We claim that momentum is conserved, yet most movi .h4 o g55ln,l)ld9ya)hlfv yqng objects eventually slow down a )y 59),4qallhvn o5l.fdglhynd stop. Explain.

When a person jumps fr94k h 5gtih4jb 9ev)sjk8wkj lig/j ,(om a tree to the ground, what happens to the momentum of the person upoj9ihel4h) 8vs5 j94jjk(b tgw /,kgk in striking the ground?

When you release an inflated but untiedh.xv4bd d5trho +xi*v yw6m/+ balloon, why does it fly across the room?xx * dv6/ +.ihovmy+dwh4b5tr

It is said that in anvt8jbu:*n x fh9ijie 2bj8y r 2bu 7-dvc1q7.icient times a rich man with a bag of gold coins froze to death ij:ve ujb-i2qc yut x8j f7i8d1b2rn*h.7b9v 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 not been so miserly?

How can a rocket change direction when it is far out in space and is e t)amh*g/uq+g ssentially in a u*qg/t)g+mhavacuum?

According to Eq. 7–5, the longer the impact time of an impulse, th itkg 0;uh 0j0fy9ywvo t66)oie smaller the force can be for the same momentum change, and hence the smaller the deformation of the object on which the force acts. ; jot)0kvu 0ythiiy6w0g o6f 9On 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. Todsxsi 6jn,fw6 5ay, though, cars are designed to have “crumple zones” that collapse upon impaxf nw,6sis6j5ct. What is the advantage of this new design?

Why can a batter hit a pitched baseball further*t h:kepxz8/jci8qa* than a ball tossed in the air by the battz*te qx8hc:* aj8/ipk er?

Is it possible for an object to receive a larger impulse from a small fow 3*pry9*hp6.hyk cjjq gc7vh ns tsvk,4/2/prce than from a lajwpt*ngy/vpvc 7.c 2h6sk9 3k s,hqp*/ 4h yrjrge force? Explain.

A light object and a heavy object have the same kinetic energy. Which has the2-k c6amv33o qlp t0cus4 f1gd greater mom3mv4c t3du2p lg cfosa-1q06k entum? Explain.

Describe a collision in which all kine :xj oj if*n3wg,+kj:xtic energy is lost.

At a hydroelectric power plant, water is directed at high speed ag1gkm4sco-l 2qpd+jq ;t2h9 ac ainst turbine blades on an axle that turns an electric generator. For maximum power generation, should a 24mco k-+tg2hdcqs9 qlj;p1the 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-w*twone p(/r 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 dropp:t7) lm oy3osyd+d qvb/05eyke31r k ned from a height h onto a hard steel plate (fixed to the Earth), from which it rebounds at very nearly its original speed. (a) Is the momentum of the ball conserved during any part of this process? (b) If we consider the ball and Earth as our system, during what parts of the process is momentum conserved? (c) Answer part (b) for a piece of putty that falls and sticks to the steel plkred3tde7q31:yvo ml)o+ ns50/ ykb y ate.

Why do you tend to lean backward when carryin1u)lz 4zi s tioa649ib sec3.eg a heavy load in your arms?

Why is the CM of a 1-m length of pipe at its mid-point, whereasgcqkzh w70 d8.gng19, vqqwe; this is not true for your arm or le ,wc8q1gh zg0q7e;kgnd9qv w.g?

Show on a diagram how your CM shifts when you change from a lyi(i n ckpai,u e;a.u96:qg/ lmhng position to a .,mcgpul nia 9/hi6 (ea; ukq:sitting position.

If only an external force can change the momentum of the center of mass of an jdc* .u3i6ne .akte1bobject, how cajbeni 1e c* k3..tad6un the internal force of an engine accelerate a car?

A rocket following a parabolic path through the air suddenly explodes into i-cuvlp;zqb3 ;y/ (plmany pieces. What can you say about the motion ofv-u3;b(zi c p;yl/lpq this system of pieces?

