Sometimes people say .h; zuu)k)t +fmm*rix0 d )kqsthat water is removed from clothes in a spin dryer by centrifugal force throwing the water outward. What is wrong with this statemk.m ;t)uz)0 h)i*+mrdxf squ kent?

Will the acceleration of a car be the same when the carn.j qvaa zh,i/4ut;p+ travels around a sharp curve at a constant h 4 t/qinja,.avu;pz+60 km/h as when it travels around a gentle curve at the same speed? Explain.

Suppose a car moves at constant speed along a hilly road. Where does tdd1oqlti /elxok/ 1.w9t sg;f.x 0:ejhe 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 near the. 1x o9jd;ke./g/lto0 s tdwe1ixql:f bottom of a hill?

Describe all the forconh (79(iarkc es acting on a child riding a horse on a merry-go-round. Which of these forces provides the centripetal accelerat7k(onr (i 9hacion of the child?

A bucket of water can be whirled in a vertical circle without the w 1k*(:dal1owdh4lw iwater spilling out, even at the top of the circle when the b1dak:(w4lw i1 h*wl doucket is upside down. Explain.

How many “accelerators” do you .r:5l 41uaw utjc7ula0j p*ew 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 accelerations do they produce?w 0 jp*1.:t4r5j laa7euuuclw

A child on a sled comes flying over the crese9 w)*qgfi 5xst 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 i*g)wf 9xq5esas he goes over the hill. Explain this decrease using Newton’s second law.

Why do bicycle riders lean que( ,jw)t ;9aywyfp:inward when rounding a curve at high speed?

Why do airplanes bank when they tzl n.1 ao7dns7urn? How would you compute the banking angle give .ndz7 na7l1son its speed and radius of the turn?

A girl is whirling a ballx*xl5;w9m+,jdshi lpo 8 dfi. on a string around her head in a horizontal plane. She wants to let go at precisely the right time so that the ball will hit a target on the other d;+8 mjlhp* flw io.,s59xixd side of the yard. When should she let go of the string?

Does an apple exert a gravi 8fl9 c6gcuh:ltational force on the Earth? If so, how large a force? Con8u9clh6 l:g fcsider an apple
(a) attached to a tree, and (b) falling.

If the Earth’s mass were doubleuxss p-y3 j)j4 what it is, in what ways would the Moon’s orbit be differe) jxjy4ssu 3p-nt?

Which pulls harder gravitationally, the Earth on the bq-:4b 0b ubyaMoon, or the Moon on the Earth? Which a-q 0:b4b uybabccelerates more?

The Sun's gravitational pull on the Earth is much larger tha 40,,qpjvnstpn the Moon's. Yet the Moon's is mainly responsible for the tides. Explain. [Hint: Consider q0pnj s,4v pt,the difference in gravitational pull from one side of the Earth to the other.]

Will an object weighei3ht9yn7jj6hm 5u x* more at the equator or at the poles? What two effects are at work?yum *hn j3e7h5i6jx9t Do they oppose each other?

The gravitational force on the Moon due to .pf:sfqrjj3 3a9d; fcf1 8bs gthe Earth is only about half the force on the Moon due to the Sun. Why i rqs s8jg:f3a. jf19pfdfc3b;sn’t the Moon pulled away from the Earth?

Is the centripetal acceleration of Mars in its orbit around the Sun larger or +m :*wra,t0 sgzf tz.qsmaller than the cen +z*r.0zs mawtg,f:tqtripetal acceleration of the Earth?

Would it require less speed to launch a satellite (a) toward the eas7nv.mf yw 2o5nz+aglll 4j .k4t or (b) toward the west? Consider the Earth’s rota7jkv ng4f 2ml4n5 l a+.yw.olztion direction.

When will your apparent weight be the greatest, a 5 k:)ndht:ctis measured by a scale in a moving elevator: when the elevator (a) accelerates downward, (b) accelerates upward, (c) is in free fall, (d) moves upward at constant speed? In which case would yotthnk:i )c :d5ur 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 l7ae3s l5hlzp 0ong periods in outer space could be adversely affected by weightlessness. One way to simulate gravity is to shape the spaceship like a cylindrical shell that rotates, with the astronauts walking on the inside surface (Fig. 5–32). Explain how this simulates gravity. Consider (a) how objects fall, (b) theze7ls5alhp3 0 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 “a25,ae ls *thytpparent weightlessness” between steps.2ths, a*ley 5t

The Earth moves faster in its orbit around the Sun in January than in July. Iznxsd w/-3q3ody(+l r0 pd4pcs9 ,lbw msf 7q5s 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 ydf bq+o rs3zq 5wp/ 39ldwsl pm(, n-ds407xcmain factor is the tilt of the Earth’s axis relative to the plane of its orbit.]

