We claim that momentum is conservebw(v* 7uv.qje d )axtu) b7.xyd, yet most moving objects eventually slow down and stop. Ex b7jvqwv by.))xx d .(aut*eu7plain.

When a person jumps from a tree to the ground, what happens to the momentum .zpl..mq.xi hc- k*vk of the pe x-*.i.m v.cplkqhzk. rson upon striking the ground?

When you release an inflated but untipc)unm0qn4d14wpaoc ro(a5 ) ed balloon, why does it fly across the roomno1d c)u )qnp0m rocwa a544p(?

It is said that in ancient times a rich man with a bag of gold coins +qg+3zohw-kqxe kw+uhn82. gfroze to death while stranded on a frozen lake. Because the ice was frictionleh3xwggkq+ oe2-w . +hkn8q+zu ss, 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 space and isgk*chcfy86 /vm scx:, essentially ccf:6/,*h mvxksc8yg in a vacuum?

According to Eq. 7–5, the longer the impact tim3tk)zvihdh;ip1to3fz+ h8q qr /lj4.e 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 val 1;+zktq3 /plfvrd hi.hjz )i438htoque 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 wi mmp4u5 -z*6/ g) h:tlatqhejzthstand collisions. Today, though, cars are designed to have “crumple z4-hzz gqe*5h tulj) mmt6p :/aones” that collapse upon impact. What is the advantage of this new design?

Why can a batter hit a pitched baseball further than a ba..sybphh0x.) gz2g g yll tossed in the air by the ba.g.g 0gh2sy)pzbh. yx tter?

Is it possible for an object to receive a larger impulse from agq owpi p-x+,wsq+-k/ small force than from a large foks-oq+ g,ipw/ w q-px+rce? Explain.

A light object and a heavy object have the same kinetic elx6wms 038tj inergy. Which has the great6i 8mj0w tlxs3er momentum? Explain.

Describe a collision in which all kinetic ene1ma b8t oivp:6o*0 u1,eg8gusb4 flbjrgy is lost.

At a hydroelectric power plant, waterkxuhv7m:.n0p) .b c yy is directed at high speed against turbine blades on an axle that turns an electric generator. For maximum power generation, should the turbine blades be designed so that the water is br bkcy.u:hny xm7p0.)v ought to a dead stop, or so that the water rebounds?

A squash ball hits a wall at a/ukw 45*vtgogyaw; i: 45 $^{\circ} $ angle as shown in Fig. 7–30. What is the direction (a) of the change in momentum of the ball, (b) of the force on the wall?

A Superball is dropped from a height h onto a hard sg/s b8ni392 a uz48vb d:sfhigteel 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 (vi ssf8 2 3 hzagbnbui8:d94g/b) for a piece of putty that falls and sticks to the steel plate.

Why do you tend to lean backward when carrying a heavy load in your 6e*5ml no6 tsxarms?

Why is the CM of a 1-m length of pipe at its mid-plg)1k3t6 rq ovl up7k703zqhzoint, whereas this is not true for your7u0pg3k3tlz7hkz 1 lqor)q6v arm or leg?

Show on a diagram how your CM shifts when you change from a lying position oihjaak,gi90 r.42 iwto a si04 rwo.i9i,h k jga2aitting position.

If only an external force can change the momentum of the center of mass of at3 ntwsrx;6 7rn object, how can the internal force of an engine6rsxw 3n;tr t7 accelerate a car?

A rocket following a parabolic ps0-p.ef aist/ ath through the air suddenly explodes into many pieces. What can you e i-astf0ps./say about the motion of this system of pieces?

