Is it possible for an object moving with a constant speed to accelerate? Explai)wz;7yi)xd. 1 pzuqb xxdp))xz 7u.b; yw1qzin.

  Consider a particle moving with constant speed such that its acceleration jmp wq.vzrcqe *fd;:np 0l 2 :z;i-3roof constant magnitude is always perpendicular pmze i: d r*-q 2jlc;;qpn3z.v0wof:r to its velocity.

  An object moves in a circular path a9hl, hjj-vop zs0)9qum* 8swxt a constant speed. Compare the direction of the o mj90*hpl-)wu8qj,zsv s xoh 9bject's velocity and acceleration vectors.

  When an object experiences uniform circula edw/yogdf3bo w(p 7,*r motion, the direction of the acceleraf*gw 7 3dpby (/woe,odtion is

  Consider a particle moving with constant speed such that itv) pby /2 jbdcoj(pu vp(xe1o24lb (:vs acceleration of constant magnitude is always perpendicular to its veloc v: /2p2vbbj1u( 4ydop (vxlpb)( ejcoity.

  What type of acceleration does an object movi/ xr4 ,vkpy/0hdmxkb2ng with constant speed in a circular path expe/x0, k/xd4bp2myv hrk rience?

  What force is needed to ma4leoo1zju g; ,ke an object move in a circle?

  When an object experiences uniform circular motion, the direction of ty fzdfnz1k4 :6he net forcykzfzf 6d 41:ne is

  A roller coaster car is on a track that forms a circular loa 3vlteu*,z6o ,vjrk3op in the vertical plane. If the car is t3k3j*oatvzu6 ,vr,le o just maintain contact with track at the top of the loop, what is the minimum value for its centripetal acceleration at this point?

  A roller coaster car (mass = M) is on a tracr da;s3 bp/xri.;wxs3e 2v)y gk that forms a circular loop (radius = r) in the vertical plane. ;3w s)rp3r 2eg / .xy;vbasxid If the car is to just maintain contact 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-circular arc gy b v6e:st0he( jg6.luntil it is going straight up. Just as the plane l 0e6bvtyse :jg6 h(g.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 radi4iym p+n, 2qmrus $r$ 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 at a constant speed v. Then it goes ava4b45ym) vg1kd8rz hround the same curve at half of the original speed. Wha 1h5mb8vy4a v4rg) dzkt 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 -w.dwghhx44-7f zvy:i c1h7 6jm cujja constant speed v. Then it goes around a curve of radius 2r at speed 2cd6fj7 ig w ux7h1jc -.yhvj4mzh:4 w-v. What is the centripetal force on the car as it goes around the second curve, compared to the first?

  A car of mass m goes around a banked curve of radius r with speedaq6ope1/gu ,*lklh1xz i3(kq v. If the road is frictionless due to ice, the car can still negotiate the curve if the horizontal component of the normal force on the car from the road is equal in (1ul z,ahp/ kl6eoq1q3* kx gimagnitude to

  Two horizontal curves on b sq9jth( 3y*+ywj6pt a bobsled run are banked at the same angle, but one has twice the radius 9ps6+*tjy tw 3 bqyh(jof the other. The safe speed (no friction needed 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 thqrp94z ta2inn61v+b/fae g; ge Olympic bobsled track is not constant, but increases upward from the horizontal. Coming around a turn, the bobsled team will igavarn+p;/ 9net zi q 12bf6g4ntentionally "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 circular p l9q nx5ds+qf 0o8l;fpath to have both centripetal and tangential accelerq0 lopq9;fn5 dl8fs+xation?

  The gravitational force between two ogh2) q.y2; -ffgub0pldzob;xbjects is proportional to

  The gravitational force between two objects is inversely proportional tosmd;gt-r*bz /

  Two objects attract each other gravitationally. If the 29.vl i9e;;yaz zlsv ndistance between their centers is cut in half, the gravitational f.9ely zivas;2 ;n lv9zorce

  Two objects, with maswu o.0s0fwpe1ses $m_{1}$ 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 massed tfj7e(t* frxp g )zfv0f24t;s $m_{1}$ 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 universal gravy p wgw,7vk5qx1q, q,vitation.

  Compared to its mass on the Earth, the mass a i 8,nsdsb +.io:yo(js*1u tmof an object on the Moon is

  The acceleration of gravitcxf6qd h 6odx h6(ii2)y on the Moon is one-sixth what it is on Earth. An objecfd)ohii(c6 h66xqx 2dt of mass
72 kg is taken to the Moon. What is its mass there?

