We claim that momentum is conserved, yet most moving objects eventually slo -3u *gl jim/c j+gq9,top ,jl*qreel*w down and stop. Explo qq+g9l,/r ig*j*cllep jej3 -, t*umain.

When a person jumps from a tree to the ground, what happens to6*yac gk-8ev x the momentum of the person upon striki6cxg8y v -ke*ang the ground?

When you release an inflated but untied balloon, why doe 6.6jn(btykp9ekgkk8 s it fly across the roomk nytj.bkk(8ge69 pk6?

It is said that in ancient times a rich man 4 gzs bc+ e:d;th;o6i lggbj;5with a bag of gold coins froze to death while stranded on a frozen lake. Because the ice was frictionless, he could not push himselfg65sg;ci:dt;z e log4 b;j+bh to shore. What could he have done to save himself had he not been so miserly?

How can a rocket change direction when it is3a2fv940- uodwa lghf)x ;x ys far out in space and is essentially in a vacu0x 3uvla ydf)fax2-9;sw 4gh oum?

According to Eq. 7–5, the longer the impact time of an impulse, tdltq7l)r8pwt/fllys kw** kn21 vf-8 he smaller the force can be for the same momentum change, and hence 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 fraclf *k2-ltky)dlw/wf7q88 p tn l*rv1sture or death.

Cars used to be built as rigid as possiblew(jsw j75f v+r to withstand collisions. Today, though, cars are designed to have “crumple zones” that collapse up5 jw+ swj7rfv(on impact. What is the advantage of this new design?

Why can a batter hit a pitched baseball further than a ball tossed in +c* s18uga6jbpva xm*the air by the battera+ 6s *acxjvg1mpb*8u ?

Is it possible for an object to receive a larger i kbwnm3: h03eyrigk :dy::pp7mpulse from a small force than b:k0 n k:3wei:3hyr py m:gpd7from a large force? Explain.

A light object and a heavy object have the same kinetic energy. Which hak2 -vw ilscj1s9oqa bj1cu 841s the greater m18q jlsiv-42s1 c 1j9buowc akomentum? Explain.

Describe a collision in which all kinetic ener;k2 p)hb z sk23ej6yevgy is lost.

At a hydroelectric power plant, water is directed at high speed against tux/odnk0 mu7,n5 f *qnsrbine blades on an axle that turns an electric generator. For maximum powersdo5u 7f x0knn,* nqm/ generation, should the turbine blades be designed so that the water is brought to a dead stop, or so that the water rebounds?

A squash ball hits a wallmg(oty5 /qj/5 yola7i) w,s tq at a 45 $^{\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 h7ltc q,t0s( hm onto a hard steel plate (fixed to the Earth), from which it rebounds atmt (lhcts7,q0 very nearly its original speed. (a) Is the momentum of the ball conserved during any part of this process? (b) If we consider the ball 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 lean 91 js+vz8 gg1ug36c*vbgsey qs, 7idmbackward when carrying a heavy load in your arms?

Why is the CM of a 1-m length of pipe at its mid-point, whereas thi8+by b*b ga)qts is not true for ygbqtbb*+y a )8our arm or leg?

Show on a diagram how your CM san ls85gxixwz0bptheg.:(m,f; b rm)pd( z 5+hifts when you change from a lying position to a sitn5ag85xm bxzws:0mp;ztr+ib. lg((ef )ph d,ting position.

If only an external force can change the momentum of the center of mass o-tt o88wb,wjbtl75 *t etszf 3f an object, how can the internal tz7oeftb5 - 3,8jbstt *l8wtwforce of an engine accelerate a car?

A rocket following a parabolic path through the air sudger i96.ydmt nf68:qg denly explodes into many pieces. What can i edy.r6ft m68g9:g qnyou say about the motion of this system of pieces?

