We claim that momentum is conserved, yet most moving objects eventually x.o x7+ki5us2v j5yc pph2ligp8tfpok 262x/slow down and 7k5v2kpj8i / p6pi+5 x 2 sh gxt2ooluy2f.cpxstop. Explain.

When a person jumps from a tree to the ground, what k +n nal tt,akcg4p,6r/hp,9/ sv5wybhappens to the momentum of the person uk/ , wp, cr6hntlp49/5 sabgyt,nka+vpon striking the ground?

When you release an inflated but untied balloon, why does it ;utl j 9c-hmyoxd r +6ya;t5q/fly across the room?hjx toyr5-d9m lc ;yu;+6tq/ a

It is said that in a.uyskno 4371c )ge sictclvn7 y. k3u/ncient times a rich man with a bag of gold coins froze to death while stranded on a frozen lake. Because the ice was frictionless, he could not push sco cut n/us1773nv4el).ci gy3k.y khimself to shore. What could he have done to save himself had he not been so miserly?

How can a rocket change direction when it is far ohw:jme ke: q ;a7a:,lsut in space and is essentially in a vakam:ea s: ql7;we j:,hcuum?

According to Eq. 7–5, the longer the impact time of an impul3oiv lb2:r /7-6msq6;qkljp kyydo/ w se, 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 this basis, explain the value of air bags, which are mb6oqo qyv7 wj ;k/6/- rkis yp:2ll3dintended 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 collid 6m32,b8t 2hskkha,bpelq/ r *acol4 sions. Today, though, cars are designed to have “crumple zones” that collapse upon impact. What is the advantage of th4 qhtm*k8s l k ,elbr2p6a/oa, 2chbd3is new design?

Why can a batter hit a pitched baseball furthlj b1u no-6m1qer than a ball tossed in the air by the batterlnomqj1b-6 1u?

Is it possible for an object to receive a larger impulse from a smal bvso8eg:+3w fl force than frosoewb vf:g83+m a large force? Explain.

A light object and a heavy object have the same kinetic energy. Which ha zx5ssh f4umf0nlob r-;k28 q/s the greater momentum? Expla5;n0 ff8hls s -mkq/xzo24bur in.

Describe a collision in which all kinetic e1ywc)st -x: cy9j sbe1nergy is lost.

At a hydroelectric power plant, water is directed at high speed8 eoc.*k gnv7y dup4si ebi 0i)1(wm+o against turbine blades on an axle that turns an electric generator. For maxo8w ginse.1dyv i0(+ei7c ub*)mpko 4imum 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 xq8 s krg,qp/n-.mu )yat 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 heigh++ k9*medlyxks(9 vcq3 rrtyxkw,c4/ t h onto 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 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 plaxrdk*xyy+s c vt/(mkr+,e 93kclq4w9te.

Why do you tend to lean backward when carrying a heavy load in your armvxmf4 +a:9r tms?

Why is the CM of a 1-m length of pipe at its mid-point, whereas thio)-qo8e8pl avc5r k c6s is not true for your ar6)vp5crl coaok8e - q8m or leg?

Show on a diagram how your CM shif +b wrbhq //k5wnj6 z+qbh+a,tts when you change from a lying position to a sitting posb5kjb ,hb+q+qr at w/6/ +znhwition.

If only an external force can chanetydr-/jd 8cmyd 5z7aw 6/+8xayfuu; ge the momentum of the center of mass of an object, how can theu6fc dd8y/;j auwtr8m5 ae7/ yy-d xz+ internal force of an engine accelerate a car?

A rocket following a parabolic path through the air suddenly explodes iw:hid 39fsb:u;/cfr 4nz7wxnnto many pieces. What can you say about the motioncwsw3 izdx ;u7b: h49f :nf/nr of this system of pieces?

  What is the magnitudkao2yvsr9;t 9 e of the momentum of a 28-g sparrow flying 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. What is t9xs)ihqm:/ v 9/uic jvhlvtm)y1w(g6he skier’s chang9vhsm9c)i: uwil(hq1)/jx ty 6vv /gm e in velocity?    m/s

  A 0.145-kg baseball pitched at 39 m/s is hit on a horizontal line drive stra5rbw7 cdaz9z4ight back towardb7a9 r4z5wz cd the pitcher at 52m/s If the contact 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 th*tjr7p z y/fz-rows a 6.40-kg package out horizontally with a speed of 10 m/s Fig. below Calculate the velocity of the boat immediately after, as/jp7ft*z- r yzsuming 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 kkeb3n emo7; ,5t01dwuz uk8 bexerted on a rocket, given that the propelling gases are expelled abnokb7mtk z3 5e0u,k8eu w1;d t a rate 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 apulx ;ng 9st56t $4.1 \; m/s$ 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 travelsl7 .m e n9ajzq3w,yk9f alone on alevel frictionless track with a constant speed of j a39 wne7kmly, q9zf.18m/s A 5350-kg load,initially at rest, is dropped onto the car. What will be the car’s new speed?    m/s

