Is it possible for an object moving with a constant speebi* mu6gv(24 joxt7u(qu98h ino)e tu d to accelerate? Explai2thon7 e48im9qutu b6gx ouv*(u ji()n.

  Consider a particle moving with constant speed such that8:dbf6xcce4rt 9:qapglj; em 9kg n89 its acceleration of constant macjk a9:t8l cefnx49g;dqm6p9g e:r 8bgnitude is always perpendicular to its velocity.

  An object moves in a circular path at a constant speed. Compare the di( p2.9sl l zmecwmyb47rection of ymbm7.p 9c(zwe2 lsl4 the object's velocity and acceleration vectors.

  When an object experiences uniform circular motion, th. d+ubc*(6 4-wqjec72vmanr.mz hw kae direction of the acceleration 4jrm aw2n.+mq-*7eu cchwdv. a6kz(bis

  Consider a particle moving with constant speed ,-g -z,yt mqxbsuch that its acceleration of constant magniqbtmx, ,-zyg- tude is always perpendicular to its velocity.

  What type of acceleration does an object moving with constant speed in ,6io,tbv82 z1sli fj*v qnp( za circular path experience? v8 topq,i2vfz,6s jinz1* (lb

  What force is needed q3tod5/04vj s14 )mesbu fxoitz b:-ato make an object move in a circle?

  When an object experiences uniform circular motion, th t- fyq)g.2o.klh/n1 rz ryo;re direction of the net forceqrrton/2.yhg. z -r1fk ;lo )y is

  A roller coaster car is on a track that forms a circular loop in the verticalrbyxic.;-vn,w(d8 mu plane. If the car is to just maintain codvw(r8bxim,; c. un -yntact 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 track7 rkma; z+h o -fwq9:exdtmm82r,f)ji that forms a circular loop (radius = r) in the vertical plane. If the car is to just maintain contact with the track at the top of the loop, what+2;r8t xqr wf7 dahom-zjfm,ik)9:me is the minimum value for its speed at that point?

  A pilot executes a vertical dive then foly.9f bfhnsb wl:w6n/-y y.b ,olows a semi-circular arc until it is going straight up. Just as the plane is at its lowest point, , hybb ys-l/n96ow. :nfyfb.w 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;2ovmp8cbfjsz b5eqc+.c5 y ; radius $r$ 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 constan/wvkg 9u(ab/e6ngig5iay k,nl 1y: b7t speed v. Then it goes around the same curve at ig5v9/ uab,alngkge(:iy k1y76 w/n b half of the original 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 uy6vw(-8kmm-s vd6sq speed v. Then it goes around a curve of radiuqmwuk6(v6-s8ydv-s ms 2r at speed 2v. 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 irkys qe:wb y: 1l5q+k(c8d:zspeed v. If the road is frictionless due to ice, the car can still negoticwk l +sqq b:zek(r 1d:5y:yi8ate the curve if the horizontal component of the normal force on the car from the road is equal in magnitude to

  Two horizontal curves on a bobsledka5 u ,aqp/p(h run are banked at the same angle, but one has twice the radius of the other. The safe speed (no friction needed to stay on the run) for the smaller radius curve is v. What is the safep /(uqkh5 pa,a speed on the larger radius curve?

  The banking angle in a turn on the Olympic bobsled track is osa8rwre.2aj)dokfc9( t) x* not constant, but increases upward from the horizontal. Cominj*sc )xrf8o wea)9t2dr.( kaog 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 3j0 -dth4/w8op6ofmq- jfe jnobject moving around a circular path to have both centripetal and tangential0wej j/ n-h d3-fjoft6po8q4m acceleration?

  The gravitational force between two objects is proportional to hy0c.9bhdcho+1r/ll58enhj 3 nzb 3l

  The gravitational force between two objects is inversely proportion) zxyv r3,jv kncj,66aal to

  Two objects attract each other gravx8zh6xf4,,p;oo vv e ditationally. If the distance between their centers is cut in half, the gravitz xx,d,eohof4vp8v ;6ational force

  Two objects, with masse(bu2 8 ;-bjqwl sqiuf6s $m_{1}$ 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 massesvr qnm0cd/9a t:8u6hc $m_{1}$ 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 gravitat d)s2ef avwd/08d(ndeu1 w*t hion.