  As a rocket moves away from the Earth's surface, the rocket's wez,)laz4 lbx )vp0o d4:k shr,n-i5lvvight

  A spaceship is traveling to the Moon. At what point is it beyond the pull of E8*bav: s/ t -bab(b4xrh.uh kdstc*r,ard4rshtab *: (rckvb x,b st* -/.8bhuath's gravity?

  Suppose a satellite were orbiting the Earth just above th x bhffc32t6m,u x+h02znhff9e surface. What is its cent2x f,2xzhf3mfhn+u0 tc6 bf h9ripetal acceleration?

  A hypothetical planet has a mass of half that of the Earth and a ra7 u k +*)gmdhu 0:py*ppmonmc/z*yh; kdius of twice that of the Earth. What is the acceleration due to gravity on the planet in terms of g, the acceler/m*cupz7:y ) +pgnkpkd*h*;m0m ho yu ation due to gravity at the Earth?

  The acceleration of gravity on the Moon is onesg *ys;h 9ndb)-sixth what it is on Earth. The raddssy*)b gnh9;ius of the Moon is one-fourth that of the Earth. What is the Moon's mass compared to the Earth's?

  Two planets have the same surface gravity, but planet B has twicoi8u k:pfq+; 0wxkhx+78cxo vg vf l:3e the radius of planet A. If planet A has mass m, what is the mass of pfkv8w0l;v3 ix7xfo+gu q+k ::8xh coplanet B?

  Two planets have the same sui;pf u1gll - 5h5mtwdu7hr/*l rface gravity, but planet B has twice the mass of planet A. If planet A has radius r, wh u - p/tdllfmghr*wu1;5i7l 5hat is the radius of planet B?

  Consider a small satellite moving in a cij vx.v jsl qqur4s2h..;qkz+e:g 5a5a rcular orbit (radius r) about a spherical planet (mass M). Which expression gives this satellitq5.2rx ag ;s.s+lah: .qukqj4z5 vjve e's orbital velocity?

  Satellite A has twice the mass of satellite B, and rota 4)fp(v.e d iz;fr*ytltes in the same orbit. Comp.; lidfvtpy f)*4e(rzare the two satellite's speeds.

  A person is standing on a scale in an elevator accelerating downward. Compare tbxtndk4,ny 8 5he reading on t,b ydn85 k4tnxhe scale to the person's true weight.

  Who was the first person to realize that the planets move in elliptical patha tpiff kr-xx0pcc)02 izl 24+s around the Su ci+)txf 0irk2pfz 0acp- 2lx4n?

  The speed of Halley's Comet, while traveling in its elliptical or j4e4*yq)r ; nqorj )z8vodr+sbit around the qedjrsjn z;)+4 yq)ro8rv* 4 oSun,

  Let the average orbital radius of a planet (6f q)z egntfc+1,nnjbe R. Let the orbital period be T. What quantity is constant for all plannecj,1 )t6( ffnq ngz+ets orbiting the Sun?

  A planet is discovered to orbit around a star in 1 e/8yagozvm2 xurd)5 2 bt*lueu1fg6the galaxy Andromeda, with the same orbital diameter as the Eartuou 8 z*y1vtrg6gfm xa12e2lbe/ud5 )h around our Sun. If that star has 4 times 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 distancex/jus;k(ti+usji 32 r from the Earth to the Sun is defined as one "astronomical unit" (uut(s;2rxki ji+s j3/ AU). An asteroid orbits the Sun in one-third of a year. What is the asteroid's average distance from the Sun?

State Kepler's laws.: 5 mbh(guvozy 8rw99w

  List the four fundamental forces9 a2dixb6zk; r in nature.

  An object moves with a co ge*jiul/1 sf2nstant speed of 30 m/s on a circular track of radius 150 m. What is thfg*2ulj i1e/ se acceleration of the object?

  The maximum speed around a leloe1ijq*t 9f *i6v0cioh +l:evel curve is 30.0 km/h. What is the maximum speed around a curve with twice the radius? (Assume all other e t9fh6v+ *iieiq c*joo1l: l0factors remain unchanged.)

  What is the centripetal r)3bz+ ott l/(q qpp-kacceleration of a point on the perimeter of a bicycle wheel of dit-ltopr(zk/3)b q+p qameter 70 cm when the bike is moving 8.0 m/s?

  A point on a wheel rotating at 5.00 rev/s is located 0.200 m from the km, bp(r:li(zuo./np axis. What is the centripetal acceleration /mpl(:bz(kp.ruoni,?

