Sometimes people say that water is removed from clothes in a spin dryer by centh* 6ndg 7-9y8z j0vxjrxxa9pgrifugal force throw7x0j9ngzr-6vxpgy 9x j*8 hdaing the water outward. What is wrong with this statement?

Will the acceleration of a car be the same when the car travels around a shaaa bgypa 6mq8xplhs4 cp1 8,04rp curve at a constant 60 km/h as pqp04sa pyb86caxa481,h mgl when it travels around a gentle curve at the same speed? Explain.

Suppose a car moves at constant speed along a hill+ 8yst /2a 3jxwjd.he/f5glvv us/ t2ukve+0fy road. Where does the car exert the greatest and leasts/tdavjk 5 .ulx/fve3hg 0 ue+2tf/jyvw 82s+ 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 a -v 9eby:)z xx:ouya2bcting on a child riding a horse on a merry-go-round. Which of these forces provides the centripetal acceleration of the chiz:o 29eyxx) u- aybvb:ld?

A bucket of water can be whirled in a vertical cirjc* u 2 z- 2,fr;xokt*bk+feyycle without the water spilling out, even at the top of the circl 2 ,kjfryf utzx;o+bk-c2*ey *e when the bucket is upside down. Explain.

How many “accelerators” do ykas,qz , 4y-hoou have in your car? There are at least three controls in the car which can be used to cause the car to accelerate. What are they? What accel4-kz qo, ,asyherations do they produce?

A child on a sled comes flying over the cres5eh. +edkbi. p 1:hm e1 k/rd99syordrt 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 m1presd: he.91dr+ry5/9ekho k. bid normal force between his chest and the sled decrease as he goes over the hill. Explain this decrease using Newton’s second law.

Why do bicycle riders lean inward when rounding a curve at higqmr+sy9;mj unpo /k8 -h speed?

Why do airplanes bank whenn+ e0l9jdgo+spptn3dk-okf:4 /9uvy they turn? How would you compute the banking angle given its sejd:4/pon-opy fk+nl9u 3tg+sv k09dpeed and radius of the turn?

A girl is whirling a ball on a string around;+ sn .gx 5ulymh/x(wp her head in a horizontal plane. She wants tosy5.hx( x/+ ug l;nmpw 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 string?

Does an apple exert a gravitational force onm9l- mnt 5;t3 r/iztyi the Earth? If so, how large a force? Considerti-nty9m/mi z;t lr35 an apple
(a) attached to a tree, and (b) falling.

If the Earth’s mass were double what it is, in what ways would theou5ly ahv, h9,z26b6xog-rwrpk:f (h Moon’s orbit ,pf ko9b (5h,6rz 2axo yhh6 urgvwl:-be different?

Which pulls harder gravitationds1ew 8t+ jx hv.5g5kually, the Earth on the Moon, or the Moon on the Earth? Which accelerates dsuw8x.jv5e+gth k15more?

The Sun's gravitational pull on the Earth is much la/4tr(gxz gu4 bb el5j0slh1 i(rger than the Moon's. Yet the Moon's is mainly responsible for the tides. Explain. [Hint: Consider the difference in gravitational pull from one side of the Earth to the ot15tz gh 4urje gb0x( bsi(ll4/her.]

Will an object weigh more at the equasqnm5:,fzv8c7j jw+ wtor or at the poles? What two effects are at wozn: w5w,fjm7 sv8j cq+rk? Do they oppose each other?

The gravitational force on the M:4f j-b5moulooon due to the Earth is only about half the force on the Moon due to the S: jbo4l -fuo5mun. Why isn’t the Moon pulled away from the Earth?

Is the centripetal a;j 6gmu4ce8pna v-tr 5 unhu,1cceleration of Mars in its orbit around the Sun larger or smaller than the hg81uu- ,4e 5rntnvjap;mc6u centripetal acceleration of the Earth?

Would it require less speed to launch a satellite (a) toward the east or dctiqe zi+c ;oes;k 0jb*6 1o3(b) toward the west? Consider the Earth’s rotat i+q1 c*t6kboeised 3;;cjz0oion direction.

When will your apparent weight be the greatest, a 2aeo-;s0uvw)hfr x1 ss measured by a scale in a moving elevator: when the elevator (a) acce hvw- o)sure a10fx2s;lerates downward, (b) accelerates upward, (c) is in free fall, (d) moves upward at constant speed? In which case would your weight 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 outer space coulr8 +dt,yr/aci ir:*iy d be adversely affected by weightlessness. One way to simulate gravity is to shape the spaceship like a cylind/ ,i +*:itriad8yycrrrical 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 think of.

