We claim that momentum;pbr. 2 y4ul yb)fu-/mf9f r :oeaiez7 is conserved, yet most moving objects eventually slow down and s i97p:fl)ra- fmz. 2;b/4f ro uuybyeetop. Explain.

When a person jumps fro.;,c8v6ckqmnvg,n xb m a tree to the ground, what happens to the momentum of the person upon striki6nn8 kgvq,;mcv x ,b.cng the ground?

When you release an inflated m;ml.h2ojmwr ;*y3ov9,) dzi)cy3gstwekc 9 but untied balloon, why does it fly across the roomc y)o3m hmeki c.3wvg slr,9owd9j*)y2;tzm;?

It is said that in ancient times a rich man with a bag of gold coi+*l wilz9oi8 vdk) o.uns froze to death while stranded on a frozen lake. Because the ice was frioi+)uv 89d l io.wkl*zctionless, 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 fk(9zf ; / :dgtzm4vxamar out in space and is essentially in a vacu zkx/4;t gm(:v fdma9zum?

According to Eq. 7–5, the longer the impact timemsc)em7 k,fl+ pm2nk .gjm k13 of an impulse, the smaller the force can be fok1me )7p3m2c glk msf+k,.mn jr the same momentum change, and hence the smaller the deformation of the object on which the force acts. On this basis, explain the value of air bags, which are intended to inflate during an automobile collision and reduce the possibility of fracture or death.

Cars used to be built as rigid as possible to withsiuuh * b4)k2o/hnzzcu q4 p-e*tand collisions. Today, though, cars are designed to have “crumple zones” that collanuqkzcpo4)u ub / hz -h4ei**2pse upon impact. What is the advantage of this new design?

Why can a batter hit a pitched base :p7-7 m :k-vid2c3rv dt.ora1jxpcyxball further than a ball tossed in the air by the batt-p7c213-yao .rx 7:mv:dtr kid jpcvx er?

Is it possible for an object t9xo23 jr sh7r:.dhn/ zcnxe 7qvq. 0wio receive a larger impulse from a small force than from a large f/nr. qwrx9e x7n0d 7vhjzi2h3c:qos.orce? Explain.

A light object and a heavy object have the same kinetic energy. Which ha- iu2vy)mbh o)cv2 nx7s the greatv2uv-b7m 2nch)xo y i)er momentum? Explain.

Describe a collision in which all kinetic energy is los fiuj4-4w yi.d5xlw9;cmxs( mt.

At a hydroelectric power plant, water is directed at high speedfk/tb 147s)9q otzs tpw 5mc1t against turbine blades on an axle that turns an electric generator. For maximum power generation, should the turbine blades b/7f1 9 1s5cqzmtpo)tbs 4wttke designed so that the water is brought to a dead stop, or so that the water rebounds?

A squash ball hits a wall axai48 u7ldav,)k2sn)o-uy v yt 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 pl.4 4 -auq xxub2idi8i.koo.kgate (fixed to the Earth), from whio2.ui8a g4 ioxqi.u .-kxkd4bch it rebounds at very nearly its original speed. (a) Is the momentum of the ball conserved during any part of this process? (b) If we consider the ball and Earth as our system, during what parts of the process is momentum conserved? (c) Answer part (b) for a piece of putty that falls and sticks to the steel plate.

Why do you tend to leai n7+n-.udwwi) qgpn52 -c(o fx ,qamin backward when carrying a heavy load in your arms?

Why is the CM of a 1-m length of pipe at its mid-point, whereas )lnf c,)otf.g0ub2x qthis is not true for your arm or. noc,2qx)lg)f fbut0 leg?

Show on a diagram how your CM shifts when you change from a i+usu llm.*o4/ yfgq4 lying position to a sitting positio l4su+.oi g4lq*f /yumn.

If only an external force can chanq ezn6b0ut4+v nvk5 f0nq 1aq;ge the momentum of the center of mass of an object4n+qabtn1v0 fe qn;0 5 zuvqk6, how can the internal force of an engine accelerate a car?

A rocket following a parabolic path through the air m9-n-hc2ul v)+1pzkpz iqd,5 cjva7gsuddenly explodes into many pieces. What can yo2czl) 9mh,dzckng7 -5pi-j qup a1vv+u say about the motion of this system of pieces?

