We claim that momentum is 1qt26)lo 2e2x;qnyriu d q/zaconserved, yet most moving objects eventually slow down and stop. Explierao26 t1/ndzqxl;y2u) q q2ain.

When a person jumps from a trevs;+c ; nslvj96ue(ga e to the ground, what happens to the momentum of the person upon s; +69 ne;v(vsglcju satriking the ground?

When you release an inflated but untied balloon, why does lvxfux6mz855 n, zae*it fly across the room?5x fv 5luzmx8,az *6en

It is said that in ancient times a rich man with a bas.jelpw8 06,v6 zetlo3h0 zv hg 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 himself had he not beenhe03p6j vtzzsl h6 ,l.v8 0eow so miserly?

How can a rocket change direction when it is far out in space and is essentiallyff ok6 w:)a8wnx8el0o l 8 k6)af:x80ownowf ein a vacuum?

According to Eq. 7–5, z8jjhwx:p y(4 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 force acts. On this basis, explain the value of air bags, which are intended to inw8yjx h zj:(4pflate during an automobile collision and reduce the possibility of fracture or death.

Cars used to be built as rigid asj7ngx;/-; u p1spnaulevh12a possible to withstand collisions. Today, though, cars are designed to have “crumple zones” that collapse upon impact. What is the advantage of tax ;j;l/ u1ppen -1nv7hsua2ghis new design?

Why can a batter hit a pitched baseball further th h5 )bjz.clh+can a ball tossed in the air by the bat.zbl c5h)j+hcter?

Is it possible for a8)wizf j osx+os:ii7 d ;y,dr;n object to receive a larger impulse from a small force thanwdi,;jdoys io+s:iz7 f; r)8x from a large force? Explain.

A light object and a heavy object have the same kint4c g c5 u h2l/8qm:*xe4vkhhxetic energy. Which has the greater mo tlch:c5u24ghh km8ve*/q 4xxmentum? Explain.

Describe a collision i8a hjapw:/c/h n which all kinetic energy is lost.

At a hydroelectric power plant, water is directed at high speed against turbine ,8 kn5b:+suh fjf r5wi8fwd45llya9s blades on an axle that turns an electric generator. For maximum power generation, should the turbine blades be designed so that t ,ha 5l9yfrb uws:wd85fnl is+5j8fk4he water is brought to a dead stop, or so that the water rebounds?

A squash ball hits a wall ai 6+n1oaji+ oa2:uumrt 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 fr)x3y5jhsj n3 xom 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 piec3jy)n js5xh3x e of putty that falls and sticks to the steel plate.

Why do you tend to le ;pjj,zw,q y1c8. rmqxan backward when carrying a heavy load in your arms?

Why is the CM of a 1-m length of pipe at its mid-pox 6ongau 0 ptif39*-pkh7f)hzz7s 8 rjint, whereas this is not true for youra-hkr6gfz 73n9jpp0o tzu)i7 x*hs 8f arm or leg?

Show on a diagram how your CM shifts when youz(d ts:flji, 3z0r31v8nx fts change from a lying position to a sitting posi(:srtz , 3ifjdv38xtsf1n l0 ztion.

If only an external fo av2kt q:b/0py 4on0evrce can change the momentum of the center of mass of an object, how can the internal fka by 0opvv2tq4/en:0orce of an engine accelerate a car?

A rocket following a parabolicznan4sx wo2c )eh54i5 5 vpq;r path through the air suddenly explodes into many pieces. What can you say about the motion of this sysnx p swhv5q;z4n5a52 ce4oi r)tem of pieces?