Explain how a runner experiences “free fall” or “apparent weightlessc*tvuwba,n+) k( qr:f 1lq+n6e s0krkness” betweebu+nrqns1+:k0v a lrek f6c), t*kq( wn steps.

The Earth moves faster in itsaa g w1yp/do(nnc612g orbit around the Sun in January than in July. Is the Earth closer to the Sun in January, or in July? Explain. [Note: This 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 orb /2 wpgca1 d(1gn6oaynit.]

The mass of Pluto was not known until it was discovered to have a moon. Explaif +.1wt3.8py achrxhoc8h yz9n how this discovery enabled an estimate of Pluto’s masryctxo p.f3hh88ay .cz+1wh 9s.

  The Sun's gravitational pull on them+r r30s0jjq e Earth is much larger than the Moon's. Yet the Moon's is mainly responsible for r+j30r s0mqejthe 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 co7uf53q3wz t 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 orbi ,ij t7iwsjmy t19bm69u5aubw8lk+2n t around the Sun, and the net force exerted on the Earth. What exerts this force on the Earth? Assume that the Earth's orbit is a circle of6i8wj2bm9nam+s kt1yu ulb7ij , tw59 radius 1.50$ \times 10^{11} \mathrm{~m}$ . [Hint: see the Tables inside the front cover of this book.]    $\times10^{22}$

  A horizontal force of 210 N is exerted on yk1 t8iten + i;ml0cw3a 2.0-kg discus as it rotates uniformly in a horizontal circle (at arm’s length) of radiun3;kmy810tt+ ci wei ls 0.90 m. Calculate the speed of the discus.   

  Suppose the space shuttlxoq e /hz6*8rd vg/k0ge is in orbit 400 km from the Earth'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 terms of g , the gravitational acceleration at th 8xoeh/*kg 0dg6z rq/ve Earth's surface. $\approx$    g

  What is the magnitude of the acceleration of a speck of clay on the edge o/ j c9 etb61qr.l;odn wydz*u)f a potter’s wheel turning at 45 rpm (r9b6e*);wtr. jo /d 1qyudcnzlevolutions per minute) if the wheel’s diameter is 32 cm?   

  A ball on the end of a string is revolved at a uniform rate in a vewk: ;f :vrm/sertical circle of radius 72;v /fe: r:smwk.0 cm , as shown in Fig. 5-33. If its speed 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 1050-kg car cl 01g b* l5nqhx2wcqfdp7 7k5kan round a turn of radius 77 m on a flat road if the coefficient of static friction between tires and road is 0.80? Is thiqh5dpl5bf27gw0k1*l c nxqk 7 s result independent of the mass of the car?   

  How large must the coefficiennw:1e 3fu*o*dp f d.0 cfxg(pmusqs6-t of static friction be between the tires and the road if a car i *6 quenf1m.sudf 3sc0wf(*d:pgoxp- s to round a level curve of radius 85 m at a speed of 95km/h ?   

  A device for training astronauts and jet fi- /qxw ln:nv/7c)uqcyghter 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 n)7:vcxun/-cq / yq lwis 7.85 times her 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 a rotating turntable of variable9 dey. *sa*wme speed. When the speed of the turntable is slowly increased, the coin remains fixed on the turnta s.e*ed m*a9ywble until a rate of 36 rpm is reached and the coin slides off. What is the coefficient of static friction between the coin and the turntable?   

  At what minimum speed must a roller coaster be traveling when upside x rew./j9/ww9nam/c t-:fl(f nlh3qgdown at the top of a mrnh99w3:a fl/j cng(q .le/-/tw wxf circle
(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) crosses the rouxv1qv4e dnf,/c,wud;nded top of a hill (radiusend1v xv,d4c/uf; , qw =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-diameter Ferr r0 5d*r-qg mqg /l.mshtha/w2ux6pg3is wheel need to make for2a5t6ug*/q/. x- r3d ggwhlmp0qmshr the passengers to feel “weightless” at the topmost point?    rpm

  A bucket of mass 2.00 kg is whirled in a vertical circle of radius 1ccjky4icc/ a ((s 62qc.10 m. At the lowest point of its motion the tension in the rope supporting the bucket is 2c ac(c(jk sicq 26/c4y5.0 N.
(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 particle 9.00 cm froji de-(+ 4h/)joit*vkvctb2 vv)uti9m the axis of rotation is to experience 9hit - (*vtjv/cv +)ubk2oti)dijev4an acceleration of 115,000 $\mathrm{~g} $'s?    rpm

