Sometimes people say that water is removed from c0k: s kxe bk9ueb,s 3e8oq-zc*lothes in a spin dryer by centrifugal force throwing the ,u3skbe 8 bek zxo*e-s:09ckqwater outward. What is wrong with this statement?

Will the acceleratiowqk(hm1 2l6 uhi iv4o/n of a car be the same when the car travels around a sharp curve at a constant 60 km/h as when v/hhlwqik(m1io62 u 4 it travels around a gentle curve at the same speed? Explain.

Suppose a car moves at constant speed along a hilly road. Where doe ozm-/kenv*u/p/)h mzs the car exert 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 hv-z/ u*oz/m)p emn /knear the bottom of a hill?

Describe all the forces acting on a child riding a horse on a merry-gdr* (3t5 , egcnbj:yfzo-round. Which of these forces provides the centripetalzgje5 3:rfyc* (nt b,d acceleration of the child?

A bucket of water can be whirled in a vertical circle without the water spi- ypymrn c92s0lling out, even at thenypsryc- 9 m20 top of the circle when the bucket is upside down. Explain.

How many “accelerators” do you have in your car? There are at least thr-l d(seogx-0 mee controls in the car which canl--d(xe mo gs0 be used to cause the car to accelerate. What are they? What accelerations do they produce?

A child on a sled col m- n9bszi6(n5/s yedmes flying over the 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 hill. Explain this decrease using N(6l es in snmby59-zd/ewton’s second law.

Why do bicycle riders s.z(ao sr7odzi98 o7 zlean inward when rounding a curve at high speed?

Why do airplanes bank when the8lm.vrg wjf: j+p ;g;ey turn? How would you compute the banking angle given its speed and ravgj lr8:efpmw;.+g; jdius of the turn?

A girl is whirling a ball on a string around her head in a horfjrzr jg49* :pbxk 68d2 qje7qizontal 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 qg7j28j94 qr z:6xkbej dp*fr. When should she let go of the string?

Does an apple exert a gravitati0gtgp/ 9a8doethc0 s3onal force on the Earth? If so, how large a force? Consider an dsoe9hg/ g t3tp80ca0apple
(a) attached to a tree, and (b) falling.

If the Earth’s mass were double what it is, in what ways would v gvae1wmol;)pw5d 23the Moon’s orbit be differente w) 1dmwop2;a35vvgl?

Which pulls harder gravitation 80cnxa 3qhoi-z/7uhpally, the Earth on the Moon, or the Moon on the Earqhaxp 70h z3 un/c8o-ith? Which accelerates more?

The Sun's gravitational pull on the Earth is much large(gj)jt kt-pz*h en9m -r than the Moon's. Yet the Moon's is mainly responsible for the tides. Explain. [Hint: Consider the difference in gravitational pulj*) mj- p(nzeghtk-t9 l from one side of the Earth to the other.]

Will an object weigh more at j* frqxhn0 qu+ 2hn,b2the equator or at the poles? What two effects are at work? Do they oppohb nrfn*2hqq 2xj 0,+use each other?

The gravitational force on the Moon due to the Earth is only about half the for* i+jhrqo ai ,-ac31b :v6walrce on the rc1+r wijav-*i6 ob,3al: qhaMoon due to the Sun. Why isn’t the Moon pulled away from the Earth?

Is the centripetal acceleration of Mars in it2nfi;-fxz +)w.szgi s v)m6y ws orbit around the Sun larger or smaller than the centripetal accelerationiigs n f6.y- zzf)xmsvw+);w 2 of the Earth?

Would it require less speed to launch a satellite gycg815 .m(nxutla*q(a) toward the east or (b) toward the west? Consider the Earth’s rotationa( 1xc8tgy*gm.u 5 lqn direction.

