We claim that momentum is conserved, yet most movi,3p -g- ktp fzqv5cxm;w.ioz(ng objects eventually slow down and stop. Excg3p oiz-kf wmvz(,q;p t 5.x-plain.

When a person jumps from a treqadl*/3z d/jjjs w ap6a8:0koe to the ground, what happens to the momentum of the person 8/z:dp0j*w/ aqa 6ojaksjd 3l upon striking the ground?

When you release an inflated but untied balloon, why does it j kqg*airb*xkib93(c */ iex1,eszl( fly across the roomexe (/s b* kj3*i9 (xqbgirz*ial1,ck?

It is said that in ancirykehp jyor lp*zuf+,:66+l64k 4gra ent times a rich man with a bag of gold coins froze to death while stranded on a frozen lake. Because the ice was frictionle f pprr6ea 4y+4ljy*zou:gr,kl66kh +ss, he could not push himself to shore. What could he have done to save himself had he not been so miserly?

How can a rocket change direction when it is far out in space and is essentialljjx8s ig) (*pmy m)g8 x i(ps*jjin a vacuum?

According to Eq. 7–5, the longer the impact time of an imo s msy3h-bdd/i7 z x(7v72lgipulse, the smaller the force can be for the same momentum change, and b-g y2oisv dhd/7z7xl s(im37hence the smaller the deformation of the object on which the force acts. On this basis, explain the value of air bags, which are intended to inflate during an automobile collision and reduce the possibility of fracture or death.

Cars used to be built as rigid6cz .59ah;8xzlux.pa 4txpcpttqx 2 . as possible to withstand collisions. Today, though, cars are designed to have “crump86t.axtx;.lh. u4qz ap2 cptc x59 xzple zones” that collapse upon impact. What is the advantage of this new design?

Why can a batter hit a pit(;ah:rmx my 4sched baseball further than a ball tossed in the air by thm ayx(h:4 ;rsme batter?

Is it possible for an object to receive a larger impulse from a fvo21gpe.:m o co.: cllor9z0 small force than fromop:vf oc92le1l.ogr:.oc 0mz a large force? Explain.

A light object and a heavy object have the same kvq*q. 28tu,u3r hx ipeinetic energy. Which has the greater momhrp .q3i8 et,xv*uuq2entum? Explain.

Describe a collision in which a7cyswnn1 3 *uwll kinetic energy is lost.

At a hydroelectric power plant, water is directed at high speed x87a(wg: 5 gyqbdqi:r:lsjh. against turbine blades on an axle that turns an electric generator. For maximum power generation, should the turbine bladegsiq.5 :bhya q :jd7g(8w:lxr s be designed so that the water is brought to a dead stop, or so that the water rebounds?

A squash ball hits a wall at a 4y do: idn-yh m9x. yk/41 )asdr-ttpg(5 $^{\circ} $ angle as shown in Fig. below. What is the direction (a) of the change in momentum of the ball, (b) of the force on the wall?

A Superball is dropped from a height h onto a hard 82p hn ukk36xb75crrs7 9rcursteel plate (fixed to the Earth), from which it rebounds at very nearly its original speed. (a) Is the momentum of the ball conserved during any part of this process? (b) If we consider the bukurxcrp36br5 s2rkc 779 8hn all and Earth as our system, during what parts of the process is momentum conserved? (c) Answer part (b) for a piece of putty that falls and sticks to the steel plate.

Why do you tend to le+raib u,th cz/,u h-zs,ikb+ 3an backward when carrying a heavy load in your arms?

Why is the CM of a 1-m length of pipe at its mid-point, whereas tho+rj:k un) .x hnbce3avn-.ye0d r 8v)is is not true for your ax)nc8yn 0v-a.+j h3b . noedr :kevr)urm or leg?

Show on a diagram how youkp,1 g2sjmcb* r CM shifts when you change from a lying position to a sitting pos ,21gcjbk ps*mition.

If only an external force can change the mom kxe:.nfs/e) kbkqua2dw ,,j4entum of the center of mass of an object, how can the internal force of an engine acceleraa,bexn/4f)eq,ud sw j k2:.k kte a car?

A rocket following a parabolic path throu*ttrti x0gdz l4e lwvo: 2 r77f)ce5b7gh the air suddenly explodes into many piei7ecr4 vdl:) 72zt*7ftxt5 0l oberwgces. What can you say about the motion of this system of pieces?

