We claim that momentum is conserved, ,t* ,posvnmho5*; cne yet most moving objects eventually slow down annh,n5e m*,osv ;poc *td stop. Explain.

When a person jumps from a tree to the ground, what happens to the momentum oyd) koy()b mh2f the person upondym()h )oby2k striking the ground?

When you release an inflated but untied balloon, why does makh +kjcl,k6*n9c*j )m ns)qit fly across the room? kj9hkjsl+q*a))nkc6c m ,mn*

It is said that in anciec7 ;ckld(66btk+ nqyqnt times a rich 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 himself had he not been so mikk+ ;q7n( 6lc yqt6dbcserly?

How can a rocket change direction wheny6pmg nvo*r9z ,5 n0, ef2ypwj it is far out in space and is essentially in a vacu6 ngj pf0w 2n ,yvm,5repz*o9yum?

According to Eq. 7–5, the longer the impact time of an impulse, the smaller t :z9qa/cib +yphe 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 thz /ac pb+yq9i:e 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 coj,-7yieebq.q790r p e ylrh1ullisions. Today, though, cars are designed to have “crumple zones” that collapse upon impact. What is the y91el7u riqp.b-,reye q j 7h0advantage of this new design?

Why can a batter hit a pitched basebalbxy p*9aego7 e45yqop4 h;n6 ql further than a ball tossed in the air by t5o4qe *bhgy p7 e;6q94nopya xhe batter?

Is it possible for an object to receive a larger impulse from a smal.4lon;fo5 vgw m)jan*l force than from a l)onvl mang* ;w. 5fj4oarge force? Explain.

A light object and a heavy object have the same kiniy0h* a2e- y0; zcoajj.xf k;oetic energy. Which has the greater momentum? Exp2;*xj 0 of.ciyh za;-ajeko0ylain.

Describe a collision in which all kinetic ekgzi15 e bg)l7p wql m;*u3vo5nergy is lost.

At a hydroelectric power pu3 b)wcj:u d0g36eg kulant, water is directed at high speed against turbine blades on an axle that turns an electric generugwu3 cg063 j:)d kebuator. For maximum power generation, should the turbine blades be designed so that the water is brought to a dead stop, or so that the water rebounds?

A squash ball hits a 7/z: v8y mbyedwall at 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 hard1 dunfoku d10, 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 partfuu1d,do 10nk of this process? (b) If we consider the ball and Earth as our system, during what parts of the process is momentum conserved? (c) Answer part (b) for a piece of putty that falls and sticks to the steel plate.

Why do you tend to lean backwxsj,x v .jt(l+9:/zsf7* om bbcdysc 0ard when carrying a heavy load in your arms?

Why is the CM of a 1-m length of pipe at its mid-point, whereas s .d:g,ar :rt3(nc c6ooy :fyithis is not true fyns:3.dc ft:r (ac 6i, r:ogyoor your arm or leg?

Show on a diagram how your CM shifts when you change from a lying pom* j 58 hfsls4mp h8iitr92n(wsition to a m ih8ji4*s2(59sh f t8nrwpmlsitting position.

If only an external force can change the momentum o5fh ,1h:9 n zrr3rqpzbbu 61usf the center of mass of an object, how can the internal force of an engine accelerate a zpz 9 5u ,h:r31fbq urr6bsn1hcar?

A rocket following a parabolic path through the air suddenp1 b0.5auolc8hx 7my5 ky+jjnly explodes into many pieces. What can you say about x7u.5p5kco n bjla1y0h8 jym+ the motion of this system of pieces?