The mass of Pluto was not known until it was dao2qziq bpcmi+d ,wlk(u (7)5iscovered to have a moon. Explain how this discovery e 5qpmw o((iiz)bc2q7ud, alk+ nabled an estimate of Pluto’s mass.

  The Sun's gravitational pull nyy ghlz7;9eh e vp3:.on the Earth is much larger 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 other.]A child sitting 1.10 m from the center of a merry-go-round moves with a speed of;lzye 7ngy:vh3p9. eh 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 19o;c t-i/p:q-wf4ujub 80 $\mathrm{~km} / \mathrm{h}(525 \mathrm{~m} / \mathrm{s})$ 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 orb 5 m7efbk4oy:xit around the Sun, and the net force exerted on the Earth. What exerts th5bx ye7 m4f:kois 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 of 210 N is exerted on a 2.01uwagoy+th(hvk. /d 3f sj;q ;-kg discus as it rotates uniformly in a horizontal circle (at arm’s u(jvy;gh1/so;w3ktafd .+ qhlength) of radius 0.90 m. Calculate the speed of the discus.   

  Suppose the space shuttle is in orbit 400 km from the Earth's surface, and ehk,* rlecb3v :kdi cw+/)z,ucircles the Earth about once every 90 minutes. Find the centripetal acceleration of the space shuttle in its orbit. Express your anc3 / k*w ):rhd,ue,+ebilvk czswer in terms of g , the gravitational acceleration at the Earth's surface. $\approx$    g

  What is the magnitude of t0ec1 yciim8v4t21q fau ;ymh, he acceleration of a speck of clay on the edge of a potter’s wheel 2mv,4m 1 yh ccqei;ft81aui y0turning 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 in a verticadv;tm *o92zv11 k9a tc ss8nudl circle of radius 72.0 cm , as shown in Fig. 5-33. If its speed isct dvv1suot ma29s*d8 9 ;nzk1 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 can round a turn o)du t9m rdbk**f radius 77 m on *b t*dm9drku) a flat road if the coefficient of static friction 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 theagkq/hc+k 1o/ xs0lm7 tires and the road if a car is to round a level curve of radius 85 m ghsc+k /k ol7mxq/1a0 at a speed of 95km/h ?   

  A device for training astronauts and jl fnk0mnrn 08t(t9*fqjtp2nz r+;q*net 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 rota2 t nqrrm qntz0f9ln0+;**jpk8(tnfnting?    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 turn-8n y+ qu gj4pvkix- 9v5s,kfqtable 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 off. What is the coefficient of stat x q8+fnivk4 v-qpj9su5y -,gkic friction between the coin and the turntable?   

  At what minimum speed must a roller coaster be traveling wh1jn a q(oa(90hjc2f xhen upside down at the top of h9qc 0n1jha(aj2x o(fa 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 h 2 * l0goxg4ldfd3c0sthe driver) crosses the rounded top of a hildl* 0ol30dhc2g 4xgs fl (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 wr fj*)8wlv d:xheel need to make for the passengers to feel “weightless” at the topmw*)djf8lx v:rost point?    rpm

  A bucket of mass 2.00 kg is whirled in a verticall26(q kve mfrk,ab/j) circle of radius 1.10 m. At the lowest point of its motion the tension in the rope supporting the bucket,kqklf6j)v/m( abe2r 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 )-0cvyq(cou( ykuzi 3.00 cm from the axis of ro q3-kcuo y0iuz(c(y v)tation is to experience an acceleration of 115,000 $\mathrm{~g} $'s?    rpm

  In a "Rotor-ride" at a carnival, people are rotated in a cyo dq+xn3(zn8bja).l 2edl7 q nlindrically walled "room." (n (2x38.jz+n edbnd aqqol7)lSee 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 rb,zm ur8.tt9dotated in a circle on a frictionless air-hockey tabletop, and is he ,t9tu .rbm8dzld in this orbit by a light cord connected to a dangling block (mass m ) through a central hole as shown in Fig. 5-
36. Show that the speed of the puck is given by