  What is the magnitude of the momentum of a 28-g sparrow flyinlj9:+iif t ft+l u+b0tg with a speed of 8.4 mj+f+itl lt f:ui0+b 9t/s    $kg\;m/s$

  A constant friction force +bapl6za - +*di)jt2 rpr1m. d+h wtmvof 25 N acts on a 65-kg skier for 20 s. What is the skier’s ch+r16+t tpprwih)aza.m d+ dbv*l2- jmange in velocity?    m/s

  A 0.145-kg baseball pitched at 39 mq7kt/ x45gzz s,f9a uy/s is hit on a horizontal line drive straight back toward the pitcher at 52m/s If the contact time between bat and bfq9 a,/z5g7xyk4uszt all 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 horizontally with a sp:kyd kk,r)p,geed 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 26.0yg) :,kkrpk,d kg, and that of the boat is 45.0 kg. Ignore water resistance. The velocity of the boat is    m/s

  Calculate the force exetmq- th /ub2*d:yi8lz qzo 78wrted on a rocket, given that the propelling gases are expelled at a rate of 1500kgmtq h8qu:id- bz8/tw 2oly7 *z/s with a speed of $ 4\times10^{4 }$ (at the moment of takeoff).$a\times10^7$ N a =   

  A 95-kg halfback moving qg oob w.itoe;,0 y9/.lyx ;jwat 4.1m/s on an apparent breakaway for a touchdown is tackled from behind. When he was tackled by an 85-kg cornerback running at 5.5m/s in the same directi .9ye/ o;0;oig wqy,l.b jtwxoon, what was their mutual speed immediately after the tackle?    m/s

  A 12,600-kg railroad car travels alone on a i2itwhi),1xp level frictionless track with a constant speed of 18m/s A 5350-kg load,initially at rest, is dropped onto the capi2 ih1 i),wxtr. What will be the car’s new speed?    m/s

  A 9300-kg boxcar traveling at 15m/s strikes a second boxcaty.x j*l*m:;kh t .wybr at rest. The two stick together and move off with a spmjt*yhl.. t ;* xkybw:eed of 6m/s What is the mass of the second car?    m/s

  During a Chicago storm, winds can whip horizontally at speeds of 100km/bjiyyh03 4 rbs3k:p 4vh If the air strikes a person at the rate of 40k3syrbhjb3: py0i4 vk4g/s per square meter and is brought to rest, estimate the force of the wind on a person. Assume the person is 1.50 m high and 0.50 m wide. Compare to the 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 ptd,tpm)8n /ystes;)8,eg aq 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 with the tracks, what is the speed of td)e)8g; ns e ma ,ptqyt,/ts8phe car after 90.0 min?$\approx$    m/s

  An atomic nucleus inuav4m4y mn.k.*rd i: litially moving 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 original nucleuslmy:duvnmr .. a*k4i4 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 andn)p ph:r9h3pk1mf*o o emerges cleanly at 170m/s If the block is stationary on a frictionless surfpmoph ):pr * nf31h9koace when hit, how fast does it move after the bullet emerges?    m/s

  A 975-kg two-stage rocket is t vs6d 0jn*:vr xp s(u8qw-oun)raveling 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 spacev kwm)r3btu7i.lx2u0s np s1; with a velocity of 115m/s Tsuip2ubv)t3sw n0rx ;lk m.17o alter its course by 35.0 $^{\circ} $, its rockets can be fired briefly in a direction perpendicular to its original motion. If the rocket gases are expelled at a speed of 1750m/s how much mass must be expelled?    kg

  A golf ball of mass 0.045 kg is hit off the tee at a speed of 45m/s(h2k3u4p uiq(1vd v:utfmg z1 The golf club was in contact wihfkz314pm(ug qu1i2 utdv v:(th 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 to rest it)i;54li*** qrbnt pe 6tzcgx n a time interval of 8.0 mstb;ii * 6rz lt)n *54*eqctgxp. (a) What is the impulse given to the nail?    kg*m/s
(b) What is the average force acting on the nail?    N

