We claim that momentumw ;6u7j-1u,mv(x- n;)zk hnw l -qsmqiejav7d is conserved, yet most moving objects eventually slow downq 7 - mh-mw; ;jia)jsvdunu (7k6zq, wl-ve1nx and stop. Explain.

When a person jumps from a tree to the ground, what hap*g ;)dvzafd+s6yp2 cxp0 z n:kpens to the momentum of the person upon striking tha;sfg*n+yp xz0 6v2c): dpdkze ground?

When you release an inflated but untied balloon, why does it fly acrosrvagnl 63-/6uzci)nn s the room?rlu z6 nigv3ca)n6/n-

It is said that in ancient times a rich man with a bag of gold coins froze g b9z;1iakm6t to death while strt 9;i6g1bazm kanded on a frozen lake. Because the ice was frictionless, he could not push himself to shore. What could he have done to save himself had he not been so miserly?

How can a rocket change direction when it is far out in s-+ vg sh 8erly99wguq-pace and is essentially in a vacuysg99ge8wul- h-q +vrum?

According to Eq. 7–5, the longer the n( vfji1 0-olgimpact 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 inflate during an automobile collision and reduce the possibility of ign-ovl 1(0fjfracture or death.

Cars used to be built as rigid as possible to withstand collision s6 0/gd5tgeut zgnakwww+ q1ayax.63yi3+u,s. Today, though, cars are designed to have “crumple akgw6d,6ts +w3x1w30yin. a e/agqty 5guzu+zones” that collapse upon impact. What is the advantage of this new design?

Why can a batter hit a pitched baseball further than a ball tossed in the aiwr3v2p5q 7-rzn 4xpbjr by the battepq nrbwz x327j-p5v4rr?

Is it possible for an object to receive ag laso zmi71e -fp7q-- larger impulse from a small force than from-1f7ozmqe -i-spg7 al a large force? Explain.

A light object and a heavy object have the same kixbm61n( owcj 0netic energy. Which has the greater momentum? Explaib0x1o j6nw(m cn.

Describe a collision in which all kineti.ly.h ev)a)sru: d1 6by.mt yhv7s,yw c energy is lost.

At a hydroelectric power plant, water is directed av5mf +xg 8acw4t high speed against turbine blades on an axle that turns an electric generator. For maximum power generation, should the turbine blades be designed sg+fca4 v8wm 5xo that the water is brought to a dead stop, or so that the water rebounds?

A squash ball hits a wall b ehc2l3(o6 aiat 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 f e4 ()zxlc qw3.;f9qzb uk:lmyrom 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 momen:4zkeqb .9;wq)mux yc3f z (lltum conserved? (c) Answer part (b) for a piece of putty that falls and sticks to the steel plate.

Why do you tend to lean bysb3y; vl.: qd ,u4ypwackward when carrying a heavy load in your arms?

Why is the CM of a 1-m length of pic23 qn9sdb qm(z *9sffpe at its mid-point, whereas this is not true for your arm orsfq 3*n( d9csmq z9b2f leg?

Show on a diagram how your CM shifts when you chan-8ntz)vknl4 sps a55n ge from a lying position to a sitting position)ankt 5 nv-z8sspl45n.

If only an external force can change the momentum of the center of mass o0u4 bq5ag jxt)f an object, how can the internal force of an engine acc4q5gt bj0au) xelerate a car?

A rocket following a parabolic path through the air suddenly explodes intogsp2 ibtv qwt7.f r s.)y/4xo7 many pieces. What can you say about the motion of this systes ) 2fw s4igo7/x.ty7 prbtv.qm of pieces?

