We claim that momentum is conserved, yet most moving objects eventually slow dow (;q o:m(m+fef-q2 ntvg kj5wnkm ;qgw tnf-oqe mn( 2+:fvj(5n and stop. Explain.

When a person jumps from a tree to the grhg cn80 kf86bmha1c2b ound, what happens to the momentum of the person upon striking the groundbn6h1gb8 m k8cah2fc0?

When you release an inflated but untief y-xfd4/6uzr d balloon, why does it fly across the room?dr6xuy /-fz4f

It is said that in ancient times a rich man with a bag ofvn;.)wqt m)xo7z 59jrfvglt. gold coins froze to death while stranded on a frozen lake. Becauog79 )w trn.ljv;. z)v5 qtfmxse the ice was frictionless, he could not push himself to shore. What could he have done to save himself had he not been so miserly?

How can a rocket chanx;5t jskc, bkv(n3rc :ge direction when it is far out in space and is essentially in b :;(cvk3sn5 ,xkc tjra vacuum?

According to Eq. 7–5, the longer the impact time of an impulse, the sx/v(7jb.r7wgox7 /8a bd, vju djh 74xhgfow0 maller the force can be for the same momentum change, and hence the smaller the deformation of the object on which the force acfjv(vbaj h7r /jxw/ 0x.7 u, b7gghd4x7 wdo8ots. 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 r-r,q8vbik liox2q.0-xcz ffo n8l)) to withstand collisions. Today, though, cars are designed to have “crumple zones” that collapseifn)2vr8r-lo c)x 0.qoq i-,zf8k bxl upon impact. What is the advantage of this new design?

Why can a batter hit a pitched baseball further than a ball toxfb k;:i-*nb sqhf0. : 2eq3ogywx*zussed in the air by y.z k2x fhobn;f3: x0sw:-*u*bi gqqethe batter?

Is it possible for an object to receive rw;/ v qydx0*+lanw:c a larger impulse from a small force than from a la:wx0rcn/+vd qwal y;* rge force? Explain.

A light object and a heavy object have the same kinetic energy. Whi g 3uph9i2f(j-aa el+wch has the greatepel +fg 2u3a9jwi a(-hr momentum? Explain.

Describe a collision in which all kinetic energy is lostr5;pp ;z1dzfrsaro82 .

At a hydroelectric power plant, water is 1n ql cd*xl.5ily6*z2h.lms 7tfqub f6no; i8directed at high speed against turbine blades on an axle that turns an electric generator. For maximum power generation, should the turbine blades be de6lcul fh7 5n.dt lyioibs.61n;8*z *f lm2qxq signed so that the water is brought to a dead stop, or so that the water rebounds?

A squash ball hits a wall a,q/ueqo j po(a0:nd-e58kkad t 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 onto a hard steel plate (fixe. -n4qi0wr wu)szwg4z; zc1p td 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, duringz) ;4prwzw-q14g uns 0c tw.zi 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 b.z:j1v c0e+9 chtd oolackward when carrying a heavy load in your arms?

Why is the CM of a 1-m length of pipe at its mid- (*skr qxrsc5570e.0do/4j*v iimt3juyk srxpoint, whereas this is not true for your arm or* *jjxdr55i4sor 0t/kykiq.x 7 escs03vmr(u leg?

Show on a diagram how your CM shifts when you chanl09jyp)ol 5ac6m 9 tzfge from a lying position to a sitting po99ctl jlpoy56) 0 azmfsition.

If only an external force can change the momentum of the center of mass of an 1b2gp41o t 4t:cbx ubaobject, how can the interobp 41uxa:gc12b 4tbtnal force of an engine accelerate a car?

A rocket following a parabolic path through the airajdp+df5uytb.g,xxd 7 s1;1 o suddenly explodes into many pieces. What can you say about the motion of this systep,at xd1d1y; gou7+ xds5j. fbm of pieces?