  What is the magnitude of the momentum of a 28-g spiv83zkn )ded *vvh35xarrow flying with a speed of $8.4 \; m/s$    $kg \; m/s$

  A constant friction force of 25 N acts on a 65-2zyy f /htal+ub2s;9lkg skier for 20 s. What is the skie+yh u lz2tyb;fla/9s2r’s change in velocity?    m/s

  A 0.145-kg baseball pip.k uvm1 x)e7nd4-i: yc0mt qetched at 39 m/s is hit on a horizontal line drive straight )q1 .p7cten x-d :e mmkv0iyu4back toward the pitcher at 52m/s If the contact time between bat and ball is $3\times10^{-3}$s calculate the average force between the ball and bat during contact.    N

  A child in a boat throws a 6.40-kg package out horizib3jqtr9 bjz. maey4 u9;gv)9eyv c 34ontally with a speed of 10 m/s Fig. below Calculate the velocity of the boat immediately after, assuming it was initially9bvqy3v 4 btiju3ee4 gca)zj;rym99. 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 rocket, given that the proow)kx 2vn0 x0vpelling gases are expelled at a ratex)w00o vxkn 2v 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 moving ay(duu7r -r i*wt $4.1 \; m/s$ 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 travelk25h3t 6 lourbv3m3:rmeq;so s alone on alevel frictionless track with a constant speed of 18m/s A 5350-kg load,initi m ;orquro35m:3shlk3et b2 6vally at rest, is dropped onto the car. What will be the car’s new speed?    m/s

  A 9300-kg boxcar tra43v-wckjx 3wui 0s+v i2z:ck xveling at $15 \; m/s$ 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 spee+khb9myqgc7 l w ;xov,6 ,cef6ds of 100km/h If the air strikes a person at the rate of 40kg/s per square meter and is brought to rest, estimate the force of the wind on a person. Assume the person is 1.50 m high and 0.50 m wide. Compare to the typical maximu6m,wfhg7 + 6ckqy;e9 bo,c vlxm 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 o etc )e;qgj+(rn a level track. Snow begins to fall vertically and fills the car at a rate of 3.5kg/min Ignoring;c geet)+q(r j friction with the tracks, what is the speed of the car after 90.0 min?$\approx$    m/s

  An atomic nucleus initially moving at 420m/s emits an alpha particle in the qy8qh804:tju+yulg j (9n rsvdirection 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( tglhq04n y vs+q9urj8 uj8:y the alpha particle have when it is emitted?    m/s

  A 23-g bullet traveling 230m/s penetrates a 2.0-kg block of wourhgf-mh0, x1od and emerges cleanly at 170m/s If the block is stationary u-m,h0 1 xrhgfon a frictionless surface when hit, how fast does it move after the bullet emerges?    m/s

  A 975-kg two-stage rocket isp.:dng6l rn/ h traveling at a speed of $5.80\times10^3\mathrm{~m/s}$ with respect to Earth when a pre-designed explosion separates the rocket into two sections of equal mass that then move at a speed of $2.20\times10^3\mathrm{~m/s}$ relative to each other along the original line of motion. Let “A” represent the upper stage (that moves away faster) and “B” represent the lower stage.
(a) What are the speed and direction of each section (relative to Earth) after the explosion? $v'_A$   m/s  ----待选择----away from the Earthtowards the Earth  $v'_B$   m/s  ----待选择----away from the Earthtowards the Earth 
(b) How much energy was supplied by the explosion? [Hint: What is the change in KE as a result of the explosion? $a\times10^8$ a =    J

  A rocket of total mass 3180 kg is travd ; inq.ehh,t:1af 8mheling in outer space with a velocity of 115m/s To alter its course by 35m81 tf.eh ;nqhid :,ha.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 b a) xut,6)fqrthe tee at a speed of 45m/s The golf club was in contact with tf)x uq6bra ,)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 :uv n8 (rh8katv epx)/igjs658.5m/s and comes to rest in a time interval of 8.0 ms. (a) What is the impulse kr8an5)hj gs:v/ 6xpteu(iv 8given 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 speed v=25m/s strikes xyl,96q. r r9zzl+ ywna 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 e.5f0wlcghksglm 0-xgmp u++ .ngineer in charge of the crashworthiness of new automobile 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 impact until it is brought to rest. (a) Calcul w+mk0fupl+x0 ggghc 5-..s mlate 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 running37k0zd pwp3k j+iie)x6d f2lv at 4m/s to the east and is stopped in 0.75 s by a head-on tackle by a tackd) 3e03id+2zl7p6 k jwixpfvk ler 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 4g) cwzarp-o4mo hf61tennis ball (mass 0.060 kg) points in the +x direction and is given by the graph of4)fmapoz o14 g 6hc-rw Fig. 7–33 as a function of time. Use graphical methods to estimate
(a) the total impulse given the ball    N*s
(b) the velocity of the ball after being struck, assuming the ball is being served so it is nearly at rest initially.    m/s