  What is the magnitude of tho1z h2vk9b x+c-lgj 3ce momentum of a 28-g sparrow flying with a speed 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 th wfj cf)2-4dxee skier’s change in velocity?dx -w2ffc)j e4    m/s

  A 0.145-kg baseball pitched at tsne 1vvjv:0 g -c5*td39 m/s is hit on a horizontal line drive straight back toward the pitcher at 52m/s If the contact time between bat and ball :v-0en 1d t*tjv5 csvgis $3\times10^{-3}$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 wjwsr9y5mv yvvrwi :/g(h n4+s td2+45gqmn- horizontally 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 qg vhr y:-d5(+2g ym4w n9st+j5/s wvw4ivrmn 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 rocketnck/oja2; l7l/s pg5j, given that the propelling gases are expelled at c/ng5l;/ojs 2la k7pja rate of $1500 \; kg/s$ with a speed of $ 4\times10^{4 } \; m/s$ (at the moment of takeoff). F =    $\times 10^7 \; N$

  A 95-kg halfback movinna3jejp.l3b7wioa a1kjbu+u) ;( ig, g 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 trb,vfkw d+bhno 79a3j3avels alone on alevel frictionless track with a constant speed of 1 bho+v 7f dja3nbw3,9k8m/s A 5350-kg load,initially at rest, is dropped onto the car. What will be the car’s new speed?    m/s

  A 9300-kg boxcar traveling y kr;9at1w+c kv;fc7vat $15 \; m/s$ 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 cajv fw)5 / yw3vz2m,ekxn whip horizontally at speeds of 100km/h If the air strikes a person at the rate of 40kg/s per square meter and is brought to rest, esti2/fwjz3 w,yvk5mvx e )mate 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 on ); ci: qjf(fm;d-uglo a level track. Snow begins to fall vert-md;f: gc uqfljo;() iically 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 alph4 p.hc flnh)w+a particle in the direction of its velocity, and the remaining nucleus slows to 350m/s If the alpha particle has a mass of 4.0 u and the original nucleus has a mass of 222 u, what speed4)fpl ch+hn. w does the alpha particle have when it is emitted?    m/s

  A 23-g bullet traveling 230m/s penetrates a 2.0f,yszofe,50o jwo3uahjr 8 1 g- 8u0uf-kg block of wood and emerges cleanly at 170m/s If the block is stationary on au0 ,f1oh gu 0 ow j3yjar-5zff,8e8uos frictionless surface when hit, how fast does it move after the bullet emerges?    m/s

  A 975-kg two-stage rocke l*.x9/i,dhzxb iqu5eam - o2yg; x7oht is 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 traveling in outer spatdlh4;ypv1ii c74x14 no(g azce with a velocity of 115m/s To alter its coursp x4;o 41(thldyz7i 1avn igc4e by 35.0 $^{\circ} $, its rockets can be fired briefly in a direction perpendicular to its original motion. If the rocket gases are expelled at a speed of 1750m/s how much mass must be expelled?    kg

  A golf ball of mass 0.045 kg is hit off the tee avq5 ;lh3tq i*o48aam rt a speed of 45m/s The golf club was a iqv8o45*;mhratql3 in 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 na q(izzw 26 h1 le(yarjf1sd3l-il at a velocity of 8.5m/s and comes to rest in a time interval of 8.0 ms. (a2 wj l31zzsf hyi((l6e q1-adr) 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 speed v=25m/s strikesk8;dkkplc ,8q 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 crashworthin;p q:: 7;wmcn3hrqwqpess of new automobile models. Cars are tested by smashing them into fixed, rn;pmwq; w:qcp q7h 3:massive barriers at 50km/h (30 mph). A new model of mass 1500 kg takes 0.15 s from the time of impact until it is brought to rest. (a) Calculate the average force exerted on the car by the barrier. $\approx$$a\times10^5$N a =   
(b) Calculate the average deceleration of the car.    m/$s^2$

