We claim that momentum is conserved, yet most moving objects eventually slow,h tnbtg4 .s4 :ee s,+ xiczqik/;s(we down and stop. Explaik.bwe sz(i,e ,shcqg 4ntt+:x4; sie/n.

When a person jumps from a tree to the ground, what happensp-,q2 sjg5r, 2p pvvy t-kwj)zrk94ql to the momentum of the person upon striking the ground? jqr-2-gskz v, v9qr), jpl52kyptw p4

When you release an inflated but untied balloon, why dox 9*upwic/qo i30co/4gxjn5mes it fly across the room?uwg5 ipj4//moc* x9co q03xni

It is said that in ancient times a rich man with a bag of gold coins frozer:xj;:d2n kl3 r30uv etnaynfv 7h(*o to death while stranded on a frozen 73:rvtjehyn;n(n*douak: 23v f l0r xlake. Because the ice was frictionless, he could not push himself to shore. What could he have done to save himself had he not been so miserly?

How can a rocket change direction when it is far out in spacyxg3v 2qzk3nnkj )w(vz3o* ;te and is essentially in a vac2q(3 *tnn gvz3wx) vjo;kkzy3 uum?

According to Eq. 7–5, the lonc)v zd;+p1m,en5 (4wjpi ne ppger the 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 value of air ba)v+p, e1n 4d; jz(cme nwp5ippgs, which are intended to inflate during an automobile collision and reduce the possibility of fracture or death.

Cars used to be built as rigid as possible to withstand collisions. Todayli7 zyyuyg9w5j ,fxe490 o8qt , though, cars are designed to have “crumple zones” that collapse upon impact. Wha z0qilwf7o j5uy yg48xyte,9 9t is the advantage of this new design?

Why can a batter hit a pitched baseball further than a ballc(iw. re,xk1z 5 xmo(f31wnmy tossed in the air by the batfx (e,wm. 351ino( c1kzxmy wrter?

Is it possible for an objec,hw4) pwn q 4ao .sat-f:d mwt4wjdu*/d 7mf,ft to receive a larger impulse from a small force than from a large force? Expl d-:wm/o pdw.td *mfajf4,w nafq47w,t4 )sh uain.

A light object and a heavy object have the same kinetic energy. Wh f;gi5ica,z7f+a w9mjich has the greg+ famj5iic;f97,a zw ater momentum? Explain.

Describe a collision in which all kineti/3ic jez5,ple nvq2x-c energy is lost.

At a hydroelectric power plant, water is directed at hi54ckw ai pc;/d/zyl:ygh speed against turbine blades on an axle that turns an el y k ci//zy5capdw;:l4ectric 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 45*ok eqt(e4*l /tma; -g eb8zks $^{\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 ytfo0++xx8ux7 )-aczwd ) g zao(hs: ph onto a hard steel plate (fixed to the Earth), from which it rebounds at very nearly its original speed. (a) Is the momentum of the ball conserved during any part of this process? (b) If we consider the ball and Earth as our system, during what parts of the p(o+zyus: w )-cotzxf px7aax+8 d)h g0rocess 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 backward when carrying a heavy load in yo8(c4l q.jvg 7trjv *ipur arms?

Why is the CM of a 1-m length of pipe at its mid-point, whereas this is nodn8d7l* cv62p;ivve nt true for yo7n*;n 2de vvdvc i86plur arm or leg?

Show on a diagram how your CM shifts when you change from a lying pf :up6xava: rst:y 1d wzs1o0/osition to a sitting posit xvd:0a rou:tzw:6s1a/ s1y fpion.

If only an external force can changh88xbgym 7p o.4tf:vv e the momentum of the center of mass of an object, how can the in fg:yh tbv7 8.xm84vopternal force of an engine accelerate a car?

A rocket following a p8/ l*etpqjqkmh9;7xk b,z( f carabolic path through the air suddenly explodes into many pieces. What can you say about the motion of this systebk h qpz t(xk/7lq me8j*,;fc9m of pieces?