  From what maximum height can a 75-kg perswa7wspj :o5oc3)z8laj i (x w0on 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 xaz a0w(c8j5s7j:p3wi l w oo)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 direction) wp*aq/ /kes0c oith a speed of collides head-on with a 0.220-kg ball at rest. If tso/ e/ pk*0cqahe collision is perfectly elastic, what will be the speed and direction of each ball after the collision?Let A represent the 0.440-kg ball, and B represent the 0.220-kg ball. $v'_A$    m/s  ----待选择----eastwest  $v'_B$    m/s  ----待选择----eastwest 

  A 0.450-kg ice puck, moving east with a speed of 3m/s has a head-on collision wl0fan 6jal-0 d2:bj7f4x cw jnith a 0.900-kg puck initially at rest. Assuming a perfectly elastic collision, what will be the speed and direction of each object after the collision?Let A represent the 0.450-kg puck, and let B refa 2f006j dlb47ln cajjn-:w xpresent 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 *e efy ojada,6;4voj 3equal mass undergo a perfectly elastic head-on collision. If one bal*aj3j do6vfe;y oe4 ,al’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 opposite direction. ) v'$_A$ =    m/s v'$_B$ =    m/s

  A 0.060-kg tennis ball, moving with a d;e1gi,riflwdm 0u1.speed of 2.5m/s collides head-on with a 0.090-kf rdi iw0um. d;,1el1gg 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'$_A$ =    m/s v'$_B$ =    m/s

  A softball of mass 0.220 kg that is moving with +kiu2v6rl;k. wg l9yja speed of 8.5m/s collides head-on and elastically with another ball initially at rest. Afterward the incoming softball bounces backward wiu klv i9j2wy6l+g.k; rth a speed of 3.7m/s Calculate
(a) the velocity of the target ball after the collision    m/s
(b) the mass of the target ball.    kg
(Let A represent the moving softball, and let B represent the ball initially at rest.)

  Two bumper cars in an amusement park ride collide elastically as ovh+ln)2s 91 ny) mmtppne approaches the other directly from the rear (Fig. 7–34). Car A has a mass of 450 kg and 9th)v 21 mpp+ns)nmlycar 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 elast4+ k( ue obiq,c+0xzb5kn5 rxtic head-on collision with a second ball initially at rest. The second ball moves off with halz5xc ,e(orbx0qi5tnu+ k b +4kf 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 frictihlkwe+ bv-j22bx6u3lx4 5jd fonless 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 landj43xe2 x2dlw b 5j-6kf ubh+lv? [Hint: Both leave the incline moving horizontally.]$\Delta x_{m}$$\approx$    m $\Delta x_{M}$$\approx$    m

ake the general case of an object 0rplvgrh tt ab89q,;8of 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 pendul24hqbi:8zl l wxx8h-h um experiment, projectile 1 results in a maximum height h of the pendulum equal to 2.6 cm. A second projectile causes the the 2ix8h 4hzlwq:x 8-hlbpendulum 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 travelin 9 jdb6 iq08x9.iu2jjghwc c-ng 230m/s buries itself in a 3.6-kg pendulum hanging on a 2.8-m-long string, which makes the pendulum swing upward in an arc. Determine the vertical and horizontal components of the pendulum’s disi8g- jbc9 jijqdun9x2c . 6hw0placement.vertical$\approx$    m horizontal =    m

