We claim that momentum is conserved, yet m(xa+xlua/o iu ooz y1t8 2s1x8ost moving objects eventually slow down and s s8t uix(a1/xzy+ox182la oo utop. Explain.

When a person jumps from a tree to the ground, what happens to the momentun (b8/k ju67) zoipczpx9hct/m of the person upon strikinui8hbxtzj9c 6 7/ o )zpc(p/nkg the ground?

When you release an inflated but untied balloon, why does it fly across the +vh,o+n(gzsp ,sj;krw s+ z6 zroom+,+z6hp (z vkng z;srsswj o+,?

It is said that in ancient times a riqa ul6 a04gre+ch man with a bag of gold coins froze to death while stranded on a frozen lake. Because the ice was frictionless, he could not push himself to shore. Whau6a+ elr4g q0at could he have done to save himself had he not been so miserly?

How can a rocket change direction when it is far o8 xfgewec1) +uj- 6zprut in space and is essentially in a vacuumezfxjp 1u)+r6-cgwe8 ?

According to Eq. 7–5, the longer the impact time of an impulse, the smk7.vi7w l x2sgaller the force can be for the same momentum change, and hence the smaller the deformation of the object on which the force acts. On this basis, explain the value of air bags, which are intended to inflate during an automobile collision and reduce the pogs2i.x7l7w v kssibility of fracture or death.

Cars used to be built as rigid as possibl7qbdf5w8p4 +h1 vsvqpe to withstand collisions. Today, though, cars are designed to have “crumple zone8 qh1svqv b dpp4f57w+s” that collapse upon impact. What is the advantage of this new design?

Why can a batter hit a pitched baseball further than a balsmux .(wj36a/j onl :ul tossed in the air by thom.:u/n 6wljju(3s ax e batter?

Is it possible for an objechxmfjiu , 69c3 q1 n+oulq/.jyt to receive a larger impulse from a small force than from a large force? Eh.6jnij 1/lo9 f3u,xumq+qc yxplain.

A light object and a heavy object have the same kinetic energy. Which hwe a,;ky7c1hi as the greater akh7 iy, e;1cwmomentum? Explain.

Describe a collision in which all kinetic--(f+vhx6ofaep o pa 9gry:;j energy is lost.

At a hydroelectric poxu))*il sw-by wer plant, water is directed at high speed against turbine blades on an axle that turns an electric generator. For maximum power generation, should the turbine blades be design)x )i -yslwub*ed so that the water is brought to a dead stop, or so that the water rebounds?

A squash ball hits a wall at -vj dqyo6fbr*1vkbha )v5 .o)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 st(4wqrh3ylas h/t5v a-eel 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 th-s4/whar3ylht q5a (v is 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 plate.

Why do you tend to lean w ps oh,njpft.5 5k42hbackward when carrying a heavy load in your arms?

Why is the CM of a 1-m length of pipe at its mid-point, whereas this is notff1y+3hqx9 ltf l rr)13mcrb4 true for youf4 m3 yq9 crrx)l3t+1frl1b fhr arm or leg?

Show on a diagram how your CM shifts when you change from a lying position to dy6 / c1ro-u) zxdj+wt-itr;fa sitting positioy / z6idt rtud)ow;fcj+-- r1xn.

If only an external force can c rq)va ee640 x(w,a2l rqmgcx,hange the momentum of the center of mass of an object, how can the internal force of an engine accelerate axceaq m le g,) v6xqar(2w40r, car?

A rocket following a parabolic path through the air suddenly eegyfh kh:,ev o. 7b(-sxplodes into many pieces. What can you e( f:7. hskohyveb-g,say about the motion of this system of pieces?