  What is the magnitude of the momentum of a 28-g sparrow flying with a spee eq8jgii* , a-q5fm8edd of $8.4 \; m/s$    $kg \; m/s$

  A constant friction force of 25 N acts on a 65-kg skier for 20 s. What is tmyh5z)nb,8,/tcsvx b1aza* 4;- t ryrl7t sf ehe sks1,s t/vb 7fnhyma y5,clza ;84tt)rx b-z*reier’s change in velocity?    m/s

  A 0.145-kg baseball pitched at 39 m/s is hit on a horizontal line drive styuqpmpb 0gwk7: , + uv.h1yu5jraight back toward the pitcher at 52m/s If the contact time between b0u kup,p:v .5qmw1+7ubgyy jhat 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 horizontal6muf1xhnww+wru xx49 j3 2a(jk -ayx*ly with a speed of 10 m/s Fig. below Calculate the velocity of the boat immediately after, assuming it was initially at rest. The mass of the child is 26.0 kg, and that of thukxy1axw6nw wj3 9uax-4mrhjx *+ (2fe boat is 45.0 kg. Ignore water resistance. The magnitude of the velocity of the boat is    m/s

  Calculate the force e78 vaho ncuck(a7z l9+xerted on a rocket, given that the propelling gases are expelled at a rate naohkv9l78u (c+ c7zaof $1500 \; kg/s$ with a speed of $ 4\times10^{4 } \; m/s$ (at the moment of takeoff). F =    $\times 10^7 \; N$

  A 95-kg halfback moving aab(r pl,)nd*xuu .o9v t $4.1 \; m/s$ 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 frictionles bj pp8 (ufaa (k3ne aahngxdi5-)w:3:s track with a constant speed of 18m/s A 5350-kg load,initially at rest, is droppe8kjnh) u(d: anag5(3 ap-xif: wabp3ed onto the car. What will be the car’s new speed?    m/s

  A 9300-kg boxcar traveling m8yc uf*h6u7jat $15 \; m/s$ 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 horizontaln 0o2s)yhlgzpmz8 3u vz- -+kjq,uv.fv4cu3 wly at speeds of 100km/h If the air strucf qz,8n.24mzsvw3 o)v+0u -vgz-y 3 phj kluikes a person at the rate of 40kg/s per square meter and is brought to rest, estimate the force of the wind on a person. Assume the person is 1.50 m high and 0.50 m wide. Compare to the typical maximum force of friction $\mu\approx1.0$ between the person and the ground, if the person has a mass of 70 kg.    N
$F_{on person}$  ----待选择----<> $F_{fr}$

  A 3800-kg open railroad car coasts along with a constant speed of 8.6m/s ov1 :/qds unif+n a level track. Snow begins to fall vertica snu+i vd/q:f1lly 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 pa )ezd nxf2h6svphl0.7rticle 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 masvf0. hh6)p27e sxdzl ns 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 tn/jj:o 0)xjx of wood and emerges cleanly oxn:)tjxjj0/ at 170m/s If the block is stationary on a frictionless surface when hit, how fast does it move after the bullet emerges?    m/s

  A 975-kg two-stage rocket is tracvi4 n1b a(w ufc.yv*5a/9js gveling 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 stjehu r/q*b4; gwo7( velocity of 115m/s To alter its course b* ;oj/t (7swubg4rqehy 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 then9w )6xe bvwh c g/a6)m:s843xonleue tee at a speed of 45m/s The golf club was in contbe3l9 o6w u8exw g/6en csvn)4m :ah)xact 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 rv hkk7kv41n2s bo-3 kvms)ke 2est in a time im 2)7v4b1hsn k vk23-kkskeovnterval of 8.0 ms. (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 speejm e+ s03.xi7df:m iywd 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 crashworthiness of new automob .6;sz r2gqibjile models. Cars are tested by smashing them into fixed, massive barriers at 50km/h (30 mph). A new model of mass 1500 kg takes 0.15 s from the time of qz.sbrj2 i 6;gimpact 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 toydd1pifh.+fo6 y 8)en the east and is stopped in 0.75 s by a head-on tackle by a tacklerh)poff6+y.ey di8 1n d 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) points in the +x dir dkb9o vuio at-*:3bd,b2fa, yection and is given by the graph of Fig. 7–33 a9f-*d,t23b a dbb :oiakyv,ou s a function of time. Use graphical methods to estimate
(a) the total impulse given the ball    N*s
(b) the velocity of the ball after being struck, assuming the ball is being served so it is nearly at rest initially.    m/s

