We claim that momentum is conserved, yem:puj v96zgf -t most moving objects eventually slow downpj9v6zm-uf : g and stop. Explain.

When a person jumps from a tree to the ground, what happens to the momentum o*75mrs. of7cncol:j470a2f r b ye mt/5cq jgof the person upon str2j5/j0trocy l ns.7b mqe7c57mfo* agr:4cofiking the ground?

When you release an inflated but untied balloon, why does it q6- gj9+inrzkp90 j pcfly across the room?j-r6kc 9zpq9 0pijg+n

It is said that in ancient times a rich man with a bag of gold coins 0f)jpl g3xcy.froze to death while stranded on a frozen lake. Because the ice was frictionless, he could not push himself to shore. What could he have done to save himself had he not0pgjfy x)lc.3 been so miserly?

How can a rocket change direction when it is far out in space andro(k/qio z)u077au ru is essentially in u0o) 7zu/ar7kuroq i(a vacuum?

According to Eq. 7–5, the longer the impact time of an impulse, the smc7 a: kog2rrzr+k0b*pfn: *lkaller the force can be for the same momentum change, and hence the smaller the deformation of the object on which the force act2l: gf0p*rkck z*k n+obarr:7s. On this basis, explain the value of air bags, which are intended to inflate during an automobile collision and reduce the possibility of fracture or death.

Cars used to be built as rigid as possible to withstand collisions. Today, thg (vk)0ix.skver v-;hough, cars are designed to have “crumple zones” that collapse upon impact. What is the advantage of this new i.hrx e vk) kv(vg0;s-design?

Why can a batter hit a pitched baseball further than a b /4jxr/o3vx fjv9l(jms4os mw2 k*d2t all tossed in the air by the batter?jvss t2(v k*/4/wl9d34 m fomjjx oxr2

Is it possible for an object to rec b t+tu5 m402znrh-b-tcc nef9eive a larger impulse from a small force than from a large force? Explarhft -u 4c9tbbz+ 2c5nn- 0temin.

A light object and a a zqkk0;qh+d;v sh a:*heavy object have the same kinetic energy. Which has the greater mom0;ha dah+*:k;szv qkqentum? Explain.

Describe a collision in which all kinetic energy is lo* fnso-32 8x5*sswg;r7siw a5ywfxonst.

At a hydroelectric power plant, water is directed at high speed against h) j:ih115gpm7ouglah ( pox ss2 7h4bturbine blades on an axle that turns an electric generator. For maximum power generation, should thh hb a) x o154 ggl7hup:p2h7jsism(o1e 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 w x:(k t wc.i8xd)g-ph2 ba tta3j.u0xcall at a 45 $^{\circ} $ angle as shown in Fig. 7–30. What is the direction (a) of the change in momentum of the ball, (b) of the force on the wall?

A Superball is dropped from a height h onto a hard steel plate (fixed to the nb/ /qpg1v9dp5 /hmxym2,pws 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 s5vmp /x,bg pwy9/mhnq /12dpof putty that falls and sticks to the steel plate.

Why do you tend to lean backward when carrying a heavy load in your arms?5nb,sby2tf*lyk2p.. bv 8eu a

Why is the CM of a 1-m length of pipe atj.8x6p2 btscgebbb3yl+g:x 2 its mid-point, whereas this is not true for your arm or x6tb8 :y+ x2lbeg cpsb.b3jg 2leg?

Show on a diagram how your CM shifts when you change from a lyivu2fu;rlf8 6 f4a y1ixm-nvt5 ng position to a sitting pof54xvyf; 2 fl18-nr 6tuviamu sition.

If only an external force can change the momentupd n6:s tuq6*tm of the center of mass of an object, how can the internal 6p* tu tn:6dsqforce of an engine accelerate a car?

A rocket following a parabolic path through the air sd9 w(m- ; ptib5khy*ebuddenly explodes into many pieces. What can you say about the moty pw 5-e*tbd;9mhikb( ion of this system of pieces?