  What is the magnitude of the momentum of a 28-g sparrow fly67 nva glhbh jt1)c8d(ing with a speed of $8.4 \; m/s$    $kg \; m/s$

  A constant friction force of 25 tdys5 p 7di.v7N acts on a 65-kg skier for 20 s. What is the skier’s changeds 5.vt 7yid7p in velocity?    m/s

  A 0.145-kg baseball pitched at 39 m/s is hit on a horizontal line drive st76tp41wfdy1(egzz ve2ku l .*ivvbh 1raight back toward the pitcher at 52m/s If the contact time betweenuz1 p*veb2y7v ezkdlg4.1th( ivw6 1f 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 horizont+c7lvgvrha7wagbpqx214la g3x l29 4ally with a speed of 10 m/s Fig. below Calculate the velocity of the boat immediately after, assuming it was initially at rest. The mass of the child is 26.0 kg, and that of the boat is 45.0 kg. Ignore water resistance.1gvx+gql hla7x72a24gavr w 4lc93 b p The magnitude of the velocity of the boat is    m/s

  Calculate the force exerted on a rocket, given that the propelling gases : 4gbgfb:a-,sh6gb da vmw vu:bp:j (3are expegdb:m:f v3asb (w gv4bhj:6u ,: abp-glled at a rate of $1500 \; kg/s$ with a speed of $ 4\times10^{4 } \; m/s$ (at the moment of takeoff). F =    $\times 10^7 \; N$

  A 95-kg halfback moviybbh qp1c-fg31sp .n gmi :m93ng at $4.1 \; m/s$ on an apparent breakaway for a touchdown is tackled from behind. When he was tackled by an 85-kg cornerback running at $5.5 \; m/s$ in the same direction, what was their mutual speed immediately after the tackle?    $m/s$

  A 12,600-kg railroad car travels alone on alevel frictionless trd -e9t0iodzj iuq;h1ct25e,fack with a constant speed of 18m/s A 5350-kg load,initially at rest, is dropped onto the car. Whatjiqfu0hc1ete; itzodd 2- 59 , will be the car’s new speed?    m/s

  A 9300-kg boxcar traveling a:2xhe.+nie dqhp (bc)t $15 \; m/s$ 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 horizonm)-v)m 3ruaku:o mr1rtally at speeds of 100km/h If the air strikes a person at the rate of 40kg/s per squm :1oa)3k)mmrrv u-ur are 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 coaj-*lpot9 p5;e/z/9li tv wgmtsts along with a constant speed of 8.6m/s on a level track. Snow begiwt/llv*m5;p 9jep/toi 9t gz-ns to fall vertically and fills the car at a rate of 3.5kg/min Ignoring friction with the tracks, what is the speed of the car after 90.0 min?$\approx$    m/s

  An atomic nucleus initially moving at 420m/s emits an alpha particle in the dird*+ci8vl shr2ection of its velocity, and the remaining nucleus slows to 350m/s If the alpha particle has a mass of 4.0 u and the original nucleus has a mass of 222 u, wha+cid 2 r*h8lvst 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 emergerzzc)syv- ; b*s cleanly at 170m/s If the block is stationary on a frictionless surface when hit, how fast does it move afterr-s) *bzyc ;vz the bullet emerges?    m/s

  A 975-kg two-stage rocket is ts -f b6jwvzp gbi(2q634n)tej raveling 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 mao(waphf6:bu 2ss 3180 kg is traveling in outer space with a velocity of 115m/s To alter its coursf6w:2ap o bhu(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 gq vr2p1vqfv m,0xy,3d )uflb/olf club was in conta dqxp0u,b1,3rqmyf) lvv2/ v fct with the ball for $3.5\times10^{-3}$s Find (a) the impulse imparted to the golf ball,    kg*m/s
(b) the average force exerted on the ball by the golf club.    N

  A 12-kg hammer strikes a nail at a velocity of 8.5m/s an )(;macti()wmhs0n xpd comes to rest in a time interval of 8.0 ms. (a) What is the impulssmt) mxh)iw0p; na((c 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=i szt6),2ry k)rxa(r e0.06kg 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 engineer in charge of the crax8 pdjyt4pc kza *f,uz s(mb(v818x3eshworthiness 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 the average force exerted on the car by the barriec mbkef1z(8x(pv jd84ayx uzs83 ,*tpr. $\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 s by 8gmbtv 8ea) m2a head-on tackle by a tackler runna)b8t2 mme 8gving 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 0.060ef+ q -db/xu5z kg) points in the +x direction a5u+b-fzeq/d x nd is given by 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 75-kg person jum a wm2n/e a3pp(ub yx:z38ncj8p 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 breaking strength (force per unb y23e zwpxcna8nm ua 38(p/:jit 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 kf7pkc ly gme890fgfi5 mrw 56l1d(tt4g moving 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 and55lwi gpe1yt7 rt0c6 lf4g(f k8mmfd9 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 pdu;b* zs-*qwe 1wzxe3n-ws- head-on collision 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 the 0.450-kg puck, and let B rezue s1z-wd*ewp sx-bq 3 *;nw-present 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 mktdq .w )i/u2lass undergo a perfectly 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 movingdk./l itwq)u 2 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, m 44*:xgio.u-cs d teloukh99ooving 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 Assox9-oul . cd :kois94* tge4uhuming 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 0.2cwdh.5 v9yau*20 kg that is moving with a speed of 8.5m/s collides head-onu9.vy a5cw*d h and elastically with another ball initially at rest. Afterward the incoming softball 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 pasgj-5hf) r4r zpc .d4ly q24kkrk ride 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/sqjs4zy flc4d4 k5 k-p .rrhg2) calculate
(a) their velocities after the collision v'$_A$ =    m/s v'$_B$ =    m/s
(b) the change in momentum of each.$\Delta p_{\mathrm{A}}$$\approx$    kg*m/s $\Delta p_{\mathrm{B}}$$\approx$    kg*m/s

