We claim that momentum is c5x j v rmn+uza2/a 2qo.4itev6onserved, yet most moving objects eventually slow dowurj25mv /toezv4a x+q ni6.a2n and stop. Explain.

When a person jumps from a tree to the ground, what happens tlh 5jdbb z)3tr 2m82dno the momentum of the pers3)d8nzb5rm lh2t jd2bon upon striking the ground?

When you release an inflated but untied balloon, why does it fly across th2bu +0 lb1s6rhiteds.s7x7 mc o;kr+me room? m l17b+t rkme o;susx6d.+ rs7cb0ih2

It is said that in ancient times a ric 3 2c tva bl;y1rx.9mk5mkt+iz7 c/tagh 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. What could he have done to save hims tcmt tb i ;2ckxk +z79g3y15vr/.aalmelf had he not been so miserly?

How can a rocket change direction when it is far outu 3ak0z( jjbh0 in space and is essentially in a vacuu (ahj30 j0bzkum?

According to Eq. 7–5,f4w / qz7uwk rl)o*yp3 the longer the impact time of an impulse, the smaller the force can be for the same momentum change, and hence the smaller the deformation of the object on which the fouy7l /qr4w k)* pfoz3wrce acts. 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. Todwsgkb,i+lx a3u9mn w773 de, iay, though, cars are designed to have “crumple zones” that collapse upon impact. Whanikux b3w 7,9deai,+w3sgm 7l t is the advantage of this new design?

Why can a batter hit a pitched basebfl8/n/c 79u kqrwelnx f qoh7d+ uq*:y2z.6v oall further than a ball tossed in the air by the battfqql/orwx+:/q.o7k9*n yn7d u86l vcf uz2 heer?

Is it possible for an object to receive a larger impug 7xip*x;z 2fulse from a small force than from a lg7 i2fzxx* p;uarge force? Explain.

A light object and a heavy objecto( + b;qxnkso6a ml(;fvy3mf9 have the same kinetic energy. Which has the greater mome+v( ys39qm;(f; lbx6moaknfo ntum? Explain.

Describe a collision in which all kinet6e,i7vk(q dr gic energy is lost.

At a hydroelectric power plant, water is directed at high s)//r dl;5ifllm w.mkkpeed against turbine blades on an axle that turns an electric generator. For maximum power generation, should the turbine blades be designed so that the water ldkl. m liw/)m5/rfk;is brought to a dead stop, or so that the water rebounds?

A squash ball hits a wall atoea+fz cmgo .9;t.g)u 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 stf5 i 1o1. yo-zvcx7yn1c poop)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 this process? (b) If we consider the ball fnzo)cyc7 x v1 .o5p1 p-o1iyoand 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 backward when carrying a heavy +.3krnwvqbk8 z k.wz, -kg*pxload in your arms?

Why is the CM of a 1-m length of pipe at its mid-poin yuy9-o9jh 1fbt, whereas this is not true for your a obuyfj9-h9 y1rm or leg?

Show on a diagram how your CM shifts when you change b lsau086n*n dfrom a lying position to a sitting posianub* 6ldn80 stion.

If only an external force ct lh/y 5ta.2myan change the momentum of the center of mass of an object, how can the internal force of an engine accelera5yla tm.hyt /2te a car?

A rocket following a parabo-jj ,doo eyld2st 4,57 u9tktclic path through the air suddenly explodes into many pies7oe4j, d9uktdtjc y, 5- l2otces. What can you say about the motion of this system of pieces?

  What is the magnitude of the momentum of a 28-g sparrow flying with a spe +kkwizo848*fdp t*q4 srdf3ied of $8.4 \; m/s$    $kg \; m/s$

  A constant friction force of 25 N acts on a ldl23( gvs tf865-kg skier for 20 s. What is the skier’s changs8gl 3v2(fd lte in velocity?    m/s

  A 0.145-kg baseball pitched at 39 m/s is hit on a hhn a1rjf :x 2bt;yhd5yjp7:v)orizontal line drive straight back toward the pitcher at 52m/s If td1p fht 5v:ynjh:xja by;7 2r)he 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 horizontally with a spa fjgw7o1l3h,eed of 10 m/s Fig. below Calculate the velocity of the boat immediately after, assuming it was initially at rest. The mass of the child is 26.0 kg, and that of the boat is 45.0 kg. Ignore water resistance. Theofw,7g h3 jl1a magnitude of the velocity of the boat is    m/s