  A 9300-kg boxcar traveffkh kvdtm5 i: +0e;zx z3km5pl i,1w5ling at $15 \; m/s$ strikes a second boxcar at rest. The two stick together and move off with a speed of $6 \; m/s$ What is the mass of the second car?    $m/s$

  During a Chicago storm, wind;gerjs 3/j rm4y 0jm4o1r - 4ounc9rbjs can whip horizontally 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 for ebo4m n 1r-g 43r/jrm; rjus9jco04jyce 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 alonv ul671pzv y3hz-4mfiq /c3xeg with a constant speed of 8.6m/s on a level track. Snow 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- zcy zm uvpx3hl/7ief6413vq min?$\approx$    m/s

  An atomic nucleus initially moving at 420m/s emits an alphai 3ypub2,yfq1 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 ofpf2by, 1 3iyqu 222 u, what speed does the alpha particle have when it is emitted?    m/s

  A 23-g bullet traveling 230m/s peneya;s:cd )k/ yidh0lu8trates a 2.0-kg block of wood and emerges cleanly at 170m/s If the block is stationary on d8sku0/c y;y )lhi: daa frictionless surface when hit, how fast does it move after the bullet emerges?    m/s

  A 975-kg two-stage rocket is traveling at a9, tls6bx kr,k 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 with a vx htd w.m)0j.pelocity of 115m/s Txd j.)w0 pmht.o 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 the tee at a speed of 45m/s Tdfr6xwp2 rta 86f, mm3he golf club was in contact witx 86rfa63f2 mm wtr,pdh the ball for $3.5\times10^{-3}$s Find (a) the impulse imparted to the golf ball,    kg*m/s
(b) the average force exerted on the ball by the golf club.    N

  A 12-kg hammer strikes a nail at a velocity of 8.58cwvvbyxwb0p 4/0 4p nm/s and comes to rest in a time interval of 8./bvcv ww4p b0xny0p480 ms. (a) What is the impulse given to the nail?    kg*m/s
(b) What is the average force acting on the nail?    N

  A tennis ball of mass mp rad-1 tq,+ut=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 charxvq 3rx+6. h3b ect zp+dwx6v+ge of the crashworthiness of new automobile models. Cars are tested by smashing them into fixed, massive barriers at 50km/h (30 mph). A new model of mass 1500 kg takes 0.+ x63 +tqpvr hw dv.xc+xz6eb315 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 icgb4 qzk ;d+ wz8tn.i4s stopped in 0.75 s by a head-on tackle by a tac4ziwq 4;tk .d8bn+gzckler running due west. Calculate
(a) the original momentum of the fullback    kg*m/s
(b) the impulse exerted on the fullback    kg*m/s
(c) the impulse exerted on the tackler,    kg*m/s
(d) the average force exerted on the tackler.    N

  Suppose the force acting on a tennis ball (mass 0.060 kg) points.z// fv,krqo y e:ngl4d.f ks5 in the +x direction and is given by thoe z.sk//4f kqlrvfdn.5: g, ye 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 breaking the la6d 2btbd; +syy8p,glbyr+ ;fower leg bone of either leg? Ignore air resistance and assume the CM of the person move y;lsy;fb6brpy,++tbg2 da 8d s a distance of 0.60 m from the 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 colli2*;l* :oa nscb nhh m774kcg;qgb a.osdes head-on with a 0.220-kg ball at rest. If the collision is perfectly elastic, what will be the speed and direction of each ball after the collision?Let A represent the 0.440-kg ball, and Baol *gsoachkc*2bn:hb;m 4sn . ;7g7 q 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, m*zpc/i4bo h3o*s.h :)enk1d lwgt0mj 6h uvz*oving 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 c:h*k*imv szd.)j/ugo13zhoehn0 4*wb6lptand 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 perfectly elastic head- 4 -(r(qmn.mo nkq1qenon 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 af - re.mqmn(q no4(1knqter 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, moving with a speed of 2.5m/s collides head-on witfm3wom g4/dok +(es0v ax 3ho5h 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 0.090-kg ball.)m3owd kx3o+ (vhma4/sfge05ov'$_A$ =    m/s v'$_B$ =    m/s