  A 95-kg fullback is running at 4m/s to th/e enb145wx/.z 7hvdnv7fozje east and is stopped in 0.75 s by a head-on tackle by a tackler running 5j7eh.be 7w/zfznvv nx/ o4 d1due 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 0.060zd5zxqyv 2uuu.h; 1l+ kg) points in the +x direction and is given by the graph of Fig. 7–33 as a functq5x12 uzz.+v ;duuhyl ion 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 person jump without breaking the z-ckr tmgdw- . 45 wz3(hhbw8yhhe25 qlower leg bone of either leg? Ignore air resistance and assume the CM of the perso- kh4tr zwb5w(gqe-w82zh m h3h.5cydn 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 directionf.kjvb6ic,c nd 6j (;p) with a speed of collides head-on wd pj cic6n;b j(,vf6.kith a 0.220-kg ball at rest. If the collision is perfectly elastic, what will be the speed and direction of each ball after the collision?Let A represent the 0.440-kg ball, and B represent the 0.220-kg ball. $v'_A$    m/s  ----待选择----eastwest  $v'_B$    m/s  ----待选择----eastwest 

  A 0.450-kg ice puck, movingqmjg0 v xw-hg)q/ y1.a east with a speed of 3m/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 q/-) h1agymgj .vxw0q 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 equ6 nzkbf4m7ha )al mass undergo a perfectly elastic head-on collision. If one ball’s initial speed was 2m/s and the otheabfh64n)km 7zr’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, mi/ pho8 t6v br6y1dna)kk)h/ coving with a speed of 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 bac 6b8y// a)ivnkp1hkdrt6) holl 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 gt)ity z79hh/ speed of 8.5m/s collides head-on and elastically with another ball initially at rest. Afterward the incoming softball bounces backward with a speed of 3.7m/s Calculat9h7 tht/gi)y ze
(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 collideiivo /n1 qsv-c q9j4um6/g,vk 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 kg6 kn -vvi1ui/c/g4s vqq9jm, o, 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 secondk0h;svgju:na, seb 1iw( f1g 7 ball initially at rest. The second ball moves off with:gsa 0g s;wfev,jn 1(iu17bhk 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 frictioz7 o0lgno (.rpnless incline as shown in Fig. 7–35, and elastically strikes another cube at the bottom t0prozlg.n7 o(hat is only one-half its mass. If the incline is 30 cm high and the table is 90 cm off the floor, where does each cube land? [Hint: Both leave the incline moving horizontally.]$\Delta x_{m}$$\approx$    m $\Delta x_{M}$$\approx$    m

ake the general case of an oknh1w+ 0gp-t eh g :bg))26y fm8qopugbject 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 experimenthfk i99xjue-sp 787th , projectile 1 results in a maximum height h of the pendulum j7x9fhu-7h it s9kp8e equal to 2.6 cm. A second projectile causes the the pendulum to swing twice as high, $h_2=5.2\mathrm{cm}$ The second projectile was how many times faster than the first? $v_1$ =    $v_2$ ([color=rgba(0, 0, 0, 0.85)]Round to three decimal places)

  A 28-g rifle bullet tr a8+ gf y;ojrvih h(gh9h.p 1e29shos.aveling 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 compongss9 .h2h fo h.(h 9gvy;eai+18rj phoents of the pendulum’s displacement.vertical$\approx$    m horizontal =    m

(a) Derive a formula for the fraction of kinetic energy los dq51ycq;u2y dgo )h6yt, $(\Delta\mathrm{KE/KE})$ 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,prtt il2mmuh x7+t3m47t0a e. into two pieces, one of e. am m0pltu724mtx+th ir7t 3which 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 particle. ) KE'$_A$ =    J KE$_B$ =    J

  A 920-kg sports car collides inhi s.h(0 sl7rsto the rear end of a 2300-kg SUV stopped at a red light. The bumpers lock, the brakes are locked,lshs0hr(i. s7 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 height of 1.50 m and rebounds to a height lsq0f 3 fg70ik9uo y8xg3k n(kof 1.20 m. Approximately how many rebounds will the ball make before losing 90% of its energy?osf9y8 k(qg u g0ix3f3nk07lk   