  A 0.280-kg croquet ball makes an elastic head-on collision with a second b)*lvpx bz5,4dy mid6ball initially at rest. The second ball moves ovdb4yd i*)m,pzxlb5 6ff 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 cu+e*mn x d fqyr6 pr25ljk;d+6xbe slides down a frictionless incline as shown in Fig. 7–35, and elase kr rd2;x f+y6j +p*lmqd6x5ntically strikes another cube at the bottom that is only one-half its mass. If the incline is 30 cm high and the table is 90 cm off the floor, where does each cube land? [Hint: Both leave the incline moving horizontally.]$\Delta x_{m}$$\approx$    m $\Delta x_{M}$$\approx$    m

ake the general case of an objec3fuwi5rm;m9 dubis+q7 .,4h f nbx)mct 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)m otg63b.bgvnh.0s qxx 3aj*, projectile 1 results in a maximum height h of the pendulum equal to 2.6 cm. A second pgv6 ms3xxt) a*j.nq03o.g b bhrojectile 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/s4i bso us7 zf6x03bq;d buries itself in a 3.6-kg pendulum hanging on a 2.8-m-long string, which makes the pendulum swing upward in an ars0s3q 64 bzoubx f7d;ic. 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 energ+x2/plse0k y wy lost, $(\Delta\mathrm{KE/KE})$ for the ballistic pendulum collision of Example 7–10. (b) Evaluate for m=14g and M=380g

  An internal explosion breaks an object, initially at rest, iaajkq2/ ;+wn n)e e9jjnto two pieces, one of which has 1.5 times the mass of the other. If 7500 J were released in the explosion, how much kinetic energy did each piece acquire? (Letjw+;2 e9e )nnjqka/aj 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 SUVs:c8v1 ,7v*tenz . ael4x yajh stopped at a red light. The bumpers lock, the brnhzv estx:vy1j8lc e. *,a4a7 akes 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 of 1.50 m and rebounds to a h6r b7ahyexgmz;8usl4z7 ;z6 aeight of 1.20 m. Approximately how many rebounds will the ball make before losi gzy6 6 a7z4e;s z78maxu;hlbrng 90% of its energy?   

A measure of inelasticicla5rcsh:8 b+ty in a head-on collision of two objects is the coefficient of restitution, e, definedblahsc8 cr :+5 as$e=\frac{\nu_\mathrm{A}^{\prime}-\nu_\mathrm{B}^{\prime}}{\nu_\mathrm{B}-\nu_\mathrm{A}},$
where $\nu_\mathrm{A}^{\prime}-\nu_\mathrm{B}^{\prime}$ is the relative velocity of the two objects after the collision and $\nu_\mathrm{B}-\nu_\mathrm{A}$ is their relative velocity before it.
(a) Show that e=1 for a perfectly elastic collision, and e=0 for a completely inelastic collision.
(b) A simple method for measuring the coefficient of restitution for an object colliding with a very hard surface like steel is to drop the object onto a heavy steel plate, as shown in Fig. 7–36. Determine a formula for e in terms of the original height h and the maximum height h’ reached after one collision.