  What is the magnitude of the momentum of a 28-g sy8vj/ su; fnm3ly,c-hqzhrwu.;ou.0l pf,r 3 parrow flying with a speed of 8.4hvynu80f/ y3wm,rr, h solu-cpuz jl.q.; ;f3 m/s    $kg\;m/s$

  A constant friction force of 25 N acts on a 65-kg skier for 20 s. What is the sk mnuh1ssr .y*7ier’s change in vel1nyh7 sm su.*rocity?    m/s

  A 0.145-kg baseball pitched at 39 m/s is hit oenyon29 ht.b+4 nfpt8n a horizontal line drive straight back toward the pitcher at 52m/st bo4yp ef8+.9th2nn n 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 6.40-kg package out hor) s 0s bm+pok qez,wgzw()t7/sizontally with a speed of 10 m/so0 + zqwtzgwbs/ me())p k,7ss Fig. below Calculate the velocity of the boat immediately after, assuming it was initially at rest. The mass of the child is 26.0 kg, and that of the boat is 45.0 kg. Ignore water resistance. The velocity of the boat is    m/s

  Calculate the force exerted on a rocket, given that the propelling gases are lc8- 22w :uqykupg-v uexpelled at a rate of 1500kg/s with a speeypuuwu 2l8: 2 kc--vqgd of $ 4\times10^{4 }$ (at the moment of takeoff).$a\times10^7$ N a =   

  A 95-kg halfback moving at 4.1m/s on an apparent breakaway fn ofj ttkl7/*9or a touchdown is tackled from behind. When he was tackled by an 85-kg cornerback running at 5.5m/s in the same direction, what was their mutual*lt/j tfnk 7o9 speed immediately after the tackle?    m/s

  A 12,600-kg railroad car travels alone on alevel frictionless track with a constjge:bf/8t jxszrady79xct9u9 zt s l8(. bh 28ant speed of 18m/s A 5350-kg load,initially at rest, is dropped onto the car. What w9c: z fjatsxt7gebb8( hlx t9d.j28sy 8z9ru/ill be the car’s new speed?    m/s

  A 9300-kg boxcar traveling at 15m/s sg (fbuh, ,u.2ho8lifze v,.x rtrikes a second boxcar at rest. The two stici f(ogh.r,,b eh8lz.xuv 2 ,ufk together and move off with a speed of 6m/s What is the mass of the second car?    m/s

  During a Chicago storm, winds can whip horizontally)q dl7.4 (iqsfh z7oaz at speeds of 100km/h If the air strikes a person at the rate of 40kg/s per square meter and is brought to rest, estimate the force of the wind on a person. Assume the person is 1.50 m high and 4) z .qoqhlda77z(fis 0.50 m wide. Compare to the typical maximum force of friction $\mu\approx1.0$ between the person and the ground, if the person has a mass of 70 kg.    N
$F_{on person}$  ----待选择----<> $F_{fr}$

  A 3800-kg open railroad car coasts along with a constant speed of 8 o6e((jd2c:( dx+lojqrj h e xgyud(59.6m/s on a level track. Sn(ux2g( o(hq5j69d(crjjeyol :ed d +xow 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 an alpha particle in *m :spcp+libj3 m6nhjt2;;3xirhvp* the direction of its velocity, and the remaining nucbr*;tp6j;slvic j+pph x3n h32 *m:m ileus slows to 350m/s If the alpha particle has a mass of 4.0 u and the original nucleus has a mass of 222 u, what speed does the alpha particle have when it is emitted?    m/s

  A 23-g bullet traveling 230m/s penetrates a 2.0-kg block of wood and emefv2tq:e /n3bhf +m-r xs.7 mpbrges cleanly at 170m/s If the block is stationary on a frictionless surface when2/ f btv7-nmf:sme.b h+p3qrx hit, how fast does it move after the bullet emerges?    m/s