  What is the magnitude of the momentum of a 28-g uda.r n7coo -5kx:*zo sparrow flying with a speed of $8.4 \; m/s$    $kg \; m/s$

  A constant friction fou+q 0cr(mxr;j rce of 25 N acts on a 65-kg skier for 20 s. What is the skier’urm ;xjqr+(c0s change in velocity?    m/s

  A 0.145-kg baseball pitched at 39 m/s is hit on a horizontal li95;0ufgiutgalys1uxmy2g6/ ne drive straight back toward the pitcher at 52m/s If thi0tsf51u g96 ua/lx 2mu yygg;e 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 horizontal)pb2cn. 4r**lyxavq e .l:atd ly 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 isr l*c al .pxa4*:n.bqvd)t ye2 45.0 kg. Ignore water resistance. The magnitude of the velocity of the boat is    m/s

  Calculate the force e) v9yr/uaz-wp.onm4vxerted on a rocket, given that the propelling gases are expelled at a rate onv-a9/romp z)v4 .yw uf $1500 \; kg/s$ with a speed of $ 4\times10^{4 } \; m/s$ (at the moment of takeoff). F =    $\times 10^7 \; N$

  A 95-kg halfback moving al/m6vw cqy4 ;2c)dsx ct $4.1 \; m/s$ 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 frica)m-aa3, wp u:+ 7dejxq 7cc1pgvn2 wktionless track with a constant speed of 18m/s A 5350-kg load,initially at rest, is dropped onto the, cj wa)pag1-qx 3pm:c7w7kd vena +2u car. What will be the car’s new speed?    m/s

  A 9300-kg boxcar travzuyb ;0p,mpy 9-zirj )s*7nbeeling 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 horizontally at speeds o:k5rzi ba424ly- .m(ep.bnwdd n-h ryf 100km/h If the air strikes a person at the rate of 40kg/s per square meter and is brought to rest, estimate the force of the wind on a person. Assume the person is 1.50 m high and 0.50 m wide. C4bihyb dkenlrz5.2a- rm(-nd4yw :p .ompare 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/ssp :lr l14pp8g on a level track. Snow begins 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 aftep:p1 4gllps8rr 90.0 min?$\approx$    m/s

  An atomic nucleus initially moving at 420m/s: l1siih q*b2p emits an alpha particle in the directionl 1*spb hiiq2: of its velocity, and the remaining nucleus slows to 350m/s If the alpha particle has a mass of 4.0 u and the original nucleus has a mass of 222 u, what 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 clelqcqu /1w7ot)h3yb 18j r 1cokanly at 170m/s If the block is stationary on a frictionless surface when hit, how fast does it move after the bul8hy )q3lb/1cocw7jk or1tqu 1 let emerges?    m/s

  A 975-kg two-stage rocke11p-9t;uscxgrw0 h x jew9 q+xt is traveling at a speed of $5.80\times10^3\mathrm{~m/s}$ with respect to Earth when a pre-designed explosion separates the rocket into two sections of equal mass that then move at a speed of $2.20\times10^3\mathrm{~m/s}$ relative to each other along the original line of motion. Let “A” represent the upper stage (that moves away faster) and “B” represent the lower stage.
(a) What are the speed and direction of each section (relative to Earth) after the explosion? $v'_A$   m/s  ----待选择----away from the Earthtowards the Earth  $v'_B$   m/s  ----待选择----away from the Earthtowards the Earth 
(b) How much energy was supplied by the explosion? [Hint: What is the change in KE as a result of the explosion? $a\times10^8$ a =    J

  A rocket of total mass 3180 kg is traveling in outer spac2g*zx9scj -ww)7wwxiaj4 dqz+-4 z b te with a velocity of 115m/s To alter its 2 bdcz z)--wtj+*sqwj xi4z xawgw 794course 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 kg2bo2 5fm dii+qxubj1r)3hsk4 is hit off the tee at a speed of 45m/s The golf club was in hk2+qoisj4)ubf 35r ib1 xm2d contact with the ball for $3.5\times10^{-3}$s Find (a) the impulse imparted to the golf ball,    kg*m/s
(b) the average force exerted on the ball by the golf club.    N

  A 12-kg hammer strikes a nail at a velocity of *;lrmhule .d98.5m/s and comes to rest in a time interval of 8.0 ms. (a) What isdue.l ;ml9r* h the impulse given to the nail?    kg*m/s
(b) What is the average force acting on the nail?    N