  What is the magnitude of the momentum of a 28-g sparrow flyi9:yecp8xo, zb(ank y2ps 4 u*qng with a speed of 8.4 m4 qxe:pzak2pn, *yubc8 osy9(/s    $kg\;m/s$

  A constant friction force of 25 N act 610oe1vczyayd25wjd:5w l bns on a 65-kg skier for 20 s. What is the skyvw d e5za 1l0 y2n:6bdj5oc1wier’s change in velocity?    m/s

  A 0.145-kg baseball pitched at 39 m/s vlm/sl 2ub :,smwu7 ;d,fp 1bgis hit on a horizontal line drive straight back toward the pitcher at 52m/s If the contact time ,b 7lwu;pg/d1ssmf m 2,lv:bubetween bat and ball is $3\times10^{-3}$s calculate the average force between the ball and bat during contact.    N

  A child in a boat throws a 6.40-kg package out horizontally wplcle/9 e17inp- sff3ith a speed of 10 m/s Fig. below Calculate the e7 n3p1fsecf/ -il9plvelocity of the boat immediately after, assuming it was initially at rest. The mass of the child is 26.0 kg, and that of the boat is 45.0 kg. Ignore water resistance. The velocity of the boat is    m/s

  Calculate the force exerted on a rocket, gi/ e+:5by2r eid5prdwkven that the propelling gases are expelled a5k:r +5/i y2bpwdredet a rate of 1500kg/s with a speed of $ 4\times10^{4 }$ (at the moment of takeoff).$a\times10^7$ N a =   

  A 95-kg halfback moving at 4.15nenqpir2n5p )o/yclq0f it9f5:z(z m/s on an apparent breakaway for a touchdown is tackled from behind. When he was tackled by an 85-kg cornerback running at 5.5m/s in the same direction, what was their mutual speed immediately after te: l5cqon/) pt0 5yrip(zq nni zf52f9he tackle?    m/s

  A 12,600-kg railroad car travels alone on alevel fricti:bvldevm4 s m7a49ha2 onless track with a constant speed of 18m/s A 5350-kg load,initiaem9 hb4vm d:s7l2a av4lly at rest, is dropped onto the car. What will be the car’s new speed?    m/s

  A 9300-kg boxcar traveling at 15m/s fv6-tw5ixa kwvh) dp-e 2)2xi strikes a second boxcar at rest. The two stick together and move off with a speed of 6m/s What is the masswi2))xdathpei -f2x6 5vw -vk of the second car?    m/s

  During a Chicago storm, winds can whip horizontallqf:;4y : vuwwr )9yxejy at speeds of 100km/h If the air strikes a person at the rate of 40kgx;::jwqvuyrf w 4y)9e/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 6 .-pn ia) bo:n: a8qhdzpz7ih8x0hp xwith a constant speed of 8.6m/s on a level track. Snow begins to fall vertically and fills i ai0h6pqodbx p-8nhx.a)pn :7 z:hz8the 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 par+u nr3v.82fudovbecgd 80 j -rticle in the direction of its velocity, and the remaining nucleus slows to 350m/s If the alpha particle has a mass of 40o8 v+ fngr2cb jvr8.ed-u3ud.0 u and the original nucleus has a mass of 222 u, what speed does the alpha particle have when it is emitted?    m/s

  A 23-g bullet traveling 230m/s peun mwh3l*o y00netrates a 2.0-kg block of wood and emerges cleanly at 170m/s If the block is statiy0lw3*onm u0 honary on a frictionless surface when hit, how fast does it move after the bullet emerges?    m/s

  A 975-kg two-stage rocket is traveling at a k1;edch/keai4 5s y g0speed 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 vel yzu*s 7 hy*p .fti7iu:x0()issw 0sjmocity of 115m/s To alter its course by 35.0 0) shi0 :u7i.fzumxpsjw*siyty s(* 7$^{\circ} $, its rockets can be fired briefly in a direction perpendicular to its original motion. If the rocket gases are expelled at a speed of 1750m/s how much mass must be expelled?    kg

  A golf ball of mass 0.045 kg is hit off the tee at a speed of 45m/s The golfcf, e )nl ls pudh4*93-rris8b club was in contact wit)hp 9rlcb8 sef,irn3d4-l us*h 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 rest in aph v x:a/sv-m b4*cb.y time interval of 8.0 ms. (a) What is the impulse giveypv bc4:* .hbavsx /m-n to the nail?    kg*m/s
(b) What is the average force acting on the nail?    N

  A tennis ball of mass m=0.07:q v14x4 yvbbutro6 ru lm.4g6kg and speed v=25m/s strikes a wall at a 45 $^{\circ} $ angle and rebounds with the same speed at 45 $^{\circ} $ (Fig. 7–32). What is the impulse (magnitude and direction) given to the ball?   kg*m/s to the  ----待选择----leftright 

