Is it possible for an object moving with a constant speed to accelerate? Exua7hir+ na1 9fwmw ;e,plain.9e,ahnw;a wim rf7u+1

  Consider a particle m*pidn1st.r:g oving with constant speed such that its acceleration of constant magnitude is always perpendiculg pnsid :r*.1tar to its velocity.

  An object moves in a circular path at a constant speed. Compare the directiojfbh jn 4;+qe3vgslmv2+1 qhiq(0h)zn of the o hq)4qzes3v+jj(v2n im1 b+ hq0flh;gbject's velocity and acceleration vectors.

  When an object experiences uniform circular motion, the direction of thenb. s-g*dh,m z:ckuj q3, .vie acceleratiods.jm,zhv : uqkein g3b-c.*,n is

  Consider a particle moving with constant speed such that idrm s*.i 0nhz:yr;n aki4,a( cts acceleration of constant magnitude is always perpendin,iar 4himz.ad;k cr s0n*( y:cular to its velocity.

  What type of acceleration does an object moving with constant speed in a circun, 7el1 -: zgzy9ncc t:z)kqukqj36yk lar path ecky6 zqj l,- 31:z7kz:)ugtc k9qenn yxperience?

  What force is needed to make an object move in a circleh2g5 dd+ ky yz53ijt0t?

  When an object experiences uniform circular motion, the directut gwsor1z2 am -vg:tp/3en aaw31i4 )ion of the net forceaervp1mowt)2ngi4 :s-z 3/3 atwa1 g u is

  A roller coaster car is on a track that forms a circular loop in dgx9s 11cyy 8tthe vertical plane. If the car is to just maintain y1y tg19dcsx8contact with track at the top of the loop, what is the minimum value for its centripetal acceleration at this point?

  A roller coaster car (masmn, *v9ow r es4lu:33mbxi,l ps = M) is on a track that forms a circular loop (radius = r) in the vertical plane. If the car is to just maintain contb,emi xs3rwo49l pn v ,*:mu3lact with the track at the top of the loop, what is the minimum value for its speed at that point?

  A pilot executes a vertical dive then follows a semi-cijcozahl,uir0k 6je+y 9ccq/b9. i ;n3rcular arc until it is going straight up. Just as the plan+/9 k3a9nycejo.; qui bjccirlz , 6h0e is at its lowest point, the force on him is

  A coin of mass $m$ rests on a turntable a distance $r$ from the axis of rotation. The turntable rotates with a frequency of $f$. What is the minimum coefficient of static friction between the turntable and the coin if the coin is not to slip?

  A car goes around a curve of radiu5 i- 0 cwo*fh rguvjaovf;i3-omkvc5:z 3f7 f*s $r$ at a constant speed $v$. What is the direction of the net force on the car?

  A car goes around a curve of radius r axfwy 1/n69gfg.;w0 yu5qtld7m fbx t ,t a constant speed v. Then it goes around the same curve at half of the omt nyg; 57ylfxtx9q ,1b0d wuf/w6g.friginal speed. What is the centripetal force on the car as it goes around the curve for the second time, compared to the first time?

  A car goes around a curve of radius r at a constant speed v. Then it goes aroun6o eybiew8az0,d1cm5,y rkm 8d a curve of radius 2r at speed 2v. What is the centripetal force on the car as it goes around the second curve8km,0eymo 1cez85 i6, yadrwb, compared to the first?

  A car of mass m goes around a banked curve of radius 3rgcug89l pjluqv v8es .8t29aq7g/qf d:ul 8r with speed v. If the road is frictionless due to ice, the car can still negotiate the curve if the horizontal component of the normal for/c89gg:7 8.8eu9u8fq trqgqa s ljpvu2ll v3dce on the car from the road is equal in magnitude to

  Two horizontal curves on a bobumb n/sl +r42-j)nxveh*) zu fsled run are banked at the same angle, but one has twice the radius of the other. The safe speed (no friction nj-vx) re+u2bnz4 )/mus* hlfneeded to stay on the run) for the smaller radius curve is v. What is the safe speed on the larger radius curve?