  What is the magnitude of the momentum of a 28-g sparrow flying with a s;gw:orkkt21jcj bv+ cu5y ;u)h 1epy9peed 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 isu( )l pn 6gdpa/9omz(y the skier’s change in velopoyudmgp/9lz ( an)6(city?    m/s

  A 0.145-kg baseball pitched at 39 m/s is hit on a horizo+wjndcoek)5j.at + -z ntal line drive straight back toward the pitcher at 52m/s If the cont t kanj-c+)ej d+.owz5act 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 6 7j7fqpxr n+1p.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, a1xrfj77q ppn+nd 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 exp.w73 -ux6c vyzx.mzby elled at a rate of .y637xym -cbxuzwz.v $1500 \; kg/s$ with a speed of $ 4\times10^{4 } \; m/s$ (at the moment of takeoff). F =    $\times 10^7 \; N$

  A 95-kg halfback movinh 4 hbvp7z25 4zzkqp6ag at $4.1 \; m/s$ on an apparent breakaway for a touchdown is tackled from behind. When he was tackled by an 85-kg cornerback running at $5.5 \; m/s$ in the same direction, what was their mutual speed immediately after the tackle?    $m/s$

  A 12,600-kg railroad car travels alone on alevel frictionle:lxyksif3j0l g 2,/ dkv6rq; hss track with a constant speed of 18m/s A 5350-kg load,yx0;l,sh6vf dk r2 qk:/j3lgiinitially at rest, is dropped onto the car. What will be the car’s new speed?    m/s

  A 9300-kg boxcar traveling atgc8qo-s4 5 mxp $15 \; m/s$ strikes a second boxcar at rest. The two stick together and move off with a speed of $6 \; m/s$ What is the mass of the second car?    $m/s$

  During a Chicago storm, winds can whip horizontally at speeds of 100km/h If nv plnr)) e:cns)pn4*;*lg 6fauya(tthe 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 a)4pl*v:ntcl(af)nngy* u6); e ns prand 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 carqoi)8u(rx* 6a )jz9q/djgdaiq l0q+ p coasts along 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 /p 86djo uqi)0(l* 9j qgarid +qax)zqwith the tracks, what is the speed of the car after 90.0 min?$\approx$    m/s

  An atomic nucleus initially m0r2 b9s+d5)y )3n)6 cmpftwx7ito3uvrtmd s v oving at 420m/s emits an alpha particle in the direction of its velocity, and the remaining nucleus slows to 350m/s If the alpha particle has a mass of 4.0 u and the ort3c)s wv+vi6 )0unstdf prymdm x52t 39)rob7iginal 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 zvd -0q x;br/ qbpc8+hil74qx.l0mhp2.0-kg block of wood and emerges cleanly q.bzlp 8 lhidvm+ qp bx/-h07r4qc;0 xat 170m/s If 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 traveling ivscf/z/24xjkq/ ja/kvhe/7 at a speed of $5.80\times10^3\mathrm{~m/s}$ with respect to Earth when a pre-designed explosion separates the rocket into two sections of equal mass that then move at a speed of $2.20\times10^3\mathrm{~m/s}$ relative to each other along the original line of motion. Let “A” represent the upper stage (that moves away faster) and “B” represent the lower stage.
(a) What are the speed and direction of each section (relative to Earth) after the explosion? $v'_A$   m/s  ----待选择----away from the Earthtowards the Earth  $v'_B$   m/s  ----待选择----away from the Earthtowards the Earth 
(b) How much energy was supplied by the explosion? [Hint: What is the change in KE as a result of the explosion? $a\times10^8$ a =    J

  A rocket of total mass 3180 kg is traveling in outer space with a vedhj0y5cf v8fo.u y o ww0;0y4zlocity of 115m/s To altew;wf djzfvo0y .uy08yo05ch 4r 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 xvu6cay 5un80The golf club was in conta cv a8uxyn60u5ct with the ball for $3.5\times10^{-3}$s Find (a) the impulse imparted to the golf ball,    kg*m/s
(b) the average force exerted on the ball by the golf club.    N

  A 12-kg hammer strikes a nail at a velocity of 8.5m/s and comes t.acl8hogj4 vjdm: pmlf y7 0a 4y1i+s+o rest in a time interval of 8.0 ms. (a) What is the impulsea0i:op74d8c l +4 h1lym.fmvjs+y ag j given to the nail?    kg*m/s
(b) What is the average force acting on the nail?    N