(a) Derive a formula for th((whn j(j 9ejm9y)dlw e fraction of kinetic energy lost, $(\Delta\mathrm{KE/KE})$ for the ballistic pendulum collision of Example 7–10. (b) Evaluate for m=14g and M=380g

  An internal explosion breaks an object, initially at resr94lh2eqnc5hd 1cdu;s9 j uh*t, 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 thehnlu2h4 u9s 1he5d*jcd ;9qrc lighter particle. ) KE'$_A$ =    J KE$_B$ =    J

  A 920-kg sports car collides into the rear end of a 2300-kg; xs 1pu5sx0sb SUV stopped at a red light. The bumpers lock, the brakes are locked, and the two cars skid forward 2.8 m before stopping. The police officer, knowing that the coefficient of kinetic friction between tires and road is 0.80, calculates the speed of the sports car at 1bs0 ;sspxxu5 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 m. Apbqw q4.+ dozq(b 8psm2proximately how many rebounds will the ball make before losing 90% of its energqs( md+.bpqq24w8obz y?   

A measure of inelasticitytwo4upi0 u) wgr3vz ,5 in a head-on collision of two objects is the coefficient of restitution, e, def p3)u4rv wgt05,uzow iined 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 intr-q7vfooapv,5 9 r/yc o two pieces, 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 inqf95co,vyprvr a/ o7- 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 direction at 5.5m/s co- -g khq3f-4rc x3iu37f,tu5bvbnghii ww8 k)llides head-on with a 10.0-kg object moving in the g i543 gki kv37)-fn-wt qwcbu-uxri3b8,hfh-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 a second nucleus, an eoyn ;;+o4ksh electron, and a neutrino. The electron and neutrino are emitted at right angs nky;e4 oh;+oles 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 mas6 -u(ke.:r4ah3yg-;o*w l sx pvrxubgs $m_\mathrm{A}=0.400$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 collis5camaves,m )7lw kr.6ion between two objects of equal mass, each having initial speed the t e s.rkav,75wa)mc lm6wo move off together with speed v/3 What was the angle between their initial directions?    $^{\circ} $

  Two billiard balls of equal mass move at right angles andj:w6h.ojzti7qxxv1 a 72 y3hd 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 7x.1t6 j7zavo xwqiyjdh3:2h 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) makes a pern dwtj4k429eo fectly elastic collision with another atom at rest. Aftwtd4no4j k29eer the impact, the neon atom travels away at a 55.6 $^{\circ} $ angle from its original direction and the unknown atom travels away at a -50 $^{\circ} $ angle. What is the mass (in u) of the unknown atom? [Hint: You can use the law of sines.](Let A represent the incoming neon atom, and B represent the target atom) $m_B$   u

  A neon atom (m=20u) makes a n6olsqsukxe55 l 42k:perfectly elastic collision with another atom at rest. After the impact, the neon atoon ss5l4xq2k 6lk5 ue:m 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 s3 dbceiwi0 w8((3 fwl 6txb/gxhown in Fig. 7–38. Specify relative to thii w 6/b3(tlgf ww 8d0e(3xbcxe left-hand 1.00-kg mass.    m

  The distance between a carbon 6jc3l 74ov83 gf6 ohmvqwzbp-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 front of the car.t ,g(je/gkme bn1qg ;/ 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 thrb gj//(tee;,gq ng1m kee 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, is us pm5nk43y w9p, /n3kwjk-0ebh sd;yna ed as a ferryboat. If three cars, each of mass p k;mn pawn/d9- 5jk,bsew03h4 y yk3n1200 kg, occupy its NE, SE, and SW corners, determine the CM of the loaded ferryboat.$X_{CM}$ =    m $Y_{CM}$ =    m