  The banking angle in a turn on the Olympic bobsled track is not constant, b*fl3a e.lpv/iut increases upward from the horizontal. .fpvlei l/a* 3 Coming around a turn, the bobsled team will intentionally "climb the wall," then go lower coming out of the turn. Why do they do this?

  Is it possible for an object moving around a circularr*7yf p-/, d sy mhmid34(zl7pwat lq3 path to have both centripetal and tangential acceleration(dt w,f yp7l*s-7yh/ pr 3idq3ma4zml ?

  The gravitational force between two objects is proporti mq+5lsm k*b: /2lpxwb1yzyt*onal to

  The gravitational force p *.xq-ygrl 90d .wypwbetween two objects is inversely proportional to

  Two objects attract each other gravitationally. If the distance between their x( 35fftbejqyy -yp3)centers is cut in ha p5) 3(ffyx3eytby-jq lf, the gravitational force

  Two objects, with massen1z3qo(xchy3. sy.w2nvj p f3s $m_{1}$ and $m_{2}$, are originally a distance r apart. The gravitational force between them has magnitude F. The second object has its mass changed to 2$m_{2}$, and the distance is changed to r/4. What is the magnitude of the new gravitational force?

  Two objects, with mas,):t3-z5s ldd rjhrhkfuq6.xses $m_{1}$ and $m_{2}$, are originally a distance r apart. The magnitude of the gravitational force between them is F. The masses are changed to 2$m_{1}$ and 2$m_{2}$, and the distance is changed to 4r. What is the magnitude of the new gravitational force?

State Newton's law of univexy m on)x bdurn409-i1rsal gravitation.

  Compared to its mass on f:z*di /n 66 haknd9pethe Earth, the mass of an object on the Moon is

  The acceleration of gravity on the Moon is one-sixt:dogu s y u, 0h3a+sgjc//3 6wngn,dxch what it is on Earth. An object ofgc nx+ 6/wdsa,gd j3y:cgun 0, s3/uoh mass
72 kg is taken to the Moon. What is its mass there?

  As a rocket moves away from the Earth's sur5 y7)bpin8+x7t+a. y9jdubsz3mq enju-q (m wface, the rocket's weight

  A spaceship is traveling to the nnfmwsc . 1x.28 yyjqz9ccpl/: poz/0Moon. At what point is it beyond the pull of Ea/zp1 cw fp:9 yy2/ .l qcznxcnoms0.j8rth's gravity?

  Suppose a satellite were orbiting the Earth just above the surface.qud), z.exq/s What is its centrisdz)que x/q ,.petal acceleration?

  A hypothetical planet has a mass of half that of the E 2et: gl(ysd2b9 ma.gharth and a radius of twice that of the Earth. What is the acceleration due to gravity on the planet in terms of g, the acceleratioeb:.h2adgl( y2 sm9gtn due to gravity at the Earth?

  The acceleration of gravity on the Moon is one-sinwx c /,.7ed79glpgprxth what it is on Earth. The radius of the Moon is one-fourth that of the Earth. What is the Moon's mass compared to t rp g7l7c e.xn/g,dw9phe Earth's?

  Two planets have the same surface gravity, but(wbd-0ws rgyvld:lv 5zd(fhl/rw a+o*e :6w: planet B has twice the radius of planet A. If planet A has mass m, what is sd:/awg 5hd vo:l (bwl0y+fw r6wzed*l- r(v:the mass of planet B?

  Two planets have the same surface gravity, but platqgqkx)9nwj-e6o6fx6bw 0ef ,m4m*b o, pl9r net B has twice the mass of planet A. If planetpfn-w9jwq46r6t9xx0 * 6obq)em,e ,l gok bm f A has radius r, what is the radius of planet B?

  Consider a small satellite moving in a circular orbit (radius r) about a z zb0xob/f/ s*spherical planet (mass M). Whichbx*s zboz/ 0/f expression gives this satellite's orbital velocity?