  A tennis ball of mass m=0.06kg andd.08:dadh pnr n1le -t 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 charllqp,h/um 9cnrur ax5nd* l:2sv*,i7ge of the crashworthiness of new automobile models. Cars are tested by smashing them into fixed, massive barriers at 50km/h (30 mph). A new model of mass 150h l 2xn/:,lnavms,9urpi u5rcdq7**l0 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 runningwa b,bbwq4p0 cnsk,8 , at 4m/s to the east and is stopped in 0.75 s by a head-on tackle by a tackler running dub4cwn,sp bwq0ab8k, , e 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) points in the +x dir/, htd6) mbfw,k)lc umection and is given by t ftm))c6/luh,bm,k dwhe 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 heii5xh2s:k2bqo h:jj:l ght can a 75-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 breakinghj ohlb2xk sijq5 2::: strength (force per unit area) of bone is $170\times10^6\mathrm{~N/m^2}$ and its smallest cross-sectional area is $2.5\times10^{-4}m^2$ [Hint: Do not try this experimentally.]    m

  A ball of mass 0.440 kg moving east (+x diz . gfv+lar14pm.j0xi rection) with a speed of collides head-on with a 0.220-kg ball at rest. If the collision is0a.g .l4z1+xf mivp rj 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 speed0ptw34g bt- )ow vxy4u of 3m/s has a head-on collision with a 0.900-kg puck initially at rest. Assuming a perfectly elastic collision, what will be the speed and direction of each object after the collision?Let A represent the 0.450-w4twpt0 -yo4 vgb) 3uxkg 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 eq: f9 m7 kbavkv7 +b,ft:5-5sgf plpbvzual mass 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 movbv9 mb-5:apgbk5 z+7 skp:7tv vf fl,fing 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, moving with a speed of 2.5m/s collides hea n e/uar1,d.in*cr :jed-on with a 0.090-kg ball initially moving away from it at a speed of 1.15m/s Assuming a perfectly elastic collision, what are the speed and direction of each ball after the collision?(Let A reprec :1/enurai d,.*renjsent 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 skp .cbdh6p00.x/oqul f+7ep kpeed of 8.5m/s collides head-on and elastically with another ball initially at rest. Afterward the inp0+.0x7d.cq /kkfhpp lo 6beu coming 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 park ride 0a6tt59*jgspgsu-z vmi 2 o (ccollide 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 -u59 szt g j(top*6s20m cavgicar 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-jt e;n 03/u6x8 m2omnm0d1azy1kbltbon collision with a second ball initi ob6 m u mmlyx3/e1b0n0tdnz2j tk;18aally at rest. The second ball 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 slides down a 9 feti.v37 lizr/rt*pfrictionless incline as shown in Fig. 7–35, and elastically strikes another cube at the bottom that is only one-half its mass. If the incline iseiitzf.rp vlr7/*93t 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 lrvtd)z ri1odgld3uni 7oy00/ bbh/;he;q.2 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 og c*yup (i u6bzz* 3 aj-re85snol)0wexperiment, projectile 1 results in a maximum height h of the pendulum equal to 2.6 cm. A second o0ncjz3* usw-)8 ipar5 bly6oz( *eguprojectile 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 prjshxji5d ,,rd.+ar8)yzt b4endulum hanging on a 2.8-m-long string, which makes the pendulum swing upwzxrty+8isb j h4r,a.d5rdj ), ard in an arc. Determine the vertical and horizontal components of the pendulum’s displacement.vertical$\approx$    m horizontal =    m

(a) Derive a formula for the fraction of kinetic wslyb5pkc 6r-h1-* vienergy 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, into two piecd+laezy ,+8bc es, 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? (Let A represent the heavier particle, and B represent the lighter particlely+d+c z8,ab e. ) KE'$_A$ =    J KE$_B$ =    J

  A 920-kg sports car collides 0szq65qgkfn /into the 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 cark6fg0/z5n qqs 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 om(gmo1iu*8 qn f 1.50 m and rebounds to a height of 1.20 m. Approximately how many rebounds will the ball make before losing 90% of itsi mq(*um1 ng8o energy?   

