We claim that momentum is conserved, yet most moving objects eventually slow d5lkqafdc;n 21own and stop.52knl1cdq fa ; Explain.

When a person jumps from a tree to thepi 07zy1 u6 pwdrb4m:a ground, what happens to the momentum of the person upon striking mz6i payd714w:0bpruthe ground?

When you release an inflated but untied balloon, why does it fly c : g*wj-z.c :m;j/;c ziaam62qwn bhxacross the room?;- jn:zam;bw: g/a.mxhq ic2c*jwz6 c

It is said that in ancient times a rich man with a bag of gold coins fro h; jikdh0 *so3/kt)ku32binoze to death while stranded on a frozen lake. Because the ice was frictionless, he could not push himself to shore. What could he have done to save/j h kukodt3knb* ioi)3s h;02 himself had he not been so miserly?

How can a rocket change direction whri; j *qr .(:e-exs:l n*hremkwl-z0ren it is far out in space and is essentially e *r*l-h iql:smew0xrznr:;r-(.jekin a vacuum?

According to Eq. 7–5, the longer x7jk i+tvl;pfqe7f07to30 o jthe impact time of an impulse, the 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 thepf3k x;7t qv0ltjo+07f ioj 7is 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 rigid as possible to withstand collisions. ,8oq3l :f/noh mchn 5nToday, though, cars are designed to have “crumple zones” that collapse upon impact. Whn5/hnn,:m 3f8loqhoc at is the advantage of this new design?

Why can a batter hit a pitched baseball further than a ball tossedqa)t6g:pr -30q*im zeh g61 ndgzwqn4 in the air by th4peggtzz-q agrhn6*n3:mqd60 q) 1 wie batter?

Is it possible for an obje5cwc,m4 l 2 blqs8w-jxct to receive a larger impulse from a small force than from-swwcjl5cxl4 2b,m8q a large force? Explain.

A light object and a heavy object have the same kinetic energy. Whicvcp1)+ o p(dla n- yse7qzzu s7*k4zu1h has the greater mome zk4q+)p7o 1uz szds( c velyu7a1-pn*ntum? Explain.

Describe a collision iaqcox7g+ sm9 9+2oed pn which all kinetic energy is lost.

At a hydroelectric power pl u/m3r v/ 0qgbnf. aa-kt afp0(6hh-ppant, water is directed at high speed against turbine blades on an axle that turns an electric generator. For maximum power generation, shoa t .-/qumhrpa-a6 fhvbpfkp(/ 0 3n0guld 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 wal qr bsodcf76./90oa9nedlb*nl at a 45 $^{\circ} $ angle as shown in Fig. 7–30. 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 +fhc*q5 /oz aphard steel 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 ball and Earth as our system, during what parts of the process is momentum conserveda/* qz5+ fchpo? (c) Answer part (b) for a piece of putty that falls and sticks to the steel plate.

Why do you tend to lean back ttqhfaz1zu v82 s0zm01x6z6q ward when carrying a heavy load in your arms?

Why is the CM of a 1-m length of pipe at its mid-point, whereas thk7d d, j7ur/n8f1zv *m)qhxdu is is not true fodd7n7 / 1vqjuu,fh8 dk)rx z*mr your arm or leg?

Show on a diagram how your CM shifts when you change from a lying position to a b,dutl 1 v*9cx*2ix kasitt2k91a*ut,xc*x id bl ving position.

If only an external force c ef9is:un a5)-lx1vrran change the momentum of the center of mass of an obrfvne: 5li) au1sx9 -rject, how can the internal force of an engine accelerate a car?

A rocket following a parabolic path through the air suddenl+vhlujirszn0 m2v kp(7 sqjk*/) fk+n 4 r1.qvy explodes into many pieces. What can you say abo 2 )kkj0m(4n++lrs rjpz *q.iknsvhuvqv/f17 ut the motion of this system of pieces?

