We claim that momentum is conserved, yet most moving objects eventmkx-k fn3;d i,8bz)ldually slow down and stop. Expl8xbd 3znmfd-,l )ki ;kain.

When a person jumps from a tree to the ground, what happgx tx1z3mx2 f85or,a3 ziyp t.ens to the momentum of the person upon stz2x,gp31tiym5f.t8z a 3rox xriking the ground?

When you release an inqyhuau /+-av ;flated but untied balloon, why does it fly across the room avyu/h-u;+ aq?

It is said that in ancient times a rich man with a bag of y cv. iuyhk+rm/)/jd/gold coins froze to death while stranded on a u d rv+/cj ./hi/ymky)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 il-rwk2rq c db)5nqnv s0n+d r,)l/s5 kn space and is essentially in aql rd/lrkqn- 5wk2n,d)rbsn05 )+svc vacuum?

According to Eq. 7–5, the longer the impact timep6z *z6/irhsqn0oq p /s(cnv2 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 as zn (hp6vo/rqq*c 6zp0/2isncts. On this basis, explain the value of air bags, which are intended to inflate during an automobile collision and reduce the possibility of fracture or death.

Cars used to be built as rigid as possible to withstja76 th5: wt/;ujp3 bdogdd-p and collisions. Today, though, cars are designed to have “crumple zones” that ;wo6dp hat tdpdu5/jg -7bj3: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 air b:kk j7 2tlpopcq,6nq o;vf *;iy the batter?k2olqn:pkj pv; t fo ,*q;6c7i

Is it possible for an object idd0p; ukk/a8sj ,0po to receive a larger impulse from a small force than frsj8ad0dup o/pi;,kk0 om a large force? Explain.

A light object and a heavy object have th w c cp*j -vb,3ewv;a2cpi8,sqe same kinetic energy. Which has the greater momentu pev,csi *j2a3b,q8wvcw -;pc m? Explain.

Describe a collision in which all kine3mm3 ,optu if:k-lk 6ftic energy is lost.

At a hydroelectric power plant, water is directed at high speed against turbinemv jt+d);/ec v blades on an axle that turns an electric generator. For maximum power generation, should the turbine blades be designed so that the +;t ed)vj/cmv water is brought to a dead stop, or so that the water rebounds?

A squash ball hits a wal vh0:i +e4cyk:8bcwesl 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 hard steel plate (fixed to the Earq2ute/fn f .1rth), 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 momentume/1n 2rfq.u tf conserved? (c) Answer part (b) for a piece of putty that falls and sticks to the steel plate.

Why do you tend to lean backward when carrying a heavy load in your arm w)wzp*q+ctjm*0b,n2 tjn ot,s?

Why is the CM of a 1-m jdy 0/svk 9y;-ev0f iylength of pipe at its mid-point, whereas this is not true f0ev-sfkv;jy dy 90i/yor your arm or leg?

Show on a diagram how your CM shifts when you change from a ly7e ix( x1cw7oeing position to a sit7e oxeix w1c(7ting position.

If only an external force can change the momentsv; :fa:jtm/ bum of the center of mass of an obj/jfat; b:vsm: ect, how can the internal force of an engine accelerate a car?

A rocket following a parabolic path through the air suddenl(w .pzzq*m;ply explodes into many pieces. What can you say about the motionzqzwl; ppm.( * of this system of pieces?

  What is the magnitude +i.yat)5gktcpb dhd9k*gu6 1 of the 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 i tmrwgqki (,4yprgd 9,: ci5s+s the skier’w,spd gc5k: q4 t+i( rgim9y,rs change in velocity?    m/s

  A 0.145-kg baseball pitched at 39 m/s is hit on a horizontal line drivk wgbpi8a j5*,e straight back toward the pitcher at 52m/s If the contact time between bat and ball isb ji wga,kp85* $3\times10^{-3}$s calculate the average force between the ball and bat during contact.    N

  A child in a boat throws a 6.40-kg package out horizontally with a speed hxwa*k m2tk0ja, /d0z nd4i3sof 10 m/s Fig. below Calculate the velocity of the boat immediately after, assum 2askwx 3m,d0/akzn0j *4i htding 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 magnitude of the velocity of the boat is    m/s

  Calculate the force exbm l f.f1xsh/p00u.,wijk(v7kb j a5uerted on a rocket, given that the propelling gases are expelled at a rate/ 0u,kw0v( pj.l ia7bm xjh1ku s.bff5 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 - )gfi w isf g7e-jz5bn vh:m5j+)s3jkat $4.1 \; m/s$ on an apparent breakaway for a touchdown is tackled from behind. When he was tackled by an 85-kg cornerback running at $5.5 \; m/s$ in the same direction, what was their mutual speed immediately after the tackle?    $m/s$