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

  Redo Example 5-3 , precisely this time, by not qn (-b jgc(3mt ih d8nsfx-8+fignoring the weight of the ball which revolves on a string 0.600 m lo c8(qg+xhjt f bmndin 3s-8(f-ng. 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 tro8o6.rb2iz oo mk9f u-aveling 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 5 zgkojbj99h8$ 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 evasi/dtv l6 edp1:3wbpo m0jv3,qrve 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 tangentityn+tke3ogqw5pk o5 82jgoh+ipd* -* al and centripetal components of the net force exerted on the car (by the ground) in Example +o5tgki 5p -qo3tojn ge*d+hpy k*2w8 5-8 when its speed is 15$ \mathrm{~m} / \mathrm{s}$ . The car's mass is 1100 kg . F$_{tan}$ =    F$_R$ =   

  A car at the Indianapolisio,he1 r-fuh/ ee3; ;jakb:g c 500 accelerates uniformly 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 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 betweeoee,;:ebf/urk3 c1hh-ia; j gn the tires and the road to provide this acceleration with no slipping or skidding? $\approx$   

  A particle revolves in a horizonta;dc t 4nczn1kxzl541 y.i0xa il circle of radius 2.90 m . At a particular instant, its acceleration is 1.nnk5;.c dy404 zci atlxx11iz05 $\mathrm{~m} / \mathrm{s}^{2}$ , 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 ::jac/z3-;c ywhu y djtxd w,d00ga.e on a spacecraft 12,800 km (2 Earth radii) above tx/ d wtw0hy,0- juj:y 3e dz;:.daccgahe Earth’s surface if its mass is 1350 kg.   

  At the surface of a certain planet, the gravitational m+,0qsktc 6r9.mn otw acceleration g has a magnitude0 ,q6romn9kt +tmwcs . of 12 m/s$^2$ A 21.0-kg brass ball is transported to this planet. What is (a) the mass of the brass ball on the Earth and on the planet   
(b) the weight of the brass ball on the Earth and on the planet? $W_{Earth}$   $W_{planet}$  

  Calculate the acceleration due to gravity on the M; e zr8x3ouo.koon. The Moon's radius is 1.74 uxz.8 or3ke o;$\times 10^{6} \mathrm{~m} $ and its mass is 7.35 $\times 10^{22} \mathrm{~kg}$ .   

  A hypothetical planet h 41viru..x3 :dc)a+rwv kixpsas a radius 1.5 times that of Earth, but has the same mass. What is the acceleration due to grras1ix.4xr pi3uvkw + ).vc: davity near its surface?   

  A hypothetical planet has a mass 1.66 times that of Earth, but the sxkbu5(p6oy( xn/w- tdame radius. Wh(t(xp b5x6 uy o-dn/wkat is g near its surface?   

  Two objects attract each other gravita d s3 k,kyvok- (4 7h(j+/6a;trj5tvpkvdv zxetionally 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 valu::+f f iiq.k3u-m k fiajff;c2cso )b:e of g , the acceleration of gravity, at (a) 3200 m cc):2j: a qm oi+fkf3f:;is-.i kfuf b   , and (b) 3200 km    , above the Earth's surface.

  What is thedistance from the Earth’s center to a point 3* 8skcgw37tgpxco f, outside the Earth where thegravitational acceleration due to the Eartk,sfgpt73c 8g* w3 ocxh is $\frac{1}{10}$ of its value atthe Earth’s surface?   $\times10^7$

  A certain neutron star has five times f9 x g:l1q9pnx:qk4v kthe mass of our Sun packed into a sphere about 10x:nq :gpkv9 xqk91 4fl km in radius. Estimate the surface gravity on this monster.    $\times10^12$

  A typical white-dwarf star, which o)+6ztoco5zxue1 flc ,nce was an average star like our Sun but is now in the last stage of its evolution, is the size of our Moon but has the mass of our Sun. What is the surface gravi )z f 6c+oo,zx15tulecty on this star?    $\times 10^7$

  You are explaining why adcu;1 a7rtq0u stronauts feel weightless while orbiting in 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 by calculatin7dauu10tc ; rqg the acceleration of gravity 250 km above the Earth’s surface in terms of g.   