A measure of inelasticity in a head-on collision of two objects is the coeffitothwo0v4,aldf:x u2c /q9x- cient of restitutiqxlo4xt a:hwd , -v /tf0u2c9oon, e, defined as$e=\frac{\nu_\mathrm{A}^{\prime}-\nu_\mathrm{B}^{\prime}}{\nu_\mathrm{B}-\nu_\mathrm{A}},$
where $\nu_\mathrm{A}^{\prime}-\nu_\mathrm{B}^{\prime}$ is the relative velocity of the two objects after the collision and $\nu_\mathrm{B}-\nu_\mathrm{A}$ is their relative velocity before it.
(a) Show that e=1 for a perfectly elastic collision, and e=0 for a completely inelastic collision.
(b) A simple method for measuring the coefficient of restitution for an object colliding with a very hard surface like steel is to drop the object onto a heavy steel plate, as shown in Fig. 7–36. Determine a formula for e in terms of the original height h and the maximum height h’ reached after one collision.

  A wooden block is cut into two pieces, one with three times the mass f2r5z ece-njry0h /j) of the other. A depression is made in both faces of the cut, so that a firecracker can be placed in it with the block reassembled. The reassembled block is set on a rough-surfaced table, and the fuse is -en0ye2fcrr)hj / zj5lit. 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 directq*q2k 5n slr iaa3l*:gion at 5.5m/s collides head-on with a 10.0-kg oblqng**:q2skia 5 l3ra ject 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 a secoibg+uxbjf (ya gl /bz1)--z1und nucleus, an electron, and a neutrino. The electron and neutrino are emitted at right angles and have momeizg+)-1 (u bjy- z/b x1lfuagbnta 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 masi4vu0vmm nkk x/t).d3s $m_\mathrm{A}=0.400$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 inelaafbopnlo+. l5xuf)/ k4 w)1sustic collision between two objects of equal mass, each having initial speed the two move off together with speed v/3 What was the angle xlou/+a u4kl no1.b5 fwspf))between their initial directions?    $^{\circ} $

  Two billiard balls of equal mass move0ftby:07c veviju uo5z h;5 ;l 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 positive y axis (Fig. 7–37). What is the final diru:eov uytb;5h f50 i;l0c7j vzection 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 elyxwbl 1e 3bwp9x,j1 i7astic collision with another atom at rest. After txl,1e3 y i9ww7x jbbp1he impact, the neon atom travels away at a 55.6 $^{\circ} $ angle from its original direction and the unknown atom travels away at a -50 $^{\circ} $ angle. What is the mass (in u) of the unknown atom? [Hint: You can use the law of sines.](Let A represent the incoming neon atom, and B represent the target atom) $m_B$   u

  A neon atom (m=20u) makes a perfectly elastic collision : /s w4fsk9xpiwith another atom at rest. After the impact, the neon atom trax9sfs4wk: p i/vels away at a 55.6 $^{\circ} $ angle from its original direction and the unknown atom travels away at a -50 $^{\circ} $ angle. What is the mass (in u) of the unknown atom? [Hint: You can use the law of sines.](Let A represent the incoming neon atom, and B represent the target atom) $m_B$   u

  Find the center of mass of the three-mass system shown in Fig. 7–38. Speccyu4a3 .aoves 7n7c7jdxua2 t v t.6;dify relative to the left-hand 1.004ux v3va67 .7ycdejus;tca. nt oad27 -kg mass.    m

  The distance between a k 7jzws 3dvfz3gc r234carbon 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 1050hv:a3j hje du6er6w02 -kg car is 2.50 m behind the front of the car. How far from the front of the car wilhrvdwj 0ee hu j:62a36l the CM be when two people sit in the front seat 2.80 m from the front of the car, and three people sit in the back seat 3.90 m from the front? Assume that each person has a mass of 70.0 kg.    m