  A 12,600-kg railroad car travels alone on alevel frictionless trac8ikd 5kosl7x29 iw4 r .:rmqsuk with a constant speed of 18m/s A 5350-kg load,initially at rest, is dropped 7iu lioxm d s k9r4r52q.s:w8konto the car. What will be the car’s new speed?    m/s

  A 9300-kg boxcar travelio)7vip ki3aco+kkwg p koc)i )6*yw4.ng 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 horizontalljv;+lfdiz/ffc9xm4a,;t0v yf s +,hxy at speeds of 100km/h If the air strikes a person at the rate of 40kg/s pe l+ ;xd4 +v,c;yxtv9mfj0saz,fih f/fr square meter and is brought to rest, estimate the force of the wind on a person. Assume the person is 1.50 m high and 0.50 m wide. Compare to the typical maximum force of friction $\mu\approx1.0$ between the person and the ground, if the person has a mass of 70 kg.    N
$F_{on person}$  ----待选择----<> $F_{fr}$

  A 3800-kg open railroad car coasts along with a constant speed of 8.6m/s on a lv7u6 d vy-iussx51m c0(hc kekk,n6n7evel track. Snow begins to fall vertically and fills the car at a rate of 3.5kg/min Ignoring friction with the tracy0din-kv, ne67h k(kus v xu scc67m51ks, what is the speed of the car after 90.0 min?$\approx$    m/s

  An atomic nucleus initially movy wvq)zwvcy(v 8* ks;5b+6sjoing at 420m/s emits an alpha 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 nucleusj+s)wby(8 kv qvz5; svcwo6*y 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 penetrates a 2.0-kg block of wood and emergesh,y r 9/ ae.qm9ryf6es cleanly at 170m/s If the block is stationary on a f/6fqh9ersy9r yma., e rictionless surface when hit, how fast does it move after the bullet emerges?    m/s

  A 975-kg two-stage rocket is traveling h a+hbsk6 je 2zlh79q0at 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 isc7pm h-fwzvcb8 5jw;0 traveling in outer space with a velocity of 115m/s To alter its coursc m;f 5cpwh70-8jzb vwe 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 at a speed of 45m/s The golf cj7+os+d1 y wbblub was in contact with the bal+oby ws 17bdj+l 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 a(ht:4 os lda r2wd: ym 8mn+5)htt4nmtnd comes to rest in a time interval of 8.0 ms. (a) What is the impuls4wh dtotn8l)+m(htn:tym:2r ma ds54 e 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 strikey- r;u +w4lxjm(gm dh;s 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 crashwo1. 3w .yi *dm0gc ,qbt9mpzmn*wi p+corthiness 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) Calculate themipbg*tm,* z1 qow.i +c mw.dy 30pcn9 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 stopped in 0.75 k; r3 jrkio)6mjmky98s by a headkjy)9oj ;8 krr6k3imm-on tackle by a tackler running due west. Calculate
(a) the original momentum of the fullback    kg*m/s
(b) the impulse exerted on the fullback    kg*m/s
(c) the impulse exerted on the tackler,    kg*m/s
(d) the average force exerted on the tackler.    N

  Suppose the force acting on a tennis ball (mass 0.060 kg) po9q-yd-i,lhovoz : -t *kkot 7oints in the +x direction and is given bki lod zt---,*: 7qoykoo9 tvhy the graph 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 iw /p d3ltrj nm9,0f5z75-kg person jump without breaking the lower leg bone of either leg? Ignore air resistance and assume the CM of the person moves a distance of 0.60 m from the standing to the seated position (that is, in breaking the fall). Assume the breadn t0r3ifzpw/j m9 l5,king 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 mok9*:xx h w 2qxdzd 6qv,jg0/ynving east (+x direction) with a speed of collides head-on with a 0.220-kg ball at rest. If the collision is perfectly elastic, what will be the speed and direction of each ball after the collision?Let A represent the 0dw/zg*vkj x:06nyx hqqd29,x .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 colq8-bvt ss v36blision with a 0.900-kg puck initially at resq8-b 6vbv3sst t. Assuming a perfectly elastic collision, what will be the speed and direction of each object after the collision?Let A represent the 0.450-kg puck, and let B represent the 0.900-kg puck. v'$_A$ =    m/s ----待选择----eastwest  v'$_B$ =    m/s ----待选择----eastwest 

