on the Earth is this? $F_{Earth-planets}$ =   $\times 10^{17}$ ${F_{Earth-plantes}}$ \ ${F_{Earth-sun}}$=    $\times 10^{-5}$

  Given that the acceleration of gravity at the surface of Mars is t+qz e xrm. x+st8fzi1l0rxbx9 3k7q- 0.38 of what it is on Earth, and that Mars’ radius is 3400 km, determine the mass ofq terxx-+3x8r10fqx+7 tk l zbmsiz9 . Mars.    $\times 10^{23}$

  Determine the mass of thga5a 93j*ku2dz:g nkce Sun using the known value for the period of the Earth and its distance from the Sun. [Note: Compare your answer t*kn2 ku:ag3 5d9ajgzco that obtained using Kepler’s laws, Example 5–16.]    $\times 10^{30}$

  Calculate the speed of a satellite moving in a stable circular orbit abeu6se4m(rk +8 fc4zwaout the Earw+u 4ma(e4 f8cs rkze6th at a height of 3600 km.    $\times 10^3$

  The space shuttle releases a satellite into a c e qpa-(+e9rgks8k;lfircular orbit 650 km above the Earth. How fast must th( kfe8 qk+la -;p9egsre shuttle be moving (relative to Earth) when the release occurs?    $\times 10^3$

  At what rate must a cylu n*q6 kyqt, 1u7iz,yeindrical spaceship rotate if occupants are to experience simulated gravity of 0.60 g? Assume the spaceship’s diameter is 32 m, and give ,uitqeu*1y7 y ,k6zqnyour answer as the time needed for one revolution. (See Question 21, Fig 5–32.)   

  Determine the time it takes for a satellite to7 cll if:0wlc3c )gzv8 orbit the Earth in a circular “near-Earth” orbit. A “near-Earth” orbit is one at a height above the surface of the Earth which is very small compared to the l8z)l0vgi3 7cccwf:l radius of the Earth. Does your result depend on the mass of the satellite?    s ~    min

  At what horizontal velocity would a satellite have to be launched from the topa p4v ch,7 q-k;,episb of Mt. Everest to be placed in a circuls b, 7iah4vepp,-kc; qar orbit around the Earth?   

  During an Apollo lunar landing,ffz -h:3l/vkgsao 7w h** tym mission, the command module continued to orbit the Moon at an altitude of about 100 km. How long did it take to go around the hhalsytm*vw o-g,:3/7 zf*kf Moon once?    s

  The rings of Saturn are composed of 9+ ydrtrmp; vq+8 msm efo.4m2chunks of ice that orbit the planet. The inner radius of the rings is 73,0r.4yq mo 8femm t2v9;r+spmd+00 $\mathrm{~km}$ , while the outer radius is 170,000$ \mathrm{~km}$ . Find the period of an orbiting chunk of ice at the inner radius and the period of a chunk at the outer radius. Compare your numbers with Saturn's mean rotation period of 10 hours and 39 minutes. The mass of Saturn is 5.7 $\times 10^{26} \mathrm{~kg}$ .


$T_{\text {irner }} $ =   
$T_{\text {outer }} $ =   

  A Ferris wheel 24.0 m in diameter rotates oncl. yu*r5ak cci3d4hb( e every 15.5 s (see Fig. 5–9). What is t (yubrk*cdcl ah.435i he ratio of a person’s apparent weight to her real weight (a) at the top, and (b) at the bottom?
(a)    (b)   

  What is the apparent weight of a 75-kg astronaut 4200 (ie,12.0kbc dhx5 qf0fwke .tpl:xc0hlaa5k km from the center of the Earth 5kxe1b d i e20qc k5h,hptlaxkl:f(00 .a.cwf's Moon in a space vehicle (a) moving at constant velocity,     ----待选择----towards the Moonaway from the Moon 
(b) accelerating toward the Moon at 2.9 $\mathrm{~m} / \mathrm{s}^{2}$ ?     ----待选择----towards the Moonaway from the Moon 

State the "direction" in each case.

  Suppose that a binary-star system consists of two stars of xt u/e chgvy/9y5(zggjm) 6 m/fwt 1-lequal mass. They are observed to be separated by 360 million km and th/g/)/ ct 96umyvfgz5xmet - y(w gj1lake 5.7 Earth years to orbit about a point midway between them. What is the mass of each?    $\times 10^{29}$

  What will a spring scoqnpgpt4 :,/qs) yj;gale read for the weight of a 55-kg woman in an elevator that moves jotq/nsp)g : 4,q yg;p
(a) upward with constant speed of 6.0m./s   
(b) downward with constant speed of 6.0m./s   
(c) upward with acceleration of 0.33 g,   
(d) downward with acceleration 0.33 g   
(e) in free fall?   