  What is the magnitude of the momentum of a 28-g sparrow fly fya4mrt xfr u5k049 /j:lp5pping with a speed of $8.4 \; m/s$    $kg \; m/s$

  A constant friction force of ihw v88*6h iuay6m qw625 N acts on a 65-kg skier for 20 s. What is the skier’s change in veuiaih8v*68 mwqhw 6 6ylocity?    m/s

  A 0.145-kg baseball pitched at 39 m/s is hit on a horizontal line dw8,s+: pbm(cr+v sp kjrive straight back toward the pitcher at 52m/s If the contact time be: 8p sjscbk(+ pv+rm,wtween 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 h88hy0t:6h soy 2jqch 6.40-kg package out horizontally with a speed of 10 m/s Fig. below Calculate the velocity of the boat immediately after, assuming iq2c8ot0h hsh6 y:8 jyht was initially at rest. The mass of the child is 26.0 kg, and that of the boat is 45.0 kg. Ignore water resistance. The magnitude of the velocity of the boat is    m/s

  Calculate the force exerted on a rocketv1 r q1brvb ;j5xqc(zq ).)vkn, given that the propelling gases are expellqv kx; qrzc(1bv 5nj.v)rb1)q ed at a rate of $1500 \; kg/s$ with a speed of $ 4\times10^{4 } \; m/s$ (at the moment of takeoff). F =    $\times 10^7 \; N$

  A 95-kg halfback movi -q,ouoa7 q*ring 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 frictionlnds;/vxg;dg(tq1: gv ) ;q.tlqa ( s,kfnzv) zess track with a constant speed of 18m/s A 5350-kg load,initially at rest, is dropped onto the car. What will be the ct gsgq svknnvv,l ;:q z/dt )1aq()df;x;g.( zar’s new speed?    m/s

  A 9300-kg boxcar traveling atsx.wy (7y3mw8h 9waa plwwm30 $15 \; m/s$ 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, 4y3teq l;g(dv,v/p9 j.oeov.)lbn sq winds can whip horizontally at speeds of 100km/h If the air strikes a person at the rate of 40kg/s per square meter and is brought to rest, estimate the force of the wind on a person. Assume v3; .)qoe ,/n9ets db.p4ovgvq(y j llthe 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 coaej),o he w1f)4 rieuqn;dq )v-sts 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 tracnew, )r)f;vu qe 4e i-1)oqdjhks, what is the speed of the car after 90.0 min?$\approx$    m/s

  An atomic nucleus initially moving 5opn6cwjf,ob,x f8z9vf ;g 6 mat 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 nucleus has a mass of 222 u, what speed does the alp f6z px; fv5m6ofon,98gbcj,wha particle have when it is emitted?    m/s

  A 23-g bullet traveling 230m/s penetrates a 2.0-kge6 ne/y1k wlks-(a9lw fl3yg7 block of wood and emerges cleanly at 170m/s 9-1esw/f ( y3l7wlylk ag6k neIf 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 travelingh rgx. )+ i (vkem8vcup1ba7u43crgl6 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 velocity *iukalm9m-4: bguac+ of 115m/s To alter its course blg+9m* 4-kcu:ba iamuy 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 The g)- ellr q/-u0nfqjk5v olf club was in contactlvf l0-e5rkn/-uq )jq 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 to rebiz; o 1(;5yk jo1fvbtk */lzpst in a time interval of 8.0 ms. (a) What is the impulse given to the nao;51z( *z1fyt/ ok lbkjbpvi ;il?    kg*m/s
(b) What is the average force acting on the nail?    N

  A tennis ball of mass m=0.0 buape qea14;66kg 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 crashworthinesili+ ni j3v0e3s of new automobile models. Cars are tested by smashing them into fixed, massive barriers at 50km/h (30 mph). A new model of masl i j3en3v0i+is 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 isg;jq7b9gg(2 e* n9m9 idnsidr stopped in 0.75 s by a head-on tackle by aneidd*g(q9;jb2sg mig 7 r n99 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) pointsa 8if(f 3hytul9xz/ d. in the +x direction and isd z89ffh3l(x/y i. tau given by the graph of Fig. 7–33 as a function of time. Use graphical methods to estimate
(a) the total impulse given the ball    N*s
(b) the velocity of the ball after being struck, assuming the ball is being served so it is nearly at rest initially.    m/s