  From what maximum height can a 75-kx n9 kt+-rngabkf8pv5u(93wkg 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 pfa(n v p9r5k tkx 3-bgwu8n+9kosition (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 mox*c rzzsi 4: * udrscp5plq;,,ving 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 directp qzi5xcz s*d,scu*4lp ;, :rrion of each ball after the collision?Let A represent the 0.440-kg ball, and B represent the 0.220-kg ball. $v'_A$    m/s  ----待选择----eastwest  $v'_B$    m/s  ----待选择----eastwest 

  A 0.450-kg ice puck, moving east with a speed of 3m/s has a hh dw mapt, 5*)tpri-j(yfx6l r+:7mea ead-on collision with a 06(7yrf * 5-m:wl ajxdpeitp+a), tr mh.900-kg puck initially at rest. Assuming a perfectly elastic collision, what will be the speed and direction of each object after the collision?Let A represent the 0.450-kg 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 collisiongcbvyj de0 g2q5;vggn s *v92io g*9k4. If one ball’s initial speed was 2m/s and the other’s was 3m/s in the opposite direction, what will be their speeds after the collision?(Let A represent the ball moving at 2.00 m/s, and call that direction the positive direction.Let B represent the ball moving at 3.00 m/s in the oppod22 cgvg94*ig s kye j*0b;59qvgvgnosite direction. ) v'$_A$ =    m/s v'$_B$ =    m/s

  A 0.060-kg tennis ball, moving with a speed of 2.5m/s collides he3zrmo.rm)wnn wb y3q5p6s*3ead-on with a 0.090-kg ball initially moving away from it at a speed of 1.15m/s Assumin*mnw3zsmw)36y3r 5 qp e no.brg a perfectly elastic collision, what are the speed and direction of each ball after the collision?(Let A represent the 0.060-kg tennis ball, and let B represent the 0.090-kg ball.)v'$_A$ =    m/s v'$_B$ =    m/s

  A softball of mass 0.220 kg that is moving with a speed of 8.5m/s 3uz6 ,rpn;yiecollides head-on and elastically with another ball initially at rest. Afterward the incoming softball bounces backward with a speedpz6 i e;,r3uny 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 elastic6mj*jn h3j59pyq (a n0:edckoally as one approaches the other directly from the re adh:3mcpkjj6 j5nqen 9*0(oyar (Fig. 7–34). Car A has a mass of 450 kg and car B 550 kg, owing to differences in passenger mass. If car A approaches at 4.5m/s and car B is moving at 3.7m/s calculate
(a) their velocities after the collision v'$_A$ =    m/s v'$_B$ =    m/s
(b) the change in momentum of each.$\Delta p_{\mathrm{A}}$$\approx$    kg*m/s $\Delta p_{\mathrm{B}}$$\approx$    kg*m/s

  A 0.280-kg croquet ball makes an elastic head-on collision with a sec +0hsv0aun 3 1wetfa+z (mh,mhond ball initially at r0,an mu3hhve1s(h +ztwm0+ af est. The second ball moves off with half the original speed of the first ball.
(a) What is the mass of the second ball?    kg
(b) What fraction of the original kinetic energy $(\Delta\mathrm{kE/KE})$ gets transferred to the second ball?   

  In a physics lab, a cube slides down a frictionless incline as shown iz 9jbf9:tl6dan Fig. 7–35, and elastically strikes another cube at the bottom that is only one-ha9 bzjad 96:ltflf 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 objey10(yshpj hcd2qw s64ct of 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 experimenkt 1kj2cb+w r0t, projectile 1 results in a maximum height h of the pendulum equal to 2.6 cm. A second projectile cau0t2crwkkb 1 +jses 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.; bvhh1qgzcm9*i531jlq8 pii6-kg pendulum hanging on a 2.8-m-long string, which makes the pendulum swing upward in an arc. Determine the vertical and horizont h5h 1i 1c9*jpiilqvgz3q m;b8al components of the pendulum’s displacement.vertical$\approx$    m horizontal =    m