  A 17.0-kg monkey hangs from a cord suspended from the ceiling o 1o7n) oc+j)wonx 7oscab- as1f an elevator. The cord can witba)1sjoa )ocnc1x7 7n+wo os -hstand a tension of 220 N and breaks as the elevator accelerates. What was the elevator’s minimum acceleration (magnitude and direction)? a =   

Show that if a satellite orbits very near the surface 4 kc ;d*) 0i3ygoaaw6z+cufjoq/ i)p xof a planet with period T , the density (mass/volume) ofj)w* z)x;o dc/+k0aufg ao yc4qi pi63 the planet is $\rho=m / V=3 \pi / G T^{2}$ .
(b) Estimate the density of the Earth, given that a satellite near the surface orbits with a period of about 85 min .

  Use Kepler’s laws and the period of the Moon (27.4 d) to determine the per15l rq(m rwa8siod of an artifici8r(asqlw15m ral satellite orbiting very near the Earth’s surface.    s

  The asteroid Icarus, though only a . h4waydk;l/i few hundred meters across, orbits the Sun like the planets. Its period is 41ial; ky.wd/ h40 d. What is its mean distance from the Sun?    $\times 10^{11}$

  Neptune is an average distan*i pt2n) v31msaj8 ipl87 twfsce of 4.5 $\times 10^{9} \mathrm{~km}$ from the Sun. Estimate the length of the Neptunian
year given that the Earth is 1.50 $\times 10^{8} \mathrm{~km}$ from the Sun on the average.    $\times 10^2$

  Halley’s comet orbits thetw)+iiw jj940nbso+j sp 34yo Sun roughly once every 76 years. It comes very close to the surface of the Sun on its closest approach (Fig. 5–39). Estimate the greatest distance of the comet from the Sun. Is it still “in” the Solar System?ypj 49034tsojn+wo)i +swbi j What planet’s orbit is nearest when it is out there? [Hint: The mean distance s in Kepler’s third law is half the sum of the nearest and farthest distance from the Sun.]    $\times 10^6$

  Our Sun rotates about the centem+tmw4czq 2jk k3xfd0s/48sb r of the Galaxy $\left(M_{G} \approx 4 \times 10^{41} \mathrm{~kg}\right)$ at a distance of about 3 $\times 10^{4}$ light-years $\left(1 \mathrm{ly}=3 \times 10^{8} \mathrm{~m} / \mathrm{s} \times 3.16 \times 10^{7} \mathrm{~s} / \mathrm{y} \times 1 y\right)$ . What is the period of our orbital motion about the center of the Galaxy? $\approx$   $\times 10^8$

  Table 5–3 gives the mass, pl-4 l/kq e dmp755/(mrydpdjg eriod, and mean distance for the four largest moons of Jupiter (those discovered by Galileo in 1609).q / ld -ed5/(4 mmg7rypjdkpl5
(a) Determine the mass of Jupiter using the data for Io.$M_{\substack{\text { Jupiter- } \\ \text { Io }}}$ =    $\times 10^{27}$
(b) Determine the mass of Jupiter using data for each of the other three moons. Are the results consistent?
$M_{\substack{\text { Jupiter- } \\ \text { Europa }}}$ =    $\times 10^{27}$
$M_{\substack{\text { Jupiter- } \\ \text { Ganymede }}}$ =    $\times 10^{27}$
$M_{\substack{\text { Jupiter- } \\ \text { Callisto }}}$ =    $\times 10^{27}$

  Determine the mass of the E t(gf6zad53 sbyhw .k4arth from the known period and distance of the Moon. y th6gfz53s(k4b.d wa    $\times 10^{24}$

  Determine the mean distance from Jupiter for each of Jupiter’s x6wwxg+/6f,haz j1c3ba-:p8gd eqi hmoons, using Kepler’s third law. Use the distance of Io and the periods given in Table 5–3. Compare to the values in the eh8a6 fg +,ix/6 wb3z- qhxpwgca 1:jdTable.
$r_{\text {Farip }}^{r}$ =    $\times 10^3$
$r_{\text {Guarymale }}$ =    $\times 10^3$
$r_{\text {Culimio }}$ =    $\times 10^3$

  The asteroid belt between Mars and Jupiter consists of manu3*lzl 2-l w1jcwr za/y fragments (which some space scientists think came from a planet that once orbited the Sun but wa3*lz-wl j zul/2r1ca ws destroyed).
(a) If the center of mass of the asteroid belt (where the planet would have been) is about three times farther from the Sun than the Earth is, how long would it have taken this hypothetical planet to orbit the Sun?$\approx$    y
(b) Can we use these data to deduce the mass of this planet?

