We claim that momentum is conserved, yet most moving objects eventually slow dox(eot6/c8toju d 0 z2gg8 mt8dwn and stop. Explt t0jd8ce/ o( xg 6g2doz8u8tmain.

When a person jumps from a tree to the ground, what happens to the +yfrzzh)fei *g 6p9 1smomentum of the person upon strikinp9ifzfz)e*y+h1rg 6 sg the ground?

When you release an inflated but untied balloon, why does it fly acrosskgylc(,s, j 2c the room c(,,ycls 2gjk?

It is said that in ancient times av lz*y*ztl q;h )q7mo; rich man with a bag of gold coins froze to death while stranded on a frozen lake. Because the ice was frictionless, he h7;ot*mq*l lvz)y;q z could not push himself to shore. What could he have done to save himself had he not been so miserly?

How can a rocket change direction when it is far out in space an);g3kjd cjb :9kvecyvs .b* r.x:p2r vd is essentially in a vac cp;g sykvjb:bjr*:r 3 )ev9c.d.2k xvuum?

According to Eq. 7–5, the longer the impact time of qj)13wnzrtw/d:bs; x +. ka++gxditr 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 this basis, explain the value of air bags, which are intendrgwq +xt+xas/;b 1n.i 3d)r z+:ktjwded 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 collisxu3vd5 u7 4xlsions. Today, though, cars are designed to have “crumple zones” that collapse upon impact. What is the adv xx43l5d 7uuvsantage of this new design?

Why can a batter hit a pitched baseball further than a bj ;2 ikp prilxc498 b((jaov0: ,jheoqall tossed in the air by the battj,ppebx0r4; 8hvj2ica: o9j oi k (lq(er?

Is it possible for an ob e2-q)e m6 d)z/9fetrjezty1tject to receive a larger impulse from a small force than from a large force? teey19zj)tt qr6de- f/)me z 2Explain.

A light object and a heavy obj+k1tnl7d krw5ect have the same kinetic energy. Which has the greater momentum? Explai57d ntwrlk+1k n.

Describe a collision in which all kinet f0p3qyn/wm .i,tud 9a,b,sxwic energy is lost.

At a hydroelectric power plant, w-5aqf,ap,;dnl, pp:i1 fhcpxater is directed at high speed against turbine blades on an axle that turns an electric generator. Falcf, 5,-d nppp; f:1qph,aixor 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 /p: wi:td a-viat 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 hard stm 5qeixr- d/vncq )c4:9nyp ;deel 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 sy)mqdec;cx 4rv pi yn q5d:n/9-stem, 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 backward when carrying ae 6 g0x+rsqnz)f)y o0s heavy load in your arms?

Why is the CM of a 1-m length of pipe at i2g qmcjh)ei )ba( :ja-ts mid-point, whereas this is not true for your aracaj(qge-jb: 2 h)m)i m or leg?

Show on a diagram how your 91bwiynpqx4bh . g0a ,CM shifts when you change from a lying position to a sitting positpwb 0,nyhxq g 4ba9.1iion.

If only an external force can change the momentum of the center r/j 3;dqgu 48vou(8m(hw f occof mass of an object, how can the internal force of an engine dcqmr4u83jf / go;h(w(cv o8u accelerate a car?

A rocket following a parabolic path through the air suddenly explodesw)s m)0ctpnkw4sqj ea8o;;v- into many pieces. What ca- s;j)mk)w 4sc etvnaow;p80qn you say about the motion of this system of pieces?