  Satellite A has twice the mass of satellite B, and rotates zdeh m*-u+ c9bc: qvl1in the same orbit. Compare the two : l ev*1chzmu bcq+9d-satellite's speeds.

  A person is standing o*cix3xw8a lnxj4l5ttc,gcp .8 ab/l+ n a scale in an elevator accelerating downward. Compare the reading on the scale to the person 5t/*i g8 wax ltl +,83anp.4cjxcxbcl's true weight.

  Who was the first person to realize that the planets move in ellipticaj/t zlfoq8;+r l paths around the Sun?q/8rflz otj;+

  The speed of Halley's Comet, while traveling in its elliptical orbit around tx+jyeq2p s *yuim 6g58(vi ,q9ne*tfe he S*,veexjus*2f8qyt9g q+eiyp i (n56 m un,

  Let the average orbital radius of a planet bexl.p7wjj+u(iu. ialbivk1 -2dpj9xj;dd(9x R. Let the orbital period be T. What quantity is constant for alludv-1ji+ x j2alwji j.9i9(xkp;(p7dxub .d l planets orbiting the Sun?

  A planet is discovered to orbit around a star in the galaxy Andr2sa :ad gb+pg8omeda, with the same orbital diameter as the Earth around our Sun. If that star has 4 time:pbag asg2d 8+s the mass of our Sun, what will the period of revolution of that new planet be, compared to the Earth's orbital period?

  The average distance from the Earth to the Sun is defined aswv3fqt v;b73k one "astronomical unit" (AU). An asteroid orbits the Sun in one-third of a year. What is the astet wv33 bk;vqf7roid's average distance from the Sun?

State Kepler's laws.m.slomlt+mv : 2 8b+ra

  List the four fundamental i8guxg-rs-*06f7z lv rrf9wuforces in nature.

  An object moves with a constant speed of 30 m/s on a circular track of03:q pvs7 .zkwcrdt, nq7h;bi radius 150 m. What is the accele;hi ptb d rcvn., k77w:zq03sqration of the object?

  The maximum speed around a level curve is 3077p wae9b(k axv zre)3.0 km/h. What is the maximum speed around a curve with twice the radius? (Assume all other factors remain ux9a(wpv zbe e3rk7a 7)nchanged.)

  What is the centripetal accelp gzntt0.+,yr eration of a point on the perimeter of a bicycle wheel of diameter 70 trg+.,0pn tyzcm when the bike is moving 8.0 m/s?

  A point on a wheel row4 ,qud:h;j8bmdn(j : sopb:atating at 5.00 rev/s is located 0.200 m from the axis. What is the centripetal acceleration?:jo 8;pn,j wdq( abbdh:s u4:m

  How many revolutions per minute must a circular,p za lh86hd9 fxr9+yc7 rotating space station of radius 1000 m rotate txa 6cl r8 hdf9zp79y+ho produce an artificial gravity of $9.80 \; m/s^2$?

  A motorcycle has a mass of 250 kg. It goes around a 13.7 m radius turn at 9t g5(4qaheb(7 pfobs( aia 85u6.5 84bobf a hs ie7((qt55ua p(agkm/h. What is the centripetal force on the motorcycle?

  A 0.50-kg mass is attached to the end of a 1.0-m string.cm0gc43a:k 8daj hoj: The system is whirled in a horizontal circular path. If the maximum tension that the string can withstand is 350 N. What is the maximum speed of the mass if the string kadom::cgj c3 j40ah8is not to break?