  A science-fiction taf9 p2ve1bdkvgs : (hp5le describes an artificial "planet" in the form of a band completh2 5pvf(1g9p:k sdbevely encircling a sun (Fig. 5-40). The inhabitants live on the inside surface (where it is always noon). Imagine that this sun is exactly like our own, that the distance to the band is the same as the Earth-Sun distance (to make the climate temperate), and that the ring rotates quickly enough to produce an apparent gravity of g as on Earth. What will be the period of revolution, this planet's year, in Earth days?   

  Tarzan plans to cross a gorge by swinging in an arc from a hanging vine (Fzmej b23 b x(/6ndhik9ig. 5–41). If his arms are capable of exerting a force of 1400 N on the vine, what is the maximum speed he can tolerate at the lowest point of his swing? His m e 9b/ (6bhmdkxz3in2jass is 80 kg, and the vine is 5.5 m long.   

  How far above the Earth’s surface will the acceleration of gravi;0 fy8uj ds(w 9b(wxbsty be half what it is on the9bswy s bx;udw(j08f( surface?    $\times 10^6$

  On an ice rink, two skaters of equal mass grab hands and spin in a ww g6o(0r-jnemutual circle once every 2.5 s. If we assume their arms are each 0.80 m long and their individual masses are 6nw60wo e-jrg( 0.0 kg, how hard are they pulling on one another?    $\times 10^2$

  Because the Earth rotates once per day, the apparent acceleration of gu +cmk :-g(1bnnhh fz(ravity at the equator is slightly less than it would be if the Eaz1nuh:m-(c(gf +nbh krth didn’t rotate. Estimate the magnitude of this effect. What fraction of g is this?    $\times 10^{-1}$

  At what distance from then-eb)ev-we m hsd(o7w xp9i5/ Earth will a spacecraft traveling directly from the Earth to the Moon experience zerove-eho) xw-75w(bs d /e9nip m net force because the Earth and Moon pull with equal and opposite forces?    $\times 10^8$

  You know your mass is 65 kg, but when you stand on kp2a6 by)9m,d s+vmqfu) s 4:8xnabpga bathroom scale in an elevator, it says your mass is 82 kg. What is the a4m6q28kab: psa f xu m+vpbgy,)n9d )scceleration of the elevator, and in which direction?     ----待选择----upwartddown 

  A projected space station consists of a circular tube that will ro;q mx e(7si+ztvaz.5wtate about its center (like a tubular bicycle tire) (Fig. 5–42). The cirs me xvqwa+. z(it;z75cle formed by the tube has a diameter of about 1.1 km. What must be the rotation speed (revolutions per day) if an effect equal to gravity at the surface of the Earth (1.0 g) is to be felt?$\approx$    $\times 10^3$

  A jet pilot takes his aircraa9eprk3( /xoaft in a vertical loop (Fig. 5–43).
(a) If the jet is moving at a speed of at the lowest point of the loop, determine the minimum radius of the circle so that the centripetal acceleration at the lowest point does not exceed 6.0 g’s.    $\times 10^3$
(b) Calculate the 78-kg pilot’s effective weight (the force with which the seat pushes up on him) at the bottom of the circle    $\times 10^3$
(c) at the top of the circle (assume the same speed).
   $\times 10^3$

Derive a formula for the mass of a planeq7mzw-m; jdk)e)pto 2fvo8 v eb 7orhf183rd3t in terms of its radius r, the acceleration due to gravity at its surface and) v z m-e )hvk2fr7f8wom; 3rb8oeodtp13d7jq the gravitational constant G.

A plumb bob (a mass m hanging on am9(.t;p ge yja string) is deflected from the vertical by an anyem .(;gajp9 tgle $\theta$ due to a massive mountain nearby (Fig. 5-44). (a) Find an approximate formula for $\theta$ in terms of the mass of the mountain, $m_{\mathrm{M}}$ , the distance to its center, $D_{\mathrm{M}}$ , and the radius and mass of the Earth. (b) Make a rough estimate of the mass of Mt. Everest, assuming it has the shape of a cone 4000 m high and base of diameter 4000 m . Assume its mass per unit volume is 3000 kg per $ \mathrm{m}^{3}$ . (c) Estimate the angle $\theta$ of the plumb bob if it is 5 km from the center of Mt . Everest.