  What is the magnitude of the mome,+x*wx y-5d viz+fd5m, ayndx ntum of a 28-g sparrow flying with a speed of $8.4 \; m/s$    $kg \; m/s$

  A constant friction force of 25 N njfab6zo+ - 8 p/ o1k,yqodzg4 vx)qp/acts on a 65-kg skier for 20 s. What is the skier’s change p-pod 1 a j8 oz/no4+qz kqgvfb)/,xy6in velocity?    m/s

  A 0.145-kg baseball pitched at 39 m/s,8 2)n c5re2qshjkstz is hit on a horizontal line drive straight back toward the pitcher at 52m/s If the contact time between bat and ball i rhj)q,2k8 ts se5c2nzs $3\times10^{-3}$s calculate the average force between the ball and bat during contact.    N

  A child in a boat throws a 6.40-kg package outh tlku;2r5/s6x*emo z horizontally with a speed of 10 m/s Fig. below Calculate the velocity of the boat immediately after, assuming it was initially at rest. The mass of the child is 26.0 kg, and that rl5tsh2*/ez6 o m k;uxof the boat is 45.0 kg. Ignore water resistance. The magnitude of the velocity of the boat is    m/s

  Calculate the force exerted on a rocket, given that the propelyvbw( . t+2.e4-mfgjfob y4gzling gases are expelled at a r f2-g4.(jgwfy+.4zty obmv be ate of $1500 \; kg/s$ with a speed of $ 4\times10^{4 } \; m/s$ (at the moment of takeoff). F =    $\times 10^7 \; N$

  A 95-kg halfback moving at 0u,z 1jjun32 bbkal2w $4.1 \; m/s$ on an apparent breakaway for a touchdown is tackled from behind. When he was tackled by an 85-kg cornerback running at $5.5 \; m/s$ in the same direction, what was their mutual speed immediately after the tackle?    $m/s$

  A 12,600-kg railroad car travels alone on alevel frictionless traw;8fti/plgp7 / kan: iksmvl;+ e:j k d2.da:lck with a constant speed of 18m/s A 5350-kg load,initially at rest, isnk;7if.s dv:lkl lag kpi;m 8et+j:wd/a:p2 / dropped onto the car. What will be the car’s new speed?    m/s

  A 9300-kg boxcar travelin,b ok,5xaf.ds ,bol- sg at $15 \; m/s$ strikes a second boxcar at rest. The two stick together and move off with a speed of $6 \; m/s$ What is the mass of the second car?    $m/s$

  During a Chicago storm, winds can whip hs 5xrjx6eyphl(tl6rg2( ) d)j orizontally at speeds of 100km/h If the air strikes a person at the rate of 40kg/s per square meter and is brought to rest, estimate the force of the wind on a person. Assume the person is 2dr(js6)trp)elgyj6xh5 (x l 1.50 m high and 0.50 m wide. Compare to the typical maximum force of friction $\mu\approx1.0$ between the person and the ground, if the person has a mass of 70 kg.    N
$F_{on person}$  ----待选择----<> $F_{fr}$

  A 3800-kg open railroad car coasts along with a constant speed of *t) ayu.b0nki 8.6m/s on a level track. Snow begins to fall vertically and fills the car at a rak)*0a nti yub.te of 3.5kg/min Ignoring friction with the tracks, what is the speed of the car after 90.0 min?$\approx$    m/s

  An atomic nucleus initially moving at 420m/s emits an alpha patc0 cpse3.y5n3d4+ vdtvy;k urticle in the direction of its velocity, and the remaining nucleus slows to 350m/s If the alpha particle has a mass of 4.0 u and the original nucleus has a mass of 222 u, what speed does the alpha particle ha cyd3+5vp tt3yuv40s.kecdn ; ve when it is emitted?    m/s

  A 23-g bullet traveling 230m/s pm8dbw ehdog)nnd05lu/lg bn4.i/u0 ,enetrates a 2.0-kg block of wood and emerges cleanly at 170m/s If the block is stationary on a fri4 d8.n euoubd nni/g,w)l0 b0d/5lh mgctionless surface when hit, how fast does it move after the bullet emerges?    m/s

  A 975-kg two-stage rocket is traveling at a speed of.gjyxs+pd- l 0 $5.80\times10^3\mathrm{~m/s}$ with respect to Earth when a pre-designed explosion separates the rocket into two sections of equal mass that then move at a speed of $2.20\times10^3\mathrm{~m/s}$ relative to each other along the original line of motion. Let “A” represent the upper stage (that moves away faster) and “B” represent the lower stage.
(a) What are the speed and direction of each section (relative to Earth) after the explosion? $v'_A$   m/s  ----待选择----away from the Earthtowards the Earth  $v'_B$   m/s  ----待选择----away from the Earthtowards the Earth 
(b) How much energy was supplied by the explosion? [Hint: What is the change in KE as a result of the explosion? $a\times10^8$ a =    J

  A rocket of total mass 3180 kg is traveling in outer space withpsr2a/c +7rge a velocity of 115m/s To alter its course by 35 ae+2rcg/p7rs.0 $^{\circ} $, its rockets can be fired briefly in a direction perpendicular to its original motion. If the rocket gases are expelled at a speed of 1750m/s how much mass must be expelled?    kg

  A golf ball of mass jbs9y6 dm jbw-;vxx:40.045 kg is hit off the tee at a speed of 45m/s The golf club was6vxywb b:j md9 xs4j;- in contact with the ball for $3.5\times10^{-3}$s Find (a) the impulse imparted to the golf ball,    kg*m/s
(b) the average force exerted on the ball by the golf club.    N

  A 12-kg hammer strikes a nail at a velocity of 8.5m/s +b3(szi;ca0usk:(3sce -+z1pze ybfr o9nzg and comes to rest in a time interval 93s eef1s ckbc0(n+-oyz(gzuz;i+bpzs3 ra : of 8.0 ms. (a) What is the impulse given to the nail?    kg*m/s
(b) What is the average force acting on the nail?    N