  You are the design engineer in charge ony 8l3ylvhs7t 2b 9t *cfb8n5ff the crashworthiness of new automobile models. Cars are tested by smashing them into fixed, massive barriers at 5b8l bh3 vtn8t*2y n7c9y5fsfl0km/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 the east and is stopp+9lnaglzl( oez8-:ih ,w; tlled in 0.75 s by a head-on tackle by a tackler running due wesl-l9onaz le(h+wt;i l 8lgz,:t. 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 +zchap.r1b,j ball (mass 0.060 kg) points in the +x direction and is given by the grh rbcz1ap.j+, aph of Fig. 7–33 as a function of time. Use graphical methods to estimate
(a) the total impulse given the ball    N*s
(b) the velocity of the ball after being struck, assuming the ball is being served so it is nearly at rest initially.    m/s

  From what maximum height can a 75-kg person jump without breaking the low* td1l/k9ym 4qit; eyjer leg bone of either leg*qjkyl;/yi t dt41m9e? Ignore air resistance and assume the CM of the person moves a distance of 0.60 m from the standing to the seated position (that is, in breaking the fall). Assume the breaking strength (force per unit area) of bone is $170\times10^6\mathrm{~N/m^2}$ and its smallest cross-sectional area is $2.5\times10^{-4}m^2$ [Hint: Do not try this experimentally.]    m

  A ball of mass 0.440 kg moving east (+x dftile5)5z 4-sw;w is)ex mpu5irection) with a speed of collides head-on with a 0.220-kg ball at rest. If the collision is perfectly elastic, what will be the speed and direction of each ball after the collision?Let A represent the 0.440-kg ball, andt ;ul5)) ewizms -p5fse 5wix4 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 col ,0a5:yxvchqp h/ aj9jlision with a 0.900-kg puck initially at rest. Assuming a perfectly elastic collision, what will be the speed and direction of each object after thqjx:5ph0va ay/,9ch j e 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 collision: jin8k wvf31j. If one ball’s initial speed was 2m/s and the other’s was 3m/s in wkj j3:nif81 vthe 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, 1s jly( w,qi3dmoving 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, wha13yjlsq(w,id t 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 0.2fp1f)8q8kc4ci egvtt0hymg.l vw5u.9z n8 ,e 20 kg that is moving with a speed of 8.5m/s collides head-on and elastically with another ball initially at rest. Afterward the incoming sfvc tg, 8k80g8ephlue45 cz.ni 1mtvwq 9f.)yoftball bounces backward with a speed of 3.7m/s Calculate
(a) the velocity of the target ball after the collision    m/s
(b) the mass of the target ball.    kg
(Let A represent the moving softball, and let B represent the ball initially at rest.)

  Two bumper cars in an amusement park ride collide rhjk5:2s f: mtl0r ui(elastically as one approaches the other directly from the rear (Fig. 7–34). Car A has a mass of 450 kg and car B 550 kg, owing to differences in passenger mass. If car A approaches at 4.5m/s and car B is moving at 3.7m/s calcula:5k ltfir r( hms:0j2ute
(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 second)zwi ;/vzh)g evtk,t7 ball initially at rest. The second ball moves off with halz/;etzhv7ktgi )v w),f 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 in Fig. 7–39lxb-mi uly7+ 5, 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 cubei9xl y 7u-mbl+ land? [Hint: Both leave the incline moving horizontally.]$\Delta x_{m}$$\approx$    m $\Delta x_{M}$$\approx$    m

ake the general case+7 h :t,6vnd, lhozkrn of an object 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 experiment, projectile 1 results in a myahgsi7t9v 72e -el7y aximum height h of the pendulum equal to 2.6 c ael yysgh27e-i9t7v7m. 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 traveling 230m/s buries itself in a 3r-, z5 h+7e)lforuzyf.6-kg pendulum hanging on a 2.8-m-long string, which makes the pendulum swing upward zl)rz-f+f 5 y7o,eru hin an arc. Determine the vertical and horizontal components of the pendulum’s displacement.vertical$\approx$    m horizontal =    m