When will your appar xpcx lh8(jm6mi3(rs+ent weight be the greatest, as measured by a scale in a moving elevator: when the elevatoxr m6(3 (l+xp miscj8hr (a) accelerates 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 could be adversezrhzpt0 ty/2 81px (r3aclv+ qly affected by weightlessness. One way to simulate gravity is to shape the spaceship like a cylindrical shell that rotates, with the astronauts 0(yzr8r31ltp qc2+ ah tv /zpxwalking 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 vm z15;7tovg-ipepn 0experiences “free fall” or “apparent weightlessness” between st; i5p-vn7mvgo0eztp1 eps.

The Earth moves faster in :c9*pvv wo(mkg8k 9q:qj fz0lits 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 p(q9v8cp jqv:f*:g k0k mo9wzllane of its orbit.]

The mass of Pluto was not known until it wasaq)3vap5ny k 35gnd;d discovered to have a moon. Explain how this discovery enabled an estimate of Pluto’s mass nk)qdv53;n5 p3 gydaa.

  The Sun's gravitational pull on the Earth is much largtblxw (g ,p*t0er than the Moon's. Yet the Moon's is mainly responsible for the tibp,tg (xwt 0l*des. 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 1, p)zkha*+r) af; cvue980 $\mathrm{~km} / \mathrm{h}(525 \mathrm{~m} / \mathrm{s})$ 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 acca9nht d(k )g)0-yketceleration of the Earth in its orbit around the Sun, and the net force exerted on the Earth. What exta 0(tkchd)-)gyk 9enerts this force on the 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 of9ge,2 i;op dsa krk.5n 210 N is exerted on a 2.0-kg discus as it rotates uniformly in a horizontal circle (at arm’s length) of radius 0.90 m. Calcuik59,sprg k; o ane2d.late the speed of the discus.   

  Suppose the space shuttle is in orbit 400 km from th8,s* -)ufpy g9wvdo0 :yzyk jxe Earth's surface, and circles the Earth about once every 90 minutes. Find the centripetal acceleration ofyxj wvokz9gyf, psu 0)-8y*d: the space shuttle in its orbit. Express your answer in terms 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 thec: au9ml t:n)m edge of a potter’s wheel turning at 45 rpm (revolutions per minute) if the wheel’s diac at)u::9mmn lmeter is 32 cm?   

  A ball on the end of a string is revolved at ijd8hh 4b9tm 0a uniform rate in a vertical circle of radius 7hh8 tdm49bi0j 2.0 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 elmkr o ztq(xv86/:g9 with which a 1050-kg car can round a turn of radius 77 m on a flat road if the coefficient of static frictiogkz:rvmx/e 69 oq8(tln between tires and road is 0.80? Is this result independent of the mass of the car?   

  How large must the coefficient of static friction be between the tires and the rl,7vxdy5m iefbjnm0/g2 :n lipeech7x; 4t*0oad if a cvg 5dll ,;m n: xi/t hc*0x7y07b2mefpi4jenear is to round a level curve of radius 85 m at a speed of 95km/h ?   

  A device for training afk9hk/5unpe8vv l (u 7jp9s pw ,*iy1vstronauts 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 her own weight, how fast is she rotating? ivuup59nf*v7 hlpks kwp/,89e(y v1j   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 variable4 w.-s 0xkfb(x lxlk/lz9lsp6 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 off. What is the coefficient of static frictiobkf0lxwls/xl-.xz( slk 6 4 p9n between the coin and the turntable?   

  At what minimum speed must a roller coaster be traveling when upside down at tc bz0yy6 xo3r.oynb-1he top of a circlb36rn-oo1c z by0yx .ye
(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 (inf4ld+t5s ( pitcluding the driver) crosses the rounded top of a hill (radiu(4fs+t 5 tpldis =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 to ma6r r/5rb8v ml:so ohn1ke for the passengers to feel “weightless” at ts 6vr5/8r oolh1nb:rmhe topmost point?    rpm