  What is the magnitude of the momentum of a 28-g f ggms52lz6u 92- o+ 3h/g evf)rmzngosparrow flying with a speed of 8.h m5g9)o+62 ffvzulrm2gg3 -os ez/ng4 m/s    $kg\;m/s$

  A constant friction force of 25 N acts on a 65-kg skieri b, :mg:m4isz for 20 s. What is the skier’s change iib: sm:i g4zm,n velocity?    m/s

  A 0.145-kg baseball pitched at 39 m/s is hit on a .wcfg44bol1qae,1 p 7wizf,9e xcr j5 horizontal line drive straight back toward the pitcher at 52m/s If the contact time bxi4l91rfwp 1z47 5qefg,cc we bj.a ,oetween 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 throws a 6.40-kg package out horizontally with a s0yx kr; o7o0xx58xbtqpeed of 10 m/ xq;7xbt xk oo00y85xrs 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 of the boat is 45.0 kg. Ignore water resistance. The velocity of the boat is    m/s

  Calculate the force exert ueesyy,up4 +. e+ a03io)iveded on a rocket, given that the propelling gases are expelled at a rate of 1500kg/s wiio3e0eyi,e a v.pu)4y+e d+us th a speed of $ 4\times10^{4 }$ (at the moment of takeoff).$a\times10^7$ N a =   

  A 95-kg halfback moving at 4.1m/s on an apparent breakaway for a touchdh :-pla5zs8mxn) l,hyown is tackled from behind. When he was tackled by an 85-kg cornerback running at 5.5m/s in the same direct-:) phm z 8yhl5,lasxnion, what was their mutual speed immediately after the tackle?    m/s

  A 12,600-kg railroad car t *8 emjdar,i2a+wwzi :ravels alone on alevel frictionless track with a constant speed of 18m/s A 5350-kg load,initially at rest, is dropped onto the car. What will be the car’s new spez+,8 a*i r:wami w2dejed?    m/s

  A 9300-kg boxcar traveling at 15m/s strikes a k pto3t1)3 gfzh l6yo+second boxcar at rest. The two stick together and move off with a speed of 6m/s What ipzy+k6f3 3o h)tog l1ts the mass of the second car?    m/s

  During a Chicago storm, winds can whip horizonta6)(p9t54mz(f rp qaalk g 1pdclly 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, estm(165rzfaka94 cdp t)lppg (qimate the force of the wind on a person. Assume the person is 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 8.6m/s ol i+pndxu j7 ol,*2uh:n a level track. Snow begins to fall vertically and fills the 7pln2uox:hjdu +i,l *car at a rate 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 movop7lo qy3iz(jr0z2 84z0vhas9ak kc , ing at 420m/s emits an alpha particle 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 alo0kzozsjlq2(c,k48z370 pyri a 9 h avpha particle have when it is emitted?    m/s

  A 23-g bullet traveling 230m/s penetrates a 2.0-kg block of wood and emet+ 0fnp-8qn+zdp9er)j ea 87u rxtt3 prges cleanly at 170m/s If the block is stationar )3tdrp zjnqn79x8u +a0etr8t fppe+- y on a frictionless surface when hit, how fast does it move after the bullet emerges?    m/s

  A 975-kg two-stage rocket is traj )c8vq/7 vnm;e.gmfi c oi(;wveling 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 mass 3180 kg is traveling in outer space xyb,im 9 .n6jbwith a velocity of 115m/s To alter its course by6b mi.x,b9 jny 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 the tee at a speed of 45m/s The golf c.gx*b* t+)h/mldtbp qyv- xk(lub was in cont /pq (+bg.tv)bxdykh*mlxt - *act 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 of93h 8/m6n rmfvzlm w0j 8.5m/s and comes to rest in a time interval of 8.0 ms. (a) What is the impulse given to the vmfj/ 9w8z6 n 3mm0rhlnail?    kg*m/s
(b) What is the average force acting on the nail?    N