  What is the magnitude of the momentum of a 28-g sparrow flying with ip 7l*q r;ozd3jck8b )p1y1ir6 hdjk,a speed of 8.4 miy7hk 3ikpj* , ;jdo1)q 1z cbd68lprr/s    $kg\;m/s$

  A constant friction force of 25 N acttenb6yovb;c- vlt: * ;s on a 65-kg skier for 20 s. What is the skiernlbe vb;t;v oy:-c*6t ’s change in velocity?    m/s

  A 0.145-kg baseball pit e:batpx;ku;ri044 oached at 39 m/s is hit on a horizontal line drive straight back toward the pitcher at xi4pr oa40b;;e at ku: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 throws a 1eyr;ckc :z-e 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 26.0 kg, and that of the boat is 45.0 kg. Ignore water resistance. The velocity of the boat ik -ez:r c1;ecys    m/s

  Calculate the force exerted on a rocket, given that the p.rumw ) t: jiz5lrbs 0idfd71;ropelling gases are expelled at u )zdi0r j5t7:dm;l1 r. bsfiwa rate of 1500kg/s with 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 af 4.qdk7vjme4l8g yjwd5 k-+ upparent breakaway for a touchdown is tackled from behind. When he was tackled by an 85-kg cornerback runni+758ly-4 jwfkmu j q 4kev.ddgng at 5.5m/s in the same direction, what was their mutual speed immediately after the tackle?    m/s

  A 12,600-kg railroad car travels alone on aleve,5qm)sh),nd ;vqbss v l frictionless track with a constant speed of 18m/s A 5350-kg load,initially at rest, is dropped onto the car. What will b,v ;sb5,qsvdnm h) q)se the car’s new speed?    m/s

  A 9300-kg boxcar traveling at 15m/s strikes a second boxcar at rest. The two swd -k 9cb:bvy)tick together and movbkb9)cy-dw: ve off with a speed of 6m/s What is the mass of the second car?    m/s

  During a Chicago storm, winds can whip 0 2a,x;rq26dccv bbmc 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, esti0bc 2cvdc,qmb;6ar x2mate 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 wieas z 7tqz,s8i2dp rj6 /e g83jdujs*fr .47weth a constant speed of 8.6m/s on a level trackqjep *gt e.7f8w/ddes7r4ji8 sz2sj,r azu 63. 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 min?$\approx$    m/s

  An atomic nucleus initially moving at 420m/s emits a6ec70ojyu5sivh: ssrb2*. bs ) t-q gin alpha particle in the direction of its velocity, and the remaining nucleus slows to 350m/s If the alpha particle haq 6ts:c2h5buii j)o. *bers -yg7vs0s s a mass of 4.0 u and the original nucleus has a mass of 222 u, what speed does the alpha particle have when it is emitted?    m/s

  A 23-g bullet traveling 230m/s penetrates a 2.07j 3yezu1ab t2-kg block of wood and emerges cleanly at 170m/s If the block is stationary on a frictionless surface when hit, how fast does it move after tubezy 32a7t1j he bullet emerges?    m/s

  A 975-kg two-stage rocket is traveling ac;krx6tu7f-s p, qpz7t 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 travbcqbt;s3d ix.y9 51kpeling in outer space with a velocity of 115m/s To alter its course bs 1txqck b9yd5b; 3.piy 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 d/cpgi,4qf)h 0.045 kg is hit off the tee at a speed of 45m/s The golf club was in contact with th4g )qfdih, /pce ball for $3.5\times10^{-3}$s Find (a) the impulse imparted to the golf ball,    kg*m/s
(b) the average force exerted on the ball by the golf club.    N

  A 12-kg hammer strikes a nail at a velocity of 8.5m/s and comec jw9 2ukz .q/kb5mcy6s to rest in a time interval of 8.0 ms. (a) What is the impuls/y9c . k jw5ukcmz6b2qe given to the nail?    kg*m/s
(b) What is the average force acting on the nail?    N

  A tennis ball of mass m=0.06kg and speed v=25m/s strikes a wall atga,jv q0 -yvh* 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 aumdu (gp * jx/(k7azi)ztomobile models. Cars are tested by smashing them into fixed, massive barriers at 50km/h (30 mph). A new model of mass 1500*)mx (izg7uk/a (pdzj kg takes 0.15 s from the time of impact until it is brought to rest. (a) Calculate the average force exerted on the car by the barrier. $\approx$$a\times10^5$N a =   
(b) Calculate the average deceleration of the car.    m/$s^2$