(a) Derive a formula for the fraction of kinetic ene-ghs*9ba cg*3pps 6c zrgy lost, $(\Delta\mathrm{KE/KE})$ for the ballistic pendulum collision of Example 7–10. (b) Evaluate for m=14g and M=380g

  An internal explosionv: kj g3yrq vp1dx8vcm m6j38g9e:bg: breaks an object, initially at rest, into two pieces, one of which has 1.5 times the mass of the o:yeg:vv c8v3d 1mm 9g6qj3gbr8kx jp:ther. 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 into the rear end of a 2300-kg SUV /01chs nc5k pfstopped at a red light. The bumpers lock, the brakes are locked, and the two cars ski5/n1f sh0kc pcd 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 -hln t9+kln3pof 1.50 m and rebounds to a height of 1.20 m. Approximately how many rebounds will the ball make before losing 90% of its energy? ht93np+l- n kl  

A measure of inelasticity in a he3 pixaz;(u mm1ad-on collision of two objects is the coefficient of restitution, e, defined as1 3 mxip(a;uzm$e=\frac{\nu_\mathrm{A}^{\prime}-\nu_\mathrm{B}^{\prime}}{\nu_\mathrm{B}-\nu_\mathrm{A}},$
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 tiwsr hl b(ut,pq2wi, .. 3ig-qimes the mass of the other. A depression is made in both faces of the cut, so that a firecracker can be placed in it with the block reassembled. The reassembled block is set on a rough-surfaced table, and the fuse is lit. When the firecracker explodes, the two blocks separate and slide apart. What is the ratio of dib lp,i,2g3qu.i hw tq .i(rsw-stances each block travels? ----待选择----1/91/101/81/6 

  A 15.0-kg object moving in the +x direction at 5.5)tlx 9fou*3-th 1 xlamm/s collides head-on with a 10.0-kg object moving in the -x direction at 4m/s Fil -fx9t)th al xu3m1o*nd 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 nuup8bsa::q o,icleus, an electron, and a neutrino. : oa:p8s,bqiu The electron and neutrino are emitted at right angles and have momenta of $9.30\times10^{-23}kg\cdot m/s$ and $5.40\times10^{-23}\mathrm{~kg}\cdot\mathrm{m/s}$ respectively. What are the magnitude and direction of the momentum of the second (recoiling) nucleus?    $ \times10^{-22}$    $^{\circ} $ from the momentum of the electron

  An eagle ($m_{\mathrm{A}}=4.3\mathrm{kg}$) moving with speed $\nu_\mathrm{A}=7.8\mathrm{~m/s}$ is on a collision course with a second eagle ($m_{\mathrm{B}}=5.6\mathrm{kg}$) moving at $\nu_{\mathrm{B}}=10.2\mathrm{m/s}$ in a direction perpendicular to the first. After they collide, they hold onto one another. In what direction, and with what speed, are they moving after the collision? v =    m/s $\theta$ =    $^{\circ} $ rel. to eagle  ----待选择----AB 

  Billiard ball A of masw*ueq- vv a7yh4:e7ius $m_\mathrm{A}=0.400$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 inelastc3h8//d vn;/wg6f vv+-jt oq qv/lqfo ic collision between two objects of equal mass, each having initia6t-q dvvq q/fn+8 o wc;ovj 3gh//vfl/l speed the two 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 and meet at the orp1 (zu)wrzz8 g bq0eb8awo2uc .kwwt96ro(0xigin of an xy coordinate system. Ball A is moving upward along the y axis aet16zrku(awc9b8wpzzbou w2x. ) ogr0w( 0q8 t 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) makes a perfectly elastic jdf,y0pwy 7b;collision with another atom at rest. After the impact, the neon atom trb y;7d0wf yp,javels 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 with w:.1uf3rjox0n3 hxbl.wx /k r l0zqw0another atom at rest. After the impact, the neon atom travels aw33lq kow.wj r /x.nxxu:lrzf0h0 0b1way 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-mass7miwbkgcr /z4bm2 /z7 system shown in Fig. 7–38. Specify relative to tcmkb7ib /wr zzmg4 /27he left-hand 1.00-kg mass.    m