  What is the magnitude of the momentum of a 28-g sparrow flying with a speed of7ddj0o .z0pnedjhj 7( $8.4 \; m/s$    $kg \; m/s$

  A constant friction force of 25 N a 37yp h ap9-dwdrz8e g(/ll1l5cr0bhgcts on a 65-kg skier for 20 s. What is the skier’s changle1rb3 p cry9- z 7dl/hhp5(gg 0la8wde in velocity?    m/s

  A 0.145-kg baseball pitched at 39 m/s is hit on a 6b16r0elfi tc horizontal line drive straight back toward the pitcher at 52m/s If the conte tf6bl06ric1 act time between bat and ball is $3\times10^{-3}$s calculate the average force between the ball and bat during contact.    N

  A child in a boat thr;1;c1z 8dkfuwm3 fpplows a 6.40-kg package out horizontally with a speed of 10 m/s Fig. below Calcuk1m; dpuf38f l; cp1zwlate the velocity of the boat immediately after, assuming it was initially at rest. The mass of the child is 26.0 kg, and that of 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 propelling gases are exppc 4ud 1p66jh2 vyxj)yelled at a ratyvpjy 64cj xd16 p)2uhe 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 moviv0sk c;oid58 ing at $4.1 \; m/s$ 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 track with a c/ wxsiusht)+ ;/n nmo7 *f0ikqonstant speed of 18m/s A 5350-kg load,initially at rest, is dropped onto the car. What7nx*imssnftk i0 /w/q+);h uo will be the car’s new speed?    m/s

  A 9300-kg boxcar traveling rz*y2xipv.8k rx6w i :uj:5ocat $15 \; m/s$ 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 horizontally at speeds of 1k8s f8*jy go.x00km/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 1.50 m high and 0.50 m wide. gx.s8fk* o8yj 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 8.6m/s ou- o 2r;bl .ytj7)rpum+ r0,ynjxi*ukn a level track. Snow begins to fall vertically and fills the car at a rate of 3.5kg/min Ignoring friction with thlr* )rxip7kur-;nu,+ ubyojy0 .mj2te tracks, what is the speed of the car after 90.0 min?$\approx$    m/s

  An atomic nucleus initially moving at 420m/s k;qa wxm3 2q+vemits an alpha particle in the direction of its velocity, and the rema; k+2qvw m3axqining 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 have when it is emitted?    m/s

  A 23-g bullet traveling 230m/s penetrates a ml.9a sihxq, ygd6o1 u2 k6n:n2.0-kg block of wood and emerges cleanly at 170m/s If the block is stationary on a frictionless surface when hit, how fast does it move after the bullet eh 9sx6,q.d uo1ky2lg6mnn:ai merges?    m/s

  A 975-kg two-stage rocket )wwgptx;aa ln,mxwr/n c4 w 4+meqe*.o265 pzis traveling at a speed of $5.80\times10^3\mathrm{~m/s}$ 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 mas9t-4yu qu uruth ;ky/w2saa)o8-6yhjs 3180 kg is traveling in outer space with a velocity of 115m/86oay)2st;/h tru9ha-4qu ukj- yuyws To alter its course by 35.0 $^{\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 0.045 kg is hit off roz.7;g7 2z09y zwzeko9svou the tee at a speed of 45m/s The golf club was in contact with the ball o0w7gryz 9oz s 2oeuk. 79;vzzfor $3.5\times10^{-3}$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 and cowdq3)kcy jj *+mes to rest in a time interval of 8.0 ms. (a) What is they3j+k wj*cqd ) 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 speed v=25m/s strikes a wall at a gte.-id5pj*e0(xgohq a1; zjub. wy/ 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 charge of the crashworthiness of new aut3u7ycjhp-y6ylzn ( v /pd/,nromobile models. Cars are tested by smashing them into fixed, massive barriers at 50km/h (30 mph). A new model of n,hcyy7/-lyvnppj/rd z6u( 3 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 0.75 s by:u6 (a3wvcga p/co b 74cjtag* a head-on tackle by a tackler runnc 3b/ j cagpc*4vg7 o(aw6ta:uing 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 ten)+la1xsi 4moj: 5 zbtgwr+d1 ynis ball (mass 0.060 kg) points in the +x direction and is givz: 1+)da+1 yjwgb 5srxto ml4ien by the graph of Fig. 7–33 as a function of time. Use graphical methods to estimate
(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-kg person jump without breakin9i.el y .hxj/sg 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 seated position (that is, in breaking the fall). Assume the breaking str.h .ies/xyj l9ength (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) withys4(i;6fq8fyx 4 kfom a speed of collides head-on with a 0.220-kg ball at rest. If the mify4k(q4x;ffo 8 6yscollision 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 with a spee9qfmos tucdv/+r..fez*v3 1-yda sb.d of 3m/s has a head-on collision with a 0.900-kg puck initially at rest. Assuming a perfectly e. y/d svz.9ofub c*.qvr3af1mdt-s +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 perfech+xzw.kt8 0p.32 +yy9 echaonhzi6wqtly 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 afteohha 2yc0we. y iz 63qn+ 9wz.hxptk+8r the collision?(Let A represent the ball moving at 2.00 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, f2nsf7e5k :u-hsdv 9 vmoving 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 are the speed and direction of each ball after the collision?(Let A represent the 0.060-kg t 7:de-k fusfnv2vh95sennis ball, and let B represent the 0.090-kg ball.)v'$_A$ =    m/s v'$_B$ =    m/s

