We claim that momentum is choy1 8g9yr9if+mx)r ct80f vsph bn*4 onserved, yet most moving objects eventually slow down and sto8 4y rr hf 1vsgi *0+tocf8m9nx)9ybphp. Explain.

When a person jumps from a tree to the grounu6fk7,lymf:upyk + a 3q .ykr*d, what happens to the momentum of the person uponk3* mpu+y u,ryqak67:ffyl . k striking the ground?

When you release an inflated but untied balloon, why does it fly acrfqp-tf-j4 y,voss the room?f4p j-,-fq tyv

It is said that in ancient times a rich man with a bag of gold coins fra7za-l +wtw )doze 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 himselaw)a-w+t ldz7 f had he not been so miserly?

How can a rocket change direction when it is fa md;f8x;sv+esdzi )cj1g +q mwn(3g1 tr out in space and is essentially in a va smmx3wdt++zf(n1c evsjg;1gd)qi 8; cuum?

According to Eq. 7–5, the longer the impact time of aqow *m0q4xd8 an impulse, the smaller the force can be for the same momentum change, and hence the smaller the defq4 o amxd*w0q8ormation 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 rigid as possible to withstand colliphap6n/)g p;hr fi, z :3mx-cgsions. Today, though, cars are designed to have “crumple zones” that collapse rin-3/)pp f:mch 6g,gxz ;ahpupon impact. What is the advantage of this new design?

Why can a batter hit a pitched baseball further than a ball tossed ine 5dyfj:8mx fp26lc )z the air bypx2d:8c5ef f6l) m yzj the batter?

Is it possible for an objectu ee vmt0h;05unz6 bv8 to receive a larger impulse from a small force than from a large force?v6htz0u m8bu0v ee n;5 Explain.

A light object and a heavy object have the same kinetic energy. Which has38p0pptk,o2)c0 wwe c jwbmp; the greater p0ppoe c;pj w,)k0wt3 2 wbcm8momentum? Explain.

Describe a collision in which all :ed3 ej q/pxb*kinetic energy is lost.

At a hydroelectric power plant, water 56;6rlz qr*r*tpi 8cdscs s8yis directed at high speed against turbine blades on an axle that turns an electric generator. ;z 5r** r8c ct8isdss y6rlqp6For maximum power 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 wall atjptwif/j.c.z so 6-7 o k2*ocfc3gnrp bl:0)q 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 h ontub*1i73z /jtt 8kh0rsao)jdmo a hard steel plate (fixed to the Earth), from which it rebounds at very nearly its original speed. (a) Is the momentum of the ball conser7i0taz jhk bd rj31o*ust8)m /ved 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 ba;1 x fq.n*ov.kc 4gzfbomf4 m5ckward when carrying a heavy load in your arms?

Why is the CM of a 1-m length of pipe aa(vlv vkfyf 5hsfttm0; -h:t 00 7ld4wt its mid-point, whereas this is not true-l5l0sd0h twv(;hy4f a 0t7vff: mkv t for your arm or leg?

Show on a diagram how youra ktu q*t1f9,5g:toov CM shifts when you change from a lying position to a sittitk5otouaf:1 ,* q9 gvtng position.

If only an external force can change the mw,*q jk, 0 jcnb-fhz4aomentum of the center of mass of an object, how can the internal force of an enjcn,a* h wk,0q4zbfj-gine accelerate a car?

A rocket following a pa11+i;0- .y dlstv .poqln e,kyrbt4zc rabolic path through the air suddenly explodes into many pieces. What can you s-4iz.11tdb+ r;yysq0pk lv,o ntl ce .ay about the motion of this system of pieces?