  How many revolutions per minc9 m8kd os8;tvute must a circular, rotating space station of radius 1000 m rotate to prot8d89sokv ; mcduce an artificial gravity of $9.80 \; m/s^2$?

  A motorcycle has a mass of 250 kg. It3cn amfubw, 06ta4 h3a9pphq1 goes around a 13.7 m radius turn at 96.5 km/h. What is the centripetal force on t0f4wbut ahpc196ha3m a np3,qhe motorcycle?

  A 0.50-kg mass is attached to the end of a 1.0-m string. The system is e970 wxr +yw/jiji.ytwhirled 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 striixy9 /j twry0.jew+ i7ng is not to break?

  A stone, of mass m, is attached to a strong string1xao 23h*q qvvv;o9n jl,1b ha and whirled in a vertical circle of radius r. At the exact top of the path the tension in the string is 3 times the stone's weight. The stone's speed at thi 1h jvo3;*v2qlxa9 qhanbo1v,s point is given by

  A stone, of mass m, is attached to a strong string and.y rb4iv;xq.z x/mbn*l7 a1 bn whirled in a vertical circle of radius r. At the exact bottom of the path the tension in the string is 3 times the stonba y nqli;mr /4zx.x7 vb1.*nbe's weight. The stone's speed at this point is given by

  A jet plane flying 600 q an, )y+y2tnm .u;q92bcvixlm/s experiences an acceleration of 4g when pulling out of the dive. What is the radius of curvature of the loop in which the plane is flyi2laqn,;cy)m +vtq nxyui9. b2 ng?

  A pilot makes an outside vertical loop (in which*nlcgic,-x dk:s/ 0b wmcixdy;,a6i6 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 wita6cslc-0;*, cbi:d/ixy mxiw6 dg n,kh only one-half of his normal weight. How fast is he going?

  The maximum force a pilot can stand is about seven times hicgsn6cgp +qi2e-j n-:s weight. What is the minimum radius ofe+c-sgcn : 6 pngq-j2i curvature that 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 80-m ra6uf(bt ov 9jivx/ 5b 4kc9we ,evwg*c,dius horizontal curve with the tires on the verge of slipping. How fast can this car round a second curve of radius 320 m? (Assumevt e ew(*,65w kj/4cbvugx9o9vfib, c the same coefficient of friction between the car's tires and each road surface.)

  A car is negotiating a flat curve of radiuszd8a9gut6,; cmm.s :dfvx )ys 50 m with a speed of 20 m/s. The centripetal force provia:gmc. , v)8ds xzs6dty 9mfu;ded by friction is $1.2 \times 10^{4} \; N$. What is the mass of the car?

  A car goes around a flat curve of radius 50 m at a speed of iv71n3wfn 3ml ec7c7 t14 m/s. What must be the minimum coeffi7cc i7m nnf1w3telv37cient of friction between the tires and the road for the car to make the turn?

  A car is moving with a constant speed v around a lev v2i)s 2jy;uwtel 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 yj;2s2itu wv)stay on the road?

  What minimum banking angle is required for an Olympic bobsled to negotiate (l 2pbxflo*)po(oze9x0h (rya 100-m radius turn at 35 m/sl( bpz(efy opx)o*x (2 9rh0ol without skidding? (Ignore friction.)

  A horizontal curve on a bobsled oe6li:pl 9*he run is banked at a $45^{\circ}$ 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 1000 jfpa((wf;1a rpaxa; m, banked at an angle of $45^{\circ}$, may be safely negotiated at a speed of

  A curve of radius 80 m is banked ang):b1 xtyb3ni ljn21 t $45^{\circ}$. 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 end of a string i:ft ddb04,oq dmo;tc 1s revolving uniformly in a horizontal circle of radius 014b:,otomtd;df q0c d.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 arek *b3bawf3:xs;7wj pq a, a race car accelerates at a uniform rate to 7;wfsk3w b:xb3j q*paa speed of 45 m/s in 15 s, moving on a circular track of radius 500 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 consists of a prot6) 2ekdmhws*d(tj 5ijj3e( ve on 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-kg person standing on the Earth, c+dspk4 .r:fs u9z lr9due to the Moon? The pz 99fr+sk:slcudr4.mass of the Moon 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 is F. If the masses are m :mjgdyv3uu)0k-, o y3lq)1 e txjq*qioved giuj,3 vlq30uy-d)1x*mqt) kjqoey:to half of their initial distance, what is the gravitational attractive force?