(a) Derive a formula for the frac83 qnmt88 yruition of kinetic energy lost, $(\Delta\mathrm{KE/KE})$ for the ballistic pendulum collision of Example 7–10. (b) Evaluate for m=14g and M=380g

  An internal explosion breaks an object, initially at rest, into two piecesmvmzwo9b x5bz m32o9,, one of which has 1.5 times the mass of the other. If 7500 J were released in the explosion, how much kinetic energy d5z2 m m,owvbzob9mx 39id 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 the rear end of a 2300-kg SUV stopped 4nu)c iyl zq(onu27*bat a red light. The bumpers lock, the brakes are locked4ounqc7(ln*i2u y )z b, and the two cars skid forward 2.8 m before stopping. The police officer, knowing that the coefficient of kinetic friction between tires and road is 0.80, calculates the speed of the sports car at impact. What was that speed?(Let A represent the sports car, and B represent the SUV) $\approx$    m/s

  A ball is dropped from a heig7*yz8mrria y hiaa fl7g-)oeh175m2mht of 1.50 m and rebounds to a height of 1.20 m. Approximately how many rebounds will the ball make beforlyohai yzgm 7 e7-m5r7 8ir*fmha)2a1e losing 90% of its energy?   

A measure of inelasticity in a head-on collision0xklc3/f9- /x ie/wn+tjyer j of two objects is the coefficient of restitution, e, defined anc/fkr-/jx09 w/j txi3 + ylees$e=\frac{\nu_\mathrm{A}^{\prime}-\nu_\mathrm{B}^{\prime}}{\nu_\mathrm{B}-\nu_\mathrm{A}},$
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 w3yo.nmw i7y 2sith three times the mass of the other. A depression is made in both faces of the cut, so that 73wyys n.i2mo a firecracker can be placed in it with the block reassembled. 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 di/o wx:r kxm/4rrection at 5.5m/s collides head-on with a 10.0-//xm:wor4 rxkkg 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 decays into efy2twq 0hm,p*w ff jj926yp3 a second nucleus, an electron, and a neutrino. The electron and neutw*ty2p w96pyfj f3m f20eh, jqrino 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 masa n :q e)dqf/a a7fd)h-(cuvw,2,notds $m_\mathrm{A}=0.400$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 equal1-+re (u nyeln y1po1s mass, each having initial speed the twonl 1yeypr1s( -u +oe1n move off together with speed v/3 What was the angle between their initial directions?    $^{\circ} $

  Two billiard balls of equal mass mve9: tsi:nkkag2s z5,ok9 4 (ufn*kazove at right angles and meet at the origin of an xy coo aanfs5k4e: n(* :ku ts iz9,vz29okkgrdinate 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 is  ----待选择----x directionx direction v'$_A$ =    m/s v'$_B$ =    m/s

  A neon atom (m=20u) mak chnb8o(y9 q3mes a perfectly elastic collision with another atom at rest. After the impact, the neon atom travels away at a 55.6o3mb( chy9q n8 $^{\circ} $ angle from its original direction and the unknown atom travels away at a -50 $^{\circ} $ angle. What is the mass (in u) of the unknown atom? [Hint: You can use the law of sines.](Let A represent the incoming neon atom, and B represent the target atom) $m_B$   u

  A neon atom (m=20u) makes a perfectly elastic collision- l/,y 8wrhigr with another atom at rest. After the impact, the neon atom travels away at awgrl-yh, 8/ ir 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. Specif( :oz,dam n4ocr.9 ahhq9*dwuy relatq 9.n ,dooh4carw9:(haudm* z ive to the left-hand 1.00-kg mass.    m