  What is the magnitude of the momentum of a 28-g sparrow flyi6in-: coj-ut.k xyll+ ng with a speed of $8.4 \; m/s$    $kg \; m/s$

  A constant friction force of 25 N acts on a 65-kg skier for 20 s. /2lojgf9 rx,;1 hq lr ov:*nqmWhat is the skier’s change in veloc; o /2q,vm1o9 qg:jfxl *lrhrnity?    m/s

  A 0.145-kg baseball pitched at 39 m/s is hit qr uykmit4a6h1: . l0non a horizontal line drive straight back toward the pitcher at 52m/s If the contact time betweemy6kah qnu4t0l1 r.i:n 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 n4d7cm,4xjr7 .k ,qn0nrwzrr a 6.40-kg package out 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 24czr7q7rw r ,mkdxn j,r0 4.nn6.0 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 exf6klw sh8li+ - d ev:.gxh*mn3ydzf9 (pelled at a ratks -lfi: 3lw *9neydhvdg(h.fmx+ 68ze 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 s 025kg8b ;fvbx2vj;kkf j.hp 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 2mvo;+;rfak m travels alone on alevel frictionless track with a constant speed of 18m/s A 5350-kg load,initially at2 r mm+a;o;kvf rest, is dropped onto the car. What will be the car’s new speed?    m/s

  A 9300-kg boxcar traveling ++q d)qec,a p;lysvn3at $15 \; m/s$ 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 horizontallya/fd1 im, , lwh3)fkjy 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 1.50 m high and 0.50 m wide. Compare to the typic)/fmd1h,if wa3, l kjyal 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 railrz0-( dk4,tcy .mslhivoad car coasts along with a constant speed of 8.6m/s on a level track. Snow0dc zlv.4k miy -s,th( begins to fall vertically and fills the 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 moving a1oab 3cc/r 82lcd.pvat 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 alpha parti/o2l3 1ac.8c rv bcapdcle have when it is emitted?    m/s

  A 23-g bullet traveling 230m/s penetrates a 2.0-kg block of wood and eme)ht-z-l mafbz4 z q;t;rges cleanly at 170m/s Iaz4bhz- m-)t;lqt ;zff the block is stationary on a frictionless surface when hit, how fast does it move after the bullet emerges?    m/s

  A 975-kg two-stage rocket is hphafk9y l1opxh2j: ;6)x qw *x; r:butraveling 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 outepm9 c 7 u5cr;8uchsg4mr space with a velocity of 115m/s To alter its course by m 9hcmpgu7s8 r4uc5; c35.0 $^{\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 ob ym8d y-.ez2y,o2,mxmy:kg pff the tee at a speed of 45m/s The golf club was in contact with the bal be2pm2k yz,mg8xd,:y oyy- .ml 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 o2hf4 a7o:fnw2f2wkx i yxs+x8f 8.5m/s and comes to rest in a time interval of 8.0 ms. (a) What is the impulse given to t:hx2ik8 x2fxwf4 o7ns2fw y+ahe 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 wawgv. wut :w0s:i+hx- nll 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 j+r/*h1z,cv rqdhqs 1new automobile models. Cars are tested by smashing them into fixed, massive barriers at 50km/h (30 mph). A new model q qr+cdrjhv*z1h1/s,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 cmyq(sf ,w4vs a8x3,yw.zr n8the east and is stopped in 0.75 s by a head-on tackle by a tackler running due west. Calcv ( ,ywf4w3sxanq cyzr88m,.sulate
(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 kg) points i* vw(d ncd.k-zn the +x direction and is given by the graph of Fig. 7–33 as a function of time. Us.dd(cwznk*- ve 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 he5va,y/hd . j+u/qrwdoight 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 y+/djrdqvo ha/ u5.w, standing to the seated 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) with a speed of col0z+cr pts: vjt1r gdrc(v;jux6x,6u)lides head-on with a 0.220-kg ball at rest. If the ;xc1sx ug)pt+ r0d 6(cj:uvrrz6jv , tcollision 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 speed of 3m/s x .rag8(ay 0yu:q+pa 4ea4 )wcvj4w szb ie*u3has a head-on collision with a 0.900-kg puck initially at rest. ygv wbx:.4*ey)qa+8rj azu3wecas4 pu(i 0a4 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 perfi-o2z3:wu.vaif-dlt y;mls w 7 yiu1 /ectly elastic head-on collision. If one ball’s initial speed was 2m/s and the other’s was 3m/s in the opposite disl mwz3y-u:o.1d ii -t2wa i/l7fyu;vrection, 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 moving at 3.00 m/s in the opposite direction. ) v'$_A$ =    m/s v'$_B$ =    m/s