  For a spacecraft going from the Earth tvuykpcnj .ek8.a + j:r07e 09*xfehmsoward the Sun, at what distance from the Earth will the gravitational forces due to the Sun and the Earth c0v+p*sa rjj:f.9e7cx 0mhe y8k ku. enancel?
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 ,/i8x t) adny+jz (ne f np-4bknoi.9mis $7.4 \times 10^{22} \; kg$ 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 "space-walk" at a dis8lyst a8kxyp93q )0a/j; zujktance above the Earth equal to the radius of the Earth. What is her acceleration due to gravityxk)s 0aa/89j;pyt8lu3j kz qy?

  The radius of the Earth is R. wbn r b9ol66-xfb5wb*z8 ewm5ntj9j 5 At what distance above the Earth's surface will the acceleraj8wbx6 t*m5j5nzo 996b flb5enw b-rwtion of gravity be $4.9 \; m/s^2$?

  A satellite encircles Mars aticn;b6p(z)o / msj5jm hi2z0i a distance above its surface equal to 3 times the radius of Mars. The acceleration of gravity of the sat b n2h)mcz0/jo5sizi m;(jp6iellite, as compared to the acceleration of gravity on the surface of Mars, is

  At a distance of 14000 km from some planet's center, the acceleration of gravity hlp+ nbp.-pq/hi+6musd: qb6 +hb6 6:.s-u+qlpbpd/ i mhqnp is $32 \; m/s^2$. 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 the Earth. The E:wrc 4hou+woqagg xrr1n ;* -1arth has radius r. If the object is r1 orgg :q4*rn1;cx+wwah ou-raised to a height of 3r above the Earth's surface, what is its weight?

  By how many newtons does the wes9fo1w*nvcf)0 hwzj rjfm 83calu4*m9 c t63xight of a 100-kg person change when he goes from sea level to an altitude of 5000 m? (The mean radius of the Ea3j*)fwn8hcz c490jc 9swtm1*3rl vfo mfu6x arth is $6.38 \times 10^{6} \; m$.)

  The Earth has radius r. A satellite oswseafi6b e8xu-s -1 *09mqkvf mass 100 kg is at a point 3r above the Earth's surface. Whatx-waqee6-v9*kmb8s fuis1 0s is the satellite's weight?

  A spherically symmetric planet has four times the Earth's ma;sl i8a 7asr0ee d0,bxx *7okrss and twice its radius. If a jar of peanut butter weighs 12 N on the surface of the Earth,* 08 r xo7a,l7xrsadese b0k;i how much would it weigh on the surface of this planet?

  During a lunar eclipse, the7gx(ni2w1c*;wjli/wnw f 5hp1 flc9 u Moon, Earth, and Sun all lie on the same line, with the Earth between the Moi951;fcw w pi/wf l xj2unl*w(n7hc1gon 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 tsnzg-qnte80 ,ransported 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 abou o0p0qu4vh3c yt the Earth (i.e., it just skims the surface of the Earth). What is the speed of the satellite? (The mean radius of the Ear 4pcyuqh3v00o th is $6.38 \times 10^{6} \; m$.)

  A satellite is in a low circular orbit about the Earth (i.e.,9j4qv g95r*oh ljfg e g7n-jk* it just skims the surface of the Earth). How long does it take to make one revolution around the Earth? (T 9j vglr*4e7g*ngqfh-j59kj ohe mean radius of the Earth is $6.38 \times 10^{6} \; m$.)

  A satellite is in circulo2rzfl3k02ewmf 1z 3t ar orbit 230 km above the surface of the Earth. It is observedw 03zo2fez lkmf13tr2 to have a period of 89 min. What is the mass of the Earth? (The mean radius of the Earth is $6.38 \times 10^{6} \; m$.)

  Europa, a moon of Jut6 kgcs4)jg d2kz /x2gpiter, 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 Jupitef935 j fyg0p(uz8ewns r orbits the planet with a radius of $422 \times 10^{3} \; km$ and a period of
1.77 days. What is the mass of Jupiter?

  Two moons orbit a pla+qrxcy/u ad82q eko72net in nearly circular orbits. Moon A has orbital radius r, and moon B has orbitau2qo y 8a7qkxc/+2rde l 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(zinqlm 8rns 1 ug oo:31.,fnp $7.78 \times 10^{11} \; m$ 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 orbitfm6 c:pa;9njk the Sun once. What is the average dis pjck9; 6f:namtance from Jupiter to the Sun? (The distance from the Earth to the Sun is $1.5 \times 10^{11} \; m$.)