  A bucket of mass 2.00 kg is whirled inimio iu9;gx.7 a vertical circle of radius 1.10 m. At the lowest point of its motion the tengm9u ; o.ii7xision in the rope supporting 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 9.00 cm from the ai/d1/m)nj pt0rr,9 uu yzw.dr l 1tdhx2vz 8z,xis of rotati9wd ,tj2ddyu v/zur.n10z 1 /l)mhirrtz x8,pon is to experience an acceleration of 115,000 $\mathrm{~g} $'s?    rpm

  In a "Rotor-ride" at a carnival, powmzf 6f34 /ufeople are rotated in a cylindrically walled "roof 6z3mwf4/ ofum." (See Fig. 5-35.)
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 circle on a fjt 9ow,08lncurictionless air-hockey tabletop, and is held in this orbit by a light cord connected to a dangling block (mass m ) 8t9wc0 ju nl,othrough 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 , pre/bdxu6yc ,r 51*ko zydbsup07cisely this time, by not ignoring the weight of the ball which revolves on a string 0.600 m long. In/0yr 51, bckzo*u6uxdp dys7b 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 radiupsqpax0 3*gx4s 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 masseb2n m*cm6 ta6ms $ 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 evasisxf-5.9xmyy + .uwym wve 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 and centripetal components of the net fzvx4t -mlsm /(orce exerted on the car (by the ground) in Example 5-8 when (x -vstlm4zm /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 uniforml, qni07kl;w+4hb hjycb5r/bi1 8wo quy from the pit area, going from rest to 320km/h in a semicircular arc with a radius of 220 m. Determine the tangential and radial acceleratio+cq/lwr4 hykb0i b85j1n;i hwoq,ub 7n 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 horvc+uvbqh sjsw 59vm:rdx(6 4e k:t9q,izontal circle of radius 2.90 m . At a particular instant, its ac+w x ev(sum94stjkb,9hvq:56vq :rdcceleration 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 nlearw6k(idd zs/ :vya24k38km (2 Earth radii) above the Earth’s su8en36 kd:ykrwzsa/(4 d l2ai vrface if its mass is 1350 kg.   

  At the surface of a certain planet, the gravitational acceleration g has 6s-td*5 z zxnka magnitu6 t zdns5zk-*xde 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 accelerc+ qjw9./k l8otn6wp kation due to gravity on the Moon. The Moon's radius is 1.74n98.k+6j/ k twwlp qoc $\times 10^{6} \mathrm{~m} $ and its mass is 7.35 $\times 10^{22} \mathrm{~kg}$ .   

  A hypothetical planet has a radius 1.5 timeh6 1wzc5 02sqj y:ajans that of Earth, but has the same masjza :w a2 0jsqnc516yhs. What is the acceleration due to gravity near its surface?   

  A hypothetical planet has a mass 1.66 times that of Earth, but the sameqx71q0q:vhtn ;+ 0zi0zoe tne radius. What is g nea;ttn0qi z qv+ z1nxh:q0e7oe0r its surface?   

  Two objects attract t0:y6tr g;gcbx(sg/ s each other 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 , the acceleration of gravity,1orwkd xl0 yr* m-y1w6 at (a) 3200 mr6 dw1ywyl* 0-okrmx1    , and (b) 3200 km    , above the Earth's surface.

  What is thedistance from the Earth’s centc dn0,ulpnct/ n92p4ter to a point outside the Earth where thegravitational acceleration due to th 9u4cndp0cn2,p/t lnt e 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 twosb *)o(jf;yo:ej p)g+1 husphere about 10 km in obsy ;jgjft:oewp)+h1ou(* ) radius. Estimate the surface gravity on this monster.    $\times10^12$

  A typical white-dwarf star,jk312 n/l8hqmw f(kp t which once was an average star like our Sun but is now in the last stage of its evolution, is the size/m(kjln13 2qpwt8k hf 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 21s tj vk y8+8tdfwaw2while orbiting in the space shuttle. Your friends r+tjfs ww2 yv8k1at82 despond that they thought gravity was just a lot weaker up there. Convince them and yourself that it isn’t so by calculating the acceleration of gravity 250 km above the Earth’s surface in terms of g.   