  A softball of mass 0.220 kg that is p8dxb;)a zlwa3j(s 8umoving with a speed of 8.5m/s collides head-on and elastically with another ball initially at rest. Afterward the incoming softball bounces backward with a speed of 3.7m/s Calculj(8z3)dlsabau8 w px; ate
(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 af.4j are .tdw,l y8.p,y4syzl n amusement park ride collide elastically 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 A approaches at 4.5m/s and car B is moving at 3.7,s.pwf4 l8 j4dlayye r. .zyt,m/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-o+:n,rv /5c )o prdxhfyn collision with a second ball initially at rest. The second ball moves off witdcp,hfy+5 r)vnor :x/h 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 inclqj3kse 4t* hb-wqf/n0 ine as shown in Fig. 7–35, and elastically strikes another cube at the bottom that is only qw*f-0 b khn4qs3te/ jone-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 ofr;z3hq5j ab;z 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, projectile 1 resu ll c7a2aloy+96 nwf(qlts in a maximum height h of the fl+9( lncw yo2qa7a6lpendulum equal to 2.6 cm. A second projectile 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 travelingr fvr76 6cgu7qd;(xq1i )hmfk 230m/s buries itself in a 3.6-kg pendulum hanging on a 2.8-m-long string, which makes the pendulum swing upward in an ch;u 1iqk7f6d7qfrrgxm 6)v (arc. Determine the vertical and horizontal components of the pendulum’s displacement.vertical$\approx$    m horizontal =    m

(a) Derive a formula for the fraction of kinetic energy lqmwkgne(yd. ,ed;ws*2jb8 r ( ost, $(\Delta\mathrm{KE/KE})$ for the ballistic pendulum collision of Example 7–10. (b) Evaluate for m=14g and M=380g

  An internal explosion breaks an object, initially z4+g,9arl azm / wj)asr 4ns0eat 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 piece a0 n 4+jas mlgr/aezz9r a4s,w)cquire? (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 tkh-qk )i 7t qpb*5qxb;he 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 qkpb7i-5 kxtqq*h ;b)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 SUV) $\approx$    m/s

  A ball is dropped from a height of 1.50 m and rebounds to a height of 1.20 m. )yt5rx h1q1o jApproximately how many rebounds will th jhqxyor1)1t 5e ball make before losing 90% of its energy?   

A measure of inelasticity in a head-on collision of two objects is the c 4 ,+u p.omobgnn-dljpe98x4soefficient of restitution, e, define.4s 9oj-dn48emlxo gpubn+ ,p d 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 pie)j7( 3pjlo;ijqu d,56ypve vjces, one with three times the mass of the other. A depression is made in both faces of the cut, so that a firecracker can be placed in it with the block reassembled. The reassembled block is set on a rough-surfaced table, and the fuse is lit. When the firecracker explodes, the two blocks separate and slide apart.vd5 y,pjj j(q7)u3o ;p6eijlv What is the ratio of distances each block travels? ----待选择----1/91/101/81/6 

  A 15.0-kg object moving* mefm p4 lw,qa8h/:kl r(u.oo in the +x direction at 5.5m/s collides head-on with a 10.0-kg obje/4oakwu (ql hm:*emp .l8 fr,oct moving in the -x direction at 4m/s Find the final velocity of each mass if:
(a) the objects stick together;   m/s
(b) the collision is elastic; v'$_A$ =    m/s v'$_B$ =    m/s
(c) the 15.0-kg object is at rest after the collision;   m/s ----待选择----not reasonable reasonable 
(d) the 10.0-kg object is at rest after the collision;   m/s ----待选择----not reasonable reasonable 
(e) the 15.0-kg object has a velocity of 4m/s in the -x direction after the collision. .   m/s ----待选择----not reasonable reasonable 
Are the results in (c), (d), and (e) “reasonable”? Explain
( Let A represent the 15.0-kg object, and let B represent the 10.0-kg object.)

  A radioactive nucleus at rest decays into a second nucleus, an electron. to4 p)whrjs1, and a neutrino. The electron and neutrino are emitted at right angles and have moms 1 jp.r)4thwoenta 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 mass qt lpfl5s:ai nh 7rz);i9-n7 c2q etrjv9);fa$m_\mathrm{A}=0.400$kg moving with speed $\nu_\mathrm{A}=1.80$m/s strikes ball B, initially at rest, of mass $m_\mathrm{B}=0.500$kg As a result of the collision, ball A is deflected off at an angle of 30.0 $^{\circ} $ with a speed $\nu_\mathrm{A}^{\prime}=1.10$m/s (a) Taking the x axis to be the original direction of motion of ball A, write down the equations expressing the conservation of momentum for the components in the x and y directions separately. (b) Solve these equations for the speed v'$_B$ and angle $\theta_{\mathrm{B}}$ of ball B. Do not assume the collision is elastic. $\theta_{\mathrm{B}}$ =    $^{\circ} $ v'$_B$ =    m/s