  From what maximum height can rjt4-yn*ew1u a 75-kg person jump without breaking the lower leg bone of either leg? Ignore air resistance and assume the CM of the person moves a distance of 0.60 m from the standing to the seated position (that is, in breaking the fall). Assume the breaking strength (force per unit area) of bone inruw*j -tey1 4s $170\times10^6\mathrm{~N/m^2}$ 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 movirfw7 zk u/qua)szt 2 )a c68v8k+ca8keng east (+x direction) with a speed of collides head-on with a 0.220-kg ball at rest. If the collision is perfectly elastic, what will be the speed and direction of each ball after the collision?Let A represent the 0.440-kg ball, and B represent the 0.220-kg balfu8 ) 62v8/ta8 kqz wcz7 +easku)kcral. $v'_A$    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 n h4bp4tq 40nuhead-on collision with a 0.900-kg puck i40bh44tqnun pnitially at rest. Assuming a perfectly elastic collision, what will be the speed and direction of each object after the collision?Let A represent the 0.450-kg puck, and let B represent the 0.900-kg 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 coll627/n:khpjjmduc n c5ision. 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 direct 76jpn c5 ck:md2/hnujion.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 headm3nyp(h e(fs* 5u4nf qfo .f,s-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.)v(f 5ef(y3 4suo,sh.fq pnnf*m '$_A$ =    m/s v'$_B$ =    m/s

  A softball of mass 0.220 kg that is moving with a speedwl*fq 5ph:5g+ xq09mz1 kw9utrxtqz: of 8.5m/s collides head-on and elastically with another ball initially at rest. Afterward the incoming softball bounces backward with a speed of 3.7m/s Caztu5kpqx5 1m +t0xrh9fq: w9gl w:*zqlculate
(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 rid ge /w*hlnel25yu/f:w-;a5 *a xyxb ate collide elastically as one approaches the other directly from the rear (Fig. 7–34). Car A has a mass of 450 kg and car B 550 kg, owing to differences in passenger mass. If car A approaches at 4.5m/s and car B is moving at 3.7m; 2w 5ea5 yl**ufwl/xy:-ha/ t abengx/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 baqic 3pq.oraa1dg; 6y -ll makes an elastic head-on collision with a second ball initially at rest. The second ball moves off w i3-pgdr16oqaa ; cyq.ith 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 b brr26bt(zn c.jib:*in Fig. 7–35, and elastically strikes another cube at the bottom that is only one-half its mass. If the incline is 30 cm high and the table is 90 cm off the floor, where does each cube land? [Hint: Both leave the b r:zn6bc(tbj*. r2 ibincline moving horizontally.]$\Delta x_{m}$$\approx$    m $\Delta x_{M}$$\approx$    m

ake the general case of an object *8l yue19d h8.j rqkvyx v-so2cz-u9 hof mass m$_A$ and velocity v$_A$ elastically striking a stationary object of mass head-on. (a) Show that the final velocities v'$_A$ and v'$_B$ are given by$v_{\mathrm{A}}^{\prime}=\left(\frac{m_{\mathrm{A}}-m_{\mathrm{B}}}{m_{\mathrm{A}}+m_{\mathrm{B}}}\right)\nu_{\mathrm{A}},v_{\mathrm{B}}^{\prime}=\left(\frac{2m_{\mathrm{A}}}{m_{\mathrm{A}}+m_{\mathrm{B}}}\right)\nu_{\mathrm{A}}.$(b) What happens in the extreme case when m$_A$ is much smaller than m$_B$ Cite a common example of this. (c) What happens in the extreme case when m$_A$ is much larger than m$_B$ Cite a common example of this. (d) What happens in the case when m$_A$=m$_B$ Cite a common example.

  In a ballistic pendulum experiment, pr9v (w/cffxw *7r l*tajojectile 1 results in a maximum height h of the pendulum equal to 2.6 cm. A second projectile causes the the pendulu/*w9t7*vfxwa(fr j c lm 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 32:ik, z mwz,hw.6-kg pendulum hanging on a 2.8-m-long string, which makes the pendulum swing upward in an arc. Determine the m,w z:h2 ,kwizvertical and horizontal components of the pendulum’s displacement.vertical$\approx$    m horizontal =    m