A curve of radius 67 m is banked for a design speed of wmu+,s-q-q l7io/y t q If the coefficient of static friction is 0.30 (wet pavement), at u/tq-l,si q 7 +-woqymwhat range of speeds can a car safely handle the curve?

  How long would a day be if the Earth w ldh7 g2xh7 j5xw5gw)gere rotating so fast that objects at the equator were apparently wg7w 52glxh5xjd 7ghw) eightless?    $\times 10^3$s

  Two equal-mass stars main3ifp;y*;uy ,z7mdw-lupicu f5ui4 z* tain a constant distance apart of 8.0 $\times 10^{10} \mathrm{~m} $ and rotate about a point midway between them at a rate of one revolution every 12.6 yr . (a) Why don't the two stars crash into one another due to the gravitational force between them?
(b) What must be the mass of each star?    $\times 10^{26}$

  A train traveling ats8p3nwc+gfmow w/x o636w8ff a constant speed rounds a curve of radius 235 m. A lamp suspended from the c6wf 63gww3+xp8nw/ osfmc8foeiling swings out to an angle of 17.5$^{\circ}$ throughout the curve. What is the speed of the train?   

  Jupiter is about 320 times as massive as the Earth. Thus, it has been claimed th oj3 jg:jr.r5rat a person would be crushed by the force o3r 5j.grr :jojf gravity on a planet the size of Jupiter since people can't survive more than a few g 's. Calculate the number of g 's a person would experience at the equator of such a planet. Use the following data for Jupiter: mass =1.9 $\times 10^{27} \mathrm{~kg}$ , equatorial radius =7.1$ \times 10^{4} \mathrm{~km}$ , rotation period =9 $\mathrm{hr} 55 \mathrm{~min}$ . Take the centripetal acceleration into account.    g's

  Astronomers using the Hubble Space Telesc02v2g4o. a3vpmenhs p ope deduced the presence of an extremely massive core in the distant galaxy M87, so dense that it could be a black hole (from whivpea3p2 2g.o4mh s0vnch no light escapes). They did this by measuring the speed of gas clouds orbiting the core to be 780 $\mathrm{~km} / \mathrm{s}$ at a distance of 60 lightyears $ \left(5.7 \times 10^{17} \mathrm{~m}\right)$ from the core. Deduce the mass of the core, and compare it to the mass of our Sun. v =    $\times 10^{39}$solar masses =    $\times 10^9$

A car maintains a constant speed as it trave-f4to 2* (bf mox6bqxrrses the hill and valley shown in Fig. 5–45. Both the hill and valley have a radius of curvature R. (a) H fox-6tob rm*(2q fb4xow do the normal forces acting on the car at A, B, and C compare? (Which is largest? Smallest?) Explain. (b) Where would the driver feel heaviest? Lightest? Explain. (c) How fast can the car go without losing contact with the road at A?

  The Navstar Global Po8qva) zsid)r5a6me lv3/aa4 dsitioning System (GPS) utilizes a group of 24 satellites orbiting the Earth. Using “triangulation” and signals transmitted by these satellites, the position of a receiver on the Earth can be determined to within an accuracy of a few centimeters. The satellite orbits are distributed evenly around the Earth, with four satellites in each of six orbits, allowing continuous navigational “fixes.” The satellites orbit at an altitude of approximately 11,000 nautical miles [1 naas/q))v4d8az3 6a mrlaev5diutical ]. (a) Determine the speed of each satellite.    $\times 10^3$
(b) Determine the period of each satellite. =    hours

  The Near Earth Asteroid Rendezvous (NEAR), after traveling 2.1 billioub*7ax ue2aoc(g5 jl -j .:; a, ezdom(co)lgjn km, is meant to orbit the asteroid Eros at a height of about 15 km . Eros is roughl ou,)ez*jgj2 d om5ae7lu:lc aab;(ox( cg-. jy 40 $\mathrm{~km} \times 6 \mathrm{~km} \times 6 \mathrm{~km}$ . Assume Eros has a density (mass/volume) of about 2.3 $\times 10^{3} \mathrm{~kg} / \mathrm{m}^{3}$ . (a) What will be the period of NEAR as it orbits Eros? $\approx$    $\times 10^4$sec
(b) If Eros were a sphere with the same mass and density, what would its radius be? $\approx$    $\times 10^3$
(c) What would g be at the surface of this spherical Eros?$\approx$    $\times 10^{-3}$