  A 975-kg two-stage ro*wv)mxxtsz e8) (2eniszwt 45cket is traveling 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 tra4*1uh wttl+rchr1yuc 8p ve55veling in outer space with a velocity of 115m/s To alter i*ry551 tc8euruwh +p41h vclt ts 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 -8raofxd/-zkhzi2+b u ghu qw(;yb 69tee at a speed of 45m/s The golf club was in cont6d(z 9 io hx8-h -rk2+bfauug/qzy bw;act with the ball for $3.5\times10^{-3}$s Find (a) the impulse imparted to the golf ball,    kg*m/s
(b) the average force exerted on the ball by the golf club.    N

  A 12-kg hammer strikes a nail at a velocity of 8.5mk*mt1+2xb+ qnzl ffg8 /s and comes to rest in a time interval of 8.0 ms. (a) What is the impulse given to the nail?kg+ blqt2z8x +* f1mnf    kg*m/s
(b) What is the average force acting on the nail?    N

  A tennis ball of mass m=0.06kg and speeds7 wic0ih(9wyp wan/yei)z 67 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 chargnvf *f/+wz: cce of the crashworthiness of new automobile models. Cars are tested by smashing them into fixed, massive barriers/fw :*cc nv+zf at 50km/h (30 mph). A new model of mass 1500 kg takes 0.15 s from the time of impact until it is brought to rest. (a) Calculate the average force exerted on the car by the barrier. $\approx$$a\times10^5$N a =   
(b) Calculate the average deceleration of the car.    m/$s^2$

  A 95-kg fullback is running at . gbyy(m h320afn0gfx4m/s to the east and is stopped in 0.75 s by a head-on tackle by a tackler running due west. Calcunyygf af(ghb23m.x0 0 late
(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 bwjhnfk2*ss je0q1xy qr+a l-b6 a :(;ball (mass 0.060 kg) points in the +x direction and is given by the grq:s f+lyq xb6nbej;hsw-0aj12 ka (r*aph 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 break9//gn/zrjgcx 0hzv 0t uw.ck/ hva 6tdef1 :h1ing 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 stc/z:tk 0h.gjhhv0 vd9 1xgc/e/ fa6w 1tunr z/rength (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) w k7o*uk/vgk8b sf:c5 eith a speed of collides head-on with a 0.220-kg ball at rest. If the collision *e k:fo5v/ sug8c7bkk is perfectly elastic, what will be the speed and direction of each ball after the collision?Let A represent the 0.440-kg ball, and B represent the 0.220-kg ball. $v'_A$    m/s  ----待选择----eastwest  $v'_B$    m/s  ----待选择----eastwest 

  A 0.450-kg ice puck, moving east with a speep 9w5 /orvfdip f2n8(wd 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 pu2f/f(5 w8ppi9do nrwvck, 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-on collisig2y/ 76k pfjizon. 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 colj/fg yz7pi 2k6lision?(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 7wpw*7r fd0lhwith a 0.090-kg ball initially moving awfdwp707 wr*h lay 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.)v'$_A$ =    m/s v'$_B$ =    m/s

  A softball of mass 0.220 kg that is moviotxo3g8h0j6 g ng with a speed of 8.5m/s collides head-on and elastically with another ball initially at rest. Afterward the incoming softball bounces backwardohg 8gt03j x6o 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 gp.gka myz/ vst p0q*x( *-aygtd(;3p as one approaches the otg(qkagd ;*y-t/xm0 z sv.tp * p(agpy3her 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 makes a5d dx,t+yj2in4 pn-p z:s6jitj; u3am n elastic head-on collision with a second ball initialnjmn+a;udy-x2iz 3:4t t5jjpd,p6i s ly at 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 slidesc (6xahtatsj-cz,u eq ( xt:;2 down a frictionless incline as shown in Fig. 7–35, and elastically strikes another cube at the bottojt 6uqat:;e(t(-,h2xxazscc m that is only one-half its mass. If the incline is 30 cm high and the table is 90 cm off the floor, where does each cube land? [Hint: Both leave the incline moving horizontally.]$\Delta x_{m}$$\approx$    m $\Delta x_{M}$$\approx$    m

ake the general case of an object of 0f 5a1w wvegic( fesbo343*7z5hz cqgmass 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 erdd0p 7h a8tmogw ( zjod)13m6xperiment, projectile 1 results in a maximum height h of the pendulum equal to 2.6 cm. A second projectile causes the the pendulum8td6)jahd z pmom7ro(01wg 3d to swing twice as high, $h_2=5.2\mathrm{cm}$ The second projectile was how many times faster than the first? $v_1$ =    $v_2$ ([color=rgba(0, 0, 0, 0.85)]Round to three decimal places)