  A square uniform raft, 18 m by 18 m, of mass 6800 kglj5 jk/8+ (msk yy5pxif:b(tp, is used as a ferryboat. If three cars, each of mass 1200 kg, occupy its NE, SE, and SW co5yb8+k/jk t(5mx ip:j(ly pf srners, determine the CM of the loaded ferryboat.$X_{CM}$ =    m $Y_{CM}$ =    m

  Three cubes, of sidem fho9cttzef 8 8 (7t6mrqgm:e 3rq,c2s $l_0$,$2l_0$, 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 identicat*oxuufryp:o/1y1 qh c)q2z ) l cases of tomato paste (see Fig. 7–40), each of which is a cube of length l. Find the center of gravity iptfu q ycr:1xy)z oq2/o*uh )1n the horizontal plane, so that the crane operator can pick up the load without tipping it.$X_{CM}$ =    l $Y_{CM}$ =    l

  A uniform circular plate of radius 2R has a circular hole of radius R cuzibsv 9-v(tpg)d, fuc 0 +m8let out of it. The center of the smaller circle is a distance 0.80R from the,0ipl(gc8-uvfm+ z9ed s vb)t 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 proportions are the same as those in- v6j8y 6rxoex Table 7–1, and calculate the mass of one o8jr6x yexv6 o-f your legs.    kg

  Determine the CM of an outstretched arm using Table 7–1. r4 o6 hq3oi2w:,fkd cvv7l6kh   % of the person's height along the line from the shoulder to the hand

  Use Table 7–1 to calculate the position of the CM fj6hhh ua5cy5w93rib:42 ww*zl vb91z2hstu of an arm bent at a right angle. Assume thwh3zf41u*yhzwcwabhbv965sjth9ui2 2 5: r lat the person is 155 cm tall. $X_{CM}$ =    cm $Y_{CM}$ =    cm

When a high jumper is in a position such jnb5oe c)-1.ad zq +rc5wwr7dthat his 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 CM be outside the bodo7-5 qb na5j)z+r wr.ccedd w1y? Use Table 7–1.

The masses of the Earth and Mgur-;lf0ys- j (of9gi oon 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 m apart on fricozg. .y*.k nho* 1 nred-pr,tttionless 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 cylindricaug-iudy1 y8vg9av;c+n+2abkqh2 3 i hl 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 tovcna h32u ; ia-1gg d+ki82uyv+9hqb yssed, spinning, into the air, how far above the bottom of the handle is the point that will follow a parabolic trajectory?    cm

  A mallet consists of a uniform cylindrical head of mapegk 1).ob byo68n+mdss 2.00 kg and a diameter 0.0800 m mou1.oond mbgy k +6e8p)bnted on a uniform cylindrical handle of mass 0.500 kg and length 0.240 m, as shown in Fig. 7–42. If this mallet is tossed, spinning, into the air, how far above the bottom of the handle is the point that will follow a parabolic trajectory?    d    d

  (a) Suppose that in Example 7–14 (Fig.k vlb nq;-w7ifc+)r n: 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 b v03czmld.4 2vulo,jM, are in the air and stationary with respect to the ground. A passenger, of mass m, then climbs out and slides down a rope with speed measured with rezjlm.l v 0c,42vuob3 dspect to the balloon. With what speed and direction (relative to Earth) does the balloon then move? What happens if the passenger stops?

  An 0.145-kg baseball pitched horizontally at strikes a bat and is popped se rw3/d jln0sm9hgva e+d; 3(dtraight up to a height of 55.6 m. If the contact time is 1.4 ms, calculate the average force on the ball dhv0jwd3+d(3 r; n eal/emg ds9uring the contact.    $^{\circ} $

  A rocket of mass m trba)eze l *70*ikmbd8+ uqm q+kaveling with speed $v_0$ along the x axis suddenly shoots out fuel, equal to one-third of its mass, parallel to the y axis (perpendicular to the rocket as seen from the ground) with speed 2$v_0$ Give the components of the final velocity of the rocket.$P_x$: v'$_x$=    $v_0$
$P_y$: v'$_y$=    $v_0$