  Four 9.5-kg spheres are located at the corn 9mmio 3(vlz.iers of a square of side 0.60 m. Calculate the magnitude and direction of the total gravitational force exertedm(9 .ioz l3vim on one sphere by the other three.   $\times 10^{-1} \mathrm{~N} \text { at }$    $^{\circ}$

  Every few hundred years most of the planets line up on the same side o/asmh9dn co+ 2 iij:o +b0z)hdf the Sun. Calculate the total force on the Earth due to Venus, Jupiter, ann i mah90d:s/2zo)d jh++ obicd Saturn, assuming all 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 afc4p6*w /py :n 42xkntpqv*b vt the surface of Mars is 0.38 of what it is on E 2/f4 * cpptyxvbwqnnpk*v:6 4arth, and that Mars’ radius is 3400 km, determine the mass of Mars.    $\times 10^{23}$

  Determine the mass of the Sun using the known value for the period ofc+vm q*eq9zg dkze./dh dvk 8-adl np0u5)9 h) the Earth andddgquc)hp k8mvz. k+ 9*-nev5 q9 ehl0/z )add its distance from 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 circulyd : 6id3jvrb4bz 7x;far orbit about the Earth at a height3yr6jx ;f :vbbi4d7zd of 3600 km.    $\times 10^3$

  The space shuttle releases a satellite into a circular orbit 650 km abovh5fb a1ey2a +he the Earth. How fast must the shuttle be moving (rela2hy5 aahbfe+1tive to Earth) when the release occurs?    $\times 10^3$

  At what rate must a cylindrical spaceship rotate if occupants are t j3ncst6pfc 5epw7l- *o experience simulated gravity of 0.60 g? Assume the spaceship’s diameter is 32 m, and give your answer as the time need7-cles53*wjfpt ncp6ed for one revolution. (See Question 21, Fig 5–32.)   

  Determine the time it takes for a satellite to orbit the Earth in a circulat oq;y0l+ .z:w)swj pfr “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. Do.s wfwj;+yl:zqt0p )oes your result depend on the mass of the satellite?    s ~    min

  At what horizontal velocity would a satellitel x, j ,zc ev)h:gjb67b17vnwv have to be launched from the top of Mt. Everest to be placed in a circular orbit around the Earth? lgj,ec w7jb7z:)b6 v xv,vn1h  

  During an Apollo lunar landing mission, the command module continued to orbbk39tteocu 7 em v:2+lit the Moon at an altitude of about 100 km. How long did it take to go around the Moon onteltmc+o23ubevk 7: 9ce?    s

  The rings of Saturn are cs5vy*rju /x g)q-nl j2omposed of chunks of ice that orbit the planet. The innery2-gj*n)ur 5s/x lq jv radius 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 15.5rlfz;f8n.sh;hqrcm 9e3 o:9 k s (see Fig. 5–9). What is the ratio of a person’s apparent weight to her real weight (a) at 9rmfh9sz q8k o3l;n .c ehr:;fthe top, and (b) at the bottom?
(a)    (b)   

  What is the apparent weight of a 75-kg astronaut 4200 ksw3gm 6). dkxym from the center of the Eartwxd g6m3. )yksh'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 equal mass. They augo u*douvm ,1 )b;:eo)auue*re observed to be separat,e ou u1): *o gvoad)*uu;bmueed by 360 million km and take 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 scale read for the weight of a 55-kg woma6py-)ra.t i rln in an elevator thattir.6rlpa ) -y moves
(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 6 rasc4(3:tdqo a b-,ugai o,bsuspended from the ceiling of an elevator. The cord can withstand a tension of 220 N and breaks a4q:b 6cg(ati,uo- sr 3dbaoa,s the elevator accelerates. What was the elevator’s minimum acceleration (magnitude and direction)? a =   