  A softball of mass 0.220 kg that is moving with a speed of w;tlw)v2cm) i8.5m/s collides head-on and elastically with another ball initially at rest. Afterward the incoming softball bounces backward with w2;)w imctl)v 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 parfwi6ig zd,08j k ride collide elastically as one approaches the other directly from the rear (Fig. 7–34). Car A has a mass of 450 kg and car0w6i jif,z8g d 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-onf(5 oogc6 x ;-n96eq bocb.yew collision with a second ball initially at rest. The second ball movb.enow6f9ocxg c;e-yo( b q56es 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 c14h+y48xkzd jxqm, r frictionless incline as shown in Fig. 7–35, and elastically strikes another cube at the bottom that is onlyjh4xc mx8k 41d q+r,zy one-half its mass. If the incline is 30 cm high and the table is 90 cm off the floor, where does each cube land? [Hint: Both leave the incline moving horizontally.]$\Delta x_{m}$$\approx$    m $\Delta x_{M}$$\approx$    m

ake the general case t8-9(cz avz y *k5myh4mqt dy7of 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, projectil *v9 ;ed2mdqe x 7izdgs)hre3.e 1 results in a maximum height h of the pendulum equal to 2.6 cm. A second pro3mqe r de* hz) di.7ex2v9;dgsjectile causes the the pendulum 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 i206j3dr gajdpv4quz6k 3)jda n a 3.6-kg pendulum hanging on a 2.8-m-long string, which makes the pendulum swing upward in an arc. Determine thd akd4jd)r3qa2uj3 6j06 gpvze vertical and horizontal components of the pendulum’s displacement.vertical$\approx$    m horizontal =    m

(a) Derive a formula for the fra:pkgg,w dhuq -ss9o 7 nzi:95yction of kinetic energy lost, $(\Delta\mathrm{KE/KE})$ for the ballistic pendulum collision of Example 7–10. (b) Evaluate for m=14g and M=380g

  An internal explosion breaks an object, initiallymr77um 5vemx0 at rest, into two pieces, one of which has 1.5 times the mass of the other. If 7500 J were released in the explosion, how much kinetic energy did each pmm0xv7rmu57 e iece acquire? (Let A represent the heavier particle, and B represent the lighter particle. ) KE'$_A$ =    J KE$_B$ =    J

  A 920-kg sports car collide zat-o1 ek1qc(s into the rear 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 coefficient of kinetic friction between tires and road is 0.80, calculates the speed of the sports car at impact. What was that speed?(Leac1 - k(zoeq1tt A represent the sports car, and B represent the SUV) $\approx$    m/s

  A ball is dropped from a height of 1.5 jhced9/fqdj.n;f( z/0 m and rebounds to a height of 1.20 m. Approximately how many ffdqc hej.//(9d zjn ;rebounds will the ball make before losing 90% of its energy?   

A measure of inelasticity in a head-on collision of two objects is the*j g+bppkfu () coefficient of restitution,)upf +j(gkb* p 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 two pieces, one with three times the mass dhmvfey3) bffkr+2:wk,r 4jp. uj 80fof 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. When the firecracker explodes, the two blocks separate and slide apart. What is the ratio of distances each k furjfw.bm+)8f 4f2 v:dpr,jke3 y0 hblock travels? ----待选择----1/91/101/81/6 