  Three cubes, of sidekhsg)-l9vmza+a/ 5v x/s qee +s $l_0$,$2l_0$, 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 tomatyra;k(fuvvhb; ;ocpqzd520 0o paste (see Fig. 7–40), each of which is a cube of length l. Find the center of gravity in the horizontal plane, so that the crane operatord2y;b; vpru0c50 v ;kaqz hof( 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 radius R cup,.t 8hstr5j1lsll5r1 v*x jnt out of it. The center of the smaller circle s 5ls5rv pj8jxt,.tllrh* 11 nis 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 subtraction.]   R

  Assume that your pro f-.h-my(x-kprpp xk 6portions are the same as those in Table 7–1, and calculate the masyr( p-px xp.h-kk6mf -s of one of your legs.    kg

  Determine the CM of an outstretchedqmeb1k,x/b7evx*u r )j+j 2vf/cfj- v arm using Table 7–1.   % of the person's height along the line from the shoulder to the hand

  Use Table 7–1 to calculate the position of th ,v0r-nthz gy0e CM of an arm bent at a right angle. Assume that the r,h0tg-0vnyzperson is 155 cm tall. $X_{CM}$ =    cm $Y_{CM}$ =    cm

When a high jumper is in a position such that his arms and let ( ;r1fh1p pcwn1jeokj m*3n 0.splv*gs are hanging vertically, and his trunk and head are horizontal, calculate how far below the torso’s median line the CM will be. Will this CM btw 0*(e r .o ljmsp3p*jchp11k 1;vnfne outside the body? Use Table 7–1.

The masses of the Earthpj. x3 vo,+nr--oqoj n and Moon 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 s-g c)r8 9z*dmiegyt1m 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 :09qy;/nai( ahujqvhys ri etyu.2,yl,5 x2 l cylindrical head of mass 2.00 kg and a diameter 0.0800 m mounted on a uniform cylindrical handle of mass 0.500 kg and length 0.240 m, as shown in Fig. 7–42. If this mallet is tossed, spinning, into the air, how far above the botth .u;y hii2ry yja q5(0xqe2 s:vnt,/ulaly9,om of the handle is the point that will follow a parabolic trajectory?    cm

  A mallet consists of a uniform mbn1:qar4v/tn6 oq )a cylindrical head of mass 2.00 kg and a diameter 0.0800 m mounted on a uniform ca6)nm : q/a1qvnt4robylindrical handle of mass 0.500 kg and length 0.240 m, as shown in Fig. 7–42. If this mallet is tossed, spinning, into the air, how far above the bottom of the handle is the point that will follow a parabolic trajectory?    d    d

  (a) Suppose that in Example 7ejd 76dz )nogp 38h*ije2v cl0–14 (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 9 :mdhp1iaj1f ss2 pd tr0x7l*in the air and stationary with respect to the ground. A passenger, of mass m, then climf 9ls 7:t2dpaxdm *1 0hj1pisrbs out and slides down a rope with speed measured with respect to the balloon. With what speed and direction (relative to Earth) does the balloon then move? What happens if the passenger stops?

  An 0.145-kg baseball pitched horizontally at strikes a ba2sd.m sfcoj4 rk2sc z(wkz:8w n,1 *cot and is popped straight up to a height of 55.6 m. If the contact time is 1.4 ms, 2s :ckkcwzc(8s.orjn w*sd4,ofm 21zcalculate the average force on the ball during the contact.    $^{\circ} $

  A rocket of mass m travelvvznxj -+ w/p :k)kd8+m7u06 fnfummiing 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 cor7y w,6fx 7csdk -t: 8nxmwg8hhner pocket shot shown in Fig. 7–43. Relative dimensiw n:yw7-tm, h78cxgd6xfk h8sons 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 (including space suit) acquires a speed of 2.5m/s bx/ei :ev,u;q qy pushing off with his lxv q /uqei:e;,egs from an 1800-kg space capsule.
(a) What is the change in speed of the space capsule?    m/s
(b) If the push lasts 0.40 s, what is the average force exerted on the astronaut by the space capsule? As the reference frame, use the position of the space capsule before the push.    N