  In a "Rotor-ride" at a carnival, people :z1bmjm9/*bvqq;q:innuz-i /nnyosxo 7y 3. are rotated in a cylindrically walled "room." (See Fig. 5-35.nx q.:i7b*mqny3z /;ovm qjy b1:n-io9n su/z)
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 frictionless air-hockey ta60s g9/9 cttf;w hiwibbletop, and is hel sgi;b t6 c0wwt9/h9fid 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 , preciselyx9*/ sjvab i4o this time, by not ignoring the weight of the ball whic/oxbv* 9a4ijsh revolves on a string 0.600 m long. In particular, find the magnitude 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 radius of 88 m is perfectly banked for a car traveling lz*my25+bdvt -x0iez yhki:* 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 masses3mapk, 3 1gd po.pcbc, $ 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 vertically at -0 fepq m(s5k4d .nt*f7v ufpg 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 centripetal components of therue v4b(3ems 0st 0wk+ net force exerted on the car (by the ground) in Example 5-8 b0r4u(vtes 0esk +3mw when its 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 aag/s 6v7zy7hdp n8+ nv+j)zyl rea, going from 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 t d6vh7nv/y+np+8jg)a lzy zs7he 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? $\approx$   

  A particle revolves in a ha1bzi v s0 f*g/lx+im6orizontal circle of radius 2.90 m . At a particular instant, its acceler vx+/b1fm glsa*i z6i0ation 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 gravity on a spacecraft 12,800 klnai)- hfx,*vm (2 Earth radii) above t fi,)h avl-*nxhe Earth’s surface if its mass is 1350 kg.   

  At the surface of a certain planet, thip8;w*kcif a 5e gravitational acceleration g has a magnitude*afw5c ii8kp; 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 f; tx5xciz9v 6due to gravity on the Moon. The Moon's radius is 1.7ztvxxfc;65i9 4 $\times 10^{6} \mathrm{~m} $ and its mass is 7.35 $\times 10^{22} \mathrm{~kg}$ .   

  A hypothetical planet has a radius 1.5 times that of Earth, but haem x lm6;h(*fe)mku )us the same mass. What ismuuxh( ;e)*k)le6 mm f the acceleration due to gravity near its surface?   

  A hypothetical planet has a mass 1.66 times that of Earth, bo2(bmq1t5rx ou-ixd 5o(dtu8ut the same radius. What id(xx 5(5oui -o2t8mqu b1ordts g near its surface?   

  Two objects attract each other gr;)qi)mxut 3i vs6o h1kavitationally with a force of 2.5$ \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 grav)qm. v1 s49ybbhqge:8md ,vp zity, at (a) 3200 mm) ydsze mbb9hq8:qv1g,pv4.    , and (b) 3200 km    , above the Earth's surface.

  What is thedistance from the Earth’s center to a point outside the Earth whe9d;ier +70v3xd8ax amfsyfn6 (rf n; lre thegravitational acceleration due to8(ff r6i3 n0vm ya;+rs and;7exfdxl9 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 pz* n9vt9mji,jcd n8g*acked into a sphere about 10 km in radius. Estimate the surface gravity on this monster. m9vz*ji 8gn,9 td*cjn   $\times10^12$

  A typical white-dwarf star, which once w ziw o-tk .s87 p5su6hxcum9p 82dvw6sas an average star like our Sun but is now in the last stage of its evolution, is the size of our Moon but has the6 t mhuv.px8o uz2c7d98-wpiksw5s6 s mass of our Sun. What is the surface gravity on this star?    $\times 10^7$

  You are explaining why astronauts feel weightless while orbiting m4ppepps( )1ain the space shuttle. Your friends respond that they thought gravity was just a lot weaker up there. Convince them and yourself that it isn’t so bp4p p(ema)s 1py calculating the acceleration of gravity 250 km above the Earth’s surface in terms of g.   