  A 15.0-kg object moving in the +x direction at 5.5m/s collides here c )- i, lx8yle(94kfp;zkwmad-on with a 10.0-kg object moving in the -x direction at 4m/s Find the final velocity of each mmzc)li89f;yprkel w e(k - ,x4ass 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 decays into a f57 f2grfig;dsecond nucleus, an electron, and a neutrino. The eld7ff2 f 5r;iggectron 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 ml sk9;3y -hdea9w3cpo ass $m_\mathrm{A}=0.400$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 collisi/epxp8:b 2sahon between two objects of equal mass, each having initial speed the two move off together with speed v/3 What was the angle between their ppx8eb2 h/s a:initial directions?    $^{\circ} $

  Two billiard balls of equ23 1gof bxd:zqf;nhl- al mass move 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 odh1lz;x:32 qbfnf- gspeed 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 is  ----待选择----x directionx direction v'$_A$ =    m/s v'$_B$ =    m/s

  A neon atom (m=20u) makes a perfectly elast;n9i5 g nv3ka hwpmdv(h:0a:i ic collision with another atom at rest. After the h:w vga3 mvn9kda ;5n0i:phi( impact, the neon 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

  A neon atom (m=20u) makes a perfectly elastic collision with another atom at ;bf83w 3axsoa rest. After the impact, the neon atom tbas3w o 8a3x;fravels 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 mass of the three-mass systu -jrm:; qt+vbem shown in Fig. 7–38. Specify relative to the left-hand 1.00vb ;+:r q-tumj-kg mass.    m

  The distance between a carbon atom -1+p ae j8xkp 8yhc3tf($m_{\mathrm{C}}=12\mathrm{u}$) 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 behind the fronth3ohjx .3x eskk5qz) .qi6+i k 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 from the front? Assume tha 5. 6.3+ejiq ikzxsq)kkhh o3xt 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 95en-in jfq+lp21ys g .xi(is a ferryboat. If three cars, each of mass 1200 kg, occuq1.y2peis(n i s5 gxn f-j+li9py its NE, SE, and SW corners, determine the CM of the loaded ferryboat.$X_{CM}$ =    m $Y_{CM}$ =    m

  Three cubes, of sides bpnd:yyszm08 u) r+u4$l_0$,$2l_0$, 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 paste (sv:b) *uuuh7dh ee Fig. 7–40), each of which is a cube of length l. Find the center of gravity in the horizod)uv7hub h :*untal 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 circular hole of radiu.z1vn /;w6lgnx a,uxo s R cut out of it. The center of the smaller circle is a distance 0.80R from the center C of the larger circle, Fig. 7 .u;v nznwox, ax1g6l/–41. What is the position of the center of mass of the plate? [Hint: Try subtraction.]   R

  Assume that your proportions are the same as those in Table 7–1, and calculate t)*h pdmu,k 3wzj5sgz4yesip pcf,,5( j1)mnmhe dwsmpkup s4g() m ,zz,n)5*jcjefi35 ,pm 1hy mass of one of your legs.    kg

  Determine the CM of an outstretched arm usth ch.(:jpak 7ing 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 at a right angddsq j1) rnths,6 d w))u0kt8tle. Assume that hn u tj80wr6tksd)st) dd,q)1 the person is 155 cm tall. $X_{CM}$ =    cm $Y_{CM}$ =    cm

When a high jumper is in a posi kbonfy 5rze98 ,cut*3tion such 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 this CM be outside the body? U8k5rct en,*uobf yz3 9se Table 7–1.

The masses of the Earth and Moon arex1rzn qul1e4hwc , 14*vau s;u $5.98\times10^{24}$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 frictionles 5w bm/9yo(eses 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 cylindrical head of mass 2.00,zdv8l0 vn ltnue 2r5/ kg and a diameter 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 /nu2rde8,lznv 0 5 tlvair, how far above the bottom of the handle is the point that will follow a parabolic trajectory?    cm

  A mallet consists of a unifoo i/.bmjnmm:- rm cylindrical 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 0.240 m, as shown in Fig. 7–42. If this mall.:- mm/ibonjm et is tossed, spinning, into the air, how far above the bottom of the handle is the point that will follow a parabolic trajectory?    d    d

  (a) Suppose that in Example 7–14 (Fig. 7–, u0*i3 zhqw,ppwgl4 f29), $m_{II}$=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 stationary with(go+(w)64zjvm8 x 8yjx eic ox respect to the ground. A passenger, of mass m, then climbs out and slides down a rope with speed measured with respect to the balloon. With what speed and direction (relative to Earth) does tyv(4(x wz 6je 88o )jomxg+cxihe balloon then move? What happens if the passenger stops?