  Compared to its mass on the Earth, the mo b21 xbkv2fsri lc5.;ass of an object on the Moon is

  The acceleration of gravity on th n:qo.ymh7o9 ve Moon is one-sixth what it is on Earth. An object.o h :v97onqym 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 rocke m9q1g 3e:,kqx cp: bu;uo(vket's weight

  A spaceship is traveling to the Moon. At what point is.:ycrgw,3 n of it beyond the pull of Earth's gr:w3,n.o cfyr gavity?

  Suppose a satellite were orbiting the Eartv6rg:w l3wz+dh just above the surface. What is its centripetal accelgw6dv:zl3 w+ reration?

  A hypothetical planet has a mass of half that of the Earth and a. vgfp(4(,r eii/uf 9ou33/i kve6nujgfu-tz radius of twice that of the Earth. What is the acceleration due to gravity on the planet in (/uoztvvri9n3gu3gu e/p,fe ( ui4f f-ji 6k.terms of g, the acceleration due to gravity at the Earth?

  The acceleration of gravity on the.z 41 cc+myyc/hjuce68 zzmb +sx4ny7 Moon is one-sixth 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 the Earth'sz+y hc4jyc 6bxn.scum7 1cyz+ /ezm84?

  Two planets have the same surface gravity, but planet B has twice thedk 0mmt,x:sc :ja5 66lwy jde8 radius of planet A. If planet A has mass m, what is the m :lk sdctwedy, xaj6j56 :8m0mass of planet B?

  Two planets have the same surface gravity, but planet B hm)iu7j+ zj4,bj b ;mxlas twice the mass of planet A. If planet A has radiusl,xz7; j4bij)um mj+b r, what is the radius of planet B?

  Consider a small satellite moving in a circular orbit (radius r) a; l5l/r*x5 a8k pqshyxbout a spherical planet (mass M). Which expression gives this satellite's orbital velrs l p ;/5ax58hxkql*yocity?

  Satellite A has twice the mass of satel -q thx,z42*jsl koef*lite B, and rotates in the same orbit. Compare the tw4el*kohx*tq, szj f-2o satellite's speeds.

  A person is standing on ue ju61j lsvh)v(40yga scale in an elevator accelerating downward. Compare the reading ou (0e u14lvhgjvs6y )jn the scale to the person's true weight.

  Who was the first person to realize that the planets move in elliptiop jfjumc+9,u()id 1y cal paths arouifjju u9 yo,d1mc p+)(nd the Sun?

  The speed of Halley's Comet, while ttg0rxmwjv ef55* 2n b3raveling in its elliptical orbit around the Sw f0g3net2xmr5v*b j5un,

  Let the average orbital radius of a planet be R. ao.8c ws7oy z/41rg xi xyq3*r Let the orbital period be T. What quantity is constant for allq3cy r47/ z.x1 ixrgao*8wsyo planets orbiting the Sun?

  A planet is discovered to orbit around a staebttbr..6 qdfby, 4.ur in the galaxy Andromeda, with the same orbital diameter as the Earth around our Sun. If that star has 4 times the mass 6f .bdre qty.u .b,bt4of our Sun, what will the period of revolution of that new planet be, compared to the Earth's orbital period?

  The average distancetevu ypq/el5 :qwd ,0, from the Earth to the Sun is defined as one "astronomical unit" (AU). An asteroid orbits the Sun in one-third of a year. What is the asteroid's average distance from vplw5q,y0d u/,ee:tq the Sun?

State Kepler's laws.d x7brj2/in wz-. m:1z3gqksatp6m/ b

  List the four fundamental for kl 6xfmaban1 1 rh39+lq;)qgaces in nature.

  An object moves with az 9zjpngy jb*r x ,* .nzw:y;w7xd(2jj constant speed of 30 m/s on a circular track of radius 150 m. What is the acceleration of the objbxny wn:w(jjz,zjxd* rg 9p7y2z. *;ject?

  The maximum speed around a level curve is 30.0 km/h. What is th*oi xt gqvees4*p+ g1*e maximum speed around a curve with te oe x*4qsi*t p*gg+1vwice the radius? (Assume all other factors remain unchanged.)

  What is the centripetal acceleration of a point on ya 7l0wpg ra)(4s4jtwql2p(d the perimeter of a bicycle wheel of diameter 70 cm when the bikw4 ll(w)d prtq a(s a7jg02yp4e is moving 8.0 m/s?

  A point on a wheel rotating at 5.00 rev/s is located 0.200 m f , eei, dx6upfn/qmk.2rom the axis. What is themepexifd/q k 6 u,,n.2 centripetal acceleration?