  Four 9.5-kg spheres qh b .a(ve8zcdvd2l40iwks 1f3*n d8tare located at the corners of a square of side 0.60 m. Calculate the magnitude and direction of the total gravitational3.048bs 8wqidzc* fvta12ekd d vnh(l force exerted on one sphere by the other three.   $\times 10^{-1} \mathrm{~N} \text { at }$    $^{\circ}$

  Every few hundred years most of the planen edx,1+:t9xu t9wgcwdac ; 7 qd3grv3ts 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 arenug9, vtr ;3dw3a 9qdde7gtc1wxxc :+ in a line (Fig. 5-38). The masses are $M_{\mathrm{V}}=0.815 M_{\mathrm{E}}, M_{\mathrm{J}}=318 M_{\mathrm{E}}, \quad M_{\mathrm{S}}=95.1 M_{\mathrm{E}}$ , and their mean distances from the Sun are 108,150,778 , and 1430 million km , respectively. What fraction of the Sun's force on the Earth is this? $F_{Earth-planets}$ =   $\times 10^{17}$ ${F_{Earth-plantes}}$ \ ${F_{Earth-sun}}$=    $\times 10^{-5}$

  Given that the acceleration of gravity at the surface of Mars is 0.38 of9pk+k lf(dtb 5. (:6 labbb6pyagdsa9 what it is on Earth, and that Mars’ radius is 3b.9kd d(lb+ spya9ag6fb lak:5(p6tb400 km, determine the mass of Mars.    $\times 10^{23}$

  Determine the mass of the Sun using the known value for the period of the9h; fvzh+a, kw Earth and its distance from the Sun. [Note: Compare k;hw ,f+zah9 vyour answer to that obtained using Kepler’s laws, Example 5–16.]    $\times 10^{30}$

  Calculate the speed of a satellite moving +,u3z0titi9na 6uz ffin a stable circular orbit about the Earth at a hutu if3 ,z t06znafi+9eight of 3600 km.    $\times 10^3$

  The space shuttle releases a satellite ij fo(9n e4zl2 rbfd7*dnto a circular orbit 650 km above the Earth. How fast must the shuttle be moving (r47zob 2j( efn 9dfld*relative to Earth) when the release occurs?    $\times 10^3$

  At what rate must a cylindrical spaceship rotate if occupants are to exper62y py:aa;zxztm ;d ju 9hbd;8ience simulated gravity of 0.60 g? Assum8d p:a2z9;btmjud x 6y;z;ayh e 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 satiu;qvc re2 pbp)e6nwiomw, hs 3l 47)7ellite to orbit the Earth in a circular “near-Earth” orbit. A “near-Earth” orbit is one at a height abo c m) i4uei)rp woelq627v73p;,whsbnve the surface of the Earth which is 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 ht 1ke:)m9jlsezty0x 1ave to be launched from the top of Mt. Everest to be placed in a circular orbit around the Earth? :temxz1j9 setly0) k1   

  During an Apollo lunar landing mission, the commano)c h3w c37,4 eqximzld module continued to orbit the Moon at an altitude o3i4whx c, )qlcm73ez 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 vmbose 8p-d7n1gt yr; pemr9r5;m6/h inner radius oret1m-ps gn6 h7; ;dr598 mmeyrov /bpf 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 hc a b;j0 4qumgmff,1b)7+b f-x hx/ldin diameter rotates once every 15.5 s (see Fig. 5–9). What is tflhg71;au -x+c0 ,qj b fh/ bmf4xbm)dhe ratio of a person’s apparent weight to her real weight (a) at the top, and (b) at the bottom?
(a)    (b)   

  What is the apparent weight of a 75-kg astronaut 4200 km from the centenl);z u+y u+pgoyd,t9 r of the Earth's Moon in a sp++ ,)gyytlu p9;udz onace 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 yngke xzz3j- ;p0eilpsj 1o5q/l9rs* 9+udp,of two stars of equal mass. They are observed to be separated by 360 million km and take 5.7 Earth years to orbit about a point midway betwe zj;gpp0+q-p*ylil5eo1xed j zs/,s3n k9r9 u en them. What is the mass of each?    $\times 10^{29}$

  What will a spring scale read for the weight of a 55-kg x8kr8la 0t(v ywoman in an elevator that moves vky8t(8ar x l0
(a) upward with constant speed of 6.0m./s   
(b) downward with constant speed of 6.0m./s   
(c) upward with acceleration of 0.33 g,   
(d) downward with acceleration 0.33 g   
(e) in free fall?   