  A wooden block is cut into two pieces, one wi1p0d lmvi4xg.h og7p*3m nv6sth 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. Wh6hm3nm i1p gp7g vx.ls v0*o4den the firecracker explodes, the two blocks separate and slide apart. What is the ratio of distances each block travels? ----待选择----1/91/101/81/6 

  A 15.0-kg object moving in the +x dirpg /4 0vt3g 2wmrnm ,)wqt4akjection at 5.5m/s collides head-on with a 10.0-kg object moving in the -x direction at 4m/s Find the final velocitqm jtwm)0n3k2/ gpa4,rgtw v 4y 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 deyjz(kn w:p :o9pxc31a*yqjh -cays into a second nucleus, an electron, and a new:jpjqx y-k( 1yc: ozha p93n*utrino. 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 marv); v fw*no*hss $m_\mathrm{A}=0.400$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 between two objedawar7 k(zi18 cts of equal mass, each having initial speed the two move off together with speed v/3 What was thr1aw(78 z kdaie angle between their initial directions?    $^{\circ} $

  Two billiard balls of equal mass move at right angleu 7e 9d c3rwj82d8la*3vatgwds and meet at the origin of an xy coordinate system. Ball A is moving upward along the y axis at 2m/s and ball B is mo7veltda88* wgc3 j dawr9du32 ving 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 an 23greq7 p.ca perfectly elastic collision with another atom at rest. After tqrn c23eag7p .he 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 elasti/9 dud xj+l9nz,4f dp d+ev9nrc collision with another atom at rest. After the impact, the neon atom travels away at a 554je,rf 9 xvln9d+z/ n9 +ddudp.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 Figkq my b3 nu.m3hn :dv1be 4i.4+s/sbir. 7–38. Specify relative to the left-hn3n4/i s+k1d4hu :ei r.q sbm.b3ybmv and 1.00-kg mass.    m

  The distance between a carbon ato.lp:uqf .l7u2t) dfnz m ($m_{\mathrm{C}}=12\mathrm{u}$) 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 behu.aj (*qfp0 qhind the front of the car. How far from the front of the car will the CM be when two people sit in the front seat 2.80 m from the front of the car, and three people sit in the back seat 3.90 m from the .(h 0*uqapjfqfront? 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 i oxm6 myr )pwlqo30.lt t (w3ye;nm0gg6u(/bused as a ferryboat. If im/prut. mebyow 0gt g(ol0)336wx q m l6n;(ythree 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 side8 p;khj72xulk s $l_0$,$2l_0$, and $3l_0$ are placed next to one another (in contact) with their centers along a straight line and the $l=2l_{0}$ cube in the center (Fig. 7–39). What is the position, along this line, of the CM of this system? Assume the cubes are made of the same uniform material. $X_{CM}$ =    $l_0$ from the  ----待选择----leftright  edge of the smallest cube

  A (lightweight) pallet ha22 qgl npiy-4xs a load of identical 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, soyipg 22-x4 nql 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 0 bd098oxxzk9il pb5e circular hole of radius R cut out of it. The center of the smaller circle is a distance 0.80R from the center C of th i 905ke9zo0bp 8bxxlde larger circle, Fig. 7–41. What is the position of the center of mass of the plate? [Hint: Try subtraction.]   R

  Assume that your proportions are the same as those in Table 7–1, and calcula) zfmc8 nc wln/wln:ctq*)6,kte the mass of :q* ccnczm)/ )w,n6w8llnkt fone of your legs.    kg

  Determine the CM of an outstlz869tg35e (o*wh ,r /ynuevhua dq:hx9k 7a wretched 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 posid 0ito40g m3mytion of the CM of an arm bent at a right angle. Assume that the person is 1m0g m4yi0d 3ot55 cm tall. $X_{CM}$ =    cm $Y_{CM}$ =    cm

When a high jumper is in a position such that hi hl,63p5namwchrjf0n h3n,3p s arms and legs are hanging vertically, and his trunk 3chj n 3 naph,w,lm36hr 5np0fand head are horizontal, calculate 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 Earth and Moogbgsk q j0 bi+:t(4cmd0,hxa3.pa9ixn 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 n* rlxtgi*7n* ice.
(a) How far from the woman is their CM?    m from the woman
(b) If each holds one end of a rope, and the man pulls on the rope so that he moves 2.5 m, how far from the woman will he be now?    m
(c) How far will the man have moved when he collides with the woman? He has moved    m from his original position

  A mallet consists of a uniform cylindrical head of mass 2.00 kg and a diameter 084 cb 2lw g0l1whtxts).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 tx)t twlcg 1lhw40b28she 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 kg and +y-d uuh3)w0isdps ; ya 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 ai+;duh ips-w3y0s)uydr, 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(b -sm.dz7id 2jh c nz9*u7i azalk:i*. 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 gondgl:vlh) bg975 x.wn.fc uda *aola, 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 thef9 .ln wa:5*vg.d g)hbl ax7cun move? What happens if the passenger stops?

