Sometimes people say that water is removed1r i+ed6qi yo ,llbs2lo12d.8s1wgfy from clothes in a spin dryer by centrifugal force thri2d +6so,.y2rbof18yel lwl sqg d1i1owing the water outward. What is wrong with this statement?

Will the acceleration of a car be the same when the car travels around akuvi*kt:vnq0u r5+v cor fcm/9,sx 54 sharp curve at a constant 60 km/h as when it travels around a gentle curve at the same speed? Eivc+sku /v49*u:m tocn,qf 50v r x5rkxplain.

Suppose a car moves at constant speed along a hilly road. Where does the car exeffn) r9ns4an -rt the greatest 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 neannf9-4r sanf)r the bottom of a hill?

Describe all the forces actigjqjdiiq7 736ng on a child riding a horse on a merry-go-round. Which of these forces provides the centripetal acceleratdg ijiq763jq7ion of the child?

A bucket of water can be whirled in a g3-ck;ryc, nl9mbv*gvertical circle without the water spilling out, even at the top of the circle when the bucket is upside down. Explain.g9n- rgcyvmc 3; kl,b*

How many “accelerators” do you have in your car? There are at least three cs 6 jx3teim0d-ontrols in the car which can be 6dmse-j0t xi 3used to cause the car to accelerate. What are they? What accelerations do they produce?

A child on a sled comes flying over the6 a xgxljr3ck m*k-;i9 crest 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 hr jx3 ;agc69k*xkm li-ill. Explain this decrease using Newton’s second law.

Why do bicycle riders lean inward when rounding a curve at high speqw(z l7l-vbby/9f ) teed?

Why do airplanes bank when they turn? How would you compute the banking angbnamp5 z +z-)nle given its speed and radip+) n5abnm z-zus of the turn?

A girl is whirling a ocxz 9*1slfh ,ball on a string around her head in a horizontal plane. She wants to let go at l1z9*cx o hsf,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 f s(prb5sp3)3jk 9waev5dyl0dorce on the Earth? If so, how large a force? Cd 3apr3s ) dblepyws 9v5j(50konsider an apple
(a) attached to a tree, and (b) falling.

If the Earth’s mass were double what it is, 1(nw00pv/gmi-d,z*p zrw di) zhhe* zin what ways would the Moon’s orbit be difzi- rw1pn emv 0wzgid(d/0z)*, phh*zferent?

Which pulls harder gra8 +qmd,edp amro2yslb(f 9:i(vitationally, the Earth on the Moon, or the Moon on the Earth? 2( femms8yq9dlpodb+a,ir:(Which accelerates more?

The Sun's gravitational pull on thpu mjt1)g19f w jc6c)he Earth is much larger than the Moon's. Yet the Moon's is mainly responsible u c1h1c)fj pj)w6tm9g 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 q yd1b uik-uo*b)c8 +fat the equator or at the poles? What two effects are at work? Do ki1 )*o u8-dbqufy+bc they oppose each other?

The gravitational force on the Moon due to the Earth is onlyb v(i*wi 49hqw about half the force on the Moon due to the Sun. Whw4hi*b i9 qwv(y isn’t the Moon pulled away from the Earth?

Is the centripetal acceleration of Mars in )2agy7qp+- -8ma cdgs+t kzrdits orbit around the Sun larger or smaller than the ce-)q+ata-27 yz dkdrcspm+gg8ntripetal acceleration of the Earth?

Would it require less speed to launchd lu ryo5-fha7)3iv- 3jt or-y a satellite (a) toward the east or (b) toward the west? Consider the -l-i)37r y of dj3uayh o5v-trEarth’s rotation direction.

When will your apparent weight be the greatest, as measured by a scale ,e h o/d4n+m*jniu mk3in a moving elevator: when the elevator (a) accelerates downward, (b) accelerates /jo m43kuid*nem h,+n 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 ph9ovfy+ 1*nvx2pxn t +jkfj1x.t7*wseriods in outer space could be adversely affected by weightlessness. One way to simulate gravity is to hkxx tw1+9fn 21 *xn.fsp j+ot*v7jyv 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 think of.