  After a completely inelastic collision between two objects of eq9 f9vvm 9vdy0nual mass, each having initial speed the two move off together with speed v/3 What was the angle between t9dvvf9m 9n0y vheir initial directions?    $^{\circ} $

  Two billiard balls of equal ma1 :chp *a5fvcgss 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 final direction of:1a *fpvgh cc5 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 with another atom afv tflb-q 5)w* kej9.ot rest. After the impact, the neon atom travels away at a 5). 9o*qfvft5 l- bwkej5.6 $^{\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 ao jexgd/ 0 syjh-p0/f8q 7xr36-bbgt z perfectly elastic collision with another atom at rest. After the impacqft-3sh 0 egyx0xj-7 j8bogbz6p/rd/t, 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

  Find the center of mass of the three-m5msb lsd 3o/.tass system shown in Fig. 7–38. Specify relative to the left-hand 1.00-kg mass. tbo/.5lsdm 3s   m

  The distance between a carbonjn9t5mde0c i8 0 6wtan 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 03eim tq,gf*+5uamvanr*byx*3 ik;t behind the front of the car. How far from the front of the car will the CM be when two people sit in the front seat 2.80 m from the frontar0** itb ,faunivm3mqge*5 y+k x3; t 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,1k/- f: zt63vgrhvm+htc)xmr 18 m by 18 m, of mass 6800 kg, is used as a ferryboat. If three cars, each of mass 1200 kg, occupy its NE, SE, and SW corners, determine the CM of the loaded ferryboatm-) +tmf /1x6ghkz3vc :rhrvt.$X_{CM}$ =    m $Y_{CM}$ =    m

  Three cubes, of sides hj ,vwj gb,;:g7o2 xnc$l_0$,$2l_0$, 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 idec 4 ,lmz,qk9arntical cases of tomato paste (see Fig. 7–40), each of which is a cube of length l. Find the center of gravity in the horizontal plane, so that the crane opera,a r49 cl,qmzktor 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 cut oui9l 2utjfz, (ut of it. The center ozt9f (ujiu l2,f the smaller 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 91 nqixkur 4oj,uinxu2 98pz .are the same as those in Table 7–1, and calculate the mass of one of your l.i p ruiounnqxx9 ku,82j49z 1egs.    kg

  Determine the CM of an outstretched arm using Table 7–1q/;lsvrind;zr7; 16jmregx1.   % of the person's height along the line from the shoulder to the hand

  Use Table 7–1 to calculate the positio43(jqury c i( 3qte3ngn of the CM of an arm bent at a right angle. Assume that the nrj qq3eui(gytc4(33 person is 155 cm tall. $X_{CM}$ =    cm $Y_{CM}$ =    cm

When a high jumper is in a position such tqto0dnpo4, z1 hat his arms and legs are hanging vertically, and his trunk and head are horizontal, calculate how far bpt, 1 40ndqozoelow the torso’s median line the CM will be. Will this CM be outside the body? Use Table 7–1.

The masses of the Eartq e95vpc)q jy3 75ste4kkxj-f h and Moon are $5.98\times10^{24}$kg and $7.35\times10^{22}$kg respectively, and their centers are separated by $3.84\times10^{8}$m (a) Where is the CM of this system located? (b) What can you say about the motion of the Earth–Moon system about the Sun, and of the Earth and Moon separately about the Sun?

  A 55-kg woman and an 80-kg man stand 10.0 m apart on frv4 9l wz/ tb6.9ug5hq g*osksqictionless 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 uniforx n bdn 2l4*/wciwp+-c82o fprm 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 sh8d2wn4c /+cw p*f-2p xnbroilown 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 mas7mf *--jqp2)rxdy7 ebkb1pys s 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 Fij qpy y7bmkf)2s*1x--rpd7ebg. 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 7–14 ( o xw71qqnv7:a f j/8rsnf(1qsFig. 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, ofwnjp+n6x0 k4r8 me8yvaw .-i f mass M, are in the 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 and direction (relative to Earth) does thenwkvm y0 rw 4f.ji+ap6en -8x8 balloon then move? What happens if the passenger stops?