  A tennis ball of mass m=0.06kg and speeda- 7 1zcn(h+qjkqj 2iw v=25m/s strikes a wall at a 45 $^{\circ} $ angle and rebounds with the same speed at 45 $^{\circ} $ (Fig. 7–32). What is the impulse (magnitude and direction) given to the ball?   kg*m/s to the  ----待选择----leftright 

  You are the design engineer in chargek (wo3aeb/hn;vfol a05*fxm/ of the crashworthiness of new automobile models. Cars arew /klo5( /;a3xf*avb nf0ohe m tested by smashing them into fixed, massive barriers at 50km/h (30 mph). A new model of mass 1500 kg takes 0.15 s from the time of impact until it is brought to rest. (a) Calculate the average force exerted on the car by the barrier. $\approx$$a\times10^5$N a =   
(b) Calculate the average deceleration of the car.    m/$s^2$

  A 95-kg fullback is running at 4m/s to the east and is stopped in 0)p m80u84bns pd rdgvkc.u. n-.75 s by a head-oup0bn8.r8 d- p 4dk)vcusnm.gn tackle by a tackler running due west. Calculate
(a) the original momentum of the fullback    kg*m/s
(b) the impulse exerted on the fullback    kg*m/s
(c) the impulse exerted on the tackler,    kg*m/s
(d) the average force exerted on the tackler.    N

  Suppose the force acting on a tennis ball (mass 0.060 k t(o7r6nothhc4l(ob4) inz bu kx)5v ,g) points in the +x direction and is given by the graph of Fig. 7–33 as a function of time. Use graphical methods to estimate n6(br7v)o ox45tb(o) kz, nh ihcl4ut
(a) the total impulse given the ball    N*s
(b) the velocity of the ball after being struck, assuming the ball is being served so it is nearly at rest initially.    m/s

  From what maximum height can a 75-kgh+;lkr12m )4ejyyido t7qo+cgg:y7p* w zj3m person jump without breaking the lower leg bone of either leg? Ignore air resistance and assume the CM of the person moves a distance of 0.60 m from the standing to the seatrjy;hyyio4pml 1 :ed32 +zgt*mko7w+jcg q) 7ed position (that is, in breaking the fall). Assume the breaking strength (force per unit area) of bone is $170\times10^6\mathrm{~N/m^2}$ and its smallest cross-sectional area is $2.5\times10^{-4}m^2$ [Hint: Do not try this experimentally.]    m

  A ball of mass 0.440 kg moving east (+x direction)n tbtdk/.jkevx zk(dah/ (j92k ;mr56 with a speed of collides head-on with a 0.22 z5b2kjtnh /arkm6/dek(9 v;(.j ktdx0-kg ball at rest. If the collision is perfectly elastic, what will be the speed and direction of each ball after the collision?Let A represent the 0.440-kg ball, and B represent the 0.220-kg ball. $v'_A$    m/s  ----待选择----eastwest  $v'_B$    m/s  ----待选择----eastwest 

  A 0.450-kg ice puck, moving east wit.zcoc x .zt6s.h a speed of 3m/s has a head-on collision with a 0.900-kg puck initially a. stc .z6czx.ot rest. Assuming a perfectly elastic collision, what will be the speed and direction of each object after the collision?Let A represent the 0.450-kg puck, and let B represent the 0.900-kg puck. v'$_A$ =    m/s ----待选择----eastwest  v'$_B$ =    m/s ----待选择----eastwest 

  Two billiard balls of equal mass undergo a pero;+ yj8 lynue ; l-fhlv:,tlo0fectly elastic head-on collision. If one ball’s initial speed was 2m/s and the other’s was 3m/s in the opposite direction, what will be their speeds after the collision?(Let A represent the ball moving at 2.00 vo0u jhy-en ;,lllof8:lt+; y m/s, and call that direction the positive direction.Let B represent the ball moving at 3.00 m/s in the opposite direction. ) v'$_A$ =    m/s v'$_B$ =    m/s

  A 0.060-kg tennis ball, fr, +h 8db+whxmoving with a speed of 2.5m/s collides head-on with a 0.090-kg ball initially moving away from it at a speed of 1.15m/s Assuming a perfectly elastic collision, what ar,fh8wd+bh +rxe the speed and direction of each ball after the collision?(Let A represent the 0.060-kg tennis ball, and let B represent the 0.090-kg ball.)v'$_A$ =    m/s v'$_B$ =    m/s

  A softball of mass 0.220 ptrmgf(1f9s3 dt 16xb kg that is moving with a speed of 8.5m/s collides head-on and elastically with another ball initially at rest. Afterward ts6pbt93xt (gmfdfr 11he incoming softball bounces backward with a speed of 3.7m/s Calculate
(a) the velocity of the target ball after the collision    m/s
(b) the mass of the target ball.    kg
(Let A represent the moving softball, and let B represent the ball initially at rest.)