Explain how a runner experiences “free falw to od9o4x06yme0kr/pd zs:0qe(8pw l” or “apparent weightlessness” between4 otq0/py p0 ko9o(6x8w:rm0dseez wd steps.

The Earth moves faster in its orbit around the Su*pi co+f083fuzd-jl c n 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 l c8+ju ff0zc-iod3p*the Earth’s axis relative to the plane of its orbit.]

The mass of Pluto was not known until it was discoveoy:8ud o3vx /ared to have a moon. Explain how thv 8uo3xa/y:od is discovery enabled an estimate of Pluto’s mass.

  The Sun's gravitational pull on the Earth is much largequfi2gt8j rvg q69 +2tr than the Moon's. Yet the Moon's is mainly responsible for the tides. Explain. [Hint: Consider the difference in gravitational pull from one s r9tgut8f2g2q 6i q+jvide 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 19 ;t) */5ocyizqt3 ue:mjs1dit .n kqm vj5+f,y80 $\mathrm{~km} / \mathrm{h}(525 \mathrm{~m} / \mathrm{s})$ 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 j9u k3i(l yh5-v45sevas qz/aacceleration of the Earth in its orbit 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 circl/s4 zyas ea-hu3kv 55jil( 9vqe 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 of 210 N is exertei/ r/uil6,8harmtq -od on a 2.0-kg discus as it rotates uniformly in a horizontal circle (at arm’s length) of l/u-6tm qr,i/a r ih8oradius 0.90 m. Calculate the speed of the discus.   

  Suppose the space shuttle is in orbit 400 k7,2ar t5c thnlyrzp9mob:g14m 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 the Earth's surface7cp2l,4z9b m1nt: atogyr5hr . $\approx$    g

  What is the magnitude of the accex0b0eb e14ucrca7n9l leration of a speck of clay on the edge of a potter’s wheel turnincne0 bx0r l49bceu71a g at 45 rpm (revolutions per minute) if the wheel’s diameter is 32 cm?   

  A ball on the end of a string is revolved at a uniform rate l+t- gwcp.kq:w:f w,lin a vertical circle of ra, kw:wlcgw . tp+fq-l:dius 72.0 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 ,8,s +epbqgp 5bsz+:q*da1uq -stn on 1050-kg car can 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 this repgsq bbn 8:qs 1 t,+p5doqn+ e*-za,ussult independent of the mass of the car?   

  How large must the coefficient of static frictiox)ncw 1 o;c m4qhdjh01n be between the tires and the road if a car is too)1q 0h;c chmnd4jx 1w round a level curve of radius 85 m at a speed of 95km/h ?   

  A device for training as 3b1q14 qtyjbhtronauts 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 y41bjqqt 31hbtimes 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 fod*u jvf 9nx82rom the axis of a 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 slides odv2u8n*f xj9 off. What is the coefficient of static friction between the coin and the turntable?   

  At what minimum speed must a roller coaster be traveu qd,r9mc bsu-92) mfnling when upside down at the top of a circcufb9msd-q u29,rmn)le
(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 (inc ;thpes,2 l go;,hx1xgy6ba;dluding the driver) crosses the rounded top of a hid;xl2,,agx1ebyhs o; ptg 6h;ll (radius =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 Ferris wheel need totdqj )wvv/3)ds*g7s h make for the passhv g*j7)sdd/ v)swq t3engers to feel “weightless” at the topmost point?    rpm

  A bucket of mass 2.00 kg is whirled io )kl 2g4p5nsnn a vertical circle of radius 1.10 m. At the lowest point of its motion the tension in the rope s n g)245snoplkupporting the bucket is 25.0 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.*n3vlas(m v:s8d l4a t0thyo3 00 cm from the axis of rotation is to expavy3:dl ton0 4v samh3s8(l*t erience an acceleration of 115,000 $\mathrm{~g} $'s?    rpm