  The distance between a carbon atom (ntxads9w 5 dy76d:*nd $m_{\mathrm{C}}=12\mathrm{u}$) 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 frontf -f z9lqz5osyej7o0( of the car. How far from the front of the car will the CM be when5 yz79(lz- js0foqfe o 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 by 18 m, of mass 6800 kg,k4g71i; ndrj7os9 h xz is used as a ferryboat. If three cars, each of mass 1200 kg, occupyogz rjis779; 4d1nx hk its NE, SE, and SW corners, determine the CM of the loaded ferryboat.$X_{CM}$ =    m $Y_{CM}$ =    m

  Three cubes, of side mfq8u m8 z8d dksjvo;n60f32uda5; cls $l_0$,$2l_0$, and $3l_0$ are placed next to one another (in contact) with their centers along a straight line and the $l=2l_{0}$ cube in the center (Fig. 7–39). What is the position, along this line, of the CM of this system? Assume the cubes are made of the same uniform material. $X_{CM}$ =    $l_0$ from the  ----待选择----leftright  edge of the smallest cube

  A (lightweight) pallet has a load of identical cases of tomato paste (see Fig+ 0kmr1qqtm6dus7 ir 8. 7–40), each of which is a cube of length l. Find the center of gravity in the horizontal plane, so that the crane operator 8qurkr67stm1d mi 0q+can pick up the load without tipping it.$X_{CM}$ =    l $Y_{CM}$ =    l

  A uniform circular plate of radius 2R n4wx(jy4xz++kxen0c :y;-3rsi v v a nhas a circular hole of radius R cut out of it. The center of the smaller circle is a distance 0.80R from the center C of the larger circle, Fig. 7–41. What is the position of the center of mass of the plate? [Hint: n4za x+ry v: nsnc4-xx+w(;y0ikev3j Try subtraction.]   R

  Assume that your proportions are the same as those in T 0tk(v6xjqh c+ ed 85zm by6v(*h6wegrable 7–1, and calculate the mass of one of your (6v g h ec 6dx e58w0+mqtyrb(zjh*kv6legs.    kg

  Determine the CM of an outstretched arm using Tabl 9 sl/8:m1c ocfajb3yre 7–1.   % of the person's height along the line from the shoulder to the hand

  Use Table 7–1 to calculateotbf 5s0u2;oz*,; ofzlx1lm e the position of the CM of an arm bent at a right angle. Assume that the person is 1;so e0mo21fuzfzlx5b,*t lo;55 cm tall. $X_{CM}$ =    cm $Y_{CM}$ =    cm

When a high jumper is in a position such that his arms and legs are hangpco 8a:wh 3o7oing vertically, an3 o8o7ca wohp:d his trunk and head are horizontal, calculate how far below the torso’s median line the CM will be. Will this CM be outside the body? Use Table 7–1.

The masses of the Earth and Moon are mgnj,bjlx n/b/j)/j3-hfxs cbn95i5n6s ,v c$5.98\times10^{24}$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 tkz3b+v4(s ;yr.j mslon 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 he1, tfg dvt x87vxkk0;yad 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;t 1,87t0x kxg dkfvyv, 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 u * rnahb:x.3u0.0800 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 *: 3uu. bxanhrwill follow a parabolic trajectory?    d    d

  (a) Suppose that in Examplr gxza0i -*ov0e 7–14 (Fig. 7–29), $m_{II}$=3$m_{I}$ Where then would $m_{II}$ land?    d(Round to two decimal places)
(b) What if $m_{I}$=3$m_{II}$    d

A helium balloon and its gondola, of mass M, are in the air and stat: 7,ew+3(ao w4gbeaum ajq 2oeionary with respect to the ground. A passenger, of mass m, then climbs out and slides down a rope with speed measured with respect to the balloon. With what speed and direction (relative to Earth) does t u:3ej4+2o weaq awg7b o(,maehe balloon then move? What happens if the passenger stops?

  An 0.145-kg baseball pitched horizontally at strikes a bat and isec2sc rcc0u8 * popped straight up to a height of 55.6 m. If the contact time is 1.4 ms, calculate the average fosc8 e2r *ucc0crce on the ball during the contact.    $^{\circ} $

  A rocket of mass m tr1as w1lk0d 9ixy 0 9yw4agl- effo*wb:aveling 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 showktb40 midt8rnk(s 25mf h)-hg n in Fig. 7–43. Relative(85in -skbrdm 4)httm k02fhg 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 details.