  A 17.0-kg monkey hangs from a cord suspended from the ceiling j c3c3e * mgjl8r;,kfaof an elevator. The cord can withstand a tension of 220 N and breaks as the elevator accelerates. What was the elevator’s minimum acceler l j8ckgr3e 3fj*am;c,ation (magnitude and direction)? a =   

Show that if a satellite orbits very nearcfho rx9;rh7/ the surface of a planet with period T , the density (;ho fx/hc 97rrmass/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 det/y 96bu jcebt kc:,bz5ermine the period of an artificial satellite orbiting very near the Eart9 5 t ,/ykjb:6zubbcech’s surface.    s

  The asteroid Icarus, though only a few hundred meteree8 ,s )hws6h6gq 8gris across, orbits the Sun like the planets. Its period is 410 d. What is its mes6i 86sqgeh,)e w8hrgan distance from the Sun?    $\times 10^{11}$

  Neptune is an average distance yca8da6m8*oh 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 thegntn;r :g4j 4n Sun roughly once every 76 years. It comes very close to the surface of the Sun on its closest approach (Fig. rj4gn :nntg4; 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 from the Sun.]    $\times 10^6$

  Our Sun rotates about the c-.m8 yxrqo/k xenter 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 fo1o(ylm40iq be8pxg h63eu k x0r the four largest moons of Jupiter (thosxe xk8m3hboeu6gl q0 yi(4p01 e 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 s52 tvi3 *xsjx:-n ;v wh(xwddEarth from the known period and distance of the Moon. ws ( j *niv-twv;2dxxsxd:53h   $\times 10^{24}$

  Determine the mean distance from Jupiter for each of 2unedh f (2ijfq0 ah5( w cakpw+04-kpJupiter’s moons, using Kepler’s third law. Use the distance of Io and the periods given in 22w-k 045fa( 0an iqwhhpcjudf +pe k(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 fragmenh yn3m1yf; *udts (which some space scientists think came from a planet that once orbited the S1uy*hd3 mn ;fyun 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 talc-t 6x iq,j/jce describes an artificial "planet" in the form of a band completely encixq i,-tcjc /6jrcling a sun (Fig. 5-40). The inhabitants live on the inside surface (where it is always noon). Imagine that this sun is exactly like our own, that the distance to the band is the same as the Earth-Sun distance (to make the climate temperate), and that the ring rotates quickly enough to produce an apparent gravity of g as on Earth. What will be the period of revolution, this planet's year, in Earth days?   

  Tarzan plans to cross a gorge by swinging in an a liaxsx8-8:y orc from a hanging vine (Fig. 5–41). If his arms are capable of exerting a force of 1400 N on the vine, what is the maximum speed he can tolerate at the l ax:syi8 lo-x8owest 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 gravity be hal d2u,0f zquz*92;g m-(vm:rrny zrrm cf what itu0 ( 9mz;rm qy 2c:,z2 zrdrmnr-fg*vu is on the surface?    $\times 10^6$

  On an ice rink, two skaters of equal mass grab hands and spin in a mutual .uwd+ uz9sa(nu vt6 e)v2g:r-b f3w wjcircle once every 2.5 s. If we assume their arms are each 0.80 m long and their individual masses are 60rew.tgf vswznb) +-:29dv(w36uuu a j.0 kg, how hard are they pulling on one another?    $\times 10^2$

  Because the Earth rotates once per day, the apparent accel5 *ftp4c0 yrgww+ 4euxeration of gravity at the equator is slightly less than it would be if the Earth didn’t rotat t*gwyc4f+ruewx5 4p0e. 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 directly from the Eap tw5l0cva-yal, ,p(yrth to the cpava,y p0(5 ,w-lytlMoon experience zero net force because the Earth and Moon pull with equal and opposite forces?    $\times 10^8$

  You know your mass is 65 kgvnq/ qqwuveph-cw36h hq;;k ( v(, gw5, but when you stand on a bathroom scale in an elevator, it says your mass is 82 kg. What is the acceleration of the elq 5/q w-n ;p vkv,we(vhq(c;6uhgq3hwevator, and in which direction?     ----待选择----upwartddown 

  A projected space station consists of a circul l-w5yrc90u;vphm9e . ,g d6w9j vgd)q4iuhzsar tube that will rotate about its center (like a tubular bicycle tire) (Fig. 5–42). The circle formerhjvdu eupwq)lgdm; 9is 60c9wvgy .4-9z ,5hd by the tube has a diameter of about 1.1 km. What must be the rotation speed (revolutions per day) if an effect equal to gravity at the surface of the Earth (1.0 g) is to be felt?$\approx$    $\times 10^3$

  A jet pilot takes his aircraft in a vertical loop (Fig.cecx/;, bxa j6mt3e;d 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 radirqp5r6* .ot d+wpit r:us r, the acceleration dup 5odrp :trrt6*q.wi+e to gravity at its surface and the gravitational constant G.

