We claim that momentltds/2l7q:g xdks ;4rum is conserved, yet most moving objects eventually slow dow/s:t47qgd;2 rxd sl kln and stop. Explain.

When a person jumps from a tree to the ground, what happens to thn mb;m v(hwfi5qwj) .7e momentum of the person upon ;m7v5i(j)wwq.fb hn mstriking the ground?

When you release an inflated budm1o,xv ,-hdll g3 lz3t untied balloon, why does it fly across the room? ,dvxlol3 h -d3g,zm1l

It is said that in ancient times a rice(az 3 l7*v phownmv5+h man with a bag of gold coins froze to death while stranded on a frozen lake. Because the ice was frictionless, he could not push himsp zalw7h+vm 3o5v(ne*elf 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 is essentit(q;p )q(5g f+p*mz*uij ggjq jp f:,dally i g( ftgqidz+)f(p j,p*;qqgp 5ujj*m: n a vacuum?

According to Eq. 7–5, the longer th8ybv5digq)8u 2 ,fn t hp8n4zse impact time of an impulse, the smaller the force can be for the same momentum change, and hence the smaller the deformation of the object on which the force acts. On this basis, explain the values g hyn2)5up ,bnfi8ztd84q8v 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 a:)oft2,rek+ 6qthft4*) edd i6lyobx s possible to withstand collisions. Today, though, cars are designed to have “crumple zones” that collapse upon impact. What is the advantage of th6,) do+h 2k:qd6 e* 4bexit)ytffl otris new design?

Why can a batter hit a pit7gbkr a5my0 f s67cdtr,16 puuched baseball further than a ball tossed in the air by t17p a rt7g,bsyr k6f6udc5mu0 he batter?

Is it possible for an object to receive a larger impulse from a small forc)x k(ghm pz76ud:2 v,vxyp8fce than from a large force? Expdpx6:7hvcxk y2z)f(v8 pg,mulain.

A light object and a heavy object have the same kk83zfd8f0d7b m-f eieaflp7 0inetic energy. Which has the greater mod fz37pf8 0ai -b 7flem0df8ekmentum? Explain.

Describe a collision in which all kinetic energy is los)t9jy 5 l5pxuht.

At a hydroelectric power plantsc*sts-ycf): kt+g m)wxj1 m+, water is directed at high speed against turbine blades on an axle that turns w+m) s )1mctfs+xs*y-:kgjct an electric generator. For maximum power generation, should the turbine blades be designed so that the water is brought to a dead stop, or so that the water rebounds?

A squash ball hits a wall at a 4c doj2vwualfl4 :.fa0g.;0qd5 $^{\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 plml40 7j +tdqi)nu+uix ate (fixed to the Earth), from which it rebounds at very nearly its original speed.n4 timq)07+iujxld u+ (a) Is the momentum of the ball conserved during any part of this process? (b) If we consider the ball and Earth as our system, during what parts of the process is momentum conserved? (c) Answer part (b) for a piece of putty that falls and sticks to the steel plate.

Why do you tend to lean bpdqz3 ycf8s k0-*cf.p bp a:isd3efs6mk6 b+;ackward when carrying a heavy load in your arms?

Why is the CM of a 1-m length of pipe at its mid-point, whereas this is not te) iqmwlnt dg1w/r8+9rue for w mn8rlqtg iew1d+9 /)your arm or leg?

Show on a diagram how your CM shifts when you change from a lying position tx)kf+homdam6* q f.dh ,ft//bo a sitting p,b/ dadxft q+*o )ffk6h m.h/mosition.

If only an external force can change the momentum of the center of mass lfe.m h j-ic)8of an object, how can the internal force of an engine accelerate).l8c i-hfj me a car?

A rocket following a paraborw;1 wb 4styg7lic path through the air suddenly explodes into many pieces. What can you say about the motion w7wsrg4t1by; of this system of pieces?