  A 140-kg astronaut (inb ohraep r9w9h73nko o: ;r54tcluding space suit) acquires a speed of 2.5m/s by pushing off with his legs frr4 bo5r9 ar owhhn;9epo7tk3: om 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 initially at ee)t .zn/*ym1e)ofiarest in outer space. They then push each other apart. How far apart ar.oz*)y mat e1/ei)en fe they when the lighter astronaut has moved 12 m?    m

  A ball of mass m makes a head-on elastic collision with a second ball udixy(0wcx f pqmb 0/)9yb5nx12odr+(at rest) and rebounds in the opposite direction with a speed equal to 5(x9w/pxx bc id2o0) y dbq+ numyfr01one-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 in a court casekt z).umz2/ )pkqbo/f 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 exceeding the 55-mph (90km/h) ubkp )o/k2fm /qzz.t)speed limit before applying the brakes.    mi/h

A golf ball rolls off the top xso4 5;4gvx5bd* bfyq of a flight of concrete steps of total vertical height 4.00 m.sbxy;bd*5qv4o4 g5 xf 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 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 at rnwcaa.; xp- s1est directly above it. If the bullet has a mass of 29.0 g and a speed of 510aap -w.1xs ;ncm/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 1lqyx4g1ri/ ,x yzm3*m3jh-ws.35-kg block of wood placed on a horizontal surface just in front of the gun. If the coefficient of kinetic friction between the block and the surface is 0.25, and the impact drizry xsj3g-l4, yx/wm 1hm3*q ives the block a distance of 9.5 m before it comes to rest, what was the muzzle speed of the bullet?    m/s

  Two people, one of mass 75 kg and the other of mass w5e2miottb. aa4x;v;e g u +i,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 othe i,tog 4wav+t5i;e exuma b;.2r, 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 was abouts7y3.wq bvqq/*qmi4fw wml /1dy 9qy 7 $ 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 tw jwfj8a82 lq2qo fragments by an explosion. One fragment acquires twice the kinetic energy of the other. What is the ratio of their2jfw 2q 8jal8q masses?   

  The force on a bullet is given by the formula F = 58v+*/;ysgew1vm:(c heb tstm:x66ucl0-( $1.8 \times10^{ 5}$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 massest7l:9 iqp;)gk t) 8hog8iuyvy $m_A$ = 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 radioactiveli(o0x pvth+f2w l+z2xy into an alpha particle and a smaller nucleus. What will be the speed of th xx+zop tw 0v2lhf+(i2is 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 fikrfxli gyx98d2d7 be*0r9m gs ; (kf.wred 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 slidexn:zlkbl),kgvq m x /:8tn4f,s down a 30.0 $^{\circ} $ incline which is 3.60 m high. At the bottom, it strikes a block of mass M=7kg which is at rest on a horizontal surface, Fig. 7–46. (Assume a smooth transition at the bottom of the incline.) If the collision is elastic, and friction can be ignored, determine
(a) the speeds of the two blocks after the collision,v'$_A$ =    m/s v'$_B$ =    m/s
(b) how far back up the incline the smaller mass will go. $\approx$   (Round to the nearest integer) (Let A represent mass m, and B represent mass M.)

  In Problem 79 (Fig. 7–46), what is the upper limit on mass m if it iaotgfs;m,f7+w8k wy8 s to rebound from M, slide up the incline, stop, slide down the inclig8y8 7amffk,t+ws w ;one, and collide with M again?    kg (Let A represent mass m, and B represent mass M.)

  The gravitational slingshot effect. Figure 7–47 showsl)tk*e 5qmj w ;dj8dsv1m9-aa the planet Saturn moving in the negative x direction at its orbital speed (wiae qmds8dja9t15v- wm kj)l* ;th 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