  Two bumper cars in an amusement park ride collide elasticqpu n+h ar:8n;c1ej 8hally as one approaches the other directly from the rear (Fig. 7–34). Car A has a m+h 18:unrph; aqj8 necass of 450 kg and car B 550 kg, owing to differences in passenger mass. If car A approaches at 4.5m/s and car B is moving at 3.7m/s calculate
(a) their velocities after the collision v'$_A$ =    m/s v'$_B$ =    m/s
(b) the change in momentum of each.$\Delta p_{\mathrm{A}}$$\approx$    kg*m/s $\Delta p_{\mathrm{B}}$$\approx$    kg*m/s

  A 0.280-kg croquet ball makes an elastic head-ongph ,m)2m;aebw;1 afqh e2t-w collision with a second ball initially at rest. The second ballemwh -1 b2gqaa;;mhtf e)w2 ,p moves off with half the original speed of the first ball.
(a) What is the mass of the second ball?    kg
(b) What fraction of the original kinetic energy $(\Delta\mathrm{kE/KE})$ gets transferred to the second ball?   

  In a physics lab, a cube slides down a frict1br (vsx:yj,6qquky) ionless incline as shown in Fig. 7–35, and elastically strikes another cube at the bottom that is only one-half its mass. If the incline is 30 cm high and the table is 90 cm off the floor, where does each cube lanvy ,j:()sbu6y1rqxq kd? [Hint: Both leave the incline moving horizontally.]$\Delta x_{m}$$\approx$    m $\Delta x_{M}$$\approx$    m

ake the general case ox2 7p/ er y8fpwfcdj/x):srh4f an object of mass m$_A$ and velocity v$_A$ elastically striking a stationary object of mass head-on. (a) Show that the final velocities v'$_A$ and v'$_B$ are given by$v_{\mathrm{A}}^{\prime}=\left(\frac{m_{\mathrm{A}}-m_{\mathrm{B}}}{m_{\mathrm{A}}+m_{\mathrm{B}}}\right)\nu_{\mathrm{A}},v_{\mathrm{B}}^{\prime}=\left(\frac{2m_{\mathrm{A}}}{m_{\mathrm{A}}+m_{\mathrm{B}}}\right)\nu_{\mathrm{A}}.$(b) What happens in the extreme case when m$_A$ is much smaller than m$_B$ Cite a common example of this. (c) What happens in the extreme case when m$_A$ is much larger than m$_B$ Cite a common example of this. (d) What happens in the case when m$_A$=m$_B$ Cite a common example.

  In a ballistic pendulum experiment, prc5ba ke90(g rt6-ctcz ojectile 1 results in a maximum height h of the pendulum equal to 2.6 cm. A second projectile causes the the petk6-9gbc50ac ecz ( rtndulum to swing twice as high, $h_2=5.2\mathrm{cm}$ The second projectile was how many times faster than the first? $v_1$ =    $v_2$ ([color=rgba(0, 0, 0, 0.85)]Round to three decimal places)

  A 28-g rifle bullet traveling 230m/s buries itself in a 3.6-kg pendulum han) 6(oneqsaip8uz 62aqc pb;a (ging on a 2.8-m-long stra(6 uzne; ao8p) bqapiqc2(6sing, which makes the pendulum swing upward in an arc. Determine the vertical and horizontal components of the pendulum’s displacement.vertical$\approx$    m horizontal =    m

(a) Derive a formula for the fraction of kinetic energy lost, bxcvh 78x 6d*n$(\Delta\mathrm{KE/KE})$ for the ballistic pendulum collision of Example 7–10. (b) Evaluate for m=14g and M=380g

  An internal explosion breaks an object, initially74r 1)zm 1xuuo a/ltkr at rest, into two pieces, one of which has 1.5 times the mass of the other. If 7500 J were rele )a4xkuorm u7/rl1zt1 ased in the explosion, how much kinetic energy did each piece acquire? (Let A represent the heavier particle, and B represent the lighter particle. ) KE'$_A$ =    J KE$_B$ =    J

  A 920-kg sports car collides into the ryw)o, g36 0dzhi4j wvyj3buy5 ear end of a 2300-kg SUV stopped at a red light. The bumpers lock, the brakes are locked, and the two cars skid forward 2.8 m before stopping. The police officer, knowing that the coefficie3g6ow, yi3by)vz0hjwdy 5 uj4 nt of kinetic friction between tires and road is 0.80, calculates the speed of the sports car at impact. What was that speed?(Let A represent the sports car, and B represent the SUV) $\approx$    m/s

  A ball is dropped from a heigbui87-k 5y fmvwlhu 0( 7;hjamht of 1.50 m and rebounds to a height of 1.20 m. Approximately h vu7iu0ylmk (-b; 8mwhj7f5a how many rebounds will the ball make before losing 90% of its energy?   