Show that if a satellite orbits very nearm6 /p4g. 2gpdes*miay j ,z3xz the surface of a planet with period T , the d26i ,y.4d ej* 3mpgzzx/ampsg ensity (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 the0ad:tk zc6c0czs o4uv+rd2l; period of an artificial satellite orbitinguzcr0d0 ;4dv6tclck+oaz2:s very near the Earth’s surface.    s

  The asteroid Icarus, though only a few hundred metgykmank7sz 23a1 0ou6 ers across, orbits the Sun like the ms1a zkk7ng 6u23oy0aplanets. Its period is 410 d. What is its mean distance from the Sun?    $\times 10^{11}$

  Neptune is an average dismwh:aczcmu,jk,hf55m 1); l f tance 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 the Sun roughly once every 76 years. It comes very cloi.bscj j(hv4.se to the surface of the Sun on its closest approach (Fig. 5–39). Estimate the greatest distasj v(bchj.i 4.nce 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 from the Sun.]    $\times 10^6$

  Our Sun rotates about the center of t ao6 vcdw1vr ,1qyqbz(gpr* 6*he 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 massscd4 )x-fdgu w mz9u:7f;2xo b, period, and mean distance for the four largest moons ofm d9zwx2:o;u-fcdbg7 uf) s 4x Jupiter (those 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 from the known periodwg+m/)4h 6p fld cqsq8x40lun and distance of the Moon. gs +f0pcxl4h u86)dln4 m/qqw   $\times 10^{24}$

  Determine the mean distance from Jupi 4g.wr u-ccg9ater for each of Jupiter’s moons, using Kepler’s third law. Use thewcgg .ar94-c u distance of Io and the periods 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 be, .koe*4cik(vod 7j:cmk it.xtween Mars and Jupiter consists of many fragments (which some space scientists think came from a planet that once orbited the Socikk c t*. .i7d(,kmj4oe:vxun 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 ox*x.dzck- 6u- um6gadescribes an artificial "planet" in the form of a band completely 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 todxxuu6m g-ac6 k* o-.z 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 (n x y,i,zx*k6hi7 pl)jFig. 5–41). If his arms are capable of exertil jxy*, ) kp,i7inzx6hng a force of 1400 N on the vine, 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 acceleration of gravi vm9+z7qw 6+sg1vlznsty be half what it is on the suvq1z+7zw smg6l+ nv9srface?    $\times 10^6$

  On an ice rink, two skaters of equal mass grab hands hxoi f(7; h/qd(n vq/pand spin in a mutual circle once every 2.5 s. If we assume their p/qv /7(o( idhxnfh;qarms are each 0.80 m long and their individual masses are 60.0 kg, how hard are they pulling on one another?    $\times 10^2$

  Because the Earth rotates once per day, the apparm 5mg*3;wl:ae atiyeo- 3vbg1ent acceleration of gravity at the equator is sligtmo b 5-e vl;mw:ia3aegg*1 y3htly less than it would be if the Earth didn’t rotate. Estimate the magnitude of this effect. What fraction of g is this?    $\times 10^{-1}$

  At what distance from the Earth will a spacecraft traveling .2v2rpm2pjtd*g8np 1ktc0m) cfe t7gdirectly from the Earth to the Moon experience zero net forc2g7mgktfj )28rt*v m 2pd pe10npct. ce 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 a bathroom scale in 1 3mw+xb69cqga(d s0x ifft p;ec)(dnan elevator, it says your mass is 82 kg. What is the acceleration of the elevator, and in which d;qpmcws(f0 9 ag6b+c)ddtn3 i(exf1 xirection?     ----待选择----upwartddown 

  A projected space station consist403iybftq2 eis of a circular tube that 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 (1f i3it be24qy0.0 g) is to be felt?$\approx$    $\times 10^3$

  A jet pilot takes hiw ) )pr0fvwu1d+wy9o js aircraft 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 radx0 ,/nhx:r lcgius r, the acceleration due to gn/hrgxlx:0 c, ravity at its surface and the gravitational constant G.