  Four 9.5-kg spheres are ln 0 sp)x/pwdr7ocated at the corners of a square of side 0.60 m. Calculate the magnitude and direction of the total n)xp p dw07r/sgravitational force exerted on one sphere by the other three.   $\times 10^{-1} \mathrm{~N} \text { at }$    $^{\circ}$

  Every few hundred years mus0o,t8 aawa .e 63ubxost of the planets line up on the same side of the Sun. Calculate the total force on the Earth due to Venus, Jupiter, and Saturn, assuming all four p03wubes86aaat x ,uo.lanets 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 surb8.7e z mp 9i4dqdx4hcface of Mars is 0.38 of what it is on Earth, and that Mars’ radius is 3400 km, de98b qh dc4.pdx47 mizetermine the mass of Mars.    $\times 10^{23}$

  Determine the mass of the Sun using the known value for the period of the Ea jbz-t k9 cpk9x:;suq9rth and its distance frobjsc 99:k x;uk9zqtp -m the Sun. [Note: Compare your answer to that obtained using Kepler’s laws, Example 5–16.]    $\times 10^{30}$

  Calculate the speed of a satellite moving in a stable circular orbit about thlf9d4xinw+ r; e Eanrd4w x+i9 ;flrth at a height of 3600 km.    $\times 10^3$

  The space shuttle releases a satb9 1xnk:0bc5ivzth/t6dh u m 6ak oq73ellite into a circular orbit 650 km above the Earth. How fast must the shuttle be moving (relative to Earth) when the 6tmhb: ndktbv/zco0ikxq5 6ua9 7h 1 3release occurs?    $\times 10^3$

  At what rate must a cylindrical spaceship rotate if occupants are to exu;nu8iz3 sohai -w3 u;perience simulated gravity of 0i s3uh;- 8 uawniou3z;.60 g? Assume the spaceship’s diameter is 32 m, and give your answer as the time needed for one revolution. (See Question 21, Fig 5–32.)   

  Determine the time it takes for a satellite to orbit the Earth in a circul r(85d 8nye 4*iusvzjgar “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 radius of the Earth. Does your result depend on the mass of thnv8usdjy ze ri5g( *84e satellite?    s ~    min

  At what horizontal velocity would a satellite have to be l hc.x+: pfc p;4s3ee c-ur2lkxaunched from the top of Mt. Everest to be placed uc4;rce.- echk:sxpfp32l+xin a circular orbit around the Earth?   

  During an Apollo lunar landing mission, the command module ci5ybkbz23u wzi g6oa:sn-my*9- dl:bontinued to orbit the Moon au-wo n lby62ia-m izz5sg 3 9*b::dybkt an altitude of about 100 km. How long did it take to go around the Moon once?    s

  The rings of Saturn are composed of chunks of ice that 5v,: ;ezsv gvcorbit the planet. The inner radius of the rgvv5vs: ce;z,ings is 73,000 $\mathrm{~km}$ , 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 once every 15.5 s (se+qtuv k(2+ow.s2 uvoee Fig. 5–9). What is the ratio of a person’s apparent weight to her real weight (a) at the top, and (b) at the u.ovvt+2 ( s2o keuq+wbottom?
(a)    (b)   

  What is the apparent weight of a 75-kg astronaut 4200 km from the center of th0b(1y5je83z dug0tregl a kha *4grh. e Earth's Moon in a space vehicle (a) moving (yr5ar0 1.gkb3a8 *huth 0gldez4gejat 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 1icpdrl(k f/l6 - w3yps) 8qvsstars of equal mass. They are observed to be separated by 360 million km and take 5.7 Earth years toikwp/ qf- 3cvs6 ()8dlprysl1 orbit about a point midway between them. What is the mass of each?    $\times 10^{29}$

  What will a spring scale read forw; 1qz i-+t+i/b dliuk+o)zlv the weight of a 55-kg woman in an elevator that moqo-l/ d+iu;1vkbii) wl+ z+tz ves
(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 frzxc0 o8fn7(l,xo; g h*,3ih*vm ipkdwom a cord suspended from the ceiling of an elevator. The cord can withstand a tension of 220 N and breaks as the elevator accelerates. What was the elevator’s minimum acceleration (magnitude and dir h idx0fioz k ,nc*(vg;m3 *,xlwpoh87ection)? a =   

Show that if a satellite orbits very near the surface of a pla4pw v;x/lek o6net with period T , the density (mass/volume) of the plan/ 64e;klovw pxet 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 orhe iscq )**8tf the Moon (27.4 d) to determine the period of an artificial satellite orbiting very near the Earth’s surface)*t*scq8 rehi.    s

  The asteroid Icarus, though only a few hundred meters across, orbits the Sun si6lp4e6 vc q2like the planets. Its ei 6 ls2c4qp6vperiod is 410 d. What is its mean distance from the Sun?    $\times 10^{11}$