  You are an astronaut in the space shuttle pursuing a satelias4g*7mnz7 q lite in need of repair. You are in a circular orbit of the same radiusa 7s4ngq i7z*m as the satellite (400 km above the Earth), but 25 km behind it.
(a) How long will it take to overtake the satellite if you reduce your orbital radius by 1.0 km?$\approx$    h
(b) By how much must you reduce your orbital radius to catch up in 7.0 hours?$\approx$    $\times 10^3$

  The comet Hale-Bopp has a period of 3000 years. (a) Whatz (cthx9y9x. m is its mean distance from the Sun?.99cmytzhx x(   
(b) At its closest approach, the comet is about 1 A.U. from the Sun ( from Earth to the Sun). What is the farthest distance?   
(c) What is the ratio of the speed at the closest point to the speed at the farthest point? [Hint: Use Kepler’s second law and estimate areas by a triangle (as in Fig. 5–29, but smaller distance travelled; see also Hint for Problem 59).]   

  Estimate what the value of G would need to be if5w 5 *xgqsdl/jiuinz -mgo*4. you could actually "feel" yourself gravit x5m.-ng/iuqgo* z 5 ld*sij4wationally attracted to someone near you. Make reasonable assumptions, like F $\approx 1 \mathrm{~N}$ .    $\times 10^{-5}$

  The Sun rotates around the center 1 bnmh a,+rg.e6drh5 yof the Milky Way Galaxy (Fig. 5-46) at a distance of ar5,dh .em1 h+6graby nbout 30,000 light-years from the center $ \left(1 \mathrm{ly}=9.5 \times 10^{15} \mathrm{~m}\right)$ . If it takes about 200 million years to make one rotation, estimate the mass of our Galaxy. Assume that the mass distribution of our Galaxy is concentrated mostly in a central uniform sphere. If all the stars had about the mass of our Sun $\left(2 \times 10^{30} \mathrm{~kg}\right)$ , how many stars would there be in our Galaxy?$\approx$    $\times 10^{11}$

  Four 1.0-kg masses are located at the corners of a sot9 nzi v)l0d/quare 0.50 m on each side. Find the magnitude and direction of the gravitational force on i)0/z ndv 9olta fifth 1.0-kg mass placed at the midpoint of the bottom side of the square.    $\times 10^{-10}$  ----待选择----downupward 

  A satellite of mass ,48ldnr0nk2uvoe wgew+r24 c5500 kg orbits the Earth $ \left(\operatorname{mass}=6.0 \times 10^{24} \mathrm{~kg}\right)$ and has a period of 6200 s . Find (a) the magnitude of the Earth's gravitational force on the satellite, $\approx$    $\times 10^4$
(b) the altitude of the satellite.    $\times 10^5$

  What is the acceleration experr6.roettltd3 ikip n)z: :4 7uienced by the tip of the 1.5-cm-long sweep second hand on your wrerrutn3lok.dz 6pi )t i47t ::ist watch?    $\times 10^{-4}$

  While fishing, you get bore;meo( ;r uhy:s9 *eehod and start to swing a sinker weight around in a circle below you on a 0.25-m piece of fishing line. The weight makes a complete circle every 0.50 s. What is the angle that the fishing line makes with the vertical? [Hint: She;(o yu:h9mrsoe; e*ee Fig. 5–10.]    $^{\circ}$

A circular curve of radius R in a new )1 brty *ac *e1y.v5mpy*juzfhighway is designed so that a car traveling at speet* ey5v1)1u.b y*zpajfrmc *yd $ v_{0}$ can negotiate the turn safely on glare ice (zero friction). If a car travels too slowly, then it will slip toward the center of the circle. If it travels too fast, then it will slip away from the center of the circle. If the coefficient of static friction increases, a car can stay on the road while traveling at any speed within a range from $v_{\min }$ to $v_{\max }$ . Derive formulas for $ v_{\min }$ and $ v_{\max } $ as functions of $\mu_{s}, v_{0}$ , and R .

  Amtrak’s high speed train, the Ac b1oyer+6h g dwo;/ji*ela, utilizes tilt of the cars when negotiating curves. The angle of tilt is adjusted so that the main force exerted on the passengers, to provide the centripetal acceleration, is the normal force. The passengers experience less friction force against the seat, thus feeling more comfortable. Consider an Acela train that rounds a curve with a radius of 620 m at a speed of (approximately ). (a) Calcul bh+yg*woie jr6d/o1 ;ate the friction force needed on a train passenger of mass 75 kg if the track is not banked and the train does not tilt. $\approx$    $\times 10^2$
(b) Calculate the friction force on the passenger if the train tilts to its maximum tilt of 8.0º toward the center of the curve.$\approx$    $\times 10^2$