  A tennis ball of mass m=0.06kg and b8(p u+ fm1stespeed 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 ofymlj 2re:k b ft/r9xuu5:ni92 the crashworthiness of new automobile models. Cars are tested by smashing ttkyjeuu 2:mr/bxf 9r59l:in2hem into fixed, massive barriers 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 4m/s to the east and is stole5)n ha5y 4fwpped in 0.75 s by a head-on tackle by a tackler running due fanh4) 5y elw5west. Calculate
(a) the original momentum of the fullback    kg*m/s
(b) the impulse exerted on the fullback    kg*m/s
(c) the impulse exerted on the tackler,    kg*m/s
(d) the average force exerted on the tackler.    N

  Suppose the force acting on a tennis ball (mass 0.060 kg) points in the +x dkk0d dcok5zs7*d;d w4irection and is given by the graph of Fig. 7–33 as a function of time. Use graphical methods todw7 4kcdo kds*kz ;05d 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 perso 1nw(x1 w48lvvv+ enycn jump without breaking the lower leg bone of either leg? Ignore air resistancev nvv1cy84+1(el wxwn 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 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 movvwtnzs 3ut6 3e/yvv, 9ing east (+x direction) with a speed of collides hevtte uvys 6n 33/9w,vzad-on with a 0.220-kg ball at rest. If the collision is perfectly elastic, what will be the speed and direction of each ball after the collision?Let A represent the 0.440-kg ball, and 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 hjt)c1g9 g647 uw utsosas a head-on collision with a 0.900-kg puck initially at rest. Assuming a perfectly elasto6tcs swt 7jug1g9) u4ic collision, what will be the speed and direction of each object after the collision?Let A represent the 0.450-kg puck, and let B represent the 0.900-kg puck. v'$_A$ =    m/s ----待选择----eastwest  v'$_B$ =    m/s ----待选择----eastwest 

  Two billiard balls of eq9 8uc mrnr rhmws9fg ;;o,b++mual 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 their speeds after the collision?(Let A represent the ball moving at 2.00 m/s, and call that direct; hub 9w+;r9rsm rgm8nmfc+, oion 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 col0htbk2gp/ :gnlides 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.)vn2kpt gh b/0:g'$_A$ =    m/s v'$_B$ =    m/s

  A softball of mass 0.220 sbyk4f, ehxv2;cpt60 p,zb 6rkg that is moving with a speed of 8.5m/s collides head-on and elastically with another ball initially at rest. Afterward the incoming softball bounces bazs2b;v 0, p6bpk6 xe r,chyf4tckward 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 elasticd4v6k.mkz w*k+-dax w4qa 2orl+8 j pzj ppr25ally as one approaches the other directly from the rear (Fig. 7–34). Car A has a mass of 450 kg and car B 550 kg, owinkavpxk24p rk8*dd qpw6+jw- 2z5lo j . z4+mrag 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 an elastic head-on collision withjgd urhz g*3:;58aur m a second ball initially at rest. The second ball moves off with half the original srg u;gu mrjz35:da8h*peed 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 frict f x;1ix0 8pqvaap9wp2ionless incline as shown in Fig. 7–35, and elastically strikes anothxa0a9w pfxvi8 p q;1p2er 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 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 mm d;nl(av82 qxass m$_A$ and velocity v$_A$ elastically striking a stationary object of mass head-on. (a) Show that the final velocities v'$_A$ and v'$_B$ are given by$v_{\mathrm{A}}^{\prime}=\left(\frac{m_{\mathrm{A}}-m_{\mathrm{B}}}{m_{\mathrm{A}}+m_{\mathrm{B}}}\right)\nu_{\mathrm{A}},v_{\mathrm{B}}^{\prime}=\left(\frac{2m_{\mathrm{A}}}{m_{\mathrm{A}}+m_{\mathrm{B}}}\right)\nu_{\mathrm{A}}.$(b) What happens in the extreme case when m$_A$ is much smaller than m$_B$ Cite a common example of this. (c) What happens in the extreme case when m$_A$ is much larger than m$_B$ Cite a common example of this. (d) What happens in the case when m$_A$=m$_B$ Cite a common example.