  A 28-g rifle bullet traveling 230m/s buries itself in a 3.6-kg peq8.m7afz4 cykndulum hanging on aykz4aqfcm7.8 2.8-m-long string, which 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 fractilero,* j.zc ,uon of kinetic energy lost, $(\Delta\mathrm{KE/KE})$ for the ballistic pendulum collision of Example 7–10. (b) Evaluate for m=14g and M=380g

  An internal explosion breaks an object, initially at rest, into two pieceu6oqa7.19rigarv* g rs, 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 represevg9ga1*oa7rur 6rq .i nt the heavier particle, and B represent the lighter particle. ) KE'$_A$ =    J KE$_B$ =    J

  A 920-kg sports car collides into the rear end of a 2300-kg1*,spmn nu4r w SUV stopped at a red light. The bumpers lock, the brakes are locked, and the two cars skid forward 2.8 m before stopping. The police officer, knowing that the coefficient of kinetic friction between tires and road is 0.80, calculates the speed of the sports car at impact. What was that speed?(Let A represent the sportps nn1wmu* 4r,s car, and B represent the SUV) $\approx$    m/s

  A ball is dropped fro/dzb thk g,xhd-+z)s*m a height of 1.50 m and rebounds to a height of 1.20 m. Approximately how many rebounds will the bs, z- bx+*)dhkh/zt dgall make before losing 90% of its energy?   

A measure of inelasticity in a head-on collis 9iad-kt n2 d86fsu.qp4ksu(x ion of two objects is the coefficient 4qi.sska9pu6 n(f dk8ut x- 2dof restitution, e, defined as$e=\frac{\nu_\mathrm{A}^{\prime}-\nu_\mathrm{B}^{\prime}}{\nu_\mathrm{B}-\nu_\mathrm{A}},$
where $\nu_\mathrm{A}^{\prime}-\nu_\mathrm{B}^{\prime}$ is the relative velocity of the two objects after the collision and $\nu_\mathrm{B}-\nu_\mathrm{A}$ is their relative velocity before it.
(a) Show that e=1 for a perfectly elastic collision, and e=0 for a completely inelastic collision.
(b) A simple method for measuring the coefficient of restitution for an object colliding with a very hard surface like steel is to drop the object onto a heavy steel plate, as shown in Fig. 7–36. Determine a formula for e in terms of the original height h and the maximum height h’ reached after one collision.

  A wooden block is cut into two pieces wdwzy m 5s,m )t :881c/jcljwmoxl(o0, 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 reasym,jo(wcwdt5zj 1mwcm 0l:/8 s o)xl8 sembled 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 movixzce99 z:ls r4ng in the +x direction at 5.5m/s collides head-on with a 10.0-kg object moving in the -x direction at 4m/s Find z zesl994x:crthe 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 electr ,hh ap v(i+sup2)vlb.;cemqw :xy :4gon, and a np2q,v +cy4.lu)g(:;miax s evb :hhwpeutrino. The electron and neutrino are emitted 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 mg k jhzs2w95 dh77,eixjsg,8fass $m_\mathrm{A}=0.400$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 betweead +c8-uzl tfzjyx (77n two objects of equal mass, each having initial speedz77tc ayfudlxj+ (8-z the two move off together with speed v/3 What was the angle between their initial directions?    $^{\circ} $