  Neptune is an average distance o0:r:qvn/ jau 5yzgpa e.vv+8ff 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 thed w, k2 jt*k tcrfz8 s+:4pg)y,kp0ukm 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? What planet’s orbit is nearest when it is out there? [Hint: The mean distance s in Kepler’s third law8 k t:ppcf+*zu42k0),rmd ,wktysjkg is half the sum of the nearest and farthest distance from the Sun.]    $\times 10^6$

  Our Sun rotates about the c4egq. z( z.iua67vp openter 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, period, and mean distance for the four largest mo2:pj5- 9fdwokjik pr 4ons of Jupiter (tdji5k9p:pj2k -orf4 w hose discovered by Galileo in 1609).
(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 Earth frqu9, ), 3rggz:t v azlapv60ntom the known period and distance of the Moon. 09rqa:,anzug , 3) pztglt6vv   $\times 10^{24}$

  Determine the mean distance from Jupiter for each of Jupi eeu;mu:7rf ec)i -eftr 4:dy+ar/ g0ster’s moons, using Kepler’s third law. Use the distance of Io and the period :suegdree mcf ua07+r:ey-f4;t) /irs given in Table 5–3. Compare to the values in the Table.
$r_{\text {Farip }}^{r}$ =    $\times 10^3$
$r_{\text {Guarymale }}$ =    $\times 10^3$
$r_{\text {Culimio }}$ =    $\times 10^3$

  The asteroid belt between Mars and Jupiter consists of many fragme)g9v(zs0v kmde-j6.:t p yozji) e9annts (which some space scientists think came fromea-ed)9i o.9zzvjmv ) :0s(pty 6kngj a planet that once orbited the Sun but was 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 tale descririovci1/ z(d: bes an artificial "planet" in the form of a band completely encircling a sun (Fig. 5-40). The inhabitants live on the/icv(z1 ri:od 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 swil 3o;udb:j8 rpnging in an arc from a hanging vine (Fig. 5–41). If his arms are capable of exerting a force of 1400 N on the vine:ol8bp3d jr ;u, what is the maximum speed he can tolerate at the lowest point of his swing? His mass is 80 kg, and the vine is 5.5 m long.   

  How far above the Earth’s surface will the acceleratio 04bzg2j c+cjrn of gravity be half what irjbz0+jc2 gc4 t is on the surface?    $\times 10^6$

  On an ice rink, two skatersrr 6l6z; rw:x tjitp*ed 2gvg3,,xz6m of equal mass grab hands and spin in a mutual circle once every 2.5 s. If we assume their arms are each 0.80 m long and their individual masses are 60. d3wjgrz p ,t,exg*6t :i6mrr26x l;vz0 kg, how hard are they pulling on one another?    $\times 10^2$

  Because the Earth rotag3t 5lers9p-ltes once per day, the apparent acceleration of gravity at the equator is slightly less than it would be if the Earth didn’t rotate. Estimate the magnitude of this effect. What fraction of g is th tl3s-95glrpe is?    $\times 10^{-1}$

  At what distance from the Earth will a spacecraft traveling di rmpc9x 5sly2ms7m o;vs;/0berectly from the Earth to the Moon experience zero net force because theyseom ;rc2 9;ms/7vmlxb05s p Earth and Moon pull with equal and opposite forces?    $\times 10^8$

  You know your mass is 65 kg, but when you stand on a+kkm*a ;sp/qjwxu: j7 bathroom scale in an elevator, it say;xjqp/s+7kkmw :* a ujs your mass is 82 kg. What is the acceleration of the elevator, and in which direction?     ----待选择----upwartddown 

  A projected space station consists of a circular tube b)kjfy //5hhb)*mwidrg2 s 3b7 n0mqnthat will rotate about its center (like a tubular bicycle tire) (Fig. 5–42). The circle 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 ) )rhdb j/b/nmwsf7ykg0q5b *2h3nmito gravity at the surface of the Earth (1.0 g) is to be felt?$\approx$    $\times 10^3$

  A jet pilot takes his aircraft inb l 0g ux65mee55lcws 5w8on.m 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 planet in term9aw9nj /zl,,n uanjn/s of its radius r, the acceleration due to gravityn, na/jnal9j9w, nu /z at its surface and the gravitational constant G.