  In a ballistic pendulum experiment, projectile 1 results in a maximumwk,b ofr24kcqp (bp4+ height h of the pe44 +qp,fo(b rbc2kwp kndulum equal to 2.6 cm. A second projectile causes the the pendulum to swing twice as high, $h_2=5.2\mathrm{cm}$ The second projectile was how many times faster than the first? $v_1$ =    $v_2$ ([color=rgba(0, 0, 0, 0.85)]Round to three decimal places)

  A 28-g rifle bullet traveling 230m/s buries itself in a 3.6-kg pendulyb0 f; 7axl +w/zzkd.hum hanging on a 2.8-m-long string, which makes the plax/by.zh7w d +zk0;f endulum 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 v58 oiqq-wt:e i8ia+spzd 60cxg- .(: jhxlb wfor the fraction 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 twpur*d jm 1r3c;z1 sfb,tqe 8cyd),k4po pieces, one of which has 1.5 times the mass of the other. If 7500 J were released in the ebz1tur,rmd;4p*s18 ec jc yk)3dqf,pxplosion, 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 collides into thex6nhm5ps -6qk,x7 xv1+csg wiq; c9cy 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 0vg6 s6+mp hxk9xqycns 15qw-,c 7xci ;.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 ande4zy- k57muab rebounds to a height of 1.20 m. Approximately how many rebounds willy75eb4- ukma z the ball make before losing 90% of its energy?   

A measure of inelasticity in a head-on collision of two objects is the coefficnx/an3t xbk 1+r ;ahd(ient of bn / (a+3 ahxt1n;kxrdrestitution, 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 mass of the hw ( e:fir;nd lqp7;)bother. A depression is made in both faces of the cut, so that a firecracker can be placed in it with the block reassembled. The reassembled block is set on a rough-surfaced table,wq;h7:bi nf(re;d)l p 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 di3flr;+xt c)z. abgw 0jrection 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 iff +tgbwjra0.cz;3xl) :
(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 second3vans fs e96h+ nucleus, an electron, and a neutrino. The electron and neutrino are emitted at right angles an a36+n svsfe9hd 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 mass /q9/lhr4wxyi $m_\mathrm{A}=0.400$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 objectspjt n/ml+33 dp of equal mass, each having initial speed the two move off together with speed v/3 What was the angle between their initial dptn+3j/3 ld mpirections?    $^{\circ} $

  Two billiard balls of equal mass move at right angles and me7)lw osvi ya,gd+-9cy et 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 direowa,yi ysl )9c-7g+ vdction 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 anothei3a )o2tw;0fy,lpj eje.f i*mr atom at rest. After the 2ii0j t.fpo3 e)mfj,alyw*;e 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 ela47:wxmhcj ;e lstic collision with another atom at rest. 4;ljx 7:chmwe 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-massjz0fb(kzyn n1m0zz*0 system shown in Fig. 7–38. Specify relative to the left-hand 1.00-kg *yfn zb1k 0m (jn00zzzmass.    m

  The distance between a carbon atom e) i1 k02tvxu 4b2ecxtaq 4t3d($m_{\mathrm{C}}=12\mathrm{u}$) 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 at 4hjqpt1xt 6by*s 9m41*u bo2.50 m behind the front of the car. How far from the front of the car will the CM be when two people sit in the front seat 2.80 m from the front of the car, and three people sit in the back seat 3.90 m from the front? Assume that eau1*s6jt a9tbx*po144tqhm bych 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 ferrybo4gn-for +j/4tt.hr .tk liuc5 6fju p.at. If three cars, each of mass 1200 kg, occupy its NE, SE, and SW corners, determine the CM of the6j..lp5h/ji4cf+ urt uo krn-g t4t .f loaded ferryboat.$X_{CM}$ =    m $Y_{CM}$ =    m