  What is the magnitude of the-wgqpp0ub t 8rwgi 7n)4 oa,l+ momentum of a 28-g sparrow flying with a speed of $8.4 \; m/s$    $kg \; m/s$

  A constant friction atmxd5+erllv :k 1,pu6,zc:sforce of 25 N acts on a 65-kg skier for 20 s. What is the skier’s change in velocid:+t1,u eszmk :p ,allc65vxrty?    m/s

  A 0.145-kg baseball pitched at 3iz)6bfqj 7i0k 9 m/s is hit on a horizontal line drive straight back toward the pitcher at 52m/s Ifj76qib0 ) zkfi the contact time between bat and ball is $3\times10^{-3}$s calculate the average force between the ball and bat during contact.    N

  A child in a boat throws a 6.40-kg package out horizontallje0gy am:h8md h) p;3ey with a speed of 10 m/s Fig. below Calculate the velocity of the boat immediately after, assuming it was initiall:yjg)m0p a h3;em dh8ey 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 ex1a9sq*d ka 1k hlqyg2uxw l96 p.l-q4yerted on a rocket, given that the propelling gases are expelled at a r w12q 9yxkq4*qdh6p .1la gluylks- 9aate 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 at t7z:d:e ml,xq $4.1 \; m/s$ 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 aloc ed x ,27iuk e+,d14gtqzol6wne on alevel frictionless track with a constant speed of 18m/s A 5350-kg load,initially at rest, is droppewe6g,o1d,il 2qtc exz47+ kdud onto the car. What will be the car’s new speed?    m/s

  A 9300-kg boxcar travelingon,bjdvo). w ( 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 horizontcqaboi ,/q9 r;3m5vl kally at speeds of 100km/h If the air strikes a person at the rate of 40kg/s per square meter and is brought to res 9 lv;mor/kc35,a ibqqt, 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 constanamjty y)4i4oz.fs6 1q t speed of 8.6m/s on a level track. Snow begins to fall vertically and fills the car at a rate of 3.5kg/min Ignoring friction with the tracksoy )atyqij fmz46s41., what is the speed of the car after 90.0 min?$\approx$    m/s

  An atomic nucleus initially moving at 420mi*ub)w2 d6ytxfs .hi6r 9djq 9/s emits an alpha particle in the direction of its velocity, and the remaining nucleus slows to 350m/s If the a.b t hd*6yixwj26 99frdiuq s)lpha particle has a mass of 4.0 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 penetrates a 2.0-kg block of wood and emerges clea iq)wm: a.5.m jcfe 0sl*zy*shqk (b)anly at 170m/s If the block is sa*sm)hz(s*j 0b.5 c y)qfak:. emqwl itationary on a frictionless surface when hit, how fast does it move after the bullet emerges?    m/s

  A 975-kg two-stage rocket i-rnc pt5inwl9 wm1t49 s 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 space with+s+kh;yxey fr e,iz - m5kx,2w a velocity of 115m/s To alter its cours2, mi;kr y w5hfe+xksex,z y-+e 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 golfpm9nl ba+ cskybs+3t+4o 1 j.z club was in contact with the ball for9t sazyb+bjp+mlc3 s+o4. nk1 $3.5\times10^{-3}$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 :g48njig -kauiyu(h* nail at a velocity of 8.5m/s and comes to rest in a time interval of 8.0 ms. (a) What is the impulse given to the n:i4 *uj(guk 8nha-g iyail?    kg*m/s
(b) What is the average force acting on the nail?    N

  A tennis ball of mass m -neyd dr;+p5cynjqab qz3xn: ,(ac) /=0.06kg 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 en,*mxd p(c+cxbgineer in charge of the crashworthiness of new automobile models. Cars are tested by smashing them into fixed, massive barriers at 50km/h (30 mph). b (x,c+cd*mxpA 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 stopped in 9fr o pd:fs2uxs*c35k 0.75 s by a head-on tackle by a tacklecr3k5 p*2f9 fusdso:xr 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 t,6lubvtj 7,cckcdz2 ) ennis ball (mass 0.060 kg) points in the +x direction and is given by the graph of cltvb6ck 2,)z j7cud,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 jumpz124vry 6h;tynybjvq axfw(y q /1s27 without breaking the lower leg bone of either leg? Ignore air resistance and assume the Csayrq;hzx y2qf71 j 1b2y6/vn(tvy w4M 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 (+d:em (-4pafos x direction) with a speed of collides head-on with a 0.220-kg bapae :f 4s(o-dmll 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, moving east with a speed of 3m/s has a head-on collision rd cxhu ,((8 vkuj04+wrlr;tp 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 the collision?Let A represent the0pl(u 8 w,;4vkx r+thcd( rruj 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-m eb;2v3mki wth0j5(lg eob+* on collision. If one ball’s initial speed was 2m/s and the other’s wa0b jiweo mk( m*ht v;3e+gb2l5s 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 baluyf ,6u ze p;7mbijzyml( gt+98,y w:dl, moving 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 oe wy,tldy8up9iumfy z(b;m 7, +j 6g:zf each ball after the collision?(Let A represent the 0.060-kg tennis ball, and let B represent the 0.090-kg ball.)v'$_A$ =    m/s v'$_B$ =    m/s