  Two billiard balls of equal mass undergo a gech5x:pj+lq i:. a*yperfectly elastic head-on collision. If one ball’s initial speed was 2m/s and the other’s was 3m/s in the opposite direction, what will be their speeds after the collision?(Let A represent the ball moving at 2.00 m/s, and call that direction the positive direction.Let B represent the ball moving at 3.00 m/s in the q+hcg i:5x.pl ea :*yjopposite direction. ) v'$_A$ =    m/s v'$_B$ =    m/s

  A 0.060-kg tennis ball, moving with a speed of 2.5m/sg1,qh6) n ifcp collides head-on with a 0.090-kg b) fc,61gh ipqnall 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 a speed of : th(1us4mq6.im nj g3h f+qrh8.5m/s collides head-on and elastically with another ball initially at rest. Afterward the incoming softball bh1 m3(fqtg4in:6 r+q .umhsh jounces 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 elastically as one approachmirkxqx0x 0fvdh*ub q c ;152*es the other directly from the rear (Fig. 7–34). Car A has a mass of 450 kg an 0ixvhr *qq*d1xfub0 kc;5m2xd car B 550 kg, owing to differences in passenger mass. If car A approaches at 4.5m/s and car B is moving at 3.7m/s calculate
(a) their velocities after the collision v'$_A$ =    m/s v'$_B$ =    m/s
(b) the change in momentum of each.$\Delta p_{\mathrm{A}}$$\approx$    kg*m/s $\Delta p_{\mathrm{B}}$$\approx$    kg*m/s

  A 0.280-kg croquet ball makes an elastic head-on ,j6wdy)ty0 vpmw b h;245t tafcollision with a second ball initially at rest. The second bayad45j;,2hmbfttyw) w 60p t vll moves off with half the original speed of the first ball.
(a) What is the mass of the second ball?    kg
(b) What fraction of the original kinetic energy $(\Delta\mathrm{kE/KE})$ gets transferred to the second ball?   

  In a physics lab, a cube slideszx d+ih)r9-3: 2gyotpx bh0ii down a frictionless incline as shown in Fig. 7–35, and elastically strikes another cube at the bottom that i-d :9)pytob iz3ghhxiri0x2 +s 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 object of mev;a4xua+chowp3 l6 9:fh m2w ass 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, propxg n 84,gy5xkh19kk *thgmv *jectile 1 results in a maximum height h of the pendulum equal to *x9p *yg1vghn km,xk4hgk5 t8 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 traveling 230m/s buries itself in a 3.6-kg pendulum:m8zcy6tvs r 46 jz0s. d/*rpcev0tml hanging on a 2.8-m-long string, which makes the pendulum swing upward in an arc. Determine the vertical and horizontal componentsvt0pre8z z0: l/ tc6d r4jmmv.s6*ycs of the pendulum’s displacement.vertical$\approx$    m horizontal =    m

(a) Derive a formula for the fraction x jti y 50cvl25)fnfy(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 explosionafn,byb4/ p m0orr h+2 breaks an object, initially at rest, into two pieces, one of which has 1.5 times the mass of the other. If 750 +a0r2hp,rfb4ob/ mny0 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 thoks olps/ 5 csmzh,(/e);cyz-e rear end of a 2300-kg 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 impact. What was that speed?(Let A repk(z-o oc ; pcs/,zessh5)/lmyresent 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-jtk.1; dh letf4x b(t of 1.20 m. Approximately how many rebounds will thet. 41;xjbhde- f lkt(t ball make before losing 90% of its energy?   

A measure of inelasticity in a head-on cx6sxk q1 +p:k ph:lbrru (r0j3ollision of two objects is the coefficient of:6 :ljkrrs x(+p1x 3brhu kqp0 restitution, 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 m0 l8,cnwedfl (j tg4d )ov+5rinto 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 in it with the block reassembled. The reassembled block is set on a rough-surfaced table, and the fuse is lit. When the firecracker explodes, the two blocks separate and slide apart. What is the ratio of distances each b+wmt, do0 v gc8fd)e jn4l5rl(lock travels? ----待选择----1/91/101/81/6 