  A tennis ball of mass m=0.06kgdk s3 7og(p,dbjgb7v ) and speed v=25m/s strikes a wall at a 45 $^{\circ} $ angle and rebounds with the same speed at 45 $^{\circ} $ (Fig. 7–32). What is the impulse (magnitude and direction) given to the ball?   kg*m/s to the  ----待选择----leftright 

  You are the design engineer in charge of the 29h)blv/21nmnwd jvvg 95 xvw1 sq j)gcrashworthiness 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 0.15 s from the time of impa bnx vw)15j )wjv9 mhdvn9 v22ql/1ggsct 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 stodb,pc6n lf :q.fa-2coga *jv3 pped in 0.75 s by a headca.36- coan* vd:2fglpj,qf b -on tackle by a tackler running due west. Calculate
(a) the original momentum of the fullback    kg*m/s
(b) the impulse exerted on the fullback    kg*m/s
(c) the impulse exerted on the tackler,    kg*m/s
(d) the average force exerted on the tackler.    N

  Suppose the force acting on a tennis ball (mass 0.060 kg) poin fo0va5e2vkf:e 4ivq4cf5oks3da l+ :ts in the +x direction and is given by the graph of 5+sako fqa4 lvoe2id 0 ce5:4v:3ffkvFig. 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 op wvyjd*( +*0amchz7breaking 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, iyp70(hv c*mw+z*aod jn 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 collides/h- 5c- f3mi x/rnsc ,v:emlxy head-on with a 0.220-kg ball at rest. If the collision is perfectly elastic, when rm fy i/h3mcs/-lv:c5-,xx at 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 has a headpnh s2d;5t3c7u hmm3j-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 0uh ;7mst md3 np3chj25.450-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 perfectlyfg imj6;xw(w) elastic head-on collision. If one ball’s initial speed was 2m/s and the other’s was 3m/s in the opposite direction, what will be their speeds after the collision?(Let A represent the ball moving at 2.00 m/s, and call that direction the positive direction.Let B represent the ball moving at 3.00 m/s in the opposite direction. x;j wif6g )(mw) v'$_A$ =    m/s v'$_B$ =    m/s

  A 0.060-kg tennis ball, moving with a speed of 2.5m/s colli qa9)fkv ;xaq 65uy9wides 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 0.090-kg ball.f5qxwu9i a6y qa)9v ;k)v'$_A$ =    m/s v'$_B$ =    m/s

  A softball of mass 0.220 kg that is moving with a +fvpppt7/5rhm7-: +logqjwy speed of 8.5m/s collides head-on and elastically with another ball initially at rest. Afterw/ lvp7j+-rf my:pphqgo+75 tward the incoming softball bounces backward with a speed of 3.7m/s Calculate
(a) the velocity of the target ball after the collision    m/s
(b) the mass of the target ball.    kg
(Let A represent the moving softball, and let B represent the ball initially at rest.)

  Two bumper cars in a7 so0*dzwvxb *aawm-6n amusement park ride collide elastically as one approaches the m7avw* 06dx -awbzos*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/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 ma o k t-;.4qhyfy*lcfg2b)z 9jukes an elastic head-on collision with a second ball initially a l o-u2tq cgky)f 9*bfhzj;y.4t rest. The second ball moves off with half the original speed of the first ball.
(a) What is the mass of the second ball?    kg
(b) What fraction of the original kinetic energy $(\Delta\mathrm{kE/KE})$ gets transferred to the second ball?   

  In a physics lab, a cube slides down a frictionless incline as shown in Figlny.t,/y:zfme b : jl*. 7–35, and elastically strikes another cube at the bottom that is only one-half its mass. If the in t*,elm y: nz/:l.yfbjcline is 30 cm high and the table is 90 cm off the floor, where does each cube land? [Hint: Both leave the incline moving horizontally.]$\Delta x_{m}$$\approx$    m $\Delta x_{M}$$\approx$    m

ake the general case of an object k7q h,j3xgxn(a fb a27of 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 exper2 xu)8-*kmlb dvn6plm*so uh.9 qw8qhiment, projectile 1 results in a maximum height h of the pendulum equal to 2.6 cm. A second projectile causes the the pendulum to swhv98 u 6d2qb *mq.wo)m8uls*nlh-kx ping twice as high, $h_2=5.2\mathrm{cm}$ The second projectile was how many times faster than the first? $v_1$ =    $v_2$ ([color=rgba(0, 0, 0, 0.85)]Round to three decimal places)