  Two billiard balls of equal mass mov(q .d2 2);qo x2wsvjyj5s kwbve 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 w2yd(xvvbs5 ojkw)qj.; 2sq2 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 elao2fcfmj :wf1 ks,zk2,u.gx; 5eh bv4astic collision with another atom at rest. Af kgehco:m2,,b .ufz ska2fv x1w5;4 jfter 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

  A neon atom (m=20u) makes a 2 c,n 5u90h:mdh dvvdm2lzjt u tkxqf,6)d)n+ perfectly elastic collision with another atom at rest.vfdmd u ,+nql9d2xkd,2h6 ut:0cvnt)j) 5zhm After 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 2w qhe d3fx/zvadw:x 4q;6 x:,znld6 fsystem shown in Fig. 7–38. Specify relativ6envq3:zdxfhz;f x x2, /qad :lw d46we to the left-hand 1.00-kg mass.    m

  The distance between a carbon ad ,5-veu ze.sstom ($m_{\mathrm{C}}=12\mathrm{u}$) 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 the front of the car. 6:1. smp3unk t,l:mudy tc cec0f hu/6How 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 363tdc1tl :s f0 mekuum cu,yn/p:.6ch.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 2ml j82ok, v4j(tv r/ihkbhe* mass 6800 kg, is used as a ferryboat. If three cars, each of mass *h2/mj kh4rotv b2 (k8ilje,v1200 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 3relw9(gf48d6yqaq xu1n o/ o$l_0$,$2l_0$, 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 ca3w jb teqy,m7:+nu6pmses 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 operator can pick up the load ,y7njb t pemw6:qu3 m+without tipping it.$X_{CM}$ =    l $Y_{CM}$ =    l

  A uniform circular plate of radius 2R u izzb-w.y-a0has a circular hole of radius R cut out of it. The center of the smaller circle is a distance 0.80R from the center C of the larger circle, Fig. 7–41. What is the posyub--a0 zwzi .ition of the center of mass of the plate? [Hint: Try subtraction.]   R

  Assume that your proportions arl*o 7 rkx*tdr /f0o8ete the same as those in Table 7–1, and calculate the mass of ontl8k* *fertd/ 7 xroo0e of your legs.    kg

  Determine the CM of an outstretgxd(q5t ivh r7ca9)n. ched arm using Table 7–1.   % of the person's height along the line from the shoulder to the hand

  Use Table 7–1 to calculaaz ;n.k+die7 bte the position of the CM of an arm bent at a right angle. Assume that tha. dzi;+en7kbe person is 155 cm tall. $X_{CM}$ =    cm $Y_{CM}$ =    cm

When a high jumper is in a position such that his u rq4di*nq n dwx+ d7- gtwm9e17-b(k1no, dqzarms 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? Usedd97-,+1wndw goeq7trqbnidm-*k zqxnu( 4 1 Table 7–1.

The masses of the Earth and Moon ar mnmy 68wcw tnpv/ ;+3begt59ke $5.98\times10^{24}$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 frictionl8uodqi abjb -g *2uu),ess 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 uninu9 js e4yv mytq/6,v) q6gm8bform 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 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 tmv6 6y8q/mt, 9sn ug)vj4ebqyhat will follow a parabolic trajectory?    cm

  A mallet consists of a unifo5uey i6. s3ut3( l kb8akcn;0e4 sfiedrm 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 shown i l 03fi4u(y;.3ekdessb5u n ia c68ketn Fig. 7–42. If this mallet is tossed, spinning, into the air, how far above the bottom of the handle is the point that will follow a parabolic trajectory?    d    d

  (a) Suppose that in Example j;q, sk 0mlmmz-;tt)d 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 stationavm8w03 8nyi n)h o)-q edoru1qry 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 d)ue31w d8) oor8 hyvqm0in-nqirection (relative to Earth) does the balloon then move? What happens if the passenger stops?