  A tennis ball of mass:x0yqdg*zq-i4k jru+ m=0.06kg and speed 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 charge of the crashworthiness of new automovl dl+(4 yxf. o(0nkcsbile models. Cars are tested by smashing them into fixed, massive barri d(vlc.y (nls4+xk0 foers 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 n+x30 - ykrgapuqud o5lc m6-d7vi bycn28(x:in 0.75 s by a he:5diry-c g qck20 (+bnm6vdu83x7loa -yp x nuad-on 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 pd+g c(ygykvo85g*cw w 3m-0la tennis ball (mass 0.060 kg) points in the +x direction and is given by the graph of Fig. 7–33 as a function of time. Use graphical met-y *g+ ym dc3vwlgopg(5 0cwk8hods 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 height0uv;icgxf uf4z 42( qg can a 75-kg 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 seated position (thaxu;vif0 cg 4 z24(qfgut 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) wio3.7xa +e-57lotnmncyrmn ; mth a speed of collides head-on with a 0.220-kg ball at rest. If the collision is r3n;7t7cn em+oy.nm x-mo5 alperfectly 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, movil l y.sq2+iqh5)wdb ;sng east with a speed of 3m/s has a head-on collision with a 0.900-kg puck initially at 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, ad ll+h.)qb syq2; is5wnd 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 ,:iox zi er(w,fygdd-y0s*d ic47y6rmass undergo a perfectly 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 m/s, and call that direction the positive direction.Let B represent the ball,i0 goc6s,edi dz-iwfry( *y: y7rxd4 moving at 3.00 m/s in the opposite direction. ) v'$_A$ =    m/s v'$_B$ =    m/s

  A 0.060-kg tennis balse4*g1zzpx rfu1 .m- rl, moving with a speed of 2.5m/s collides head-on with a 0.090-kg ball initially moving away fropm.rrs4 *x1 f-1eugzzm 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 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 kg that is moving chxy 26a1t/lc with a speed of 8.5m/s collides head-on and elastically with another ball in/ l 2yh6ct1xacitially at rest. Afterward the 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 elastically as one approa +s:41t ee7 pzcxaeho:ches the other directly from the rear (Fig. 7–34). Car A has a mass of 450 kg and car B 550 kg, owing to differences in passenger mep+ho: c sx7ea1e zt:4ass. 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 elastici brr,9 y5o .*eo)jtru head-on collision with a second ball initially at rest. The second ball moves off with half the original speed of th eyrrto*j)ri5 ,o. ub9e 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 frictionless incline as 57n n:zvtg-e fyv s g1c28*xq ip1ej)zshown in Fig. 7–35, and elasticall : -tj2*f1)gqezz s1vg7expyi85 ncnvy 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 land? [Hint: Both leave the incline moving horizontally.]$\Delta x_{m}$$\approx$    m $\Delta x_{M}$$\approx$    m

ake the general case of an object ye hbi s5yi55,,,uptaof 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 exkofi2bqre j //4ge6s/periment, projectile 1 results in a maximum height h of the pendulum equal to 2.6 cm. A second projectile causes the the pendulum to swinf /j2soir 46 geqekb//g 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 penduyx*6f:y /qu;n zeh s q-j74zsulum hanging on a 2.8-m-long string, which makes the pendulum swing upward in an arc. Determine the vertical and horizon hxy:fysquz*s7 ue n;6j q4/z-tal components of the pendulum’s displacement.vertical$\approx$    m horizontal =    m

(a) Derive a formula for the frag h-e5ns0t;t pction 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 brzc12.i:x;hbw w..uv3*s uh o jxh4wsql8zo8 beaks an object, initially at rest, into two pieces, one of which has 1.5 times the mass of the other. If 7500 J were released in the explosiohu2s 81zwj: 4boosl*.cvb3h8i; .x.zh u wqxwn, 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 collid q58dqfnej;p7 l44cws jb(x 8ves 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?(Let A represent the sports car, and B represent the 7484bvqfq(8; 5xlnecs jd p wjSUV) $\approx$    m/s

  A ball is dropped from a height of 1.50 m and re w9*q5g(1hk7m2pfdjav nw q +7u)iucqbounds to a height of 1.20 m. Approximately how many rebounds will the ball make before losing 90% of9fhn(u j2vi7a7w cqq*kp5 qm+) dw ug1 its energy?   