A plumb bob (a mass m hanging on a strinh8pl2a.ku 3z yg) is deflected from the vertical by an angle h yku38z.p2al$\theta$ 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 Ifd1i /;k bwlt4s the coefficient of static friction is/i1kblw;sd 4 t 0.30 (wet pavement), at what range of speeds can a car safely handle the curve?

  How long would a day be if the Earth were rozdba x e e:to7/7+tkg0tating so fast that objects at the equaae/ 0o7+db:k ettx7gztor were apparently weightless?    $\times 10^3$s

  Two equal-mass stars maintain a constant distance apart o7m b3af0 x4z0s hl.yvdf 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 speed1qnzaqxr9b h.ck 5n1r;66y)k oazll. rounds a curve of radius 235 m. A lamp suspended from the ceiling swing9l) ka;b .6oa5nkqz.rcr1z h xn61qy ls 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.xcwp4kkkl pvfs0(4 .4 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 g 04pk.vc l4wsk(4fpkx '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 extr0.z zkgs 71a3yk mx: cqj.nck:emely massive core in the distant galaxy M87, so dense that it could be a black hole (from which no light escapes). They did this by meaqj kzn7ay:k kcmx0gz1:3.. cssuring 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 constanktl;fhz k9xgbub6 bk tx36gq-gb:g;+m zj+44t speed as it traverses the hill and valley shown in Fig. 5–45. Both the hill and valley have a radius of curvagbqz94z ;- k3kub +txkgfb l6;xg4 mb6g: h+jtture 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 System (GPS) utilizes a group ofl5,xd2d9cnq z88ss av 24 satellites orbiting the Earth. Using “triangulation” and signals transmitted by thes 2l8 8dsnx scv9,qaz5de 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 ]. (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.cxn- hn rj4557dg gpk51 billion km, is meant to orbit the asteroid Eros at a heh-r4d 5cg5 pnknjx57g ight of 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 pursui0d6cyt*39eflqblnf : kiz)gp xn8 ,2yng a satellite in need of repair. You are in a circular orbi:y *f3t0czx,ngk)d leiby98qfn6 2 plt 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 cg+9677u .ilct6dppdnvg0pbhas a period of 3000 years. (a) What is its mean distance from dlpu7. bg0id+7 pgc tnc9p6 6vthe 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 bt)ixeoztg(:g/ 9 4 zzpe if you could actually "feel" yourself gravitationally attracted to someone ne 9xt)i(z zte/gog4zp :ar you. Make reasonable assumptions, like F $\approx 1 \mathrm{~N}$ .    $\times 10^{-5}$

  The Sun rotates around the center of the Milky Way Galaxy (Fig. 5-46 .tytcbvd.*d .) at a distance of about 30,000 li.yb.dtv.d *tcght-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 square 0.50 1e*hjdts s*w1g r i.vwd;cybn9/qfd6. .dym1 m on each side. Find the magnitude and direction of the gravitationalm.9et;drs.1 1idq*wbs ydc*yhw. f6njvd g 1/ 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 qj-i pr3n1s1g 5500 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 experienced by the tip of w d , v5. to7cej/ks8qiwqi70athe 1.5-cm-long sweep second hand on your wrist watchq 5j8d, a oi0 wcs7vw.qk/i7et?    $\times 10^{-4}$

  While fishing, you get bored and start to swing a sinker weiteh8)b/ i m- lhf(rq.d hc,gi,ght 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? qb r hf.,dl ,i-me 8icht(/h)g[Hint: See Fig. 5–10.]    $^{\circ}$

A circular curve of radius R in a new highway is desig-)uy y42 jk0dlxy r*m yh2ex,sned so that a car traveli)d 2kehjlyx0 m 2-4s*yuyyr, xng at 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 (-r s y0(apndxe+ jdx(lu14mdtrain, 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 mass 75 kg if the track is not banked and the train m1ddj- (4+ndx(ye(p0 xl a rusdoes 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.$\approx$    $\times 10^2$