  Three cubes, of sides fij*u)bbv9(5gd8 ay t$l_0$,$2l_0$, 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 1s:7mgm)kh5r1g8 lxbl w,p km (see Fig. 7–40), each of which is a cube of length l. Find the center of gravity in the hosgp)r m xm 57k1h1lk8w, mlbg:rizontal 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 hacikkr45i5,nag 0v j.yo (pwn;s 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 iviwo.nk5kg (, ;rp4caynj50circle, 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 twk.vd627qx4 e4bhpfTable 7–1, and calculate the mass of7dkhb.p2 w4xf 64 qevt one of your legs.    kg

  Determine the CM of anppy oz25 qo( ao(m-mrmv.- my- outstretched 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 thm;gh )mru2w)+ ilg4 zqe position of the CM of an arm bent at a right angle. Assume that the person is 155 c2rhw)g qzm )m+g4;il um tall. $X_{CM}$ =    cm $Y_{CM}$ =    cm

When a high jumper is in a position such that his arms and legs are hanging vert- cr1j6tu, gdiqizb0 m.d6.irically, and his trunk and head are horij.gti i 6qdiumbrd-6 .,0crz1zontal, calculate how far below the torso’s median line the CM will be. Will this CM be outside the body? Use Table 7–1.

The masses of the Earth and Mk2a xsi48q23r)cz g2ixvry4 voon 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-kgw 7(ilm1(c69 ;rrs ijijrm1rp man stand 10.0 m apart on frictionless ice.
(a) How far from the woman is their CM?    m from the woman
(b) If each holds one end of a rope, and the man pulls on the rope so that he moves 2.5 m, how far from the woman will he be now?    m
(c) How far will the man have moved when he collides with the woman? He has moved    m from his original position

  A mallet consists of a uniform cylindrical head of mass 2.00 kg and a di.u3ok 5.nnz6xd*fn wv ameter 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. I on6dv *n.fnxk5uzw3. f this mallet is tossed, spinning, into the air, how far above the bottom of the handle is the point that will follow a parabolic trajectory?    cm

  A mallet consists of a uniform cylindrical head of mass 2.00 kg and a diameter k:pm2 l9 tki8t0.0800 m mounted on a unif98 lk i:kttm2porm 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 a parabolic trajectory?    d    d

  (a) Suppose that in Example 7–14 (Fig. gk +amh-z6dg17–29), $m_{II}$=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 m9sgatady2k;g*w: tz )ass M, are in the air and stationary with respect to the ground. A passenge2:)w;agt* zkgday9s tr, 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 move? What happens if the passenger stops?

  An 0.145-kg baseball pitched horizontally at strikes a bat and is popped straou. 26 qos;nafight up to a height of 55.6 m. s6oo;n2q. fau If the contact time is 1.4 ms, calculate the average force on the ball during the contact.    $^{\circ} $

  A rocket of mass m travelidbdkp6;rk4 8, df( xfvng 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 sdr j.urey/ m+gvwt/5 42n0eufaced with the corner pocket shot shown in Fig. 7–43. Relative dimensions are also shown. 5d0rnr/y.2+tw 4us/ egvje muShould the player be worried about this being a “scratch shot,” in which the cue ball will also fall into a pocket? Give details.