(a) Derive a formula fop.mlj+ cq)jt 9 xyg.b1r 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 x0bf-fys311 jxe krx3an object, initially at rest, into two pieces, one of which has 1.5 times the mass of the other. If 7500 J were released in the explosion, how much kinetic energy did each piece acquire? (Let A represent t1e3sx0fxfb 1 jx-k y3rhe heavier particle, and B represent the lighter particle. ) KE'$_A$ =    J KE$_B$ =    J

  A 920-kg sports car collides into thn/2op -m e ,p6hj wot7uw;icp:e rear end of a 2300-kg SUV stopped at a red light. The bumpers lock, the brakes are locked, and the two cars skid forward 2.8 m before stopping. The police officer, knowing that the coefficient of kinetic friction between tires and road is 0.80, calculates the speedww-: ;p2jecm pop6 toih/u7,n of the sports car at impact. What was that speed?(Let A represent the sports car, and B represent the SUV) $\approx$    m/s

  A ball is dropped from a height of 1.50 m and rebounds to a height of 1.20 t3 zzm6 +yeaf1f ;.pzqi2tm:zm. Approximately how many rebounds will the ball m;fm.zyaiz3ze1t fq2+ z:6t m pake before losing 90% of its energy?   

A measure of inelasticity in a gaf4h,oc tgjvk+ ul z-;cd tq9t+,5) whead-on collision of two objects is the coefficient of4gtt, 9;5hau +d-gw,o+ kvcflcz q)tj 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 y) 0vctt(i2v zpieces, one with three times the mass of the other. A depression is made in both faces of the cut, so that a firecracker can be placed in it with the block reassembled. The reassembled block is set on a rou20tv vizct) (ygh-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 direct*b:9q e)dww*f fq pi2oion at 5.5m/s collides head-on with a 10.0-kg object moving in the -x direction at 4i*f2 dwbw:o*fe 9)qq pm/s Find the final velocity of each mass if:
(a) the objects stick together;   m/s
(b) the collision is elastic; v'$_A$ =    m/s v'$_B$ =    m/s
(c) the 15.0-kg object is at rest after the collision;   m/s ----待选择----not reasonable reasonable 
(d) the 10.0-kg object is at rest after the collision;   m/s ----待选择----not reasonable reasonable 
(e) the 15.0-kg object has a velocity of 4m/s in the -x direction after the collision. .   m/s ----待选择----not reasonable reasonable 
Are the results in (c), (d), and (e) “reasonable”? Explain
( Let A represent the 15.0-kg object, and let B represent the 10.0-kg object.)

  A radioactive nucleus at rest decays into a second nucfr k .zr*vzy;vwlns40:bm . 4xleus, an electron, and a neutszv mz4.ykb *wx .0rflr:n;v4rino. 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 mass3hfb9nal ;qoog m3, *)7j5 w ibp6nfrt $m_\mathrm{A}=0.400$kg moving with speed $\nu_\mathrm{A}=1.80$m/s strikes ball B, initially at rest, of mass $m_\mathrm{B}=0.500$kg As a result of the collision, ball A is deflected off at an angle of 30.0 $^{\circ} $ with a speed $\nu_\mathrm{A}^{\prime}=1.10$m/s (a) Taking the x axis to be the original direction of motion of ball A, write down the equations expressing the conservation of momentum for the components in the x and y directions separately. (b) Solve these equations for the speed v'$_B$ and angle $\theta_{\mathrm{B}}$ of ball B. Do not assume the collision is elastic. $\theta_{\mathrm{B}}$ =    $^{\circ} $ v'$_B$ =    m/s

  After a completely inelastic collision between two objects of equal mad bp or-wqm627m4lwun s(3 a f/,e.yjass, each having initial speed the two move off together with speed v/3 What was t.u afq-p6 (ynmmbw2owr4a/ j 3el7ds,he angle between their initial directions?    $^{\circ} $

  Two billiard balls of equal mass move at r3uy fr0uvgxl*)2 2c bw g2)maeight angles and meet at the origin of an xy coordinate system. Ball A is moving upward along the y axis at 2m/s and ball B is moving to the right along the x axis with speed 3.7m/s After the collision, assumed elastic, ball B is moving along the positive y axis (Fig. 7–37). What is the final direction of ball A and what are their two speeds? direction of ball A ieyux2 u )3)2m2*g0 rvalwgbcfs  ----待选择----x directionx direction v'$_A$ =    m/s v'$_B$ =    m/s