  A 95-kg fullback is running at 4m/s to the east and is stopped in 0.75 s qu0dqk;goh33 :fu wn0by a head-on tackle by a tacklerf3do h3k:nq;0 qugu0 w 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 o.5-bl l/7uqg qkyr6jvn 8+ t0d7x lesrn a tennis ball (mass 0.060 kg) points in the +x direction and is given bntq vuls +l0 /-7 d5 q8gl.rjky6xr7bey the graph of Fig. 7–33 as a function of time. Use graphical methods to estimate
(a) the total impulse given the ball    N*s
(b) the velocity of the ball after being struck, assuming the ball is being served so it is nearly at rest initially.    m/s

  From what maximum height can a 75-kg person jump witc:e9nqq (:a twhout 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 (that is, in breaking the fall). Assume the breaking strength (force per unit area) of bone tq(nw 9cae:q: 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 movpnuhtcz4x8mxm4wh2 wbf(j1uj50 .u-ing east (+x direction) with a speed of collides head-on with a 0.220-kg ball at rest. If the collision is perfectly elastic, what will be the speed andz tjc.uhn5 1w-wu0 xbpj24x fm84(hmu 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 3kmyy0ino72tv)f3n e 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, and let B represent the 0.900-kg pucn2 0kno)fey3y7mt v 3ik. v'$_A$ =    m/s ----待选择----eastwest  v'$_B$ =    m/s ----待选择----eastwest 

  Two billiard balls of equ7 qvt+,6rt0uhc4cshgx14 ss mal mass 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 theirs s,v01+647xmhrqc4h tu gsct 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, moving with a speed of 2.5m/s collides heagmnt m03h 6ya+d-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 represent0nay hg3+mtm 6 the 0.090-kg ball.)v'$_A$ =    m/s v'$_B$ =    m/s

  A softball of mass 0.220 kg that is moving with a speed of 8.5m/s collidenk67-7ir dhq ,m ,utq4c)kfbss head-on and elastically with another ball initially at rest. Afterward th-dk7nkqci tfrm6 , 74hbq)u,se 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 oneyz. m km(8:q5x*unlne6aiy y- 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 3.7m/5l yzanm6 8.(y*e: y-uk mnqxis 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 makesd 6w,kw h+syt6ogba+5qaa h.-v7p ns9ev.6dd an elastic head-on collision with a second ball initially at rest. The second ball moves off with halfvgd,69 spq +e6bkh.dasw 6 na d +a-ty5w.7ovh 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. 71zoy xpu*jb (pz-zt*ar.7p,u –35, and elastically strikes another cube at the bottom that is only one-half its mass. If the incline is 30 cm high and the table is 90 cm off the floor, where does each cube l7 .pozty1az*( -urubpj ,zpx *and? [Hint: Both leave the incline moving horizontally.]$\Delta x_{m}$$\approx$    m $\Delta x_{M}$$\approx$    m

ake the general case of an objecf 5jyndv4wl *+ i43 jv0ox izhrl0sc4/t 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, projectuz2cgjndeiad*1m7/) ;q5zw tile 1 results in a maximum height h of the pendulum equal to 2.6 cm. A second projectile causes the the pendulum to swd1nu5g7 wt*d /ia2qc) ej zzm;ing 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-kgk ugu*f3 r9/d uu4*(gf6 jkhlk pendulum hanging on a 2.8-m-long string, whichrug udk9hf k u3j6k*/lg4*fu( makes the pendulum swing upward in an arc. Determine the vertical and horizontal components of the pendulum’s displacement.vertical$\approx$    m horizontal =    m

(a) Derive a formula for the fraction of kini;xayjfo3w 5/ etic energy lost, $(\Delta\mathrm{KE/KE})$ for the ballistic pendulum collision of Example 7–10. (b) Evaluate for m=14g and M=380g