  A softball of mass 0.220 kg that is moving with a speed of 8.5m/s collides heooq 3js:dxi :6o/m;tfad-on and elastically with another ball initially at rest. Afterward the incoming softball bounces backward with a/qo6mt3xjid o;of :s: 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 5c jjx39l3qxeride collide 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 9cex j3lq 5j3xcalculate
(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 a5u6 iin 6qj 5w(xxrs7un elastic head-on collision with a second ball initially at rest. The second ball moves off with half the original speed of the first ball. 7u xjunx(5wsi6 qr 56i
(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 a1oq 0u1.bgmn4do1tele 2d * ytgby;lxb+o4b*s shown in Fig. 7–35, and elastically strikes another cube at the bottom that is only one-half its mass. If the incline is 30 cm htub 2y 0 dd.g;eobox4oq+ t l11 4y*b1mbln*egigh 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 case5dov-ep-b 367k-l iub -yevts 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 ret4x6 oycar3:m2 v6 x ;et:nedesults in a maximum height h of the pendulum equal to 2.6 cm. A second projectile causes the the pendt3ramedeny:6 vce x46;x:to2ulum 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*69l8 hq 6 pxpapge2gml3ut6a pendulum hanging on a 2.8-m-long string, which makes the pendulum swing upward in an arc. Determine the vertical and horizontal components of the pendulum’s displacement.ver lpge2 lp66a6a39ux phqg*8mttical$\approx$    m horizontal =    m

(a) Derive a formula for the fraja+q9st kdmfi sy/,0 ,puz ;/ection of kinetic energy lost, $(\Delta\mathrm{KE/KE})$ for the ballistic pendulum collision of Example 7–10. (b) Evaluate for m=14g and M=380g

  An internal explosion breaks azo/qts d/gv()ox sz,78w sbc-n object, initially at rest, into two pieces, one of which hb,oq/xs )ovz(zt s- wd/ 8s7cgas 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 into the rear end of a 2300-kg SUV xmtrz6k+;b /)e,tcwx stopped at a red light. The bu x/cb tezxrw;t6 m+),kmpers 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 represent the sports car, and B represent the SUV) $\approx$    m/s

  A ball is dropped from a height ou0g6 ; --kkvti.coc65xu pg elf 1.50 m and rebounds to a height of 1.20 m. Approximately how many rebounds wilp5uokgu6vl xti -;e0cg-kc . 6l the ball make before losing 90% of its energy?   

A measure of inelasticity in a head-on collision of two objectsza7kht 9gvc-* iojd61pq/8 xa is the coefficient of restitution, e, defin j8/d 1zxva9-q7g kto6hic*paed 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 t z7r98xwpc :yswo pieces, one with three times the mass of the other. A depression is made in both faces of the cut, so that a firecra 87pwsyrczx9:cker can be placed in it with the block reassembled. The reassembled block is set on a rough-surfaced table, and the fuse is lit. When the firecracker explodes, the two blocks separate and slide apart. What is the ratio of distances each block travels? ----待选择----1/91/101/81/6 

  A 15.0-kg object movie9okn1b 46x 1 ,p3pn2gviykvyng in the +x direction at 5.5m/s collides head-on with a 10.0-kg object moving in the -x direction a 4kopx 26bv,n9ypg 1i31 nykevt 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 d6jp :yqd(n .pq2:bevp3z ci (c5/ 9lyemca7zfecays into a second nucleus, an electron, and a neutrino. The electron and neutrino are emit3p7ey: m l(56v .zdc:/2izbpafq9 qcycjnpe(ted 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 ma y,py8enk8a; lmiu s2-ss $m_\mathrm{A}=0.400$kg moving with speed $\nu_\mathrm{A}=1.80$m/s strikes ball B, initially at rest, of mass $m_\mathrm{B}=0.500$kg As a result of the collision, ball A is deflected off at an angle of 30.0 $^{\circ} $ with a speed $\nu_\mathrm{A}^{\prime}=1.10$m/s (a) Taking the x axis to be the original direction of motion of ball A, write down the equations expressing the conservation of momentum for the components in the x and y directions separately. (b) Solve these equations for the speed v'$_B$ and angle $\theta_{\mathrm{B}}$ of ball B. Do not assume the collision is elastic. $\theta_{\mathrm{B}}$ =    $^{\circ} $ v'$_B$ =    m/s