  An 0.145-kg baseball3xxpb mqmn+y( /s4aq; pitched horizontally at strikes a bat and is popped straight upnsbm+/ qqmx( x34y;a p to a height of 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 traveling with12 v ):quvoycv:po.yz1ppp)q rzd1/r 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 shoj.c ) w88bsnood pmv24wn in Fig. 7–43. Relative dimensions are also shown. Should the player be worried aboujd )4c vwp 2.8monbos8t 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) acquire*vlnxmg8c z eqvk(/.)s a speed of 2.5m/s by pushing off with his legs from an 1800-kg space cz)nv/k vl*qc( g.m8x eapsule.
(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 p.w uh:l4qf*9yw p2dq mass 60 kg and the other 80 kg, are initially at rest in outer space. They then puuyph94dq:lqw .2wf p *sh 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 elast 3*v:(0zf ,00ule), j1 eupj tewlim.wdmdjdtic collision with a second ball (at rest) and relj( de,wf et1ei0 )l jd3pm,. mjuw0zv u0*td:bounds in the opposite direction with a speed equal to one-fourth its original speed. What is the mass of the second ball? $m_B$ =    $m_A$(Round to two decimal places)

  You have been hired as an expert witness in a +qrx )8slafa0dj 83vh v/q)ym 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 0 fv yr8lvq+ s)8 ax/3j)mqhda15 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 flight of concrete steps ,vstllcx wh.4p6b0um./c 1fbof total vertical height 4.00 m. The ball hits four times on the way down, each time striking the horizontal part of a different step 1.0 m lower. If all collisions are perfectly elastic, what is the bounce height on the fourth bounce whenxbupmhlcvb6,40l /w .s t1cf. the ball reaches the bottom of the stairs?

  A bullet is fired vertically into 8 rrd5peqrmcy:io z ,zf,:/t3a 1.40-kg block of wood at rest directly above it. If the bullet has a mai zo rfe dq385:/c,yrz:rp ,mtss of 29.0 g and a speed of 510m/s how high will the block rise after the bullet becomes embedded in it?    m

  A 25-g bullet strikes and becomr3mv6duot3vg adc+ 37 z6dk 1oes 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 the surface is 0.25, and the impact drives the block a distance of 9.5 m before it comes to rest, whkg+71m36od ud3 vr3toz6avdc at was the muzzle speed of the bullet?    m/s

  Two people, one of mass 75 kg and the other of mass 60 kg, sit i (kn4;wv *hu-i edmu+nn a rowboat of mas kwe *uv+ n;-dh4un(mis 80 kg. With the boat initially at rest, the two people, who have been sitting at opposite ends of the boat 3.2 m apart from each other, now exchange seats. How far and in what direction will the boat move? The boat will move    towards the initial position of the 75 kg person(Round to two decimal places)

  A meteor whose mass was abkn7-x;qlv ax ;zog8( dves 7uq4 j:4xwout $ 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 9pyzy1m w; ri9explosion. One fragment acquires twiceiy9r1pz y; mw9 the kinetic energy of the other. What is the ratio of their masses?   

  The force on a bullet is give j(dmjr4qjh hs(ttm (90.kkv.n 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 masses 5k**sh)v+fc tm nu.lyv 1/fsw$m_A$ = 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 a 4+baewe0t 43:ub,svj):c+wspmsl lsmaller nucleus. What will be t)b, ve+e 0walm4wl4p t:cas3 ssjub:+ he 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 ::2udsgjogc 4 wnu.-u 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 slides down a fgy62nf.vs. e 30.0 $^{\circ} $ incline which is 3.60 m high. At the bottom, it strikes a block of mass M=7kg which is at rest on a horizontal surface, Fig. 7–46. (Assume a smooth transition at the bottom of the incline.) If the collision is elastic, and friction can be ignored, determine
(a) the speeds of the two blocks after the collision,v'$_A$ =    m/s v'$_B$ =    m/s
(b) how far back up the incline the smaller mass will go. $\approx$   (Round to the nearest integer) (Let A represent mass m, and B represent mass M.)

  In Problem 79 (Fig. 7–46), what is the upper limit on mass m if it is to rebl sowban/;yad / -20q4kwa3chmo - s5round from M, slide up the incline, h la4-wqswd02n5y3b m/o /roak;s-c astop, slide down the incline, and collide with M again?    kg (Let A represent mass m, and B represent mass M.)

  The gravitational slingshot effect.) w-fykcfh 6q4 Figure 7–47 shows the planet Saturn moving in the negative x direction atw)c 6fh 4-yqfk 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