A measure of inelasticity k r72y(lupuwp;53s whs;v 0pp in a head-on collision of two objects is the coefficient o5p pp( v2klwhwu3rsp7yu s0 ;;f restitution, 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 of the/ljmipr8 tan- .ib*: v 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 l.r:8 namjit*i/p v-breassembled 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 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 wit:)v- c5 h1hrig ccyw z)qz;rk*h a 10.0-kg object moving in the -x z*;h:c)vc z1rc) hrkw5-y qigdirection 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 nucleuf zb4oz gdhd:./f k.j0s at rest decays into a second nucleus, an electron, and a neutrino. The electron and neutrino are emittedodzjf4 :/.b.gk0dh zf 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 mg57,3eu nqlbrass $m_\mathrm{A}=0.400$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 collisionbzgm,rbgfyj 10k: h 8+ipqq4.v)jd6l between two objects of equal mass, each having initial speed the two move off together with speed v/3 What was the an)8i6jd0zkg +v ,lgrq b q14.pmf:hjybgle between their initial directions?    $^{\circ} $

  Two billiard balls of+u uvbfyh j3*1*+n jdf equal 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 speed 3.7m/s After the collision, assumed elastic, ball B is moving along the positive y axis (Fig. 7–37). What is the jv3n+du yff1 +**jbhufinal 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 perfecr rnip- ,nynf7f.; l(6ef *yvnt;q:v btly elastic collision with another atom at rest. After the impact, ;nvqv n rf*.p: n ( ,ebfti67lyfr;n-ythe 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 elj - ul*lj;zbmq) il:-bastic collision with another atom at rest. After the impact, the neon atom trav -;qmibb)lluzlj * j:-els 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 system shown in Fig. 7–38. Specify -a j c;.mpn+vgrelative to the left-hand 1.00- a.npgvcj+ m;-kg mass.    m

  The distance between a carbo jnx +f-qs9p3d zlm0m9n 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 behi 2o w8a2ooc qaio.hp0*nd the front of the car. How far from the front of the car will the CM be when two people sit in *qwoa 8c p2o2a ho.o0ithe 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 that each person has a mass of 70.0 kg.    m

  A square uniform raft, 18 m by 18 m, of tr3ztww2ee6 /2pz9(w s9yo sa mass 6800 kg, is used as a ferryboat. If three cars, each of mass 1200 kg, occupy its NE, SE, and SW corners, determine/p t ( os3tw2eaz r99zyswew62 the CM of the loaded ferryboat.$X_{CM}$ =    m $Y_{CM}$ =    m

  Three cubes, of side5z3ow s (f zn +rnhm;/ doorf6q;nlxjos,3(;qs $l_0$,$2l_0$, 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) palle y:p ahxn32l7gt has a load of identical cases of tomato paste (see Fig. 7–40), each of which is a cube of length l. Find the center of gravity in the horig:yp73x al2hnzontal 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)sbrooyp 8,p .qq1wg.p kx)qp;9 :p7vmp3 eou 2R has a circular hole of radius R cut out of it. The center of the smaller circle is a distance 0.80R from the center C of the larger ci ug7 )or8pmpq)1qp .sq pxpb ,oko9eyv;3w:.prcle, Fig. 7–41. What is the position of the center of mass of the plate? [Hint: Try subtraction.]   R

  Assume that your proportions areyo/agyct( 3mb)(nth yyf8/ p+ the same as those in Table 7–1, and calculate the mass of onoh tpf( 3 +y)y8/(cbtmy/nayge of your legs.    kg

  Determine the CM of an outstreq)qz 8lpw4y8ltched 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 blcm93i/day fsyby5 6 )ent at a right angle. Assume that the personmi93sly) y6 b/cy5fda is 155 cm tall. $X_{CM}$ =    cm $Y_{CM}$ =    cm

When a high jumper is in a position such that hism/cfx6+ joq)i 0o-9 dc lr(qbl arms and legs are hanging vertically, and 6r do)q q-lmc0/bi (o xclf9+jhis 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? Use Table 7–1.