  A 28-g rifle bullet traveling 230m/s buries itself in a 3.6-kg + 8vm4ggyxzh ,pendulum hanging on a 2.8-m-long string, which makes the pz 8+gv,h4yg xmendulum 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 kinetic energy5njx6,/ks iwk 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, oxt bl9x/*wv- gne of which has 1.5 times the mass of the other. If 7500 J were released in thex*g tv9bwx l/- explosion, how much kinetic energy did each piece acquire? (Let A represent the heavier particle, and B represent the lighter particle. ) KE'$_A$ =    J KE$_B$ =    J

  A 920-kg sports car colli)3)z zkeb ixn0zg,/* z j:wmzudes 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 n z e*, zik0)j3ugx:w)zbzmz/ 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/)fsqy9za j0a 1.20 m. Approximately how many rebounds will the ball make before losing 90% of it ja/)z90fqysas energy?   

A measure of inelasticity in a head-on collision of two objects is the coefficiy7a0f9bkg tm3 ent of restitution, e, define 37fgmtkya9b0d 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 witn9sv+a7ugyb z83ck)-+xzmf m h 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 setbsy+mgav79 3m+ zk 8-nf zuc)x 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 directiz83s7l e-: o. 3yv7pg +sqzxkoh.iklwon at 5.5m/s collides head-on with a 10.0-kg object moving in the -x direction at 4m/s Find the final velocity of each mass lh3zkl7xg s. ysvwo zkpq3i7-.:8eo+ 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, and*k/lmv0jhjzy w4q36mt,.xh; scm h*c a neutrino. The electron and neutrino are emittexwtk/6jm0yc .,hm4* ; sqv3lhz*hmj cd at right angles and have momenta of $9.30\times10^{-23}kg\cdot m/s$ and $5.40\times10^{-23}\mathrm{~kg}\cdot\mathrm{m/s}$ respectively. What are the magnitude and direction of the momentum of the second (recoiling) nucleus?    $ \times10^{-22}$    $^{\circ} $ from the momentum of the electron

  An eagle ($m_{\mathrm{A}}=4.3\mathrm{kg}$) moving with speed $\nu_\mathrm{A}=7.8\mathrm{~m/s}$ is on a collision course with a second eagle ($m_{\mathrm{B}}=5.6\mathrm{kg}$) moving at $\nu_{\mathrm{B}}=10.2\mathrm{m/s}$ in a direction perpendicular to the first. After they collide, they hold onto one another. In what direction, and with what speed, are they moving after the collision? v =    m/s $\theta$ =    $^{\circ} $ rel. to eagle  ----待选择----AB 

  Billiard ball A of masswvrtcu 63/-,vuz 4*x rdcm lo+ $m_\mathrm{A}=0.400$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 ozdjq: ;)p(hj ihw)vl+bjects of equal mass, each having initial speed the two mo +(j djhv)i:wzl ;qhp)ve off together with speed v/3 What was the angle between their initial directions?    $^{\circ} $

  Two billiard balls of equal mass move at right angles and meet at the origin plabht8-wa 8/g hy0l;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 8wag ;h lyp8b0/l tha-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? 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 atnpzb.;1hz 4vlc r6 /giyyg 4;yom at rest. After thp;b;vzc4z4 i g.1 yl/nh6 ryyge impact, the neon atom travels away at a 55.6 $^{\circ} $ angle from its original direction and the unknown atom travels away at a -50 $^{\circ} $ angle. What is the mass (in u) of the unknown atom? [Hint: You can use the law of sines.](Let A represent the incoming neon atom, and B represent the target atom) $m_B$   u

  A neon atom (m=20u) makes a perfectly elastic collision wit1s. mli bbv d3dfsu/-4hr ui.qm1)bh*h another atom at rest. -hsqirm1i/vsbuf. 1hlb. )*43mb dudAfter 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 shzx2gbl (hbgza 5d;h;6 ,,tb obown in Fig. 7–38. Specify relative to the left-hand 1.00-kg b lb dhhb;g,gzb,xt(zo6 a52; mass.    m