A measure of inelasticity in a hy/pul704n nqen)uxkjg7r0( tq/+en k ead-on collision of two objects is the coefficient of resti/7k)yq+n/l rn0nu kp e jet7xq4u(g0n tution, e, defined as$e=\frac{\nu_\mathrm{A}^{\prime}-\nu_\mathrm{B}^{\prime}}{\nu_\mathrm{B}-\nu_\mathrm{A}},$
where $\nu_\mathrm{A}^{\prime}-\nu_\mathrm{B}^{\prime}$ is the relative velocity of the two objects after the collision and $\nu_\mathrm{B}-\nu_\mathrm{A}$ is their relative velocity before it.
(a) Show that e=1 for a perfectly elastic collision, and e=0 for a completely inelastic collision.
(b) A simple method for measuring the coefficient of restitution for an object colliding with a very hard surface like steel is to drop the object onto a heavy steel plate, as shown in Fig. 7–36. Determine a formula for e in terms of the original height h and the maximum height h’ reached after one collision.

  A wooden block is cut into t;7h.xvpj* a n3yrxyr /wo pieces, one with three times the mass of the other. A depression is made in both faces of the cut, so that a firecracker can be placed in it with the block reassembled. The reassembled block is set on a rough-surfaced table, and the fuse is lit. Whey/ n3*x.jhy varxr7p; n the firecracker explodes, the two blocks separate and slide apart. What is the ratio of distances each block travels? ----待选择----1/91/101/81/6 

  A 15.0-kg object moving in the +x direction at 5.5m/s collides head-on with a 1( xe9yway9n v:0.0-kg object moving x9:yw e9vya (nin the -x direction at 4m/s Find the final velocity of each mass if:
(a) the objects stick together;   m/s
(b) the collision is elastic; v'$_A$ =    m/s v'$_B$ =    m/s
(c) the 15.0-kg object is at rest after the collision;   m/s ----待选择----not reasonable reasonable 
(d) the 10.0-kg object is at rest after the collision;   m/s ----待选择----not reasonable reasonable 
(e) the 15.0-kg object has a velocity of 4m/s in the -x direction after the collision. .   m/s ----待选择----not reasonable reasonable 
Are the results in (c), (d), and (e) “reasonable”? Explain
( Let A represent the 15.0-kg object, and let B represent the 10.0-kg object.)

  A radioactive nucleus at rest deca g xp-qoa7+,)icblnjg1ftzer )sz:9,qx l3q- ys into a second nucleus, an electron, and a neutrino. The ele 9,b+ o nxq:)ltcrq1j )qgei,zs z3l-fap- 7xgctron and neutrino are emitted at right angles and have momenta of $9.30\times10^{-23}kg\cdot m/s$ and $5.40\times10^{-23}\mathrm{~kg}\cdot\mathrm{m/s}$ respectively. What are the magnitude and direction of the momentum of the second (recoiling) nucleus?    $ \times10^{-22}$    $^{\circ} $ from the momentum of the electron

  An eagle ($m_{\mathrm{A}}=4.3\mathrm{kg}$) moving with speed $\nu_\mathrm{A}=7.8\mathrm{~m/s}$ is on a collision course with a second eagle ($m_{\mathrm{B}}=5.6\mathrm{kg}$) moving at $\nu_{\mathrm{B}}=10.2\mathrm{m/s}$ in a direction perpendicular to the first. After they collide, they hold onto one another. In what direction, and with what speed, are they moving after the collision? v =    m/s $\theta$ =    $^{\circ} $ rel. to eagle  ----待选择----AB 

  Billiard ball A of masyl2v up zf,4b2s $m_\mathrm{A}=0.400$kg moving with speed $\nu_\mathrm{A}=1.80$m/s strikes ball B, initially at rest, of mass $m_\mathrm{B}=0.500$kg As a result of the collision, ball A is deflected off at an angle of 30.0 $^{\circ} $ with a speed $\nu_\mathrm{A}^{\prime}=1.10$m/s (a) Taking the x axis to be the original direction of motion of ball A, write down the equations expressing the conservation of momentum for the components in the x and y directions separately. (b) Solve these equations for the speed v'$_B$ and angle $\theta_{\mathrm{B}}$ of ball B. Do not assume the collision is elastic. $\theta_{\mathrm{B}}$ =    $^{\circ} $ v'$_B$ =    m/s

  After a completely inelastic collision between two objects of equal mass8 zahm6 34u:sn j9gp9xtefu(g , each having initial speed the two move oftjh3 g 9p( 6:4sgufe8xmun9azf together with speed v/3 What was the angle between their initial directions?    $^{\circ} $

  Two billiard balls of equal mass m xgrsxvc1i )0gob9 iw5s uq*16ove at right angles and meet at the origin of an xy coordinate system. Ball A is moving upward along the y axis at 2m/s and ball B is moving to the right along the x axis with speed 3.7m/s After the collision, assumed elastic, ball B is moving along the positive y axis (Fig. 7–37). What is the final direction of ball A and what are their two speeds? direction of ball A i 0sbxusvx5iig*61cgw1 ) 9 qors  ----待选择----x directionx direction v'$_A$ =    m/s v'$_B$ =    m/s