  A 0.060-kg tennis ball+-axzjk)zhl6 ;hu m;aig 3/e l, moving 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 tennis ball, and let B represent the 0.0+h;a-amj/ zl zeg) 6;h3xlkiu 90-kg ball.)v'$_A$ =    m/s v'$_B$ =    m/s

  A softball of mass 0.220 kg that eoi u 5nctzn /l..) ;v7zcf8wjiakd 9wh2a:* bis moving with a speed of 8.5m/s collides head-on and elastically with another ball initially at rest. Afterward the incoming softball bounces backward wit hl.)fiowa:8/ t5kibn;u z.*ve9 dc2n7jza wch 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 elasticallxsupl8:a jt/ -y as one approaches 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 mass. If car spj8la u/ -x:tA 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 elastiv 72u y c-e9jmbm*e1afc head-on collision with a second ball initially at rest. The second ball moves off y- ve2am *b1jcm uf7e9with 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 frictionless incline as shown in Fig. qa cod u)dbn.zbd 2(1.7–35, 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 eachbcuq1 .)dbond.dz 2(a cube land? [Hint: Both leave the incline moving horizontally.]$\Delta x_{m}$$\approx$    m $\Delta x_{M}$$\approx$    m

ake the general case ol7r2ucn)m* lvwz f86io rw3-fd.vqk;f 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 pendulum5tq /q+:/fowyqzj;) wul0yrz experiment, projectile 1 results in a maximum height h of the pendulum equal to 2.6 cm. A second projectile causes the the pej/);5:yzulq w+ rf/q0ytzo wq ndulum 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-k1d hw(g(fxalz w9j1 o5mhr) 4dg pendulum hanging on a 2.8-m-long string, which makes the pendulum swing upward in an arc. Determine the vertical and horizontal components of the pendulumx hljw9mrw )( oz5hf1dg4ad (1’s displacement.vertical$\approx$    m horizontal =    m

(a) Derive a formula for the fraction of kinetic energy lx-op, +ls8 wjfost, $(\Delta\mathrm{KE/KE})$ for the ballistic pendulum collision of Example 7–10. (b) Evaluate for m=14g and M=380g

  An internal explosion breaks gq20cf- dtw;oan 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 explosion, how much kinetic ene;qcdw2g0ot -frgy 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 rear end of a 2300-kg SUV 6:/h *u x eqpnyg(x+lok.llh- c2s2orstopped 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 repreeo*6 h-2lq xk/p +.rl2xgyu( :o shcnlsent the SUV) $\approx$    m/s

  A ball is dropped from a height of 1.50 m a7v nhlel -,qb/l8llf94fgq 4jnd rebounds to a height of 1.20 m. Approximately how many rebounds will the ball make before 9l4v/qlb f,-f h 8njlel7gl4qlosing 90% of its energy?   

A measure of inelasticity in a head-on collision of two objects lm9z:r/j1rx ucrm;:h6phg - wis the coefficient of restitution, e, defi9u/-gwh::6r1 pmxjm zchr l; rned 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 t6i ,tp;v/ :ut6l 7tpai rt*bcihe 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. When the firecracker explodes, the two blocks separate and slide apart. What is the ratio of distances each block trav/uct i*tt 6,vb6i7tlpi; a:prels? ----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 a2xfxbbr9e0m. ;f bjyb-5*sjkngn52 a 10.0-kg object moving in the -x direction at 4m/s Find thj bjbsf9kmx-g;xer5y0n.5f an2 b2b*e 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 decays into a second nucleus, an electron, 1qtb jh -yf po2m(m;b5and a neutrino. The electron and neutrino are emitted at rij2m-t(bhpo mq ;b15 yfght 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 maspqcy4q25 kod+: *moc2w0x mpn s $m_\mathrm{A}=0.400$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 o t0zn3 xp3l1win54c(d1hitca bjects of equal mass, each having initial speed thca314 5d(iznlch 1tni0tw3xp e two move off together with speed v/3 What was the angle between their initial directions?    $^{\circ} $