  Calculate the force exerteii,jx0r r 8 dd:*-peucd on a rocket, given that the propelling gases are expelled at a raep:cid-r ru8 ,0dix j*te 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 movingcs83cni wbiw1m( -/n e 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 frictionless track with a cox mjqrpw5 4(t6nstant speed of 18m/s A 5350-kgxqmj6 p5t 4w(r load,initially at rest, is dropped onto the car. What will be the car’s new speed?    m/s

  A 9300-kg boxcar traveling aty-c4l *tyuh i0d 6njt) $15 \; m/s$ strikes a second boxcar at rest. The two stick together and move off with a speed of $6 \; m/s$ What is the mass of the second car?    $m/s$

  During a Chicago storm, winds can whip horizontally at speeds of 1k+n c7g v2yd-r00km/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. Assumgyckv+72r d-ne 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 9emp.eoj rg*e84miw; car coasts along with a constant speed of 8.6m/s on a level track. Snow begins to fall vertically rpwee.e8 jo9 *im gm4;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 particl+m(pg 4dbnz;ie 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 thezd+;np(mbg 4 i alpha particle have when it is emitted?    m/s

  A 23-g bullet traveling 230m/s penetrates a 2.0-kg block of wood anz.fgw29a 9 wm0yhqm4 ue; 4 nggbzy15av)k9bgd emerges cleanly at 170m/s If the block is b)9 k5y4gfn a9bwu g mm0eqgv2 .yw1z4zahg;9 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 trav vnj /zfo1+6kxeling 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 3 wn*rml /5uld4180 kg is traveling in outer space with a velocity of 115m/s To alter its course rdm/4w*l l 5unby 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 th*w/agshxk. tz, -n3 ije tee at a speed of 45m/s The golf club was ig w ,kzsi. -axt/3*njhn contact 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.8-66 v7bgotxapnwh: 0vz mbs and comes to rest in a time interval of 8.0 ms. (a) What is the impulse given to t0vt8x6v-gbzh6b.mnw po: 7 sahe nail?    kg*m/s
(b) What is the average force acting on the nail?    N

  A tennis ball of mass m=0.06kg andi2u fn 4c *.qxl9a/s +df7nefc 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 crashworthinvt3dzg p4.w .e-ba g9lwyoj(21x3vueess of new automobile models. Cars are tested by smashing them into fixed, massive barriers at 50km/h (30 mph). A new model of m94 23zgwy1(levwv.3tda- e p .jbg ouxass 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 ry6 3xxu 5komv3s;h *iuunning at 4m/s to the east and is stopped in 0.75 s by a head-on tackle by a tackler running due west. Calcuk*3m5 o u;xusixvyh3 6late
(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 e1 h nqzym,96 iikq8jqf+0cp )direction and is given by the graph of Fig. 7–33 as a function of time. Use graphical methods toqc0 8ny p1ekqq6,+i9f h)zj im 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-kmx-(p c9qd ;ck;r h-kpg person jump without breaking the lower leg bone 9m k;cph;( c-p-qk rdxof 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 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 9qf.3upt6qpc direction) with a speed of collides head-on with a 0.220-kg ball at rest. If the collision is perfect9f q3quc ppt.6ly 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 3majcjz2m6of/1g z s7.i /u sce;/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;jcos1f izz.2m//je ga76 sc u 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 c9w)p7rsxt 50bllp,z f1 zu sh9ollision. If one ball’s initial speed was 2m/s and the other’s was 3m/s in the opposite direction, what will be their speeds after the collision?(Let A represent the ball moving at 2.00 m/s, and call that direction the positive direction.Let B represent the 5,tz0l sp9 hfrs7u)b9l pw1zxball 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 o- xa:chi c /xbuy8y-3 4ozoew1f 2.5m/s collides 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, a o-u1/ew-a8b3cyz ix:4xy h ocnd 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 moving with a speed of 8.5m/s colcjle8(l) qp7s lides head-on and elastically with another ball initiall )sc8ljlq7p (ey at rest. Afterward the incoming softball bounces backward with a speed of 3.7m/s Calculate
(a) the velocity of the target ball after the collision    m/s
(b) the mass of the target ball.    kg
(Let A represent the moving softball, and let B represent the ball initially at rest.)