  A 15.0-kg object moving in the +x direction at 5.5m/s collides head-on with azz5 ,sb1uxjmanu 5 ;2muqxr25 10.0-kg object mo;a,rsxmq1jxub 55z zu m25n2uving 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 second nucleus, an electron, anda/ ejkp5z ym o(81um05 6gzq.ofa 2wwi a neut zify0ke.agow o6(qawj1/z2p 55mum8 rino. 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 mas9xxn;pj( bqi qd :6 mgn+/q+fbs $m_\mathrm{A}=0.400$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 collis/oasw. 3cbv4 gion between two objects of equal mass, each having initial speed the two move off tow.vob/a sgc 34gether 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 ori 3naah;z39vv9 f/c a5hk; ytkngin 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 direction of ball A and what are theirz9hk/f cnknaav53 ;y9vh t ;a3 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 collisio1wj q00 n4zzkpry7y) sn with another atom at rest. After the impact, the neon atom travels away at anyjr)q7zsk 04zy1w p0 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 collis3/* bjp btb7dnion with another atom at rest. After the impact, the neon atom travels away at a 55.6/nt 7*db j3bbp $^{\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 threcfjbjtkd, w( i ts yyv.7/:z98e-mass system shown in Fig. 7–38. Specify relative to the left-hand 1. .,dc:s /(tj y9i fwzjkyb7t8v00-kg mass.    m

  The distance between 61uk,;onw t90inqq d ka carbon 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. How far f-p55f jw v5pz fi+z+bqrom the front of the car will the CM be when two people sit in the front seat 2.80 m from the front of-p5pf q5vz++bf i5 zjw the car, and three people sit in the back seat 3.90 m from the front? Assume that each person has a mass of 70.0 kg.    m

  A square uniform raft, 18 m by 18 m, of mass 6800 kg, is used pq+*eh ;0v +xald5mph5r4t cmas a ferryboat. If threehvc rdlp*q05 + hmt +5x;ampe4 cars, each of mass 1200 kg, occupy its NE, SE, and SW corners, determine the CM of the loaded ferryboat.$X_{CM}$ =    m $Y_{CM}$ =    m

  Three cubes, of sidedr 7cz4yg31yov 8 gi6ds $l_0$,$2l_0$, 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 identica2nj *txv6* aobl 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, so that the crane operator can pick up the6j 2 n*vxo*tab load without tipping it.$X_{CM}$ =    l $Y_{CM}$ =    l

  A uniform circular plate of radius 2R has a circular hole ofrwt r9:f+/ mnr radius R cut out of it. The center of the smaller circle is a distance 0.80R from the center C of the larger circle, Fig. 7–41. What is the position of the center of mass of the plate? [Hint: Try subtractiontrr9+ /r: nfwm.]   R

  Assume that your proportions are the same as those in Table 7–1, argvz k40u*nvrb92sonj ju 9:1nd calculate the mass of one of youru rungzk :rn9b9*0ov2 s4jv1j legs.    kg

  Determine the CM of an outstretchct- iz8xz je -w bw.z)n c: 2*.7rrleucur.t3xed 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 the CM of an e ;1t,gbop/sl arm bent at a right angle. Assume that the person i,so ;/l t1bpges 155 cm tall. $X_{CM}$ =    cm $Y_{CM}$ =    cm

When a high jumper is in a position such that his arms and legs are hag60u() yyn ;i rm,.b4ssdhxhmnging vertically, and his trunk and head are horizontal, calculate how far below the torso’s median line the CM will be. Wyh4b;sysx m .)(ih0g 6rud,mnill this CM be outside the body? Use Table 7–1.

The masses of the Earth and Moon 8sv/l1:bcks p 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 stanr qu+ th9um2jvmx:4 /nd 10.0 m 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 un 36vu cuuuij:6iform 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 bottom of the handle is the point that will follow a paraboj3u:uuc6iu6 vlic trajectory?    cm

  A mallet consists of a uniform cylindrical head of mass 2.00 kg and a dia2)l rjk- eauw2meter 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 bottk e)waul-2 jr2om of the handle is the point that will follow a parabolic trajectory?    d    d

  (a) Suppose that in Example 7–14 (c5t uv 2x6qp:zwsnn w w)e)h4+Fig. 7–29), $m_{II}$=3$m_{I}$ Where then would $m_{II}$ land?    d(Round to two decimal places)
(b) What if $m_{I}$=3$m_{II}$    d

A helium balloon and its gondola, of mass M, are in the air and stax5y77decoin;j:j; i i t7y pk)tionary with respect to the ground. A passenger, of mass m, then climbs out and slides down a rope with speed measured with respect to the balloon. With what speed and direction (relative 5;i 77oeitpyx)k7djc:jyni ;to Earth) does the balloon then move? What happens if the passenger stops?