  Two billiard balls of equal0*y1x v,gyyr0k l cxr 4nfbw+5 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 g5yk+l bx1 0x0*fny r4v,wrcyalong 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 is  ----待选择----x directionx direction v'$_A$ =    m/s v'$_B$ =    m/s

  A neon atom (m=20u) makes a perfectly elastic collision 2s(p0k l47e z6d aveohwith another atom at rest. After the 2o hle0zsda6vp7 (4ekimpact, 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 perfectlxkm38wj9*kd m y elastic collision with another atom at rest. After the impact, the neon atom travels away at a x *mk389 djkwm55.6 $^{\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 syste ql/t7,hnm0/ggid )m/ yulyg/s0l5sa m shown in Fig. 7–38. Specify relative to tgs0sllum/5 0//tgdm)a, /y ngih lyq 7he left-hand 1.00-kg mass.    m

  The distance between a carbon atomdy3z f a)z/n*v ($m_{\mathrm{C}}=12\mathrm{u}$) 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 9dw:xt) g0o vgis 2.50 m behind the front of the car. How far from the front of the car will the CM be when two peopletwdgo9x0:vg ) 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 that each person has a mass of 70.0 kg.    m

  A square uniform raft, 18 m by 18 f5wclu9rm,dtpr k d f .)y048pm, of mass 6800 kg, is used as a ferryboat. If three cars, each of mass 9cdwt u8y,4d r.)fk50rm fplp1200 kg, occupy its NE, SE, and SW corners, determine the CM of the loaded ferryboat.$X_{CM}$ =    m $Y_{CM}$ =    m

  Three cubes, of sides o i6cbfb4-dyd.0 uh tjsnp1 jm.b0; e6$l_0$,$2l_0$, 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 bi; eo0gs 59wjidentical cases of tomato paste (see Fig. 7–40), eaej;swi 50g9ob ch of which is a cube of length 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 circular hole of radius R io z3n86*il;2jxn omhxv;n b, e2r9sxcut out of it. The center of the ;o2xn ;sr9n*xi ln3v 2mb8oj,x6 ehzismaller 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 y4he* f2z1s yal5+iquthe same as those in Table 7–1, and calculate the mass o2q i14a*h usyzf5e+ ylf one of your legs.    kg

  Determine the CM of an outstr3+uehpaeo3o1m n q+9wjjw4.n etched 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 at a right uu lnx;dncq;u*c/ 1np:dt2zf- i li)0angle. Assume that the 0-nutp2i:fd/ n1cdu* );;i uzllx q ncperson is 155 cm tall. $X_{CM}$ =    cm $Y_{CM}$ =    cm

When a high jumper is in a positicyn wh yyj84 cau)/y+(on such that his arms and legs are hanging vertically, and his trunk and head are horizontal, calculate how far below the torso’s jhcy48(/ +ny)y yw aucmedian line the CM will be. Will this CM be outside the body? Use Table 7–1.

The masses of the Earth and Moon 0w+2ow4)cye+z fsug dare $5.98\times10^{24}$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-klnckjr yik (824w xhx7d8cz8.g 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 2xp x;gry/,y q1mgo;-m mug1oq13b4wb .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. 7–42gy-wg/mbpr;1qmg;mxo13oy ,u b x4 q1. 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 e(z2se-mjf t/ sr t+7wcylindrical head of mass 2.00 kg and a diameter 0.0800 m mounted on a uniform cylindrical handle mr(e jtw-ft+z/7 e ss2of 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?    d    d

  (a) Suppose that in Example 7– h*4ce ))e uyhwt04 -lpoj8lfo14 (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 t:c: 8 x a b6rhr--(r 5huqqgtcwube6r0he air and stationary with 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 ar5bxte 0 qrhw:(r-:ug- ru68q 6cbca hnd direction (relative to Earth) does the balloon then move? What happens if the passenger stops?