  A stone, of mass m, is attached to a strong stringxm d-xv ,kz sc*zvrr r 1v1)a3ew2l25g and whirled in a vertical circle of radius r. At the exact top of the path the tension in the strink-acl5 2v *2gr e13sxr rzvx)mv ,z1wdg is 3 times the stone's weight. The stone's speed at this point is given by

  A stone, of mass m, is attached to3q; pzi;upzn c: f2+pi a strong string and whirled in a vertical circle of radius r. At the exact bottom of the path the tenpui;pnz:fpiq3;+z 2 csion in the string is 3 times the stone's weight. The stone's speed at this point is given by

  A jet plane flying 600 m/s experiences an acceleration of 4g when pulling out nop/4a k40g/j* pf1 zp;lzf:kefiv.dof the dive. What is the radiud44p.1ka/v p:*f/ e gizfkz;plfj 0nos of curvature of the loop in which the plane is flying?

  A pilot makes an outside vertical loop.e ;s, z:ss+;k jjcjirs;hw6o (in which the center of the loop is beneath him) of radius 3200 m. At the top of his loop he is pushing down on his seat with only one-half of his normal weight. How fast isj.e: +hc,zow ksjs ;rjs; i6;s he going?

  The maximum force a pilot can stand is about seven times his weight. Whatnhn 8gim8b-5i4ol*q rdzc/d 5 is the minimum radius of curvature that /d n io-5*dqlr5848hnimzbcg a jet plane's pilot, pulling out of a vertical dive, can tolerate at a speed of 250 m/s?

  A car traveling 20 m/s rounds an wto7grw-l/ x7 w10umqbc x9b7n.p r /d80-m radius horizontal curve with the tires on the ve0wr/pcbuww g 1lt-bm 7qnxdx7.r /o79rge of slipping. How fast can this car round a second curve of radius 320 m? (Assume the same coefficient of friction between the car's tires and each road surface.)

  A car is negotiating a flat curve of radius 5e q8s. ca;o;dn0 m with a speed of 20 m/s. The centripetal force p;8s dec;n. qoarovided by friction is $1.2 \times 10^{4} \; N$. What is the mass of the car?

  A car goes around a flat curve alt 3+4 : cjfn3-qrsmcof radius 50 m at a speed of 14 m/s. What must be the minimum coefficient of fric+sn:f c3 tr4-q3cm lajtion between the tires and the road for the car to make the turn?

  A car is moving with a constant speed v aroe) mz,2m8 xb czj4g8v6ideq 6sund a level curve. The coefficient of friction between the tires and the road is 0.40. What is the minimum radius of the curve if the car is to stay on thec x6d8e2v s4q 8m) ,zigm6jbze road?

  What minimum banking angle is required for an Olympic bobsled to np 75mk*0 nrkvigv; vpx2dgb:*egotiate a 100-m radius turn at 35 m/s without skidding? (Ignore72k**rv mgxvi ngd0pb;pk5 v: friction.)

  A horizontal curve on a bobsled run is banked at aearnk 8x .p:9e $45^{\circ}$ angle. When a bobsled rounds this curve at the curve's safe speed (no friction needed to stay on the run), what is its centripetal acceleration?

  A frictionless curve of radius 100 m, ba7sow 22hci .vzktxpk0c1i ;f1nked at an angle of $45^{\circ}$, may be safely negotiated at a speed of

  A curve of radius 80 m is b.mg(1u4s /i)mq2o-bn md pqfoanked at $45^{\circ}$. Suppose that an ice storm hits, and the curve is effectively frictionless. What is the safe speed with which to take the curve without either sliding up or down?

  A 175-kg ball on the endvlz-46 (r ncjf of a string is revolving uniformly in a horizontal circle of radius 0n 4lcr fzv(6-j.500
m. The ball makes 2.00 revolutions in a second. (only fill in numerial value in the blanks)
(a) Determine the speed of the ball.    $m/s$
(b) Determine the ball's centripetal acceleration.    $m/s^2$
(c) Determine the force a person must exert on opposite end of the string.    $N$

  Starting from rest in the pit omw7)nn1,ff) 1ocbbj1l puvks2r+*iarea, a race car accelerates at a uniform rate to a speed of 45 m/s in 15 s, moving on a circular track of radius j* +,firf 1omc)s2 1 bp1 bun7lv)wnok500 m. (only fill in numerical value in the blanks)
(a) Calculate the tangential acceleration.    $m/s^2$
(b) Calculate the radial acceleration when the instantaneous speed is equal to 30 m/s.    $m/s^2$

  The hydrogen atom con gohf bz/5eg:vgvo62 su7pa:5 sists of a proton of mass $1.67 \times 10^{-27} \; kg$ and an orbiting electron of mass $9.11 \times 10^{-31} \; kg$. In one of its orbits, the electron is $5.3 \times 10^{-11} \; m$ from the proton. What is the mutual attractive force between the electron and proton?