  In a "Rotor-ride" at a carnival, people are a tk2/m80 x nnm(rnajo- v*l/jrotated in a cylindrically walled "room." (See Fig. 5-8j xmr*/kmatv nnj0n2-/ola( 35.)
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 ca4f*hl mdo)t1ircle on a frictionless air-hockey tabletop, 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.)d*4m1tlao h f 5-
36. Show that the speed of the puck is given by

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

  Redo Example 5-3 , precisely tb5yo s2gm3 w+vhis time, by not ignoring the weight of the ball which revolves on a string 0.600 m long. In particular, find the magbmwo+ s5 gy32vnitude 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 4x2 :rum1jf y.xgv*lz 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 masses (q51dhvvy ewjan( x5wrf;/f 78;edgx m1p nz.$ 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 evasivesfs2pm.qb98/bl 9rml maneuver by diving vertically 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 andd usy 8pi:n,w o:n(q. csrql0; centripetal components of the net force exerted on the car (by the ground) in Example 5-8 when il,wn:qs.r0q(dui; ps 8nc:oy ts speed is 15$ \mathrm{~m} / \mathrm{s}$ . The car's mass is 1100 kg . F$_{tan}$ =    F$_R$ =   

  A car at the Indianapolis 500 acc u,q jh;e9apiw2on2k4* qe. tuelerates uniformly from the pit area, going from rest to 320km/h in p2o ehqk u 4w2j*ti.n;a9u,eqa 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? $\approx$   

  A particle revolves in a horizontal circle of radius 2.90 m . At asoh8hy:gdz7 k+g ys-m 6v yn-( particular instant, its acceleration is 1.05 oz:y6ykh(gyh- n-+8 gs 7s dmv$\mathrm{~m} / \mathrm{s}^{2}$ , 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 gravi:0plnnln7uk.vm1 :z 0dm/k osty on a spacecraft 12,800 km (2 Earth radii) above the Earth’s surface if its mass is 1350 kg.l 1zsm kvl.nndn/m::o0 up70k   

  At the surface of a cer5 .ntq:n2lf: qh*ahlytain planet, the gravitational acceleration g has a magnitude th h:fnl*an:5qqly 2.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 y79sdri 3yi 6ion the Moon. The Moon's radius is 1.74rs iyi 9i673yd $\times 10^{6} \mathrm{~m} $ and its mass is 7.35 $\times 10^{22} \mathrm{~kg}$ .   

  A hypothetical planet has a radiusv /sbnx7t5d w( 1.5 times that of Earth, but has the same mass. What is t5n(bs vxdw7 /the acceleration due to gravity near its surface?   

  A hypothetical planet has a mass 1.66 times tla5xka4phq ;* hat of Earth, but the same radius. What is g near its 4 pal;a x5qh*ksurface?   

  Two objects attract each od2g -ufwo. io.esi.avq;6k l: ther gravitationally 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 , tlq6m0-j )tp6 z9ajpn :pxz1qnhe acceleration of gravity, at (a) 3200 m0 j-pa:6lzp jtxzp)qn 1mq9n6    , and (b) 3200 km    , above the Earth's surface.

  What is thedistance froob4*9smf 7ypa m the Earth’s center to a point outside the Earth where thegravitational accel9mafsp o *y7b4eration 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 into a sphc oxi z6+r*w8pere about 10 km in radius. Estimate the si8pr*xwc +z6o urface gravity on this monster.    $\times10^12$

  A typical white-dwarf star, which oncenr9g/tf:smc 3i9 t x9ykgdyc+;/ku2f was an average star like our Sun but is now in the last stage of its evolution, i/d3m9 ygfgk+9;u t:92tc/n srfy cxiks the size of our Moon but has the mass of our Sun. What is the surface gravity on this star?    $\times 10^7$