  An 0.145-kg baseball pitched horizontally at strikes ais f3.; rx )as0 b(r/1idlwoyr bat and is popped straight up to a height of 55.6 m. If the contact time is 1/fi ry 3 a0xsrw;(dsbli.1r)o.4 ms, calculate the average force on the ball during the contact.    $^{\circ} $

  A rocket of mass m trfs6wkaj 90c3y aveling with 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 tml x96-am)xhoc i)g r1wm.. dh*9i aidhe corner pocket shot shown in Fig. 7–43. Relative dimensions are also shown.r 9dwh6-ilo* ..1 i agidam hm)cxmx)9 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 space suit) acquires a speed of 2.5m/s by puship0v p69 k lij)/ghnhfrz3 m+0mng off with his legs fromm0f 6h3 n)m0hpljgk+zp9 /vri an 1800-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 kg, are initially at p:fp; q5qzug zc 2q 8/q0roxb+rest in outer space. They then push each other apart. How far apart are they when the lighter astronaut has ;:b2o5 f q8qzq/ + zgqu0ppcrxmoved 12 m?    m

  A ball of mass m makes a head-on elastic collision with a secondmq4-)mv vjv v6 ball (at rest) and rebounds in the opposite direction with a spm -)4v vjqmvv6eed 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 involkht3lux r3(yyv( 4f33adl8 d tving 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 crasdf3( 3 3tyvut83l(hk yal 4dxrhed 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 o41 s wn0zbr*oy q7zf4gf a flight of concrete steps of total vertical height 4.00 m. 4ow0gs741 * zzrb nqyfThe 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 bottom of the stairs?

  A bullet is fired vertically into a 1.40-kg block of woouowb0wfv7h9 86 r bh/kd 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 rvhbh/kuf 07ow8 69wbembedded in it?    m

  A 25-g bullet strikes and becomes embedded in a 1.35-kg block of woo1iv,+f db0 bj 1mdhz9od placed on a horizontal surface just in front of the gun. If the coefficient of kinetic friction between the block and the9zf01hv+1 ,b o mbjddi 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 rowc)dl :nzbu 13uboat of mass 80 kg. With the boat initially at rest, the two people, who have been sitting at opponuuz 3) cdl:1bsite ends 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 wa/ka s4qr5( d-nv aant1,tbg+m s about $ 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 fragments by an exploz+ /h*uozbdgy f m8,tdn2gv -q34wy1vsion. One fragment acquires twice the kinetic energy of the other. What v1b gd /,ouvm +42 zt*dygf8-3q yznhwis the ratio of their masses?   

  The force on a bullet is given by the formv abcp6(vnp; u6 d2hy:ula 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 ,+fnq-9jlpif i:mbds5: w3yz$m_A$ = 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 i-gy:fzzn,yw c8)bpfe8x/xd / nto an alpha particle and a smaller nucleus. What will be the speed of this recoizz /fe ,gyx8x-8/fc) bd:n wypling 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) is fired:tqs );7kurwz 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 slides down alkj7 zbexip ;xf(l w:*xa1 o)+ 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 lzrexcj8 i bu t6hv,4st; -3s-eimit on mass m if it is to rebound from M, sl x e6z38 s-ijvcehr4b,t tu-;side 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 shows the planet Saturn movingy mkjwvq;0+ yod frqv6tbe*1*eo/ ,6o in the negative x direction at its orbital speed (with ry fdro *qvoe1 vm/0qy *twj6;,bk6e+oespect 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