  A 140-kg astronaut (including space suit) acquirt p:)gk i c7jv-jn84/xtezxf5es a speed of 2.5m/s by pushing off wie5j f74g pxkv :xn) jc/i-tzt8th his 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 anl9 vn4;uwe9 4z-jw1( td sbcccg04gfcd the other 80 kg, are initially at rest in oung4 -4c1w cd sc ;tfzce(gwl099j bvu4ter space. They then push each other apart. How far apart are they when the lighter astronaut has moved 12 m?    m

  A ball of mass m makes a head-on elastic collision wishb 5b;. x(zpgj,nd bk gm;u45th a second ball (at rest) and rebounds izg. db4 5gxub5ks; ,;mpnb(jhn the opposite direction with a speed equal to one-fourth its original speed. What is the mass of the second ball? $m_B$ =    $m_A$(Round to two decimal places)

  You have been hired as an expert witness inf fu 9.v5mxbx9nd;uddp0ym2 ; 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 slid 30 m. The coefficient of kinetic friction between the locked wheels and the road was measured to be 0.60. Show that the driver of car A was excepfd;xdm;b.v0nudx9f5 9u2 y m eding 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 total ukxl tg0t+ n,6vertical height 4.00 m. The ball hits four times on the way down, each time striking the horizontal pa k ut+,t0xngl6rt of a different step 1.0 m lower. If all collisions are perfectly elastic, what is the bounce height on the fourth bounce when the ball reaches the bottom of the stairs?

  A bullet is fired verti5:a m:-by+ r*jzvsp;0 4xxwf2e gzzow cally into a 1.40-kg block of wood at rest directly above it. If the bullet has zsjg+ xb:z0 v*- 5ow 4ym2wr:e;fazx pa mass of 29.0 g and a speed of 510m/s how high will the block rise after the bullet becomes embedded in it?    m

  A 25-g bullet strikes and becomes embedded in a 1.35-kg.*1/m cy olow-)ffj +exc y/mr block of wood placed on a horizontal surface just in front of the gun. If the coefficient of kinetic frictio)c.1 w-foj+*/cxmry lefm /oyn 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 d ; -g,snoull2the 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 s glln 2,-;uodwill 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 ay 1)vl*hs-5aloq x 3bxbout $ 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 suddevap;ae9si dqpt-- w5-f 9xgo(nly broken apart into two fragments by an explosion. One fragment acquires twice the kinetic energy of the other. What is the ratio of theiro-pdvpiq-s; 599w (axtga e-f masses?   

  The force on a bullet is given by 0 (hluw+ a+4oybv5ff2t3cbu6+ hqufk the formula 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 masseshnc9c. z b4 vt5t6ts1y $m_A$ = 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 atjb1md (jvpk :mpr /*8p rest decays radioactively into an alpha particle and a smaller nucleus. What will*b(p8j/jmv: pd r1kpm 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 an ad+sqe/ omvg 1 ss85;wcngle of 30 $^{\circ} $ to the horizon with a speed of 25m/s (Fig. 7–45). When it reaches the maximum height, it is hit from below by a 15-g pellet traveling vertically upward at a speed of 200m/s The pellet is embedded in the skeet.
(a) How much higher did the skeet go up?    m
(b) How much extra distance, $\Delta{x}$ does the skeet travel because of the collision? $\approx$   

  A block of mass m=2.2kg slides down :y9x ,zqgb vtg j7 9+.gt(u:ghpcp *uqa 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),f2, 6th rpff1e what is the upper limit on mass m if it is to rebound from M, slf r,he2fpf 16tide up the incline, stop, slide down the incline, and collide with M again?    kg (Let A represent mass m, and B represent mass M.)

  The gravitational slingshot effect. Figure 7–47 shows the planet Saturn movin6ejw3+ mopot h u8a-ep/d23eeg i3d-6peomte 8e w2ph+o aeu3/j n the negative x direction at its orbital speed (with respect to the Sun) of 9.6km/s The mass of Saturn is $5.69 \times10^{ 26}$kg A spacecraft with mass 825 kg approaches Saturn. When far from Saturn, it moves in the direction at 10.4km/s The gravitational attraction of Saturn (a conservative force) acting on the spacecraft causes it to swing around the planet (orbit shown as dashed line) and head off in the opposite direction. Estimate the final speed of the spacecraft after it is far enough away to be considered free of Saturn’s gravitational pull.    km/s