A measure of inelasticity in a head-on collision of toyh h9/9r3guvwo objects is the coefficient of restitution, e, deh9ug hvy3/or9 fined 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 cu(/zjh1 tnfek2by,kh 6 t into 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 sepk2(khyz,tje1 /h6fb n arate 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 direction at 5.5m/s coamf9+uy/d8 a ellides head-on with a 10.0-kg object moving in the -x directio/ efda8y9 +aumn 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 a u5dz oa /e+e2:ps*ecdecays into a second nucleus, an electron, and a neutrino. The electron andsup/*ecd+e a5oae :z2 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 m0kkq30nei qq0 ass $m_\mathrm{A}=0.400$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 objects of eq/6 o)re /m(ovh+ or0 ns*0x,nsrp vr:t/v rtzrual mass, each having 6t:/rzvnoo rh),/0e0vr /m+ ns (p*r tsrvorx initial speed the two move off together with speed v/3 What was the angle between their initial directions?    $^{\circ} $

  Two billiard balls of equal mass move at rigf gqq, (v uwr;vnh2v:1ht angles and meet at the origin of an xy coordinate system. Ball A is moving upward along the y axis at 2m/s and ball B is moving to the right along the x axis with speed 3.7m/s After the collision, assumed elastic, ball B is moving along the positive y axis (Fig. 7–37). Whau,rf1vgqnv h;v2qw(:t 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 nvhgvfxva19f2: 7ady8 4 , kduperfectly elastic collision with another atom at rest. After the impact, the neovf17yga 4k favdd2u, h9:8v xnn 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 ela68 5jz.(os7xn ohht vustic collision with another atom at rest. After the impact, the neon atj( u7hxs5.8thnoo 6zvom 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 Fig. *au6-yjs bwoie (nc19 7–38. Specify relative to the lefj w9n*oybuci a(6e1- st-hand 1.00-kg mass.    m

  The distance between a carbon(1 vh*jdd-9.qlbxa e 6cs2 uth 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 8hq:nvvyfc, fl *6uk1 2.50 m behind 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 :81k vvq nfy*fhulc6, the front of the car, and three people sit in the back seat 3.90 m from the front? Assume that each person has a mass of 70.0 kg.    m

  A square uniform raft, 18 m by 18 m, of mass 6800 kg, is used as a ferryboat. Ifa 8mha,u.5fh mr6 56ytmnmcib95rd z, three cars, each of mass 1200 kg, occupy its NE, SE, and SW corners, determine theuh.i z5 5 6m5cm,6a9f,8mnmbrahry td CM of the loaded ferryboat.$X_{CM}$ =    m $Y_{CM}$ =    m

  Three cubes, of sidez 20keu3m3mlns $l_0$,$2l_0$, 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 pasto:z1jf p+h d ah)2e)xbe (see Fig. 7–40), each of which is a cube of length l. Find the2p:ex) h+hj ofz1b)da 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 *.t usdy9+wk. du1 +qmik*s ttradius 2R has a 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 the larger circle, Fig. 7–41. What is the position of the center of mass of the plate? [Hint: Trtkks. uq ++*id ywmts19d.*uty subtraction.]   R

  Assume that your proportions are the same as those in Table 7–1, and calculatnus94sx/3 rb.3shkcz e the mas 3/s3b k szrun9cxsh.4s of one of your legs.    kg

  Determine the CM of an outs nv.5ni w+x0xlpqii *9.h n1totretched 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 arm benjek6a d2 *8jbml9i6yft at a right angle. Assume thabij y8kmaj* 626le9f dt the person is 155 cm tall. $X_{CM}$ =    cm $Y_{CM}$ =    cm

When a high jumper is in a position such -b4 d4 2r nown3o5qpwrf .sz*jthat his arms and legs are hanging vertically, and his trunk and head are horizontal, calculate how far below the torso’s median line the CM will be. Will this CM be outsid z . nf*4rw -nqso2dr45ojbp3we the body? Use Table 7–1.

The masses of the Earth andl8.7da 9ojzt /ioou 9m 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-k),swit)lb.ah i-9u0ue0 zd8 munw4 xd g man stand 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 uniforg;ya2 d yogt03m 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 pardat 2y;o3y0ggabolic trajectory?    cm

  A mallet consists of a uniform cylindrical head of mass 2.00 kg and a diamete8 l1bte9e5alr 2pt*l zr 0.0800 m mounted on a uniform cylindrical handle of mass 0.500 kg and lengtta9t*e 5p lb8rz1l2leh 0.240 m, as shown in Fig. 7–42. If this mallet is tossed, spinning, into the air, how far above the bottom of the handle is the point that will follow a parabolic trajectory?    d    d

  (a) Suppose that in Example r oj3l( euwyg-bhlm9l24c l;ji 9 1cc67–14 (Fig. 7–29), $m_{II}$=3$m_{I}$ Where then would $m_{II}$ land?    d(Round to two decimal places)
(b) What if $m_{I}$=3$m_{II}$    d

A helium balloon and its gondola, of mass M, are in the air and c8pu3i m/v zm4stationary 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 Eaz4c/ pv3i8ummrth) does the balloon then move? What happens if the passenger stops?