  An 0.145-kg baseball pitched horizontally at strikes a ba+qh 2h2 tkdyh4t and is popped straight up to a height of 55.6 m. If the contact time is 1.4 ms, calculate the average force on the ball kh+ qhythd422during the contact.    $^{\circ} $

  A rocket of mass m traveling wi .n p6.6nzbjkath 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 wf 9+jen* gn*bwith the corner 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 f*bngw+nje 9* will also fall into a pocket? Give details.

  A 140-kg astronaut (including space suit) acquires a speed of 2htbx716 y7:5bz kuqki 7e v0sv.5m/s by pushing off with hiszquk b50k hv evy 17bi7:ts7x6 legs from 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 ini.f(u lyw jtrbc q)x v+6ah..1utially at rest in outer space. They then push each o(f.h ..u1 quwxv )lc6b+ry tjather apart. How far apart are they when the lighter astronaut has moved 12 m?    m

  A ball of mass m makes a head-on elast tqo3 tx)1v+ strd79jwic collision with a second ball (at rest) and rebounds in the opposite direction with a speed equal to one-fourth its original speed. What is ther) od+s9w71 tvqtxj t3 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 8f*,jane v 4*q0nfey.dm eg;2hza+ uj 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 of kinetdjvunzy n0* jhee.+ g 8 f;*qam2,efa4ic 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 top0vo1bbye()a: g hjba2 of a flight 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 diffa 2gaj)ove(y hbb0: b1erent 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 ir(.qepn ji2 :jnto a 1.40-kg block of wood at rest directly above it. If the bullet has a mass of 29.0 g and a speed of 510m/s how high will the block rise after the bulnij.eqr p 2j(:let becomes embedded in it?    m

  A 25-g bullet strikesej- :uy,g )muc3z4 qn:vis.w*t vajf0 and becomes embedded 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 impam v:f.eji*)uny wvaj3,:q0cz 4- g ustct 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 mzuq1lqe yzm5//my 4: pass 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 u1q/:z ympm45/ y lzeqdirection 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 6 kr7pyh yft;. y/o3ppwas about $ 1\times10^{ 8}$kg struck the Earth ($m_E$=$6 \times10^{ 24}$kg) with a speed of about 15km/s and came to rest in the Earth.
(a) What was the Earth’s recoil speed?    $ \times10^{-13 }$m/s
(b) What fraction of the meteor’s kinetic energy was transformed to kinetic energy of the Earth?    $ \times10^{ -17}$
(c) By how much did the Earth’s kinetic energy change as a result of this collision?    J

  An object at rest is suddenly broken apart into two fragme0mc6qrr4j;pc fd h8g 7nts by an explosion. One fragment acquires twice the kinetic ene46cp r078hrj fcmdqg;rgy of the other. What is the ratio of their masses?   

  The force on a bullet is given by the f yd7pw2 azisa+ze5 go cd:1u55ormula 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 +c3-r 7xvlwf c$m_A$ = 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 hd*c 8talf:gvl8 xpbre3/,(34 tavui smaller nucleus. What will be the speed of this3 ,l ac h*u8gd: /xbt4(3avrp tfel8iv 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 (clapt.3zla8h( q oy target) is fired at an angle of 30 $^{\circ} $ to the horizon with a speed of 25m/s (Fig. 7–45). When it reaches the maximum height, it is hit from below by a 15-g pellet traveling vertically upward at a speed of 200m/s The pellet is embedded in the skeet.
(a) How much higher did the skeet go up?    m
(b) How much extra distance, $\Delta{x}$ does the skeet travel because of the collision? $\approx$   

  A block of mass m=2.2kg slivot /g rp:i5l- dl2cc4 qla89ldes 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 mam) 2qz),7dmlq war73 1hidl voss m if it is to rebound ,qvql3 )1d7rh2l owd7amimz)from M, slide up the incline, stop, slide down the incline, and collide with M again?    kg (Let A represent mass m, and B represent mass M.)

  The gravitational slingshot effect. Figure 7–47 .87qr jdsm nlb,; yjlqe(56frshows the planet Saturn moving in the negative x direction at its orbital speed (wifldyqbj( s l6r r7eq;jn,.8m 5th 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