  A neon atom (m=20u) makes yl4u 5)fw yiw3 w8dnk5a perfectly elastic collision with another atom at rest. After the impact, the neon atom travels away at a 5f3ynw5kldu 8 w 4)iwy55.6 $^{\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 o5xgfz (k: brif(q, 8relastic collision with another atom at rest. After the impact, tfq5(ibr :fr kzx,(8oghe neon atom travels away at a 55.6 $^{\circ} $ angle from its original direction and the unknown atom travels away at a -50 $^{\circ} $ angle. What is the mass (in u) of the unknown atom? [Hint: You can use the law of sines.](Let A represent the incoming neon atom, and B represent the target atom) $m_B$   u

  Find the center of mass of the three-mass system shown in Fig. 7–38.un dfbi4zj lg-)9vr k/:xk-p3 Specify relative to the left-hand 1.00-kg mass.)vpxf gbrdi/4 3z--k9 l:knuj    m

  The distance between a carbon at )w8p4rs1 uhrjws4yw4om ($m_{\mathrm{C}}=12\mathrm{u}$) 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. Howif *hl-qmfgp3it )*b/ far from the front of the car wi mfi-l f*t/ *qpb)hgi3ll 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 a mass of 70.0 kg.    m

  A square uniform raft, 18 m bmnu0k lip/cl x-v; f d2jxs;79y 18 m, of mass 6800 kg, is used as a ferryboat. If three ccmx -lk /i;nvs0p2dlu9fj;7x ars, each of mass 1200 kg, occupy its NE, SE, and SW corners, determine the CM of the loaded ferryboat.$X_{CM}$ =    m $Y_{CM}$ =    m

  Three cubes, of side*9f1 /wp urjhz2y g3ias $l_0$,$2l_0$, 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 pa.nih6 - ndgam;ste (see Fig. 7–40), each of which is a cube of lengtn .ai n6hm;g-dh 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 radius 2R has a circular hole of radtfb:eo 1so) r70jh-s ew8a2vsius 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.ors21ho jw tebv :sas7e-8)0f 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 Table 7–1, and ct(vl 3cudehkw-x (g 1/alculate the mass of one g3ku/(1w vtl-(x cedhof your legs.    kg

  Determine the CM of an outstretched arm using Tabdm/37vlk . hskle 7–1.   % of the person's height along the line from the shoulder to the hand

  Use Table 7–1 to calculate the pn, n.k*.5tg x y)qfiddq( ird9osition of the CM of an arm bent at a right angle. k x9*t,q. yg.qfr (dndni5d)iAssume that the person is 155 cm tall. $X_{CM}$ =    cm $Y_{CM}$ =    cm

When a high jumper is in a position such that his arms and leg 2s5bdses (o1zqkl2 0is are hanging vertically, and his trunk and head are horizontal, calculate how far bo(q0zb5i l21sekd s 2selow 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 Me-n*j*gd xzn) n 0fvr,-rl .c,yji wr8oon 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 mf 0sbgtxmg.n(-ejz8 0 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 x4m0;+ho,f n agwh(oekg and a diameter 0.0800 m moun; h,ge 0fxoma o(hn4w+ted on a uniform cylindrical handle of mass 0.500 kg and length 0.240 m, as shown in Fig. 7–42. If this mallet is tossed, spinning, into the air, how far above the bottom of the handle is the point that will follow a parabolic trajectory?    cm

  A mallet consists of a uniform cylindrical head ow *z pu+xponjdr27-n g1w w7,qf 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 t2np-zj o*1wxrg7uq + n dwp7,whe bottom of the handle is the point that will follow a parabolic trajectory?    d    d

  (a) Suppose that in Example 7–14 (F6z.bo )int 2q gvq 9:cx/)m9+uxcfnhwig. 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 2kb u,.7c xt6p(foz4xjv iydgmia :73 its gondola, of mass M, are in the air and stationary with respect to the ground. A passenger, of mass m, then climbs out and slides down a rope with speed measured with respect to the balloon. With what speed and divyupoc,fixzx.(6:i3ga7 td 7b m 2k j4rection (relative to Earth) does the balloon then move? What happens if the passenger stops?