  How many revolutions per minute must a circular, rotating spl71f7muh(w smj:b:kb ace station of radius 1000 m rotate to produce an aw:(hbub k7mlf s1 7:jmrtificial gravity of $9.80 \; m/s^2$?

  A motorcycle has a mass of 250 kg. It goes awx6 *1disjmcc1 +5vu fround a 13.7 m radius turn at 96.5 km/h. What is the centripeta+d16wc j 15vsui fmc*xl force on the motorcycle?

  A 0.50-kg mass is attached to the end of a 1.0n/g w qd3 jdqbj;5::cvvv)3ss -m string. The system is whirled in a horizontal circular path. If the maximum tension that the string cs bgcv:3ndv5;v:wjqjq/ 3 s)dan withstand is 350 N. What is the maximum speed of the mass if the string is not to break?

  A stone, of mass m, is attached to a strong string and whirled in a verttndgm;(5,j -eb 9dj uzical circle of radius r. At the exact top of the path the tension in the string is 3 times the sn9j(gjd;,b -d5 metz utone's weight. The stone's speed at this point is given by

  A stone, of mass m, is attached to a juz p xx0p6:mk-p-6ejstrong string and whirled in a vertical circle of radius r. At the exact bottom of the path the tension in the string is 3 ti6xpj j:0x -m6 epz-upkmes 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.q6 0q*oy q6wcf-iibyu+ 350 jpmgkqc pulling out of the dive. What is the radius of curvature of the loop in which the plane is flyi g63m50obf qjwyc*q 0ucqi.+ ip -6ykqng?

  A pilot makes an outside vertical loop (in which the center of the loop is by+-z 5.j )lw5c40idd yaye/ys fbg3g weneath him) of radius 3200 m. At the top of his loop he is pushing down on his seat with only one-hdlwb-s+0y. g) yfc edz ywa3/g4i5y5jalf of his normal weight. How fast is he going?

  The maximum force a pilot 0vwos3zgwb8 1 4zjku 0can stand is about seven times his weight. What is the minimum radius of curvagbzujw 80vz14 o03kwsture 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 r pa.4e )n9(0- utqtc.zxh yfjtadius horizontal curve with the tires on the verge of slipping. How fast can this car round a second curve of radius 320 m? (Assum-h) qtfy0n4at9(z.xej p cu.t e the same coefficient of friction between the car's tires and each road surface.)

  A car is negotiating a flat curve of radius 50 m rgyv3qc 7)9 oimjt; .cwith a speed of 20 m/s. The centripetal force r.mio7tccgv9 yj;q3) provided 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 14 m/i glza2e7l2 k*s. What must be the minimum coefficient of friction between thez2e *7gi lka2l tires and the road for the car to make the turn?

  A car is moving with a constant speed v around a level curve. Theu48 stoc2ihbda 3w)i8 coefficient of friction between the tires and the rahd biwts8243 co8i u)oad is 0.40. What is the minimum radius of the curve if the car is to stay on the road?

  What minimum banking angle ipr.1, :hl, ;q7*uxtq9eofsr kc7pi la s required for an Olympic bobsled to negotiate a 100-m radius turn at 35 m/s without skidding? (Ignore friction.)7,,xatc.7qsfople q1 rk9lpih* u r:;

  A horizontal curve on a bobsled rugt)8s s,5fzq w g.us n2uu9o;onhp4 -xn 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 rs8 3g4v(+ 06qjgksqh5 og khba:3fzwwadius 100 m, banked at an angle of $45^{\circ}$, may be safely negotiated at a speed of

  A curve of radius 80 m is banked aty syw9k/hxol)c-go py2ck.8 la;gmsv..0 , rz $45^{\circ}$. 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 is revolving uniformly in a horizont2hsvrwt wr rxmz8.c++i5-9 bo al circle o 9+xm8 v sr.+whbrtr2iw- zc5of radius 0.500
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 area, a race car accelewbeurc;etaoo;:m3: m2a w:x4.osg/f rates at a uniform rate to a speed of 45 m/s in 15 s, moving on a circtoef2 :mo oreg/3a;w a.b4ux; wm:s:cular 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 consi-o anj/(wg,n dsts 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(k:s5srl3+gjnqgfh/ gvo: ;,fg;ku c on a 70-kg person standing on the Earth, due to the Moon? The mass of the Moon isr vgnsfj3uf;:ohg +qs;(cg/kk 5: ,lg $7.36 \times 10^{22} \; kg$ and the distance to the Moon is $3.82 \times 10^{8} \; m$.