  Two bumper cars in a xz3w5/:dq tzan amusement park ride 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 diffetz qw/z:d5xa 3rences 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- q 9tn)+h*,n6y wrgdlgon collision with a second ball initially at rest. The second bagnwrgn h +)96tqldy ,*ll moves off with half the original speed of the first ball.
(a) What is the mass of the second ball?    kg
(b) What fraction of the original kinetic energy $(\Delta\mathrm{kE/KE})$ gets transferred to the second ball?   

  In a physics lab, a cube slides d ).eq saco;;wa nr.kx)own a frictionless incline as shown 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? [ sa;;)w x)ok.qn.ec arHint: Both leave the incline moving horizontally.]$\Delta x_{m}$$\approx$    m $\Delta x_{M}$$\approx$    m

ake the general case of an object of mas72thjbl9q: n bs 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, p cwp0idut5:bw2 :8f1qnu,w s2 xtyx ( p-mj0myrojectile 1 results in a maximum height h of the pendulum equal to 2.6 cm. A second projectile causesp w 2 yt2c0w:ujdu5m1,tsxiyp qw:f ( -x08nbm 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 pendulum ha/lc*c*l)86adi7 lkv;seuvs e nging on a 2.8-m-long string, which makes the pendulum swing upward in a; lvel*ck)s*ue/68c7 asdl ivn arc. Determine the vertical and horizontal components of the pendulum’s displacement.vertical$\approx$    m horizontal =    m

(a) Derive a formula for the fractio b*r(libsw 7f2n 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 explosionjg2p g9.( brr rn/u8cw:jl-ks5 p-cop breaks an 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 the heavier particle, and B represent the lighter pb8kprj: o-g rswlcgcr 9-.(n / j52upparticle. ) KE'$_A$ =    J KE$_B$ =    J

  A 920-kg sports car collides into the rear end of a 2300-kg SUV stopped at hei+ ubcaq-k0:uvdcegkq*a r(,mi 2*f-a- f :a red light. The bumpers lock, the brakes are locked, and the two cars skid forward 2.8 m before stopping. The police officer, ka*fu:ka-cqifc m 2(deb+ k uig*aeq, h -0-rv:nowing that the coefficient of kinetic friction between tires and road is 0.80, calculates the speed of the sports car at impact. What was that speed?(Let A represent the sports car, and B represent the SUV) $\approx$    m/s

  A ball is dropped from a height of 1.50 m and rebounds to a height of 1.20 s 3*lqfct;n n0)d91j7.cxyhnhm vq1fm. Approximately how many rebounds will the ball make before losing 90%n3d0h1f7*1tfny;m. lhq jx n)9v sqcc of its energy?   

A measure of inelasticity in a rg k3g5 7wb/hhhead-on collision of two objects is the coefficient of res3g 5bhr7kh/gw titution, 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 mapn jhz)0p guus :r2*5b.kn)3qjjmv 9 e)k*s abss 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 reassemblq .)*b zpsv5mjp h:uu2b3*j0ang)r snk9jk)e ed. The reassembled block is set on a rough-surfaced table, and the fuse is lit. When the firecracker explodes, the two blocks separate and slide apart. What is the ratio of distances each block travels? ----待选择----1/91/101/81/6 

  A 15.0-kg object moving in the +x direction at 5.5me8ox6 v8(hxj dfqsg/, /s collides head-on with a 10.0-df/eo hq (8vg j,8sxx6kg object moving in the -x direction at 4m/s Find the final velocity of each mass if:
(a) the objects stick together;   m/s
(b) the collision is elastic; v'$_A$ =    m/s v'$_B$ =    m/s
(c) the 15.0-kg object is at rest after the collision;   m/s ----待选择----not reasonable reasonable 
(d) the 10.0-kg object is at rest after the collision;   m/s ----待选择----not reasonable reasonable 
(e) the 15.0-kg object has a velocity of 4m/s in the -x direction after the collision. .   m/s ----待选择----not reasonable reasonable 
Are the results in (c), (d), and (e) “reasonable”? Explain
( Let A represent the 15.0-kg object, and let B represent the 10.0-kg object.)