  After a completely inelastic collision f6ttfb2d50uef -6/ bmmpgl1 lbetween two objects of equal mass, each having initial speed the ttgu-bd /6 lffmp05mb1 l26eftwo 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 theyrbx(q 5ojd3 n9ko ,p* 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 *xnd 95ypjr (o,kq3bo 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 per v0oer i+,o mbr,o)o ;bt36iglfectly elastic collision with another atom at rest. After thl, o60o, ) bmtore3r vboii;g+e 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 with/4,dxz8pw c cl another atom at rest. Ac dl8pcz 4w/,xfter the impact, the neon atom travels away at a 55.6 $^{\circ} $ angle from its original direction and the unknown atom travels away at a -50 $^{\circ} $ angle. What is the mass (in u) of the unknown atom? [Hint: You can use the law of sines.](Let A represent the incoming neon atom, and B represent the target atom) $m_B$   u

  Find the center of mass of the three-mass system shown in Fi-8lx ::u;zj9:h bj emhf5bssv g. 7–38. Specify relative to the left-hand 1.00-kg fj:8m:;b9b:lse h xsu5 jv hz-mass.    m

  The distance between a c 8gcbk+sd++n aarbon 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 behiph7(( dnt lsj2:pr(mqnd the front of the car. How far from t qprljshn(7 :d (pt(2mhe front of the car will the CM be when two people sit in the front seat 2.80 m from the front of the car, and 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,3yzt+olc3x o0 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 thy33x oltoz c+0e CM of the loaded ferryboat.$X_{CM}$ =    m $Y_{CM}$ =    m

  Three cubes, of sides /m2kagw v 0ldxmd4++ b$l_0$,$2l_0$, and $3l_0$ are placed next to one another (in contact) with their centers along a straight line and the $l=2l_{0}$ cube in the center (Fig. 7–39). What is the position, along this line, of the CM of this system? Assume the cubes are made of the same uniform material. $X_{CM}$ =    $l_0$ from the  ----待选择----leftright  edge of the smallest cube

  A (lightweight) pallet has a load of identical cases of tomato +oos38 m egk,5nblv; vpaste (see Fig. 7–40), each of which is a cub bnvg8 +vokms;53,eo le of length l. Find the center of gravity in 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 cirkk0c+ t /u*oticular hole of radius R cut out of it. The center of the smaller circle is a distan /ot0*i+uctk kce 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 propntb 7-zaa 3z.jortions are the same as those in Table 7–1, and calculate the mass of one of your legszbn.a-j t7za3.    kg

  Determine the CM of an outsekw 2ao6jvd 8,tretched arm using Table 7–1.   % of the person's height along the line from the shoulder to the hand

  Use Table 7–1 to cal6 9k ovdg43 x2bq)vmcoculate the position of the CM of an arm bent at a right angle. Assume that the person is 155 cm tall. dg)m6vv3oq 24 9bkcox $X_{CM}$ =    cm $Y_{CM}$ =    cm

When a high jumper is in a position such that his arms and legs are hango 9hxjwskv-odn/f**z k*1s 0hing vertically, and his trunk and head are horizontal, calculate how far below the torso’s median l-sosk*d h wfhj9 /z vk1*x*n0oine the CM will be. Will this CM be outside the body? Use Table 7–1.

The masses of the Earth an.3rf w:zkf/ko2 nmwkadt )i., d 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.9jv9 (yf.x-lr6 7ci gv0cx mvf
(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 a6fb/ y79mjgr y uniform 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 ab6y9 bj/7m gryfove the bottom of the handle is the point that will follow a parabolic trajectory?    cm

  A mallet consists of a uniform cylindrical head of macu0::v9coy1 oqmy - nm7 4pxcfss 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 7uc :v01 -qmpoxcyc4yof9n:m . 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. 7–7c3m;j c:j1 xfnw2fgc29), $m_{II}$=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 gondem d/7a zrvb* m8q r.fyl+z(z3ola, of mass M, 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 respect to the balloon. With what speed and direction (relative to Earth) does the balloon then move? What happens if +zd 3mqbzl*/ r. m8yzrfva( e7the passenger stops?