  An 0.145-kg baseball pitched horizontally at strikes a i 3mrb4he ok4d w9;0p1 0ounswbat and is popped straight up tnw3srkb;e 40pm1u 0o4hw 9oid o a height of 55.6 m. If the contact time is 1.4 ms, calculate the average force on the ball during the contact.    $^{\circ} $

  A rocket of mass m traveling with speee1mj75o gzkrbv)ba1p l d /v6.d $v_0$ 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 cowqa m .gi2x3a-rner pocket shot shown in Fig. 7–43. Relative dimensions are also shown. Should the player be worried about this being a “scratch shot,” in which the cue ball wx -iwa3 2gmaq.ill also fall into a pocket? Give details.

  A 140-kg astronaut (including space suit) acquires a speed of 2.5m/s by puq c lqv7p(85h8qb .b,8oa tbukshing off with his legs fro88o(5bt u.8qlbc h7vaq ,bqkp m 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 re -zu kh)vmp3qx;1s:q lst in outer space. They then push each othqvl3x -:pu 1k;hs)z mqer apart. How far apart are they when the lighter astronaut has moved 12 m?    m

  A ball of mass m makes a head-on elusd.-ji6g4 a dp/;rmp,eupb *astic collision with a second ball (at rest) and rebounds in the opposite direction with a speed equal to one-fourth its original speed. What ium;4a*jdei6ppu/r ,- bg psd .s 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 a8: fvh/bld0iaq84 ypzvl8l j8n automobile accident. The acci v:q8b8ypi8 dh/v la zfjl48l0dent involved car A of mass 1900 kg which crashed into stationary car B of mass 1100 kg. The driver of car A applied his brakes 15 m before he crashed into car B. After the collision, car A slid 18 m while car B slid 30 m. The coefficient of kinetic friction between the locked wheels and the road was measured to be 0.60. Show that the driver of car A was exceeding the 55-mph (90km/h) speed limit before applying the brakes.    mi/h

A golf ball rolls off the top of a flig7h+n9q+4draysr0r h5tv cg un1g; o ;s+chav*ht of concrete steps of total vertical height 4.00 m. The ball hits four times on the way down, each time striking the horizontal part of a differe +g4rntvs+rv+a ;cgohhy07u*ad n q5r1 ;s9h cnt 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 blocv ved hcv5w0)9bl1c5vk of wood at rest directly above it. If the bullet has a mass of 29.0 5hl9v v 5)1b dc0evwvcg and a speed of 510m/s how high will the block rise after the bullet becomes embedded in it?    m

  A 25-g bullet strikes and becomes embedded in a 1.35-kg block of gw7/xq3k+gpr.ezgqqr p. )k9 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 p pkeg)xg/3 r 9gz.wk7+rq q.qbefore 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 6b ohzf2 ;3irca rowboat of mass 80 kg. With the boat initially at rest, the two people, who have been sitting at opposite ends o3 zi6 ;b2ochfrf 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 cefgc2+7 * yo) u*felnabout $ 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 brokenzik9+ pkz:v* :wz9*b hughpnm v gu:3; apart into two fragments by an explosion. One fragment acquires twice the kinetic energy of the other. What is the ratio of their mhvmgzz9 bkp::* knp3uuvi: gw*;hz9+ asses?   

  The force on a bullet is given by the y9.kxr*h1ow 0c mrd4bformula 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 ahcv h9-u/io itsg( x,z6:2 ;mqiq3a v$m_A$ = 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 smalbtu/:gqqtf u u 4pswpa v.joag./-7 1,ler nucleus. What will be the speed of this recoiling nucleus if the speed of the alpha partiqgjwv1 tu.u//agau,:q. fop p7s- t4bcle 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 athx 2 8pdwiv/cp;b(pemnw:cs/ 1cjp3) 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=2.2kghk2 y3 bec0c-0 wqpx0d slides down a 30.0 $^{\circ} $ incline which is 3.60 m high. At the bottom, it strikes a block of mass M=7kg which is at rest on a horizontal surface, Fig. 7–46. (Assume a smooth transition at the bottom of the incline.) If the collision is elastic, and friction can be ignored, determine
(a) the speeds of the two blocks after the collision,v'$_A$ =    m/s v'$_B$ =    m/s
(b) how far back up the incline the smaller mass will go. $\approx$   (Round to the nearest integer) (Let A represent mass m, and B represent mass M.)

  In Problem 79 (Fig. 7–46), what is the upper limit on mass m if it is to reboul4n ,fcx4q9anho vz:*nd from M, s:hl* 4 cqn ax9zovf,n4lide 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. Figur t/6oogt*i;3 r pmvtl 8)dbvg2e 7–47 shows the planet Saturn moving in the nlv*oo gbd v2t6;)3ti /rgp 8mtegative x direction 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