  An 0.145-kg baseball pitched horizontally q7aj; p87s dgsn /uls3 :bm(xhat 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 force on the: s7hxb8pmqdsul gs3a/ (7jn; ball during the contact.    $^{\circ} $

  A rocket of mass m traveling with8g;iwsc;6 vbmvxd)y b-5bz kf1:3g eq 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 pockge.89h0 ybom yet shot shown in Fig. 7–43. Relative dimensions are also shown. Should the player be worried about this being a “scratch shot,” inm9 o yegbyh0.8 which the cue ball will also fall into a pocket? Give details.

  A 140-kg astronaut (including space suit) acquires a speed of 2.5m/s by 2*tbil( 159 c1x bkybxizy b5(hpync:pushing off with his legs from an 1800-kbxhy:( bybc5y5*1p tkl b12i xzni(9cg 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 theehm.uj hs +x8ns/)p b5 other 80 kg, are initially at rest in outer space. They then push each other apart. How far apart are they when the lij s+) 85h/phnbusex.m ghter astronaut has moved 12 m?    m

  A ball of mass m makes a he;ff9 p5p0u, uiivtzq4ad-on elastic collision with a second ball (at rest) andf uqz49pt0,i uvi p5;f rebounds in the opposite direction with a 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 witnebb *m0xyvdu e kz.c5+10:o wbrss in a court case involving an automobile accident. The accident involved car A of mass 1900 kg which crashed into station+.k1 :cwyev *rb0 0xumbdz 5boary 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 55-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 he als. *+qy4nm40zkqsme,pk r8ight 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 bounce height on the fourth bounce when the ball reaches the bottosk 8ypa*.s4 elk+ 0,nmmqz4qrm of the stairs?

  A bullet is fired vertically into a 1.40-kg block of wood at rexwwh.ia1k 28 :akm d)0fv +mujst directly above it. If the bullet has a mass of 29.0 g and a speed of 510m/s how high will the block ri ah: iu 8mfkj2akd1x.) +0wvmwse after the bullet becomes embedded in it?    m

  A 25-g bullet strikes and becomes embedded in a 1.3-,*emwm,b sy b5-kg block of wood placed on a horizontal 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 speeds,em- b, yw*bm of the bullet?    m/s

  Two people, one of mass 75 kg and the other of mfbe t, gfq558m/z0 vg7j:h zevv ;sac/ass 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 enev/5:jb v;0ze/gqsz 85amfhc, gtfv 7ds of the boat 3.2 m apart from each other, now exchange seats. How far and in what direction will the boat move? The boat will move    towards the initial position of the 75 kg person(Round to two decimal places)

  A meteor whose mass was ab 6c56 +r/pyp zjkyt3rs5ouf: xout $ 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 ap6;o.*d1qcn48 yj5jnpxg mszhart into two fragments by an explosion. One fragment acquires twice the kinetic energy of the other. Whad.j h8njo5;ng614 px mz* scyqt is the ratio of their masses?   

  The force on a bullet is git.yx5 (wokp , ohl:rj(ven by 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 masses 0dh wq.;2b 4o2ato:qb;di (c am6spoq$m_A$ = 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 radioactively into an alpha particle and a smalbr( /t i: nquo x)s(ve+ryu; 3h0u3ohxler nucleus. What will be the sp+our q3sx/u y(i)oux ner; 0htb: (hv3eed of this recoiling nucleus if the speed of the alpha particle is $ 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;2qnz 6lq 8. wg(-ozkres)z pf) is fired at an angle 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=2.2kg slidesp/4 w 3ji:hzwn 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 on mass m iojf2tqj: ht bv:43a*kf it is to rebound from2j taj: 4qko: vhtb*3f M, slide up the incline, stop, slide down the incline, and collide with M again?    kg (Let A represent mass m, and B represent mass M.)

  The gravitational slingshot effect. Figure 7–47 :-c5ppgt,3k.o:hf nyy(zi tf shows the planet Saturn moving in the negative x direction fi5-fn3:ycgk z (p, ohty.pt:at its orbital speed (with respect to 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