A plumb bob (a mass m hanging or2g0 x lnikr c9za pw1q9)t**2-pqunp n a string) is deflected from the vertical by an angle t*ln2 rr n9qig1zukqx * 2a-pwp c)p90$\theta$ 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 If 83 *gf uixt1ot yz8d,uthe coefficient of static fric,u 8u8o g13ydi*ttxfz tion is 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 rotating so fast that objects at the e3er.n+) xqgi cquator were apparentl cq+ix.gne 3)ry weightless?    $\times 10^3$s

  Two equal-mass stars maintain a constant distance apa*xkz iao6vg1*px3j- brt 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 curve of r.y 6n09dv+3rztzcm oeadius 235 m. A lamp suspended from the ceiling swings0.e r6v+9ynz dtz mco3 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 claimeghi0jevfta oavdyeo w4 l.k-5.+8 1*ed 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 's a person would experience at the equator oel a58 goa ev-0 jy iefv+t4wkh.*d1.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 Hubblee oqg4y0c12rq Space Telescope deduced the presence of an extremely massive core in the dist1q c erq24oyg0ant galaxy M87, so dense that it could be a black hole (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 as iwtc,ba .z.2iit0(3nswwb ox+ t 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?) Explain. (b) Where would the driver feel heaviest? Lightest? Explain. (c) How fast can the car go without losing contact wb+.(. xaw 0 cn3tiowib,2tw szith the road at A?

  The Navstar Global Positioning System (GPS) utilizesaa t+h2nr;-/t03b+dwrdq sbwgvpq0 * a group of 24 satellites orbiting the Earth. Using “triangulation” and sib qp 0d qhtagr;a w3vw*sr d+nb0/t2-+gnals 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 ]. (a) Determine the speed of each satellite.    $\times 10^3$
(b) Determine the period of each satellite. =    hours

  The Near Earth Asteroid Rendezvous (NEAR), after traveling 2.1 hwch,r+owp zffy:,f-2t4+in 2 j b g5ubillion km, is meant to orbit the asteroid Eros at a height of about 15 km .g2nfoh:i+,p, jh-c2w 4byr5+f utw f z 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 satellite in)bh(vlx ll9yxen ;vh 3/8q7xd need of repair. You are in a circular orbit of the same radius as the satellite (400 km above the Earth), but 257 dv 8x(;yhqlb9lvnexx/h)3l 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 is its mean distarr;p xc;1yvf 6po0s5 fnce from thep15vs;or0y r6 ffp;cx 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" vcbgdl*m:q04 ; bu v-vsgr- .vyourself gravitationally attracted to someone near you. Make reasonable assumptions, like bug-vb .c r*;0q:mdgvvvs-l4F $\approx 1 \mathrm{~N}$ .    $\times 10^{-5}$

  The Sun rotates around the center o 5 1o5j33zgucr;dzyb.i/b sczf the Milky Way Galaxy (Fig. 5-46) at a distance of about 30,000 light-years from the centerb3c1 crosz.;y3bg5u /i5zjdz $ \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 m on et4zs m,sk :d ,bku.ja-vw6h/hach side. Find the magnitude and direction of the gravitational force on a fifth 1.0-kg mass placed at the ,tjkk6sa, -h4uvz .ms: h/bwdmidpoint of the bottom side of the square.    $\times 10^{-10}$  ----待选择----downupward 

  A satellite of mass 55)i asl7nc, oid-vu zv/h4is) )00 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 eqqr-pq -alv8fc2:el4xperienced by the tip of the 1.5-cm-long sweep second q2f8 -p :qc ra4vle-lqhand on your wrist watch?    $\times 10^{-4}$

  While fishing, you get bored and start to swing a sdi0 k5j9q ne,s2+uw lkinker weight around in a circle below you on a 0.25-m piece of fishing line. The weight makes a complete circle every 0.50 s. What is the angle that the fishing line makes with the v2iu jq+n5dwk9k0 es ,lertical? [Hint: See Fig. 5–10.]    $^{\circ}$

A circular curve of rx16icd2l7ordiz-d dh :mkg+2 adius R in a new highway is designed so that a car traveling at spe6md:7 h2d+ gi -zoirdx d1clk2ed $ 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 zoclb2a 86 pw 4d/ns4g(z fl( ct;3lcqthe 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 3q(g(c6 la n4scz p8/tz;l4wb fcod2lan 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.$\approx$    $\times 10^2$