  You are explaining why astronauts feel weightless while orbiting in gcb/ekv84j9uthe 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 by calculating the acceleratc8/4j9bveug kion of 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 of s bp3va ;g(h0gbide 0.60 m. Calculate thev0g(gp;ba 3h b magnitude and direction of the total gravitational force exerted on one sphere by the other three.   $\times 10^{-1} \mathrm{~N} \text { at }$    $^{\circ}$

  Every few hundred years most of thtt b*/0wb t4ittpt: k:e 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 planets btkiw0 t /ttb: :*pt4tare 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 sur9txb2 w;ynmihr) i/k.face of Mars is 0.38 of what it is on Earth, and that Mars’ radwkrmbxy2i 9t);.nh /iius is 3400 km, determine the mass of Mars.    $\times 10^{23}$

  Determine the mass of the Sun using the known value for the period od;wj aq6s 5 5s3iejm+diqu; )ukb(kh8f the Earth and its distance from the Sun. [Note: Compare your answer to that obtained usin5mj a ;bd 65eji)s;+kwhk sq3 (u8uiqdg Kepler’s laws, Example 5–16.]    $\times 10^{30}$

  Calculate the speed of a satellite moving in a stable circulqh0g0ju.ul *a ar orbit about the Earth g*h0uauq0 .lj at a height of 3600 km.    $\times 10^3$

  The space shuttle releases a satellite into a circular orbic9j po ,e.3nent 650 km above the Earth. How fast must the s, pen 39eoj.nchuttle be moving (relative to Earth) when the release occurs?    $\times 10^3$

  At what rate must a cylindrical spaceship rotate if occupants are to o6c a.ufzceab.x,,/i9kh2(szpcv d; experience simulated gravity of 0.60 g? Assume the spaceship’s diameter is 32 m, and give your answer as the time needed for one revh.xz,a o.6cz;2kup e9a fs( v /,ccdibolution. (See Question 21, Fig 5–32.)   

  Determine the time it takes for a satellite to orbit the Earth in a circular .cp7 nai 9vw hx6g(4rp“near-Earth” orbit. A “near-Earth” orbit is one at a height above the surface of the Earth which igc69v prpa(hx.7wi4 ns very small compared to the 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 lau4bl skp75s4+5xjjs 3nnl j)wwnched from the top of Mt. Everest to be placed in a cirx )54+klj45 bpwnsjws3lsnj7 cular orbit around the Earth?   

  During an Apollo lunar landing mission, the command module co-,;wo tawkn) +t+ac santinued to orbit the Moon at an alttnaw-)s aw ;+o+c t,akitude 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 orbit the planet. The inn ypm sh537zl-;pf+m qve.3uj mer radius;p-mlj . yhsmu7zme fq+53p3v of the rings 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 (see Fig. 5–9). W.3f/l*og z)*res eknnhat is the ratio of a person’s apparent weight to her real weight (a) at the top, and (b eens*k /. 3rog*ln)fz) at the bottom?
(a)    (b)   

  What is the apparent weight of a 75-kdcg0ab755gzdhgb + h5 g astronaut 4200 km from the center of the Earth's Moon in a space vehicle (a) moving at bd55a 0 cgzdg75bgh+hconstant 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 (pdt5wo j+6*js g 1grm-iwe p+equal mass. They are observed to be separated by 360 million km and take 5.7 Earth yearsdpm -j+w se*w1g +(5ig6toprj to orbit about a point midway between them. What is the mass of each?    $\times 10^{29}$

  What will a spring scale read for the weight of a 55-kg woman in:5j qu0 rev -twod0va*su ua1/ an elevator that moves vrw1sv:0 ja0d/u5e u-*tuqao
(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 aujm51,; gy c1ud5f /v:p jhzfa cord suspended from the ceiling of an elevator. The cord can withstand a tension of 220 N anvy/5 jmcp;jg ,f:h duf15au1z d 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 of a planet with period Ti 5yxvpv2(e0m pf9as6 , the densitypx(vs0me6i f2a59p yv (mass/volume) of 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 perionc4t6e1ttlw68q b n (2cz kk(dd of an artztcnbed w6qt481nc2k6 l(k( tificial satellite orbiting very near the Earth’s surface.    s