  An 0.145-kg baseball pitched horiz38v r8 t0cy-oqze1vlcontally at strikes a bat and is popped straight up to a height of 55.6 m. If the contact time is 1.4 rv 31vcy oc8z-qel8t0ms, calculate the average force on the ball during the contact.    $^{\circ} $

  A rocket of mass m travelingmbl3 wjhr* m+) fr)3z3po ttqn8*uoi: 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–d7 *p: qvgo2jj myi/.f43. Relative dimensions are also shown. Should the player be worried about this being a “scratch shot,” in which the cue ball will also fall into a pocket? Give detailsgy/j mpq2i 7.*fjd:ov.

  A 140-kg astronaut (including space suit) acquires a speed of 2.5m/s by pushib5lunn mlq4y 1qz+d+ ua);i;ok7.au zng off with his legs frombulzz1)+q.a ;54k+yia qunoul n 7;dm 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 *b7 o+0msi: vf21 rlty2ihxizinitially at rest in outer space. They then push each other apart. How far apart are the:ixf *ilo 7br+v20is yz 2t1mhy when the lighter astronaut has moved 12 m?    m

  A ball of mass m makes a head-on elastic collision with a second ball *l dn:qopr1 4o;wdledbo8 w5+(at rest) and rebounds in the opposite direction with a speed equal l p8 odne15*bold:wo+;r dqw4to 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 expew4kh+8 rgjlv,; e )nzksdg:9prt witness in a court case involving an automobile accident. The accident involved car A of mass 1900 kg which crashed ig: 8w9vh )zl4peg;d+kr kj,snnto stationary car B of mass 1100 kg. The driver of car A applied his brakes 15 m before he crashed into car B. After the collision, car A slid 18 m while car B slid 30 m. The coefficient of kinetic friction between the locked wheels and the road was measured to be 0.60. Show that the driver of car A was exceeding the 55-mph (90km/h) speed limit before applying the brakes.    mi/h

A golf ball rolls off the top of a flig:ab5zv4,2 td5f fek yaht 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 ofy at: 52 fa5b4fd,kevz 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 vertically into a 1.40-kg block of wood a7tn n)37 ugbbmt 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 bullet bub b3g t7mn7)necomes embedded in it?    m

  A 25-g bullet strikes and becomes embedded in a 1.35-kg bloc ,goig ,4 ll(ri*cfkd5k of wood placed on a horizontal surface just in front of the gun. If the coefficient of kinetic friction between the block and the surld5*,ci ogglik(r,4f face 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 k xmj m(lw9:xs/g and the other of mass 60 kg, sit in a rowboat of mass 80 kg. With the boat :x sxmmjwl(/ 9initially 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 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 wa8 wb(2aabe7l qs 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 fragmen8wh b 0onhvo88;6u rxdw0y )ehts by an explosion. One fragment acquires th )88ewh;0r dox yo6hv nb0uw8wice the kinetic energy of the other. What is the ratio of their masses?   

  The force on a bullet is given by the formula F = 580w+ rcqff3y kvqkm5*ddc6o ,50-( $1.8 \times10^{ 5}$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 4 5(qrk7jrv zf$m_A$ = 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 avafrv5 2c 4s1i9dwgoms- n ;2clpha particle and a smaller nucleus. What will be the speed a4-roc9 vvc;fd2smni2 w5s1g 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 ta d*c -/ydgypf+gd; i7vrget) 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 slides down a 30.z q8a,1u y,dsb0 $^{\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 l (; .yeytulad +7 dmb)-u1e rmsgoo7wxh4.e. upper limit on mass m if it is to rebound from.7.-y1 thlrds mg ye xbew)o m+ealo.du74(; u 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 shows the pla (( fzaw e:ua.fkkft kx7jf5e14d6ju;net Saturn moving in the negative x direction at its orbital speed (with respect to theze7( 4 61xu.df;j5ak(kkt:efwuff j a 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