  The distance between a carbon a,5 el*yzaq e,itom ($m_{\mathrm{C}}=12\mathrm{u}$) 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 carg0dso;3y x en2 is 2.50 m behind the front of the car. How far from the front of the cadge3xn20 so y;r will the CM be when two people sit in the front seat 2.80 m from the front of the car, and three people sit in the back seat 3.90 m from the front? Assume that each person has a mass of 70.0 kg.    m

  A square uniform raft,x1 yo) / .x7mfokc-etr 18 m by 18 m, of mass 6800 kg, is used as a ferryboat. If three cars, each of mass 1200 kg, occupy its NE, SE, and SW corners, determine the CM of the loaded ferrybo-7x/)x y.1m of roteckat.$X_{CM}$ =    m $Y_{CM}$ =    m

  Three cubes, of side 60cl)at*tzdfx ,yux:w 3o -ab5*j:ewk jz1mqs $l_0$,$2l_0$, 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 identicel ,wc;v 2g 32asfcba0al cases of tomato paste (see Fig. 7–40), each of which is a cube of length l. Find the center of gravity in the horizontal plane,e,svbc gwa; 2 l03a2fc 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 ci7g0n 1reguq 1x. 3lobbrcular hole of radius R cut out of it. The center of the o.b l1ngqbx 1e0ugr37smaller circle is a distance 0.80R from the center C of the larger circle, Fig. 7–41. What is the position of the center of mass of the plate? [Hint: Try subtraction.]   R

  Assume that your proporti8 j(i(rxkq; zaons are the same as those in Table 7–1, and calculate the mass of onerx( z8jik ;aq( of your legs.    kg

  Determine the CM of an outstrtnp j: e8 nrqp1(:wja6etched arm using Table 7–1.   % of the person's height along the line from the shoulder to the hand

  Use Table 7–1 to calcula8tg9g tsj0o4z te the position of the CM of an arm bent at a right angle. Assumej z8ts490og gt that the person is 155 cm tall. $X_{CM}$ =    cm $Y_{CM}$ =    cm

When a high jumper is in a position such that his arms and legs are h6:shn1(q x8awa,m b4it ir. txo fd3s4anging vertically, and his trunk and head are horizontal, calculaw4t 36sr x1ab:x,h(n oqat sid fi8.4mte 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 Eartxw ) pg54 )s8/s +w8t ddcdpsbt-xa*wsh 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 m apart on frictionless ice. uf1wxx0 krrkgy u: g1n72f/hvm 2t w-;
(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 cylindrica+/kyt: rbjl;dr3,i x rnexw.gh,1ni-l 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–.b3rty k/w+x1egrjl-;n in xhd,:,r i42. If this mallet is tossed, spinning, into the air, how far above the bottom of the handle is the point that will follow a parabolic trajectory?    cm

  A mallet consists of a uniform cylindrical head of mass 2.00 1 ett,c 2i;fo,w 0ahfjkg and a diameter 0.0800 m mounted on a uniform cylindrical handle of mass 0.500 kg and length 0.240 m, as shown in Fig. 7–42. If this mallet is tossed, spinning, into the air, how far above the bottom of the handle is the point that will follow a parabolic ;co, tife,jf2tw10hatrajectory?    d    d

  (a) Suppose that in Examp.elfms9+ . kdi;bkh 5yle 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 gond q0m),p 5hu(a k25.+p n6kpvtlssjqxgola, of mass M, are in the air and stationary with respect to the ground. A pas jl+ .)pqpss (na0 ,gkpt 265hkuxmqv5senger, 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 the balloon then move? What happens if the passenger stops?