  A neon atom (m=20u) makes a perfectly elastic collision with 2ql uz: h,gf6miie8nb8 j6f 8aanother atom at rest. After the impact, the neon atom travels ae,mu6 b :hzj2 6lq8i8 ffign8away at a 55.6 $^{\circ} $ angle from its original direction and the unknown atom travels away at a -50 $^{\circ} $ angle. What is the mass (in u) of the unknown atom? [Hint: You can use the law of sines.](Let A represent the incoming neon atom, and B represent the target atom) $m_B$   u

  A neon atom (m=20u) makes a perfecig zblg146p ii(m.4ha5z tp 9dtly elastic collision with another atom at rest. After the impact, the nezg p bl(6gai4d.h5m ipit491z on atom travels away at a 55.6 $^{\circ} $ angle from its original direction and the unknown atom travels away at a -50 $^{\circ} $ angle. What is the mass (in u) of the unknown atom? [Hint: You can use the law of sines.](Let A represent the incoming neon atom, and B represent the target atom) $m_B$   u

  Find the center of m-j.8sdo;* ,xwja jiebass of the three-mass system shown in Fig. 7–38. Specify relativeodsbia-ej .x , w*8j;j to the left-hand 1.00-kg mass.    m

  The distance between a caxc,k2owvc;g 2 rbon atom ($m_{\mathrm{C}}=12\mathrm{u}$) and an oxygen atom ($m_{\mathrm{O}}=16\mathrm{u}$) in the CO molecule is $1.13\times10^{-10}$m How far from the carbon atom is the center of mass of the molecule?    $\times10^{-11}$m

  The CM of an empty 1050-kg car is 2.50 m beha9 kalwj4/hmkg p j95)ind the front of the car. How far from the front of the car will the CM be when two people sit in the front seat 2.80 m from the front of the car, and three people sit in the back seat 3.90 m froma/4 k99paj lgwh)jkm 5 the front? Assume that each person has a mass of 70.0 kg.    m

  A square uniform raft, 18 m by 18 m, of mass 6800 kg, is used as a ferrw,f q6/a vfdygms*t.g7a 82y dyboat. If three cars, each of mass 1200 kg, occupy its NE, SE, m dw8d/fv *yg,qag.sy6a f2t7 and SW corners, determine the CM of the loaded ferryboat.$X_{CM}$ =    m $Y_{CM}$ =    m

  Three cubes, of sides gd -u.ksckxb /0u-5ki $l_0$,$2l_0$, and $3l_0$ are placed next to one another (in contact) with their centers along a straight line and the $l=2l_{0}$ cube in the center (Fig. 7–39). What is the position, along this line, of the CM of this system? Assume the cubes are made of the same uniform material. $X_{CM}$ =    $l_0$ from the  ----待选择----leftright  edge of the smallest cube

  A (lightweight) pallet has a load of identical cases of tomato pzw kj1(um+baw6/f s u*aste (see Fig. 7–40), each of which is a cube of lewz ua 6+bjfws*/1(u mkngth l. Find the center of gravity in the horizontal plane, so that the crane operator can pick up the load without tipping it.$X_{CM}$ =    l $Y_{CM}$ =    l

  A uniform circular plate of radius 2R has a circulapw20sc 00v*m+7gz h4cp bsmx xr hole of radius R cut out of it. The center of the smal 0zb mwsp7 0c m2hvgxs4cxp0*+ler circle is a distance 0.80R from the center C of the larger circle, Fig. 7–41. What is the position of the center of mass of the plate? [Hint: Try subtraction.]   R

  Assume that your proportions are the same-y:zz5 x )enzvvdqy sj9q8 9/q as those in Table 7–1, and calculate the m5q ):qzj-9yq zvd zx8ey /vn9sass of one of your legs.    kg

  Determine the CM of an ou .q q;ozlqkj1*tstretched arm using Table 7–1.   % of the person's height along the line from the shoulder to the hand

  Use Table 7–1 to calculate the position of the CM of an arm bent e9(sq1sj z l)uat a right angle. Assume that the person is 155 cm sze( 9lq1u sj)tall. $X_{CM}$ =    cm $Y_{CM}$ =    cm

When a high jumper is in a position suc+z+t r e1a-6os t4yw o,x4ukqhh that his arms and legs are hanging vertically, and his trunk and head are horizontal, calculate how far below the torso’s median line the CM will be. Will thi+xhq t4kr1a6tu+-so o zyw,e4s CM be outside the body? Use Table 7–1.

The masses of the Earth anf 4)*y2d kgzmyd Moon are $5.98\times10^{24}$kg and $7.35\times10^{22}$kg respectively, and their centers are separated by $3.84\times10^{8}$m (a) Where is the CM of this system located? (b) What can you say about the motion of the Earth–Moon system about the Sun, and of the Earth and Moon separately about the Sun?