The masses of the Earth and Mm cw/xw(se9,d oon 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-kghoxxwa7r h n:f0ps)x:2uf8: t man stand 10.0 m apart on frictionless 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.t(x8s8 fe+ mwe i ae;n-l5p0qj00 kg and a diameter 0.0800 m mounted on a uniform cylindrican0 ml s et5; f-ex(8pqiw+8aejl 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 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 an hbwa lkcy,z-8l;ftx, /v( ;ujd 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 air;8ujy, bxl w;kflva,h/ czt(- , 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 (Fie41/vvy4t xw s**ixb 63.qa/mk owzzf g. 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,4rg.kyhuik: rgn,41 u4yl3i9mwp x8 t of mass M, are in the air and stationary with respect to th4ug.:19krnpi x34my t4 glr,hiw ku y8e 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 the balloon then move? What happens if the passenger stops?

  An 0.145-kg baseball pitched horizontally at strikes a bat and is popped i2d2 ;a(+*napoydzk bstraight up to a height of 55.6 m. If the contact timd ;a d i*kn+pz2a2o(ybe is 1.4 ms, calculate the average force on the ball during the contact.    $^{\circ} $

  A rocket of mass m traveling with sperqqgfns maf8d ;i b5t(/,,r) yed $v_0$ 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 pocket shot shown in Fig. 1g y ;z-e01nggwi(pip7–43. Relative dimensions are al;pg0gi ynz1p (e1g-i wso shown. Should the player be worried about this being a “scratch shot,” in which the cue ball will also fall into a pocket? Give details.

  A 140-kg astronaut (including spacex l3w4spchb k66. t,dt48v pvi:whnx5yrg5x: suit) acquires a speed of 2.5m/s by pushing off with his legs from an 1800-kpkhx45:l p hw.43tx ,giw8vtdxbr:nsc65 6 yvg 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 theop7 6:yru o*tx other 80 kg, are initially at rest in outer space. They then push eax: y7*6tprou och other apart. How far apart are they when the lighter astronaut has moved 12 m?    m

  A ball of mass m makes a head-on elastic collision witi1zdvbmn: kc0 8259ud*ndyjvk ib /t0h a second ball (at rest) and rebounds in the opposidvi1v0bk kj 5nt:zmb/9 2*c8iddnu0yte 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 witness in a court case involving an aui8p :(sw gyv3ztomobile 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 migsyz:v3 8 (wpeasured 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 94r1d ats9rpcvertical height 4.00 m. The ball hits four times on the way down, each time striking the horizontal part of a difp t41srcd9a9 rferent 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 bottom of the stairs?

  A bullet is fired vertically into a 1.40-kg block ofantkrzen6 q6d x 99;2vpp.d3b 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 bul6kbap9. qd 2;dv9ntz pr6 ex3nlet becomes embedded in it?    m

  A 25-g bullet strikes and becomes eyfh4 x c5* 9epowwqi -(a.yfa)mbedded in a 1.35-kg block of wood placed on a horizontal surface just in front of )yx.- *eac owfqp54 ( f9yhiawthe 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 and the other of mass 60 kg, sit in a rowboat of mw0dztj;r 2b gng 2/w beb33rb e+.zp5pass 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 direct3gpzr2r 5bbp0z we2bg.de j ;nb+3/wtion 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 agjk2 ps;g84fqbout $ 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 twowl3s:ue(93 sbo q imb. fragments by an explosion. One fragment acquires twice the kinetic energy of the other. What is the ratio of their massess3lb.mqe3w s:9b(iu o?   

  The force on a bullet is given by the dz byy*c3-u/p 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 /k6 7)1y/a(ng hey. atot fxnt$m_A$ = 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 radioact8+1g*lwf n dwfively into an alpha particle and a smallegw 8 dfn*+l1wfr nucleus. What will be the speed 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 targ64r;q zgpq2;gf 7lg mget) 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 sluth p7xr8. ai64y.xdcy3 w8 kwides 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 if it isq3x 4x4iyxw/5 ulu;ms to rebound from M, slide up the incli5wm4x3 su4xiu l;/qxyne, 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–d .xz-b k)dve+47 shows the planet Saturn moving in the negative x direction at its orbital speed de). -zv+dxkb (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