  A radioactive nucleus at rest dec-.nhy ovfvea o2:0uqqc; bd7: ays into a second nucleus, an electron, and a neuto2v 7cu;v-hqy d:af:. o0qbn erino. 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 masrn,t5uj chl1kslm,21s $m_\mathrm{A}=0.400$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 between2nelur9e) .tc5 +3popqc 4hkz two objects of equal mass, each having initial speedt)4 3ocl +9he5k.pu ecrnpqz2 the two move off together with speed v/3 What was the angle between their initial directions?    $^{\circ} $

  Two billiard balls of equal massj..:jlc gb-g 8nvri*j move 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 posit:r8* nc-gjjvb. . gjliive y axis (Fig. 7–37). What is the final direction of ball A and what are their two speeds? direction of ball A is  ----待选择----x directionx direction v'$_A$ =    m/s v'$_B$ =    m/s

  A neon atom (m=20u) makes a perfectly elastic collision with anothejic;pwm 537s.uc,sv9ydca8 or atom at rest. After the impact, the neon atom trave9vj7a .3icsp ycd,8wsm ;u5oc ls 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 elawhub 10n o2dfg::qaqbt 1v:f; stic collision with another atom at rest. After tbw:n2o g;:au:fhfd 11qt qv b0he 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-mabe.q 6p58hpk tss system shown in Fig. 7–38. Specify relative to the left-hand 1.00-khb8kpq65 .etp g mass.    m

  The distance between a c.k;vn* ydg)m7l8egq x arbon atom ($m_{\mathrm{C}}=12\mathrm{u}$) and an oxygen atom ($m_{\mathrm{O}}=16\mathrm{u}$) in the CO molecule is $1.13\times10^{-10}$m How far from the carbon atom is the center of mass of the molecule?    $\times10^{-11}$m

  The CM of an empty 1050-kg car is 2.50 m behind the fronqwo +*clkc t0.k.t yvg-3k:5 ah/cfprt of the car. How far from the front of the car will the CM be when two people sit in the front seat 2.80 m from the front of the car, and three people sit in the back seat 3.90 m from the front? Assume that each perso r 5k.y.vc ktk0cf-+ :*c3oqhw /lgaptn has a mass of 70.0 kg.    m

  A square uniform raft, 18 m by 18 m, b f8ho2h 12yglof mass 6800 kg, is used as a ferryboat. If three cars, each of mass 1200 kg, occupy its NE, SE, f21blg28o yhhand SW corners, determine the CM of the loaded ferryboat.$X_{CM}$ =    m $Y_{CM}$ =    m

  Three cubes, of sides(-*e4e6vsol p/glg y- 6kvtik $l_0$,$2l_0$, 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 identi 6jcydrj)r5t fhqlo9m/p 7s21+js w(h cal cases of tomato paste (see Fig. 7–40), each of which is a cube of length l. Find the w)s(s9r t /r26hdo7j lypmq fjh5 1cj+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 ohz 4c 3xfg-y8yf 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 position of the center of mass of the plate? [Hint: Try subtr8 z fycxh34-ygaction.]   R

  Assume that your propd.m5hc gw-k)mortions are the same as those in Table 7–1, and calculate tmhm -g5c) .wdkhe mass of one of your legs.    kg

  Determine the CM of an outstretched armdo49kpoll v10 using Table 7–1.   % of the person's height along the line from the shoulder to the hand

  Use Table 7–1 to calculate the position of the22 qomm ygaci;ji;* zqdnb+;; CM of an arm bent at a right angle. c ;b;i;ijz o2qdgy2 qn+m;m*aAssume that the person is 155 cm tall. $X_{CM}$ =    cm $Y_{CM}$ =    cm

When a high jumper is in a position such that hisadrnwo 1 ,.lj:v878u cdfqe/n arms and legs are hanging vertically, and his trunk and head are horizontal, calculate how far below the torso’s median line the CM will be. Will this C/88 co7 q ndj1f.ewr,d:vulanM be outside the body? Use Table 7–1.

The masses of the Earth and Moon aiv4*e37w3rf1pzh4 lmt-;icee a mu,k re $5.98\times10^{24}$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 8 fwt0)q5y ag4(k bgplfrictionless 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 cy, y:ha;c/-m.v 8 pepg i/jh4rh9go kfxlindrical head of mass 2.00 kg and a diameter 0.0800 m mounted on a uniform cylindrical handle of mass 0.500 kg and length 0.240 m, as shown in Fig. 7–42. If this mallet is tossed, spinning, into the air, how far above the bottom of the handle is the point that will follow a parabo-v h4ho;x y8/apecm krph./f , :i9jgglic trajectory?    cm

  A mallet consists of a uniform cylindrical head of mass 2.00 kqqb ij 3un/5gx9k3y.) z3vppdg 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 hand) 5bq339y dk vpn/j.uqgz3 ixple is the point that will follow a parabolic trajectory?    d    d