  A 55-kg woman and an 80-kg man stand 10.0 m apart on y 2l+z;juiu.tfrictionless ice.
(a) How far from the woman is their CM?    m from the woman
(b) If each holds one end of a rope, and the man pulls on the rope so that he moves 2.5 m, how far from the woman will he be now?    m
(c) How far will the man have moved when he collides with the woman? He has moved    m from his original position

  A mallet consists of a uniform cylindricadj;vb1 2f dn/,d,gmq fl head of mass 2.00 kg and a diameter 0.0800 m mounted on a uniform cylindrical handle of mass 0.500 kg and length 0.24q;f 1dnfm,dg v,d2 b/j0 m, as shown in Fig. 7–42. If this mallet is tossed, spinning, into the air, how far above the bottom of the handle is the point that will follow a parabolic trajectory?    cm

  A mallet consists of a uniform cylindrical head of mass 2.00 kg and a dinh p p-4 lw-y.y/w3+ckoe5 yjiameter 0.0800 m mounted on a uniform cylindrical handle of mass 0.500 kg and length 0.240 m, as shown in Fig. 7–42. If this mallet is tossed, spinning, into the air, how far 3 w/yh wkp-cyye+ol4n5pj .i-above the bottom of the handle is the point that will follow a parabolic trajectory?    d    d

  (a) Suppose that in Examplec x.;8gg jg *r-of ewi,7z4ntd 7–14 (Fig. 7–29), $m_{II}$=3$m_{I}$ Where then would $m_{II}$ land?    d(Round to two decimal places)
(b) What if $m_{I}$=3$m_{II}$    d

A helium balloon and its gondola, of mass M, are in the air and statiimrug2 :q7);vwcr/l honary with respect to the ground. A passenger, of mass m, then climbs out and slides down a rope with speed measured with respect/r:mr ulwv );i7c2qg h to the balloon. With what speed and direction (relative to Earth) does the balloon then move? What happens if the passenger stops?

  An 0.145-kg baseball pitched horizontally at pst9gy9;)dy4 +tbizbm4 zt4q ;6hyue strikes a bat and is popped straight up to a height of 55.6 m. If the contact time is 1.4 ms, calculate the average bth;p4g b9 e+su9iyy46) tyzt;mdqz4 force on the ball during the contact.    $^{\circ} $

  A rocket of mass m traveling witt uik8st;o l94h speed $v_0$ along the x axis suddenly shoots out fuel, equal to one-third of its mass, parallel to the y axis (perpendicular to the rocket as seen from the ground) with speed 2$v_0$ Give the components of the final velocity of the rocket.$P_x$: v'$_x$=    $v_0$
$P_y$: v'$_y$=    $v_0$

A novice pool player is faced with the corner pocketssz 8c6je(b l e m;t;onp3zy0.lyd w36 shot shown in Fig. 7–43. Relative dimensions are also shown. Should the player be worried about this being a “scratch shot,” in which the cue ball will8cmsltpe; 3 6e.0(z;s wbjzy 36nyodl also fall into a pocket? Give details.

  A 140-kg astronaut (including space suit) a jte33t1 7he+spzpjdv0 ;lv6ocquires a speed of 2.5m/s by pushing off with his legs from an 1vvjspldtp1;3hj e+ o6zet3 07800-kg space capsule.
(a) What is the change in speed of the space capsule?    m/s
(b) If the push lasts 0.40 s, what is the average force exerted on the astronaut by the space capsule? As the reference frame, use the position of the space capsule before the push.    N

  Two astronauts, one of mass 60 kg and the other 80 kgetp q ,o9(m(khs07*dkoz n 0vw, are initially at rest in outer space. They then push each other apart. How far apart are they when the lighter astronaut has moved 12 m? *(,e0mp7kqot9 vnd0(zwsh ko    m

  A ball of mass m makes a head-on elastic qc9gnb *e4g6 .3gfoxtyg v/(ycollision with a second ball (at rest) and rebounds in the opposite direction with ayyv geob*4 93 n g(.gg6ctf/xq speed equal to one-fourth its original speed. What is the mass of the second ball? $m_B$ =    $m_A$(Round to two decimal places)

  You have been hired as an expert witness inq8k;(0q f vdun a court case involving an automobile accident. The accident involved car A of mass 1900 kg which crashed into stationary car B of mass 1100 kg. The driver of car A applied his brakes 15 m before he crashed into car B. After the collision, car A slid 18 m while car B slid 30 m. The coefficient of kinetic friction between the locked wheels and the road was measured to be 0.60. Show that the driver of car A was exceeding the 5qdq;(u n8k0 fv5-mph (90km/h) speed limit before applying the brakes.    mi/h

A golf ball rolls off the top of a flight of concrete steps of total vertical mt;ggrin49 -gq1 n4xy +rpfl/height 4.00 m. The ball hits four times on the way down, each time striking the horizontal part of a different step 1.0 m lower. If all collisions are perfectly elastic, what is the 1/p g 9-nrftqrlnm4g4x; +giybounce height on the fourth bounce when the ball reaches the bottom of the stairs?