  The gravitational attractive force between two masses i5 w)so)tmd3vus F. If the masses are moved to half of their initial distanc)twuv)s5d o3me, what is the gravitational attractive force?

  For a spacecraft going from the Earth icwaps5h7 :+t toward the Sun, at what distance from the Earth will the gravitational forces due to the Sun an5 :+t7cpw hsiad the Earth 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 Moonx5ye3nu:/yr *tcu1 bx is $7.4 \times 10^{22} \; kg$ 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 distance above the Eart v4kvcl23uyy ;h equal to the ;vy2 4 3kulycvradius of the Earth. What is her acceleration due to gravity?

  The radius of the Earth is R. At what distance above the Encm * l/sjimf)d4 2 gb0ga9vt-(yq b;parth's surface will the acceleration of gravij nsmg mc/40gb;dq* pi (btl-fva)y29ty be $4.9 \; m/s^2$?

  A satellite encircles Mars at a relgv+ 00y xd-bzw-,bdistance above its surface equal to 3 times the radius of Mars. The acceleration of gravity of the satellite, as compared to the accele zlw- b, 0+-yvr0bxegdration of gravity on the surface of Mars, is

  At a distance of 14000 km from some zu,2:sta lc0tj5t0zpplanet's center, the acceleration of gravity i2zt ,0tlzp0t5:ajs ucs $32 \; m/s^2$. What is the acceleration of gravity at a point 28000 km from the planet's center?

  An object weighs 432 N on the surface e5tn;k wdu:-cof the Earth. The Earth has radius r. If the object is raised to a height oe:c 5tu ;dkn-wf 3r above the Earth's surface, what is its weight?

  By how many newtons does the wv.wk v3) l)sx mgec3k;eight of a 100-kg person change when he goes from sea level to an xs.vcl mwkge)3kv3;) altitude of 5000 m? (The mean radius of the Earth is $6.38 \times 10^{6} \; m$.)

  The Earth has radius r. A 2w*wxd);al50ft y pay satellite of mass 100 kg is at a point 3r above the Earth's surface. What is the satelliteayt2w5yp; )*xw0alfd 's weight?

  A spherically symmetric planet has four times the Earth's mass and twice ii6* wm uxk3/gyts radius. If a jar of peanut butter weighs 12 N on the surface of the Earth, how much wo yu3*wgimk /6xuld it weigh on the surface of this planet?

  During a lunar eclipse, the Moon, Earth, and Sun all lie on;acb)s,qd txtwt./0q z4vl w + the same line, with t csd vxt4l0,w;. +ztqqwt)ba/he 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 transported to the Moon4tpbbko*u 0ge ,:*qpm.
(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 about the Earth (i.e., it just ski41e/gwv ux7*s8qxe ou ms the surface of the Earth). What is the speed of the satellite? gx* 7eu u1/xvseq w84o(The mean radius of the Earth is $6.38 \times 10^{6} \; m$.)

  A satellite is in a low circular orbit about the Earth (i.e., it just skims tmtwgi7s6 4y.(pau*57k*vbo zk57hs uq: kyo she surface h7 ku5 mo.t:i(us7oyswp 7ga 5k4v*kb*zq6ysof the Earth). How long does 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 or 1w/r/7,uo;v6dz dr nrf/mjpjbit 230 km above the surface of the Earth. It is observed to have a period of 89 min. What is the mass of the Earth? (The mean radius of the Eao,v/ r df /w;jpd7zr/ 16jrnumrth is $6.38 \times 10^{6} \; m$.)

  Europa, a moon of Jupiter, has an or0sj qvok--p5 63egijw bital 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 Jupitt.ehk1sqo/ p7 er 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 planet in nearly circular or:y3j+okv cs. swfe:x(bits. Moon A has orbital radius r, and moon B has orbital radius 4r. Moon A takes 20 days to complete one orbit. How long do.ewxso f+v3 sk :yj:(ces it take moon B to complete an orbit?

  The planet Jupiter is , 7sr odc +98nqrd7bpb$7.78 \times 10^{11} \; m$ 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 Jupiter7scrl;es ).f1vah w(o 12 years to orbit the Sun once. What is the average dis)s e (.clowhva; 71fsrtance from Jupiter to the Sun? (The distance from the Earth to the Sun is $1.5 \times 10^{11} \; m$.)