  The asteroid Icarus, though only a few hundred meters across, orb e 0;jkez6sgu,)c7lt k f+ew3rits the Sun like the planets. Its period is 410 d. What is its mean distance from th6jszck+uteg0;rw,3lkf 7) ee e Sun?    $\times 10^{11}$

  Neptune is an average distance of 4.2o (a2l c/um4t(stxm4 nbqb -j5 $\times 10^{9} \mathrm{~km}$ 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 the Sun roughly once every 76 years. Itt ws i(jd +vi:r 9mse+jv2l74g s-j0lw 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 law is half the sum of the nearest and farthest distance fr-4ij(jg 97+dw lj0s:s iev+ vtm2wslrom the Sun.]    $\times 10^6$

  Our Sun rotates about the center of the yn;rqu( , eg.xd+0 uvqGalaxy $\left(M_{G} \approx 4 \times 10^{41} \mathrm{~kg}\right)$ 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,o21-z m jph7yo period, and mean distance for the four largest moons of Jupiter (those dizj o-h21yo p7mscovered 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 from the known period and distance of thp3ln4v)xae *o; u3eejf rue+ 7z-r2 nse Moon. 33* x s)2ae-+e ;lz7onjreu np vfe4ru   $\times 10^{24}$

  Determine the mean distance from Jupiter for each of Jupiter’s moons8wgl6n 8wd kg), using Kepler’s third law. Use the distance of Io and the )lwg ng68wd8 kperiods 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 fragmentsd7sd x0hbm0r+.cwzeljt161n tiq(m2 (which some space scientists think came from a planet that once orbit c7rd 0 1bjmimnhewxqs0.6d (1z+l2tt ed 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 describes an artificial "planet" in the form of a band coduwa3d rs*ov4(z lt45mpletely 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 t*d4z5lt3s4uavo dr w(he 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+c n5t gy62sztmre() r6*w vko (Fig. 5–41). If his arms are capable of exerting a force of 1400 N on the n)*mzrs(kcwt v+ 65r 6yge o2tvine, 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 w ;u4qc3dhbl vy3 x-;kiill the acceleration of gravity be half what it is on th;xkclbi dy3vhq4 3u-;e surface?    $\times 10^6$

  On an ice rink, two skaters of equal mass grab*g/ .2pkqgi)v2vuh -cqy3j jg 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 60gpv qu/22qv)3hg.*gkicy -jj .0 kg, how hard are they pulling on one another?    $\times 10^2$

  Because the Earth rotates once per day, the apparent accelerw(vj+ h2:r szpation of gravity at the equator is slightly less than it would be if the Earth didn’t rotate. Estim+(2p :w shvrzjate the magnitude of this effect. What fraction of g is this?    $\times 10^{-1}$

  At what distance from jviawuw5pn9vi1i0 n:((jyc7 the Earth will a spacecraft traveling directly from the Earth to :y1w nc7ij 0v5jini (uwp(av9the Moon experience zero net force because the Earth and Moon pull with equal and opposite forces?    $\times 10^8$

  You know your mass is 65ol/ +qne 6spdg9 ,kf-iukwc0n- 5f fi7 kg, but when you stand on a bathroom scale in an elevator, it says your mass is 82 kg. What is the acceleration of the elevatoi,k7lqs f596fc 0i+pnkfgud eo- /-wnr, and in which direction?     ----待选择----upwartddown 

  A projected space station consists of a circular tube th 69 xcnrsw)mtk ii7oka)64uj4:u 3 tdjat 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 to gravity at the surface of the Earth (1.0 g) u )4 66m4sda)joirtuwxi7k c tk9nj3:is to be felt?$\approx$    $\times 10^3$

  A jet pilot takes his aircra7anywr5 gvjv1+ ; ioq +hf6j4vft 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 planet in terms of its radius r, the aci nc 4m39)eaw*3 jyeiiceleration due to gravity at its surface and the gravitationj4yi3w m9 ai e)*eci3nal constant G.