  Two astronauts, one of mass 60 a2yuavrlm0c5kc)9.d n90f 7x2 pmf vo 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 lighter astrocmf0.x5r0mfy9cl pn v9ad 2 2u7)k avonaut has moved 12 m?    m

  A ball of mass m makes a head-on elastic collismli/m,; 4tb(gj8m0n;be vu r kion with a second ball (at rest) and rebounds in the opposite direction with a speed equal to one-fourth its orilbbun m,4mt v rkm08eijg/( ;;ginal 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 coimyq9+uop, q* urt case involving an automobile accident. The accident involved car A of mass 1900 kg which crashed into stationary car B of mass 1100 kg. The driver of car A applied his brakes 15 m before he crashed inti9q +u ypmq,*oo 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 of ts45:alvu .ltf the top of a flight of concrete steps of total vertical height 4.00 m. The ball hits four times on the way down, each time striking the horizontal part of a different step 1.0 m lower. If all collisions are perfectly elastic, what is the bounce height on the fourth bounce whenatu4:sl5v lt. the ball reaches the bottom of the stairs?

  A bullet is fired vertically inthvlk8(ed1b :io a 1.40-kg block of wood at rest directly above it. If the bullet has a mass of 29.0 g and a speed of 510m/s how high will the block rise after the bullet beco:kvbi 8e(d 1hlmes embedded in it?    m

  A 25-g bullet strikes and becomes 6j+ c af)uywwkg0 kq:(embedded in a 1.35-kg block of wood placed on a horizonta w:fqjk0u( +6cwgy) kal 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 drives the block a distance of 9.5 m before it comes to rest, what was the muzzle speed of the bullet?    m/s

  Two people, one of mass 75 kg and the other offs2(-rmmae .b mass 60 kg, sit in a rowboat of mass 80 kg. With the boat initially at rest, the two people, who have been sitting at opposite ends of the boat 3.2 m apart from each other, now exchange seats. How far and in what direction will the boat mrfeb( -.m2 masove? The boat will move    towards the initial position of the 75 kg person(Round to two decimal places)

  A meteor whose mass was p;1sr:4ehf i as1vumwdm6 19aabout $ 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 fragmenff1/6qt +tnc hts by an explosion. One fraqcft+n61f / htgment acquires twice the kinetic energy of the other. What is the ratio of their masses?   

  The force on a bullet is given by k3r x/6 l/c;vg bvel-othe formula F = 580-( $1.8 \times10^{ 5}$t) over the time interval t=0 to t = $3.0 \times10^{-3 }$s In this formula, t is in seconds and F is in newtons.
(a) Plot a graph of F vs. t for t=0 to t=3.0ms
(b) Estimate, using graphical methods, the impulse given the bullet.    N*s
(c) If the bullet achieves a speed of 220m/s as a result of this impulse, given to it in the barrel of a gun, what must its mass be?    kg

  Two balls, of massesejvevr)8:565) e0 fkyurlj sw $m_A$ = 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 alpp* pcxa6 (:lwxg llsl+ ,6f0pvha particle and a smaller nucleus. What will be the speed of this recoiling nuclsl*6w acl +0lg6x( :pfp,v xpleus 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 fi-ztt )3hgmtd) red 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=2.2(pp9t,6 1+ uj,dxutnv ie+x jgkg slides 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 g 1j2n4dlobfgg 0 k/nv)axs/u(u 6fl7is to rebound from M, slide up the incline, stop, slide down the incline, and collide with M again? /gx4j0(1 kn)lfgul obn sg7/62du vaf    kg (Let A represent mass m, and B represent mass M.)

  The gravitational slingshot effect. Figure 7–47 shows the planl09z9yp9:cca l ) zeriet Saturn moving in the negative x direction at its orbital speed (with res )ciyzl9arle099c: p zpect 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