  A bullet is fired vertic22vn(so vy7 x rx+awd*ally into a 1.40-kg block of wood at rest directly above it. If the bullet has a mass of 29.0 g and a speed of 510m/s how high will the block rise after the bullet becomes embedded +rd (xnox 7vv*2as2wyin it?    m

  A 25-g bullet strikes and becomes embedded in a 1.35-kg block of w)j(b8cz f; zuu; r6yykood placed on a horizontc) j(z r; 6ykuuby;zf8al surface just in front of the gun. If the coefficient of kinetic friction between the block and the surface is 0.25, and the impact drives the block a distance of 9.5 m before it comes to rest, what was the muzzle speed of the bullet?    m/s

  Two people, one of mass 75 kg anda89 fo5.cc rqw the other of mass 60 kg, sit in a rowboat of mass 80 kg. With the boat initially at rest, the two people, who have been sitting at opposite ends of the boat 3.2 m apart from each other, now exchange seats. How far and in what direction will the boatcqcw .o 95r8af move? The boat will move    towards the initial position of the 75 kg person(Round to two decimal places)

  A meteor whose mass was aboui jla o*f9oj--eae*g) t $ 1\times10^{ 8}$kg struck the Earth ($m_E$=$6 \times10^{ 24}$kg) with a speed of about 15km/s and came to rest in the Earth.
(a) What was the Earth’s recoil speed?    $ \times10^{-13 }$m/s
(b) What fraction of the meteor’s kinetic energy was transformed to kinetic energy of the Earth?    $ \times10^{ -17}$
(c) By how much did the Earth’s kinetic energy change as a result of this collision?    J

  An object at rest is suddenly broken apart into two fragxqkmp2 ds:/d qgn7 f:u;f,-vh ;z /zyuments by an explosion. One fragmend: p zd2 uzy gn,hxmkf -vufq;s7q/:/;t acquires twice the kinetic energy of the other. What is the ratio of their masses?   

  The force on a bullet is given by f9w)3kuro*4qarw qzmw we:(-the formula F = 580-( $1.8 \times10^{ 5}$t) over the time interval t=0 to t = $3.0 \times10^{-3 }$s In this formula, t is in seconds and F is in newtons.
(a) Plot a graph of F vs. t for t=0 to t=3.0ms
(b) Estimate, using graphical methods, the impulse given the bullet.    N*s
(c) If the bullet achieves a speed of 220m/s as a result of this impulse, given to it in the barrel of a gun, what must its mass be?    kg

  Two balls, of massesoah-got:.fxg( 41.s*abm,a wg9vyiv $m_A$ = 40g and $m_B$ = 60g are suspended as shown in Fig. 7–44. The lighter ball is pulled away to a 60$^{\circ} $ angle with the vertical and released.
(a) What is the velocity of the lighter ball before impact?$\approx$    m/s
(b) What is the velocity of each ball after the elastic collision?v'$_A$ $\approx$    m/s v'$_B$ $\approx$    m/s(Round to two decimal places)
(c) What will be the maximum height of each ball after the elastic collision?    m

  An atomic nucleus at rest decays radioactive v2t tqf,z0zl 1,*v-rlx8h txrly into an alpha particle and a smaller nucleus. What will be the speed of this recoiling nucleus if the speed of the alpha particle is * rl2z tvf lhzrx,0t1, 8tvxq-$ 3.8\times10^{5 }$m/s Assume the recoiling nucleus has a mass 57 times greater than that of the alpha particle.    m/s

  A 0.25-kg skeet (clay target) is fired at an anguiyc g+; zuri iw6q;a*-l8d4/ etq; omle of 30 $^{\circ} $ to the horizon with a speed of 25m/s (Fig. 7–45). When it reaches the maximum height, it is hit from below by a 15-g pellet traveling vertically upward at a speed of 200m/s The pellet is embedded in the skeet.
(a) How much higher did the skeet go up?    m
(b) How much extra distance, $\Delta{x}$ does the skeet travel because of the collision? $\approx$   

  A block of mass m=2.2lvat 055rsxohf -he* 3zqe70ukg slides down a 30.0 $^{\circ} $ incline which is 3.60 m high. At the bottom, it strikes a block of mass M=7kg which is at rest on a horizontal surface, Fig. 7–46. (Assume a smooth transition at the bottom of the incline.) If the collision is elastic, and friction can be ignored, determine
(a) the speeds of the two blocks after the collision,v'$_A$ =    m/s v'$_B$ =    m/s
(b) how far back up the incline the smaller mass will go. $\approx$   (Round to the nearest integer) (Let A represent mass m, and B represent mass M.)

  In Problem 79 (Fig. 7–46), what is the upper limit odsxn h 90. :l6mojkue0n mass m if it is to rebound from M, slide up the o6 .sl:mnu9d xkeh00jincline, stop, slide down the incline, and collide with M again?    kg (Let A represent mass m, and B represent mass M.)

  The gravitational sl4/y mobe+zu7kw0rz8 tingshot effect. Figure 7–47 shows the planet Saturn moving in the negative x direction at its orbital speed (with respect u/+m74w0b r8e kzzytoto the Sun) of 9.6km/s The mass of Saturn is $5.69 \times10^{ 26}$kg A spacecraft with mass 825 kg approaches Saturn. When far from Saturn, it moves in the direction at 10.4km/s The gravitational attraction of Saturn (a conservative force) acting on the spacecraft causes it to swing around the planet (orbit shown as dashed line) and head off in the opposite direction. Estimate the final speed of the spacecraft after it is far enough away to be considered free of Saturn’s gravitational pull.    km/s