  An internal explosion breaks an object, initially at rest, into two pieces, sp0xh7 o4cfzs1 kr+ x+gx,eeb 6fj5cpa *g;9l 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 acquire? (Let A represent the heavier particle, and B represent the lightxp*oaxcf 1f,gxke sc 9+b;segl j+ 4p76 h0zr5er particle. ) KE'$_A$ =    J KE$_B$ =    J

  A 920-kg sports car lty bdn-u(q/ j;m,2znye 2v4nh s9vp: collides 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?uh;t:/qevl4jpn2b y 9, m2 yvzs (nnd-(Let A represent the sports car, and B represent the SUV) $\approx$    m/s

  A ball is dropped from a height of 1.5 tzuw-u;h5/ jr+ m1xsx0 m and rebounds to a height of 1.20 m. Approximately how many rebounds will the ball make before losing 90% of its enerw5j;-m uuz +xrh1xt /sgy?   

A measure of inelasticity in a head-on collision of two ob:k ug,r bm+yy vo5k4h-jects is the coefficient of restitutionh, k vguy:+ byokr5-m4, 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 matk0dq l-nsiwacw1 bc-1v tfyg083:6jd( 5c iqss of the other. A depression is made in both faces of the cut, so that a firecracker can be placed in it(t- lak650tb3 ddn1qv8i1c0 iwjwf :ysc-cgq 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 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 witd9jeg1du au7t: e-nk h09-bcz h a 10.0-kg object moving in the 9-9kt c07bn:ua-d edjhg1zue -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 secondbx2zs ,qzk ve y,1yvrc9 pc248 l,q*nk nucleus, an electron, and a neutrino. The electron and neutrino are emitted at right angles and have ke cs2z*b4lkx8y y c,nqv,zr92vq 1p,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 mass o0e kn1tdmn.5 $m_\mathrm{A}=0.400$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 tworu9uzqe1 2 5kzm oog-be1nz1 4 objects of equal mass, each having initial speed the two move off together with speed v/3 What was the angle between thub-o1moz reez k9 4u 1n12q5gzeir initial directions?    $^{\circ} $

  Two billiard balls of equal mass move at rig2lqi8w(x nr bo .:u8coht angles and meet at the origin of an xy coordinate system. Ball A is moving upward along the y axis at 2m/s and ball B is moving to the right along the x axis with speed 3.7m/s After the collision, assumed elastic, ball B is moving along the positive y axis (Fig. 7–37). What is the final direction of ball A and what are their two speeds? directi runi:w8co (xqb28o. lon 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 conz+(xg ) frzpsh;tf:9 llision with another atom at rest. After the impact, the neon atom tnf(t9;x:g spzfhr) +zravels away at a 55.6 $^{\circ} $ angle from its original direction and the unknown atom travels away at a -50 $^{\circ} $ angle. What is the mass (in u) of the unknown atom? [Hint: You can use the law of sines.](Let A represent the incoming neon atom, and B represent the target atom) $m_B$   u

  A neon atom (m=20u) makes a perfectly elastic collision with another4h uqa: o.o +*ppz /.n9s4bkcxkrqv+x atom at rest. After p uz c.k9s*xaq+p4 o/4h r:.bov+xqkn the impact, the neon atom travels away at a 55.6 $^{\circ} $ angle from its original direction and the unknown atom travels away at a -50 $^{\circ} $ angle. What is the mass (in u) of the unknown atom? [Hint: You can use the law of sines.](Let A represent the incoming neon atom, and B represent the target atom) $m_B$   u

  Find the center of mass of the three-mass system shown in Fig. 7–38. Specify rey)y:tsjl+p89s- bm jhlative to the left-hand 1.00-kgjm js+- :ytbh8)pys 9l mass.    m