  The distance between a carbon ats-*.e)ydh l dfk1fvc( om ($m_{\mathrm{C}}=12\mathrm{u}$) and an oxygen atom ($m_{\mathrm{O}}=16\mathrm{u}$) in the CO molecule is $1.13\times10^{-10}$m How far from the carbon atom is the center of mass of the molecule?    $\times10^{-11}$m

  The CM of an empty 1050-kg car is 2.50 m behind li8 bhd-:q8pz 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 front of the car, and three people sit in the back seat 3.90 m from the front? Assume that each person has 8hl-ipzd8:q ba mass of 70.0 kg.    m

  A square uniform raft, 18 - asfd0+-apw+ umwl; dm 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 codws 0 d++a a;umlw-f-prners, determine the CM of the loaded ferryboat.$X_{CM}$ =    m $Y_{CM}$ =    m

  Three cubes, of sidesdl3yv/sw:qd kd -c;)azkj+4 : kv uy erv(,hp7 $l_0$,$2l_0$, and $3l_0$ are placed next to one another (in contact) with their centers along a straight line and the $l=2l_{0}$ cube in the center (Fig. 7–39). What is the position, along this line, of the CM of this system? Assume the cubes are made of the same uniform material. $X_{CM}$ =    $l_0$ from the  ----待选择----leftright  edge of the smallest cube

  A (lightweight) pallet has a load of identical cases of tomato paste (see Fig.g*c1 yf ct09er 7–40), each of which is a cube of lenr9* 0fc1 gtcyegth 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 radm1lipzd2tk0 1 ius 2R has a circular hole of radius R cut out of it. The center of the smaller circle is a distance 0.80R from the center C ofizp mkd 1l201t 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 the same as those in nog4uj5ehs n+a9* (pmTable 7–1, and calculate the mass of one of your5 *+sgae(npmun 9 jo4h legs.    kg

  Determine the CM of an outstretched arggg-m0vzpj)*pv tc/ 1 m 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 olhw rf5 a5(mb4n9*sjhf the CM of an arm bent at a right angle. Ass*hal(ws nb49h55rjf mume that the person is 155 cm tall. $X_{CM}$ =    cm $Y_{CM}$ =    cm

When a high jumper is in a posi* z;xf)0ccybq 7ng kfh )qzs(/tion such that his arms and legs are hanging vertically, and his trunk and head are horizontal, calculate how far below the torso’s median line the CM will be. Will this CM be outside the body? Usk*ynqf;q7sg xfc(z z0/bc )h)e Table 7–1.

The masses of the Earth and M duf* c psio8u/)4ar3sj).ktfoon 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 frictionoesm70h cx-n.less ice.
(a) How far from the woman is their CM?    m from the woman
(b) If each holds one end of a rope, and the man pulls on the rope so that he moves 2.5 m, how far from the woman will he be now?    m
(c) How far will the man have moved when he collides with the woman? He has moved    m from his original position

  A mallet consists of a uniform cylindrical head of mass 2.002j6j- idjwtwnoot(25 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 oojwd62 n2jtjwt-(5oif the handle is the point that will follow a parabolic trajectory?    cm

  A mallet consists of a uniform cylindrical head of mass 2.00 kg and a diameq u)b ;+ux1mp6twemtk )fqe6 (ter 0.0800 m mounted on a uniform cylindritmqf)wemu +et( x6;b6k)q 1pu cal handle of mass 0.500 kg and length 0.240 m, as shown in Fig. 7–42. If this mallet is tossed, spinning, into the air, how far above the bottom of the handle is the point that will follow a parabolic trajectory?    d    d

  (a) Suppose that in Exle66 b(angz 4;ep :*sbzf hcl(ample 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 and stationa+t5 f7px2 uq pzv1et-bgxp:2 rry 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 the balloon then mov pbex-x:u72 frg1p+2 vtq5 pzte? What happens if the passenger stops?