  An 0.145-kg baseball pitched horizontally at strikes a batw /fdy3r6; l5lki4idp and is popped straight up to a height of 55.6 m. If the contact time is 1.4 ms, calculate the averif4 p i;56 wl3/kdldyrage force on the ball during the contact.    $^{\circ} $

  A rocket of mass m traveling with sp:7vqg qzgew2xfa:7 qj.(()pj j t2i eufxf:(qeed $v_0$ 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./ee6/vl j8iaz z;p1f4o iz sj the corner pocket shot shown in Fig. 7–43. Relative dimensions are also shown. Should the player be worriozijsa f.lv j4p1 6z /i/e8ez;ed 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 by pusl.oz. imgc08b hing off with his legs from an 1800-k0. o8icmzl. bgg 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 4iy*uzyqs; 5u 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 l u;y4ziyq*s5u ighter astronaut has moved 12 m?    m

  A ball of mass m makes a hea;ct30)vr rkc4xneh+ / frnn5 sd-on elastic collision with a second ball (at rest) and rebounds in the opposite direction with a speed equal to one-fourth its original speed. What +t)xsv/nc05 rfrn4kh cne r; 3is 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 c 5wlq6a0ky7ii)8bf a court case involving an automobile accident. The accident involved car A of mass 1900 kg which crashed into stationarylb)wf ciq a 860k5iya7 car B of mass 1100 kg. The driver of car A applied his brakes 15 m before he crashed into car B. After the collision, car A slid 18 m while car B slid 30 m. The coefficient of kinetic friction between the locked wheels and the road was measured to be 0.60. Show that the driver of car A was exceeding the 55-mph (90km/h) speed limit before applying the brakes.    mi/h

A golf ball rolls off the top of a fs6kp3c:sb4lpb4 .n-miq xn34 qzp jk ,light 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 ls4ixsq3q lm jn4npc4,.3 -k b:p6kpbzower. 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 wonfjz/wog (g //od 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 becoo/gz(g j//fnwmes embedded in it?    m

  A 25-g bullet strikes5l(lep(qp dtjg(p 7,b and becomes embedded in a 1.35-kg block of wood placed on a horizontal surface just in front of the gun. If the coefficient of kinetic friction between the block and t,q pt5pbd(lp lj(7ge (he 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 of massu vi*pko mz3g5m(+3xg((j xte 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 3.2k3 muv+3p(m5ij *t( gx(exzgo m apart from each other, now exchange seats. How far and in what direction will the boat move? The boat will move    towards the initial position of the 75 kg person(Round to two decimal places)

  A meteor whose mass was61gn vjrur 1d3 about $ 1\times10^{ 8}$kg struck the Earth ($m_E$=$6 \times10^{ 24}$kg) with a speed of about 15km/s and came to rest in the Earth.
(a) What was the Earth’s recoil speed?    $ \times10^{-13 }$m/s
(b) What fraction of the meteor’s kinetic energy was transformed to kinetic energy of the Earth?    $ \times10^{ -17}$
(c) By how much did the Earth’s kinetic energy change as a result of this collision?    J

  An object at rest is suddenly broken apart into two fragments by an explosion. Of6 2x8kojgr u;-wr3 uone fragment acquires twice the kinetic energy of the other. What is the ratio of thxuu6-fj rwoogrk23 8;eir masses?   

  The force on a bullet is ghpbu2:mb) (nx4th, cuiven by the 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 massesb6 *n s.leap.pgyy6 s7 $m_A$ = 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 ui:l7 czbtqr:8ms 7 7asmaller nucleus. What will be the speed of this recoiling nucleus if the speed of the alpha particle is casruqitz8:7 b :7 m7l$ 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 30 l21,+/uyxz wp(xrdv k$^{\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 slides8(df:vj /yp jv: ov)wa 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), wgjvjjdj0d u-zo8c(* ux q q::9hat is the upper limit on mass m if it is to rebound from M, s0j j::(ocxgju jq-dvu* 89 zqdlide up the incline, stop, slide down the incline, and collide with M again?    kg (Let A represent mass m, and B represent mass M.)

  The gravitational slingshot effect. Figurmof:c,h,x y/t7dw3g z e 7–47 shows the planet Saturn moving in the negative x direction at itsxf7,tzm go/:y,dh3 cw orbital speed (with respect to the Sun) of 9.6km/s The mass of Saturn is $5.69 \times10^{ 26}$kg A spacecraft with mass 825 kg approaches Saturn. When far from Saturn, it moves in the direction at 10.4km/s The gravitational attraction of Saturn (a conservative force) acting on the spacecraft causes it to swing around the planet (orbit shown as dashed line) and head off in the opposite direction. Estimate the final speed of the spacecraft after it is far enough away to be considered free of Saturn’s gravitational pull.    km/s