  (a) Suppose that in Example 7–1/xvlobu uat n4-c1 dw+ 5q2ts04 (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 go ganem l(c)(q sz0i)v3ndola, 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 s)(3v 0m(el)ncaqig zmeasured 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 a5hjb-vd .n zb(up:5ib nd is popped straight up to a height of 55.6 m. I5dvj-hbbib.p nu5 z:(f the contact time is 1.4 ms, calculate the average force on the ball during the contact.    $^{\circ} $

  A rocket of mass m traveling 5wwd*i2qpfl*i; 1 nnkir7sf+ 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 th4 op ouv*i14s2 v-mwnje 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 will also fall intp o4*2i4mj svv-1 uwono a pocket? Give details.

  A 140-kg astronaut (including space suit) acquires aggh6p ws3 8p6fjai7 u) speed of 2.5m/s by pushing off with gg 686p) 3juafshwp 7ihis 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 /.tv43s ayz/ uvv;rbf mass 60 kg and the other 80 kg, are initially at rest in outer space. They then push each other apart. How far apart are they when the ligh4s.v /3/vvatz yf;rbuter astronaut has moved 12 m?    m

  A ball of mass m makes a head-on el n.jdk0og+ *wcojee/4astic 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 the mass 4e +ewjkg don /j*.0coof the second ball? $m_B$ =    $m_A$(Round to two decimal places)

  You have been hired ad00jrfnn c.+cten)b4( ) juf is an expert witness in a court case involving an automobile accident. The accident invr0)c). effi nc nn4b0d+jjtu (olved 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 exceeding the 55-mph (90km/h) speed limit before applying the brakes.    mi/h

A golf ball rolls off the top of a flight of concrete steps of total verticane+i5l sy2 fk 9pt6bd8l height 4.00 m. The ball hits four times on the way down, each time striking the horizontal part of a different step 1.0 m lower. If all collisions are perfectly2b5te9s6+y8 pdl kifn 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 at rest directlywzpkipqwmcx/2 z/-)) b/z(0n tkhro( above it. If the bullet has a mass of 29.0 g and a speed of 510m/s how high will the k-nq p zr)c2imw/(/b o(p z0x t/k)wzhblock rise after the bullet becomes embedded in it?    m

  A 25-g bullet strikes andsa/ m1m)7m bvk 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 bl mkb1/av)m7msock 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 mlrhbpyi**k5//g0o*ip xm8 x w ass 75 kg and the 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/*0ilgh owk /p5b p*xi x8ymr* 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 was about;ep bhn926iv v+7z buds0fw g8 $ 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 fragments by an explosion. O+(a/myy3ur8v sx(jqdpc +m n4y3+d4u8(apq yv mj +mc/ rs(nxne fragment acquires twice the kinetic energy of the other. What is the ratio of their masses?   

  The force on a bullet is given by the formula Fbq.1u9 s g)wg1r kimb2 = 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 atj.hc tj *23kpl;ug.$m_A$ = 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 wjoh0 e,lu0a+7 l 8k ewyyi6+pan alpha particle and a smaller nucleus. What will be the speed ofeo j7u+0 e,0phw6wiy+al 8 ylk 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 angle +(oo-j1swyrrq5yn 2lxpob,, vlh8 4 w 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 k) h :k*gtbrfl j+mwqlow52. jf3f71qp-, plp.0 $^{\circ} $ incline which is 3.60 m high. At the bottom, it strikes a block of mass M=7kg which is at rest on a horizontal surface, Fig. 7–46. (Assume a smooth transition at the bottom of the incline.) If the collision is elastic, and friction can be ignored, determine
(a) the speeds of the two blocks after the collision,v'$_A$ =    m/s v'$_B$ =    m/s
(b) how far back up the incline the smaller mass will go. $\approx$   (Round to the nearest integer) (Let A represent mass m, and B represent mass M.)

  In Problem 79 (Fig. 7–46), what is the upper limit on mass m if it is to5, 8i4xilscl8t ebyk6i l l8.5hdum: s rebound from M, slide up the incline, stop, slide down the incline, and collide with M again?kl.sd8 i8:c ull iey65tl,8xh ib4 5ms    kg (Let A represent mass m, and B represent mass M.)

  The gravitational slingshot effect. Figurkqw ar4u),;y,r lfwapn),6d8udr6t a e 7–47 shows the planet Saturn moving in the negative x direction at its orbital speed tr,ad48) d6 kfr,,n w6) ylapaurwq;u (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