  An 0.145-kg baseball pitched horics18x;lo/ v r1;hvdak zontally at strikes a bat and is popped straight up to a height of 55.6 m. If the contact tim l;1vaxd /vhc;sokr 81e is 1.4 ms, calculate the average force on the ball during the contact.    $^{\circ} $

  A rocket of mass m travelingckb7-8 o)oizq1g vcws0vs 66k-v ue0r 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 the corner pocket shot shown in Fig. 7–43. 6i i+*lht1okp(; e8pof 2ugvgRelative dimensions are also shown. Should the player be worried about this being a “scratch shot,” in which the cue ball will au o+eg( il1;p6ht2ogip* vf8k lso fall into a pocket? Give details.

  A 140-kg astronaut (including space suit) acquires a speed of8*pzo+ku2,l5kbh tr k 2.5m/s by pushing off with his legs from an 1800-+u z2pk8l tro*k5hk, bkg 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 initialb5wd9*-ea*c67x ia:r p l dakuly at rest in outer space. They then push each other apart. How far ap9akxa*p-75d :6 ulwrdbeaci *art are they when the lighter astronaut has moved 12 m?    m

  A ball of mass m makes a head-on elastic / uwygyt42u7k le6v1fcollision with a second ball (at rest) and rebounds in the opposite direction with a speed equal to one-fourth its original speed. What is the mass of tht k2 uuw 4fevg/yly716e second ball? $m_B$ =    $m_A$(Round to two decimal places)

  You have been hired as an er:. os 9b)mk.kbzp+oc xpert witness in a court case 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 s m..kb)o9s+krcz b p:olid 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 fl77bapl uf8gla+gekr 74p1n yc1ls 2*light 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 different step 1.0 m lower. If all c+cl*s2uga1 k47 pg yefnab78 1llrp 7lollisions 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 wood q6u/y q:6thds 9t*bun 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 thstthu9/dnyq 6* :bq u6e bullet becomes embedded in it?    m

  A 25-g bullet strikes and becomes embedded in a 1.35-kg block oebwfq, bwz ,y9 co.bi3;4i2vtp (:c+svt z 3ctf wood placed on a horizontal sur stc oewtibv34b;+zp( ycqw, 3:zt2 ,v i.f9cbface just in front of the gun. If the coefficient of kinetic friction between the block and the surface is 0.25, and the impact drives the block a distance of 9.5 m before it comes to rest, what was the muzzle speed of the bullet?    m/s

  Two people, one of mass 75 kg and the other of mass 60 kci n9pd)+ pd5njytu;cj-c, lnf33-cxzlan4:g, 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 direclt:-fn33p;n5x jz)junc-n + c4dpdi cac9,yltion will the boat move? The boat will move    towards the initial position of the 75 kg person(Round to two decimal places)

  A meteor whose mass was ab k5 u49tch8qilout $ 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 twop5qtq s:cnqp i6y)g/; fragments by an explosion. Otq5pynigq:c ;p 6s/)q ne fragment acquires twice the kinetic energy of the other. What is the ratio of their masses?   

  The force on a bullet is given by the fl0chxdze+z c3xk06 +r ormula 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 v ;a*mdf0t3 f(,h tzbj.lz*bp$m_A$ = 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 d09s(sj j n u-3pekh+piecays radioactively into an alpha particle and a smaller nuci(j0p 9sh uns3- p+kjeleus. What will be the speed of this recoiling nucleus if the speed of the alpha particle is $ 3.8\times10^{5 }$m/s Assume the recoiling nucleus has a mass 57 times greater than that of the alpha particle.    m/s

  A 0.25-kg skeet (clay target) is fired at ub /hjfzajh9ub1a x 9 p1)vnv*z-7+jpan 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 slc 4u6h m u6cqz6nqcz+;xjie*1c hs6;mides 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 ix(h vl+g mec6.f it is to rebound from M, slide up the incline, stop, slide down the incline, and collide with M againehv+clm .x( 6g?    kg (Let A represent mass m, and B represent mass M.)

  The gravitational slingshot effect. Figure 7–47 shows the planet Sa(8ns y( y2nhtot/duxp*o wa3+turn moving in the negative x direction at tyx( +opnd8/ o2w ht*yua(n s3its 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