  An 0.145-kg baseball pitched hor(cgpn+opql- 3qaa o /55q,mxhg6ywm1izontally at strikes a bat and is popped straight up to a height of 55.6 m. If the contact time is 1.4 ms, calculate the average force on the ball during p,(/on ql g-5w amy1p6xamo5g+ch 3 qqthe contact.    $^{\circ} $

  A rocket of mass m traveling .adbzl0o ea) 4with 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 sho/dhzhmbwc+i+ 3fo (/lwn in Fig. 7–43. Relative dimensions are also shown/ f+dw/ zi+lb hoc(m3h. 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 by 2,ajo ) nqa*edpushing off with his legs from an 1800-kg spac daqeno,j a*)2e capsule.
(a) What is the change in speed of the space capsule?    m/s
(b) If the push lasts 0.40 s, what is the average force exerted on the astronaut by the space capsule? As the reference frame, use the position of the space capsule before the push.    N

  Two astronauts, one of mass 60 kg and the other 80 kg, are initially at rest intm5m2qc 4rq;g outer spac qt2qmm;4rg5ce. They then push each other apart. How far apart are they when the lighter astronaut has moved 12 m?    m

  A ball of mass m makes a head-on elastic collision 6i6 e (pzgsz+pwith a second ball (at rest) and rebounds in the opposite direction with a speed equal to one-fourth its original speed. What is the mass of the second ball? e 6gis6( p+zpz$m_B$ =    $m_A$(Round to two decimal places)

  You have been hired as an expert witness inlpq6mt 9ou5k; a court 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 intop kq tum;5ol96 car B. After the collision, car A slid 18 m while car B slid 30 m. The coefficient of kinetic friction between the locked wheels and the road was measured to be 0.60. Show that the driver of car A was exceeding the 55-mph (90km/h) speed limit before applying the brakes.    mi/h

A golf ball rolls off the top of a flight of concrete steps of tota c;wfgg;r tg+j/yrf:gp 53) .x .as xigqyy8q7l vertical height 4.00 m. The ball hits four times on 8. fjprgy3:)ri;/x qct.ysgg+ 7 ;qggw f 5yxathe way down, each time striking the horizontal part of a different step 1.0 m lower. If all collisions are perfectly elastic, what is the bounce height on the fourth bounce when the ball reaches the bottom of the stairs?

  A bullet is fired vertically into a 1.40-kg block of wood at rest direct9bfbd l6jia;i;/ nhw ,ly 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 6 fabibh9nw,/;;jldibullet becomes embedded in it?    m

  A 25-g bullet strikes and becomes embedded in a *vlg y2h;*+whq8 :uwj:nhuq t1.35-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 suwy:wv g; *hn:q qj2u*+8tl hhurface 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 ma8mov)j+ncm 4 mss 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 nc m4momv)j8+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 wasyru*m k(t(odaz4wxp-57-cyce :z2llf-li; v 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 eyxi2lf .6t ve5c 8yf4a x6jkk:xplosion. One fragment acquires twice the kinetic energy of the 4ylv5f: y26cet k8xf6kaj .xiother. What is the ratio of their masses?   

  The force on a bullet is given by the formula F = 5 :t,by-z*te 6i53f +emyzdiibd p 7)kq80-( $1.8 \times10^{ 5}$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 ;a:lqr1 (:p teyznv ;t$m_A$ = 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 alph3p r udi5u0w7na particle and a smaller nucleus. What will be the speed of this rw5u7p n03rudiecoiling 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 angl;frmr1b1 +9 qb*osuv* silgw 5e of 30 $^{\circ} $ to the horizon with a speed of 25m/s (Fig. 7–45). When it reaches the maximum height, it is hit from below by a 15-g pellet traveling vertically upward at a speed of 200m/s The pellet is embedded in the skeet.
(a) How much higher did the skeet go up?    m
(b) How much extra distance, $\Delta{x}$ does the skeet travel because of the collision? $\approx$   

  A block of mass m=2.2kg slif eq,ho1ge 8,hdes 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 limitu0qttp3ja cr z2usjp 828p4;n on mass m if it is to rebound from M, slide up the incline, stop, slide down the incline, and collidz8s 8a0p2ju3tprn 42 c;pqtuje with M again?    kg (Let A represent mass m, and B represent mass M.)

  The gravitational slingshot effe 6v)8*a cepdyect. Figure 7–47 shows the planet Saturn moving in the negative x directi*)86pdya evecon at its 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