  The distance between a car wfxg v8/qo3-sbon 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*j+ o-qr pnw1b is 2.50 m behind the front of the car. How far from the front of the car will the CM be when two peopwbo*+pj- r 1qnle 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 m, of mass 6800 kg, is used as a ferryboat wb0*vo7 zhj vo7z+i/e. If three cars, each of mas7z0v7*hvwe z ij+/obos 1200 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 hqog )9q ra.xk2hpdp1 : r::qi$l_0$,$2l_0$, and $3l_0$ are placed next to one another (in contact) with their centers along a straight line and the $l=2l_{0}$ cube in the center (Fig. 7–39). What is the position, along this line, of the CM of this system? Assume the cubes are made of the same uniform material. $X_{CM}$ =    $l_0$ from the  ----待选择----leftright  edge of the smallest cube

  A (lightweight) pallet has a load of identical cases of , lt0ma-u8 6wai;p u*i xludo2g 1fc 5v6(xlgitomato paste (see Fig. 7–40), each of which is a cube of length l. Find the center of gravity u(2 plocwi85u0gax 1lm -digutl aiv f,*6;6xin 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 rfm h;e9wc p/o-adius R cut out of it. The center of the smaller circle is a distance 0.80R from the center C of the larger circle, Fig. 7–41. What is the position of the center of mass of the plate? [Hint: Try subtraction.]e-cm ph fo/w9;   R

  Assume that your proportions are the same as those in Tabl5 pfh(x* zb*nhe 7–1, and calculate the mass of one of your p* hn bh5*zfx(legs.    kg

  Determine the CM of an outstretchey.r )qmfp(4 4y isob+bd 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 c9t +77crwpvfe l9ca.55hmys 4:x jeyan arm bent at a right angle. Assume that the person is 155 cm tas:veay yj5wc747 fe.hr9t5 +cx mpc9 lll. $X_{CM}$ =    cm $Y_{CM}$ =    cm

When a high jumper is in a position such that his armss7knm-*ubtdg 7 c) jf4 and legs are hanging vertically, and his trunk and head are horizontal, calculate how far below the t-d* kn)7ub jf mt74sgcorso’s median line the CM will be. Will this CM be outside the body? Use Table 7–1.

The masses of the Earth and Moox 9r +pu va/wvr-z3;( doc,xm0kpan6k n 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 frictionless ice. 1w t74h.g a+yhz1q34 vknwlpw
(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 cyl06i3m+:kcmah4d f 2bzq0hazh indrical head of mass 2.00 kg and a diameter 0.0800 m mounted on a uniform cylindrical handle of mass 0.500 kg and length 0.240 m, as shown in Fig. 7–42. If this mallet is tossed, spinning, into the air, how far above the bottom of the handle is the point that will follow: m2aq+m06af03bdhki4z hc zh a parabolic trajectory?    cm

  A mallet consists of a uniform cylindrical head of masse.+ntmsuiqp q;i :3o6*9p5rqw8 hyg v 2.00 kg and a diameter 0.0800 m mounted on a uniform cylindrical handle of mass 0.500 kg and length 0.240 m, as shown in Fig. 7–42. If this mallet is tossed, spinning, into the 69;yv w5qsmg 3o:n8.*htr+ipquepq iair, how far above the bottom of the handle is the point that will follow a parabolic trajectory?    d    d

  (a) Suppose that in E agh li)i9gt:z2 )4mf w2j:lqexample 7–14 (Fig. 7–29), $m_{II}$=3$m_{I}$ Where then would $m_{II}$ land?    d(Round to two decimal places)
(b) What if $m_{I}$=3$m_{II}$    d

A helium balloon and its gondola, of mass M, are in the air anet y0gw)fg ; n 6aimn2kls,vpai8 s w:v;54e+bd 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 s;k)80: 4a,g+i2atflipvy;g vb ewwmnn6e5s 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 z2-yp.owfza-+j suogn :ajf 6yb6(2o is popped straight up to a height of 55.6 m. If the contact time is 1.4 ms, calculate the average f:oazfob-g+us2j(.62 pfoa nwz y y j6-orce on the ball during the contact.    $^{\circ} $

  A rocket of mass m traveling with s*enxf5/v.:uo:j w* ruqr ef(k peed $v_0$ 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+zjk7l*j.wbz) nph+j cch4aes 78 al4 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 will c7z)hacsw bj+ jzh 4+nllj47ape*k8.also fall into a pocket? Give details.