  What is the gravitational force on a 70-5dnujx1( *k jrkg person standing on the Earth, due to the Moon? The mass of the Moon (n 1 judkjr5x*is $7.36 \times 10^{22} \; kg$ and the distance to the Moon is $3.82 \times 10^{8} \; m$.

  The gravitational attractive force between two masses isq/t.xxvkf-h q1( r)ixcs7p * p F. If the masses are moiq7)1-*x p.rfq/s vx cpkx h(tved to half of their initial distance, what is the gravitational attractive force?

  For a spacecraft going from the Earth toward the Sun, at what dsu;9l1cbih(*eau *my,69rqc hwd ( ofistance from the Earth will the gravitational forces due to the Sun and the (9 shau9io6yfhc*cq bw(*;e urm ,l1 dEarth cancel?
Earth's mass: Me = $5.98 \times 10^{24} \; kg$ the Sun's mass: Ms = $1.99 \times 10^{30} \; kg$
Earth-Sun distance: r = $1.50 \times 10^{11} \; m$

  The mass of the Moon is7 ia:07jrhwmidyn adn5ui f 5py3286v $7.4 \times 10^{22} \; kg$ and its mean radius is $1.75 \times 10^{3} \; km$. What is the acceleration due to gravity at the surface of the Moon?

  An astronaut goes out for a "spacendv(9b4s0u vqy (w o3a-walk" at a distance above the Earth equal to the radius of the Earth. What is her acceleration d9 3y s 0uv(qn4aow(vbdue to gravity?

  The radius of the Earth is R. At what distance above the Earth;az9 d6pjt; dg5q7fi r's surface will the a d6dgfjr97 ;pt;5aiz qcceleration of gravity be $4.9 \; m/s^2$?

  A satellite encircles Mars at a distan fp vrfc7p;-g9ce above its surface equal to 3 times the radius of Mars. The accelerativcf prp fg-79;on of gravity of the satellite, as compared to the acceleration of gravity on the surface of Mars, is

  At a distance of 14000 km k6kyfgg9k)ty 25nxu. from some planet's center, the acceleration of gravity tg yx.nk y9kfug 5k2)6is $32 \; m/s^2$. What is the acceleration of gravity at a point 28000 km from the planet's center?

  An object weighs 432 N on the surface of the9b+ eatwe) r)vgq u w1/7to;sj Earth. The Earth has radius r. If the object is raised to a height of 3r above the Earv)+t; ajq w1e s )gu/wt7oeb9rth's surface, what is its weight?

  By how many newtons does the weight of a 10t8j8c (4 l cmp pu7bd.pudpy070-kg person change when he goes from sea level to an altitude of 500cplm7(80jdt4udcyu. bp p78p 0 m? (The mean radius of the Earth is $6.38 \times 10^{6} \; m$.)

  The Earth has radius r. A satellite 6n qmsljf)lyr0j /ajx em9,8+ g +/patof mass 100 kg is at a point 3r above the Earth's surface. What is t)a /0lagjlpm/ermfnjy 9t j8 sq++ ,x6he satellite's weight?

  A spherically symmetg-/cx 7whn + 3km,ig lgn3 mdt7.yyg.uric planet has four times the Earth's mass and twice its radius. If a jar of peanut butter +g3d ,m u7l3g/.mn -i .ch 7wtxkyngygweighs 12 N on the surface of the Earth, how much would it weigh on the surface of this planet?