A plumb bob (a mass m hangiv8r a, ckzf) absn*q2,ng on a string) is deflected from the vertical by an ang nva,2,rfksq 8c)b*azle $\theta$ 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 bq*vr i 2 3rpverw70mkzw; a(s2anked for a design speed of If the coefficient of static friction is 0.30 (wet pavement), at what range of speeds can a car safely handl *vr3rm w22r ipasq(;w e0k7vze the curve?

  How long would a day be if the Earth were rotatgoe j)86 jwfu3dp; *kjoe, b)bing so fast that objects at the equator were appare)bu pe ,dkej*gfwobj 38;6j)ontly weightless?    $\times 10^3$s

  Two equal-mass stars maintain as 5y1lxca 9a-b p6efy3 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 at a constant speed rounds a curke 1o -pg6c4cmshj1 .4ayeor*ve of radius 235 m. A lamp suspended from the ceigprjm41 o.o6yheks1-ecc 4a *ling 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 tmg ;)sm0/3muz ow10j 4*e iiube t,pcpa6pkw-hat a person would be crushed by the force of gravity on a planet the size of Jupiter since people can't su ewu)- 4*uo3a ;t/6m1,sipgczwipemjpb 0m0 krvive 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 Tq):nz4qk5 .y clpgmj5 elescope deduced the presence of an extremely massive core in the distant galaxy M87, so dense that it could be a black hj4 l5yc z5q:m)n. pgqkole (from which 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 w++zvhm x.gar00gt5x as it traverses the hill and valley shown in Fig. 5–45. Both the hill and valley have a radius of curvature R. (a) How do the normal forces acting on the car at A, B, and C compare? (Which is largest? Smallest?) Expw0 g+av0+x 5g mrzx.htlain. (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 Positioning Sysu a; y)ltiwpmrfv3 6f):s)( 0mrpsmr. tem (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 accurav0ssfim uayf r wt.):;3pmp) 6)(rmrlcy 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 nautical ]. (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 ts5q a2x wqcjel4pao+ f()ra /0raveling 2.1 billion km, is meant to orbit the asteroid Eros at a height ofx+0s)erafqw 5 (/a4 p2oalcqj about 15 km . Eros is roughly 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 s4z 6ql)ma7zoq;jkoj s(s-3fh atellite in need of repair. j7l6k z;qoqf sj-(s moz4 a3h)You are in a circular orbit of the same radius 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) What kp ,8bcyi qsir c,(e7z1eh9tzl(tmwu-x:k 77 is its mean distance from the Sun? 7i t(y- l,zpwt k9z71k cxhmu8i q(7e:erbcs ,  
(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 n3 zwwlt7mk /spl 41c+sv 34qgto be if you could actually "feel" yourself gravitationally attracted to someone near you. Make rp llt1+w3z7sws 4/nvgq 4 cm3keasonable assumptions, like F $\approx 1 \mathrm{~N}$ .    $\times 10^{-5}$

  The Sun rotates around the center of the Mi jp9go fg)tcct m19,cog+3uh( lky Way Galaxy (Fig. 5-46) at a distance of about p t ofuhc(c j3gg9co +9),m1tg30,000 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 squa 2s,0vja hhnni0gu+e/m 95okhre 0.50 m on each side. Find the magnitude and direction of the gravitational force on a fifth 1.0-kg mass placedna0 +0hv9s ju /g,hom2e hk5ni at the midpoint of the bottom side of the square.    $\times 10^{-10}$  ----待选择----downupward 

  A satellite of mass 5500 k0su g c3ljj):dg 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 experv+ye n87mpgrv7k8 9 q/zdaig6ienced by the tip of the 1.5-cm-long sweep second hand on your w q+ vzpe89kgyan v7ig87/dr6 mrist watch?    $\times 10^{-4}$

  While fishing, you get bored and start to swing a sinker weighta1b 4 saui*g:hipt1em)7 r)tl around in a circle below you on a 0.25-m piece of fishing line. The weight makes a compl7iirps:at4alg u em)b t 1)*1hete circle every 0.50 s. What is the angle that the fishing line makes with the vertical? [Hint: See Fig. 5–10.]    $^{\circ}$

A circular curve of m l70lovqnvsl t8/1viy,p j75 djz h--radius R in a new highway is designed so that a car traveling at speedzhp 7lotd0jqj1lm,7i -lv5y/- vnsv8 $ 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 Acela, utilizes tilt of thq7 ff.4hdbve; e 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 experienc 4h7.;fvf qebde 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) Calculate 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.$\approx$    $\times 10^2$