  An 0.145-kg baseball pitched horizontally at strikes a bat and is j vne4s,2 l*ktbdd5 2j2:v gtppopped straight up to a height of 55.6 m. If thn:k2l* 5sd vbtp22,je4t vjgde contact time is 1.4 ms, calculate the average force on the ball during the contact.    $^{\circ} $

  A rocket of mass m traveling with speec1r-tz 4 az uc/:zlld,d $v_0$ 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 face hgfrn9aiqo0e(h i9c p)7oj+ 0d with the corner pocket shot shown in Fig. 7–43. Relative dimensions are alsjehr9f(no7+i0og0 pq )hac i9o shown. Should the player be worried about this being a “scratch shot,” in which the cue ball will also fall into a pocket? Give details.

  A 140-kg astronaut (i h rp5k n8tne0a 8g/s-(9xvincmao+ y5ncluding space suit) acquires a speed of 2.5m/s by pushing off with his legs from an 1800-kg space capsul+hn 8x( ga9en8o5a0/n skvim-pyt5c re.
(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 d4tw 1jvam7e ,rest in outer space. They a741vm w,tdje 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 with a second ball (a ur2 g.patrsw-ie)o8 /t rest) and rebounds in the opposite direction) 2ao.rue-iwrsg 8/pt with a speed equal to one-fourth its original speed. What is the mass of the second ball? $m_B$ =    $m_A$(Round to two decimal places)

  You have been hired as an expert witness in a court case involving an automkelk):nbzx f6(hn t6(*j/w qoobile 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 inw6ketxjq :b( h/f)lk *o z6(nnto 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 flkx me;-b0 0uvright of concrete steps of total vertical height 4.00 m. The ball hits four times on the way down, each time striking the horizontal part of a different step 1.0 m lower. If all collisi bkve 00r-xu;mons 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 11ovjppexr ,w q3*q (gwood at rest directly above it. If the bullet has a mass of 29.0 g and a speed of 510m/s how high will the block rise after the bullet bec1op (qw*,1gr3q j pvxeomes embedded in it?    m

  A 25-g bullet strikes and becomes embedded in a 1.35-kg block of woo bt8;gh*+ ;jixx.hubod 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 ; uig;j *oh xbbh8tx+.comes to rest, what 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 y2s16ea;mz:sekuw m. n a rowboat of mass 80 kg. With the boat initially at rest, the two p6zms.w;e2uak es1 my :eople, 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 about ul b.jh +zs2:l-wx 2 m0tygl6k$ 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 v69w/vop nz) 6-euyre suddenly broken apart into two fragments by an explosion. One fragment acquires twice the kinetic energy of the other. What is the rat6)oren w- v epvu9y6/zio of their masses?   

  The force on a bullet v04ujx xz ),sl/k+seb l(;gocis given 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,/u 1 l,6qt(cey5im rnx8c fyz $m_A$ = 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 radioactivei-n.:86uwbw l kovcro45h+xyly into an alpha particle and a smaller nucleus. What will be the speed of this recoiling nucleus if the speed of the alpha par6:w -bnwryhoclo 8.5ki+4 ux vticle is $ 3.8\times10^{5 }$m/s Assume the recoiling nucleus has a mass 57 times greater than that of the alpha particle.    m/s

  A 0.25-kg skeet (clay target) is fired at an angle of 30 z05 1hgzmb427rdfnf2 4 jlodl (imm6s$^{\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 doz -t 0dcy/kt+mdpc(sft m2d;6wn 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 upp;ihorph 8a-ial.3 pb0/m obx*er limit on mass m if it is to rebound from M, slide up the incline, stop, s.8orphaxa-plm*o; b bih0 i3/lide down the incline, and collide with M again?    kg (Let A represent mass m, and B represent mass M.)

  The gravitational slingshot effect. Figure 7–47 shows the planet Saturn moving isrsi 32f q6k,b-7xxtfn the negative x direction at its orbital speed (with respect to the Sux,763tk-x fssfr bq2in) 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