  During a lunar eclipse, the Moon, Earth, and Su 2o*4dwu(h 6u+uq:-zk gi dag 89zrlhbn all lie on the same line, with the lhd izz -qgb6o gkh9w8uua 4u(d2+r:*Earth between the Moon and the Sun. The Moon has a mass of $7.36 \times 10^{22} \; kg$; the Earth has a mass of $5.98 \times 10^{24} \; kg$; and the Sun has a mass of $1.99 \times 10^{30} \; kg$. The separation between the Moon and the Earth is given by $3.84 \times 10^{8} \; m$; the separation between the Earth and the Sun is given by $1.496 \times 10^{11} \; m$.
(a) Calculate the force exerted on the Earth by the Moon, its magnitude is    $\times 10^{20} \; N$, its direction is  ----待选择----towardsaway from  the moon.
(b) Calculate the force exerted on the Earth by the Sun, its magnitude is    $\times 10^{22} \; N$, its direction is  ----待选择----towardsaway from  the Sun.
(c) Calculate the net force exerted on the Earth by the Moon and the Sun, its magnitude is    $\times 10^{22} \; N$, its direction is  ----待选择----towardsaway from  the Sun.

  A 2.10-kg brass ball is transporteuo9387zz e -gejb1/l-ted rpcd to the Moon.
(a) Calculate the acceleration due to gravity on the Moon.    $m/s^2$ (The radius of the Moon is $1.74 \times 10^{6} \; m$ and the mass of the Moon is $7.35 \times 10^{22} \; kg$)
(b) Determine the mass of the brass ball on the Earth    $kg$ and on the Moon    $kg$
(c) Determine the weight of the brass ball on the Earth    $N$
(d) Determine the weight of the brass ball on the Moon    $N$

  A satellite is in a low circular orbit a9hh( oo d.uku:bout the Earth (i.e., it just skims the surface of the Earth). What is the speed of the satellite? (The mean rad(.u:u9dhh ok oius of the Earth is $6.38 \times 10^{6} \; m$.)

  A satellite is in a l,f b9 hwlva)y8n91q moow circular orbit about the Earth (i.e., it just skims the surface of the Earth). How long doevq9bwao8,hlym 1) fn9 s it take to make one revolution around the Earth? (The mean radius of the Earth is $6.38 \times 10^{6} \; m$.)

  A satellite is in circular orbit 230 km above the surface of the Earth. It im /0upgou; xrg6(vgj 3s observed to have a period of 89 min. What is the mass of the Earth? (The meang/ogp6 (03mu;ruvgxj radius of the Earth is $6.38 \times 10^{6} \; m$.)

  Europa, a moon of Jupiter, d3acz1qh8la:-w* q6cc: zr:llohf q* has an orbital diameter of $1.34 \times 10^{9} \; m$, and a period of 3.55 days. What is the mass of Jupiter?

  The innermost moon of Jupiter orbits the planet with a radiu5d;c6 myn,cup savk 8-s of $422 \times 10^{3} \; km$ and a period of
1.77 days. What is the mass of Jupiter?

  Two moons orbit a planet in nearly circular orbits. Moon A has(1 kd4uqmrzdhl1*4ds orbital radius r, and moon B has zh(k m sd*dl41 ru4d1qorbital radius 4r. Moon A takes 20 days to complete one orbit. How long does it take moon B to complete an orbit?

  The planet Jupiter is lvl6)b)t *o,6wniqkr $7.78 \times 10^{11} \; m$ from the Sun. How long does it take for Jupiter to orbit once about the Sun? (The distance from the Earth to the Sun is $1.50 \times 10^{11} \; m$.)

  It takes the planet Jupiter 12 years to orbit the Sun once. What is the aver yi2r zchr:p fp32/4;vkqlls3s msh*1age distance from Jupiter to the Sun? (The distance from the Eq sc23iprls 4;fhrlhmp :zs k/3 1y*v2arth to the Sun is $1.5 \times 10^{11} \; m$.)