A novice pool player is faced with the corner pocket shot shown in Fig vy:0t-fznsyf19 o g+o. 7–43. Relative dimensions are:s9+y ovn fg-y0ozt f1 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 6:1zoxoera g5uty tzzvok2lc8;4p/; speed of 2.5m/s by pushing off withgez1/y o;tp: zuzoak 2 ;v 84clor65tx his legs from an 1800-kg space capsule.
(a) What is the change in speed of the space capsule?    m/s
(b) If the push lasts 0.40 s, what is the average force exerted on the astronaut by the space capsule? As the reference frame, use the position of the space capsule before the push.    N

  Two astronauts, one of mass 60 kg and the other 80 kg, are initiall-5 jslok /dngr.;nh4 ay at rest in outer space. They then push each other apart. How far apart are they w5s-k jr n;.gahnd /ol4hen the lighter astronaut has moved 12 m?    m

  A ball of mass m makes a head-on elastic c; tg4v7k1hyh7 f7 hnnmrt2xu9ollision with a second ball (at rest) and rebounds in the opposite di fh;rn 97nvh ugtx71t27 4myhkrection with a speed equal to one-fourth its original speed. What is the mass of the second ball? $m_B$ =    $m_A$(Round to two decimal places)

  You have been hired as an expert witness in a court case involxas4/sbya vxqu ;3cl(8w:kq k 3-9d rqving 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) speed limit befs3vq:8bsk-x;9 3 4(rd /u cywxaqal kqore applying the brakes.    mi/h

A golf ball rolls off the top of a flight of concrete steps a flz2o16wz r0of 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 heigh l12fro0wz za6t on the fourth bounce when the ball reaches the bottom of the stairs?

  A bullet is fired verticalo(b vlin2vfj 9n 4p76yly into 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 bjil2(oy9f nnbpv476 vullet becomes embedded in it?    m

  A 25-g bullet strikes and becomes embedded in a 1f( r3fy3vtp)e.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 drives the block a distance of 9.5 m before it comes to rest, what was the muzzle speed of the bu3 f3ervp tf(y)llet?    m/s

  Two people, one of mass 75 kg and the other of md6l)r5z c q psu/g2ga9ass 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 i65p glq)ur2zsg d/a9c n 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 aboun l6 8c;6-bpdb zmwf/ft $ 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 broke4e*ug . gj-fhen apart into two fragments by an explosion. One fragment acquires twice the kinetic eju 4 *gge.f-ehnergy of the other. What is the ratio of their masses?   

  The force on a bullet is given by the formula F = 580-(lp9.q izcex35sp-o *l $1.8 \times10^{ 5}$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 /c+k g6hmn2o )ubxk:,i 6 muat$m_A$ = 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 alpha particle and a smaluwp7 73 ;zjt2ksbd5jxyxgp- 0ler nucleus. W7ps; zj25b-7k3xyu0g ptw xjdhat will be the speed of this recoiling nucleus if the speed of the alpha particle is $ 3.8\times10^{5 }$m/s Assume the recoiling nucleus has a mass 57 times greater than that of the alpha particle.    m/s

  A 0.25-kg skeet (clay target) is fired at an angle of 32v bcbii6t0 d-0ltkdnhddyn) 1i7 7n: 0 $^{\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 30.0 ++c+ss3(a q8nojbzo a$^{\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 kg 4t9eezh2j.mass m if it is to rebound from M, slide up the incline, stop, slide down the incline,et2 gk jzh.e94 and collide with M again?    kg (Let A represent mass m, and B represent mass M.)

  The gravitational sliii2tf:8u: t;v5kxc )dt7t7achf m6vlngshot effect. Figure 7–47 shows the planet Saturn moving in the negative x direction at its orbital speed (with respdfc8 a;x57)2i :vhkcti tl6vttu:7fmect 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