A plumb bob (a mass m hanging on a string) is deflected from adqq pvy9nj :al*9e:.the vertical by an q ynev* .a9d:a:p 9jlqangle $\theta$ 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 de b;9 b hsjo2:issay(ccw;k22m sign speed of If the coefficient of static friction is 0.30 (wet pavement), at what range of speeds canhasjby ks;w o; 922cc(2b sim: a car safely handle the curve?

  How long would a day be if the Earth emikd40 y.e1 kq1b6og were rotating so fast that objects at the equator were appareniem01 6d1q y4kkegb.otly weightless?    $\times 10^3$s

  Two equal-mass stars maintain t;ubax4(l z:fa 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 roun3onhyy6k0 3mgr or*q4ds a curve of radius 235 m. A lamp suspended from th3r 0634mqogyyn*rk oh e ceiling 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 mfz/ n2 bbh/:exassive as the Earth. Thus, it has been claimed that a person would be crushed by the force of gravity on a planet the size of Jupiter since people can't survive more than a few g 's. Calculate the number of /e 2:bznxhf/b 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 Telescope deduced the presence of an extreme wmgk9iu9f2u0t4x 5 2q pogn8xly massive core in the distant galaxy M87, so dense that it could be a black hole (fro u2 54ogpnu m2qxxi8 fw0tk9g9m 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 *0t5 kyrd 7kgdas it traverses the hill and valley shown in Fig. 5–45. *k5d ktdg07 ryBoth 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?) 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 Positioning Sypnz3cd-ldyifxr0.r8,dh s2 -stem (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 nautical ].s yrc-dx p f-rid032dn,8.l zh (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. vrb7q,c/dx y21 billion km, is meant to orbit the asteroid Eros at a height of about 15 krcx7ydq vb/,2m . 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 +7 k z(tyt6s; 5pn7 glws:bprkshuttle pursuing a satellite in need of repair. You are in a circular orbit of th;t+g brpt6 (nys5 :7ls 7wkzpke 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 hasg03u*yx ;4b )y2j8mxq qzhrxx a period of 3000 years. (a) What is its mean distance from 0rz *3xxxjbqy)x qm 48;yugh2 the Sun?   
(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 if you could actually "feel"sicf3rakq g,m/p ku ,57g+t q1 yourself gravitationally attractedqrg3+t7s/ kpgu k fc,q,a 1im5 to someone near you. Make reasonable assumptions, like F $\approx 1 \mathrm{~N}$ .    $\times 10^{-5}$

  The Sun rotates arou93: z:r89zzsut gy fqind the center of the Milky Way Galaxy (Fig. 5-46) at a distance of about 3rzy8z i :u:f93tsgz9 q0,000 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 9g d+s-8vhsqwkh2 tg iz7;l+qat the corners of a square 0.50 m on each side. Find the magnitude and direction of the gravitat9gwk7 vithsqq ld8gs;++hz2- ional force on a 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 5500 kga/ q f/(o5:*rbzz xcoa1qe,qe 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 experienced by the tip of the 1.5-cm-loaf2 h5orgn pvg-q-u(0 ng sweep second hand on your rq(g 2-vhgo0n u-p5afwrist watch?    $\times 10^{-4}$

  While fishing, you ge b *-qqg; ;rxbqkn9r3ht bored and start to swing a sinker weight around in a circle below you on a 0.25-m piece of r q;bq-h3n *kxg;qb9rfishing line. The weight makes a complete 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 radius R in a new highway is designe 46lxxs g5yi5bd so that a car traveling axsx54l5ib6gy t speed $ 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,* kb9nfvn,6 unzan,;; d8c bjt tp8-wm the Acela, 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) Calculate the friction force needed on a train passenger of m-9 6*n8jn,t; ;azw8fubtcbd nnp,v mkass 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.$\approx$    $\times 10^2$