  A 140-kg astronaut (including space suit) acquires a speed of 2.5masa ef8oldg3sab6,uu;yxg( 6 . +x +ry/s by pushing off with his legs from an 1800-kg spd, fl(ya;38esrgyx+6+a. asx6ogb uu ace 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 rest in oxorso, xnmf wut5q,z176 ( v 80qr*lsouter space. They then push each other apart. How far apart are they when r7ms o r,nov6xx(tfsz*0l8,wq51 qouthe lighter astronaut has moved 12 m?    m

  A ball of mass m makes a head-on elastic collision with a second ball (ata vwquxps ;y2g,1po13 rest) and rebounds in the opposite direction with a speed equal to one-fourth its original speed. What is the mass of the secw;yox1,p21 a 3usp qvgond ball? $m_B$ =    $m_A$(Round to two decimal places)

  You have been hired as an expert witness in a court case t u hpqs(6pm-*involving an automobile accident. The accident involved car A of mass 1900 kg which crashed into stationary car B of mass 1100 kg. The driver of car A applied his brakes 15 m before he crashed into car B. After the collision, car A slid 18 m while car B slid 30 m. The coefficient omt qpph 6us(*-f kinetic friction between the locked wheels and the road was measured to be 0.60. Show that the driver of car A was exceeding the 55-mph (90km/h) speed limit before applying the brakes.    mi/h

A golf ball rolls off the top of a flight of concrete steps of to;.y4xv1ca b uatal vertical height 4.00 m. The ball hits four times on the way down, each time striking the horizontal part of a different step 1.0 m lower. If all collisions are perfectly elastic, what is the bounce height on the fourth bounce when1yv xbua.a4c ; the ball reaches the bottom of the stairs?

  A bullet is fired vertically into a 1.40-kglg (0i,ec2zj k block of wood at rest directly above it. If the bullet has a mass of 29.0 g and a sp2(0 ,elkjzi gceed of 510m/s how high will the block rise after the bullet becomes embedded in it?    m

  A 25-g bullet strikes and becomes embeddes2i x 3jyx* kx-,sofx:rl/5jud in a 1.35-kg block of wood placed on a horizontal surface just in front of the gun. If the coefficient of kinetic friction between the block and the surface is 0.25, and the impact drives the block a distanc:l/o2xx ,s3x5s j -jfxkyuir*e 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 thed)u- m52bykzj1t1ktw other of mass 60 kg, sit in a rowboat of mass 80 kg. With the boat initially at rest, the two people, who have been sitting at opposite ends of the boat 3.2 m apart from each other, now exchange seats. How far and in what direction wilkzt2 m5-yu1jd1w)tk bl 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 wassp:j7 y* cdiv* 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 suddenw0om5a xgpeztl: q..ql2e l8:ly broken apart into two fragments by an explosion. One fragment acquires twice the kinetic energy of the other. What is the ratio of theire5e. lwax:zlt q28pl.0:qogm masses?   

  The force on a bullet is given by the formula F =ah0j7)c:j4shp v8 iyv 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 terc -xb5u(0 vi7sa-j $m_A$ = 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 dx; jm*w3)4. j*q-kjjmr k f4qzsszoq) ecays radioactively into an alpha particle and a smaller nucleus. What will be the speed of this recoiling nucleus if the speed of 3f4jxok)k* 4)sw-zrmj sq .jj mz*q; qthe 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) is8ul2dew qsw50uynnc43b/en ih8 i u+: 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 slides- 6xrznwu 3jk+ 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.ux/k pg2 /,fox 9udta m if it is to rebound from M, slide up the incline, stop, slide down the incline, and collide witdutf/x. 9 2 o/akp,uxgh M again?    kg (Let A represent mass m, and B represent mass M.)

  The gravitational slingshot effect. Figure 7–47 shows the planet S4 +xb o0(tzpo: bfvk,caturn moving in the negative x direction + b0o,:tb4zvpko xf(c 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