  An 0.145-kg baseball pitched horizontally at strikes a batuo1 yi8: jtkfy3/r1v w and is popped straight up to a height o11krv ijuwo:t38yyf/ f 55.6 m. If the contact time is 1.4 ms, calculate the average force on the ball during the contact.    $^{\circ} $

  A rocket of mass m trave,hs9oa,+cfv yw,jw8 w ling 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 wff5 n0,fgcj-is faced with the corner pocket shot shown in Fig. 7–43. Relative dimensions are also shown. Should the player be worried about this being a “scratch shot,” in which the cue ball will also fall into a pocket? Give wnfg5- fjf ,c0details.

  A 140-kg astronaut (including space suit) acquires a speel2 q c3in(lx*dncg5f6d of 2.5m/s by pushing off with his legs from an 1800-kg space 26n( d*n3 fllqicx5 cgcapsule.
(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 iysnv1ls cw 1yi91tz60 98gztthe other 80 kg, are initially at rest in outer space. They then push each other apart. How far apart are vn i 1 y9w s9tszty6clg1z08i1they when the lighter astronaut has moved 12 m?    m

  A ball of mass m make9n cmo;l yc3x6yl1ezi+k d ie(/-i* tks a head-on elastic collision with a second ball (at rest) and rebounds in the opposite direction with a speed equal to one-fourth its(ei/cm3 xiyli+ dz*kn ect6 1k9l-o;y 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 involving ny;8m( y.-ht-wf s+zh)sx unr 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 5-h( ntfurs mzx-.wy ;ysh+n8)5-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 tota2x188jds/6bq zerhgn l 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 hh6g/x21n s8 dqbr 8jezeight on the fourth bounce when the ball reaches the bottom of the stairs?

  A bullet is fired vertically into a 1.40-kg b )bfltspx q-7.lock of wood at rest directly above it. If the bullet has a mass of 29.0 g and a speed of 510m/s hof- t)sl px7.qbw high will the block rise after the bullet becomes embedded in it?    m

  A 25-g bullet strikes and becomes embedded in a 1.35-kg block of wo+/ .jcwpzb ee7:/o wilod placed on a horizontal surface just in front of the gun. If the coefficient of kinetic fri+ .oljp7 w/izwc/e:be ction between the block and the surface is 0.25, and the impact drives the block a distance of 9.5 m before it comes to rest, what was the muzzle speed of the bullet?    m/s

  Two people, one of mass 75 kg q: v;ktyxic)q)n.e*o and the other of mass 60 kg, sit in a rowboat of mass 80 kg. With the boat initially at rest, the two people, who have been sitting at opposite ends of the boat 3.2 m apart from each other, now exchange seats. How far and in what direction will the bok x)qqt:*v ceno;.i)yat move? The boat will move    towards the initial position of the 75 kg person(Round to two decimal places)

  A meteor whose mass wa* :x sjttf.za,s 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 apar.y 9ch6f*wgaus8 q4f :bh9msmt into two fragments by an explosion. One fragment acquisy:qh fw49 mgsu.9a*fmh bc6 8res twice the kinetic energy of the other. What is the ratio of their masses?   

  The force on a bullet is given by the formula F = 580b ,( mrvm u,2;,v iyt6j2poohj-( $1.8 \times10^{ 5}$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 massesx3qq ivr9w evz1n arf*( o9:4,o8hyo g $m_A$ = 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 sm8//pzhr z ejp); dx;io-7rmpmaller nucleus. What will be the 8h);od pp/p ezz /xm7jimrr-; 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 offl)h w- sr0wb3 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 slides downjqbo42v(z l)j* qbtw 3 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 ixvmq8d:t0o7 a s the upper limit on mass m if it is to rebound from M, slide up the incline, stop, slide down the inclat8o0qxd v :m7ine, and collide with M again?    kg (Let A represent mass m, and B represent mass M.)

  The gravitational slingshot effect. Figure 7–47 shows g )b,jxtuujzs kec1 c::dk,/;the planet Saturn moving in the negative x dirt1 xbju:kd g,zejk: ,;ucsc/) ection 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