We claim that momentum is conserved, yet mca-mbe45v . terfd0t2yq2 3etost moving objects eventually slow down and stop. 2yv20eq5mbtd e fc 3ar.t-te4Explain.

When a person jumps from a tree to the ground, what happens to the momentum o)knp25uvdy:xd nqve32 7an 2cf the person ucv nqd272exv5n: 3dan py2k)upon striking the ground?

When you release an inflated but untied balloon, why doejj ,y0(qqo vt+2 qmmq1s it fly across the room? jjm+qq1 t,m2qqovy 0(

It is said that in ancient tihmvsdhn-l34x ,q.f 9umes a rich man with a bag of gold coins froze to death while stranded on a froz9x3ms,dh -4uhn q.flven lake. Because the ice was frictionless, he could not push himself to shore. What could he have done to save himself had he not been so miserly?

How can a rocket change d zn9cj4 r30cem/ rutd b(utjes2pv(- :irection when it is far out in space and is essentially in a 0pz:mc ( uv 4cd9te2( jt-3juer bs/nrvacuum?

According to Eq. 7–5, the longer the imjddoezl9 *b) /pact 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 aio* )j9ddeblz /r 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 possiblqorf 9lfkaz w1,+6rc6e to withstand collisions. Today, though,ffw cr6 qrk1a9,z lo6+ cars are designed to have “crumple zones” that collapse upon impact. What is the advantage of this new design?

Why can a batter hit a pitched baseball further than a f; g 68mycj*fkqd b7r+ball tossed in the air by the batter?68;rycdbk *7+gfmj fq

Is it possible for an object y dcfive.izk i2a6q-/rf *j: 6to receive a larger impulse from a small force than ii:a2 - *6icq6.j zryk/fvfd efrom a large force? Explain.

A light object and a heavy of+pa3,r zdb4m; nf2kpbject have the same kinetic energy. Which has the greater momentu4bp z fpa3d,mk;2 +fnrm? Explain.

Describe a collision in wk e2g zpxjii*/)lx9a9d59 3nbo dovb8p isr(3hich all kinetic energy is lost.

At a hydroelectric pxxbas5 q5y:4ub okms 9( b;9qbower plant, water is directed at high speed against turbine blades on an axle that turns an electric generator. For maximum ;q 599u qyoasb5x(xbk :4bsmbpower 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 atkf9*v kb+vq yd(,3dtq a 45 $^{\circ} $ angle as shown in Fig. below. What is the direction (a) of the change in momentum of the ball, (b) of the force on the wall?

A Superball is dropped from a height h onto a hard steel plate (fixed ew:zd: sk-w yd,;-oyzto the Earth), from which it rebounds at very nearly its original speed. (a) Is the momentum of the ball ezzs -kdyw::w,o ;d-yconserved 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 backward when carrying a /ckt q4 zqme ..v:vfa/heavy load in your arms?

Why is the CM of a 1-m length of pipe at its mid-po(jh d- vkf;j9 owis-;9 ahty(jint, whereas this is not true for kt(9fjshd- oja(w-;vi; j9 yhyour arm or leg?

Show on a diagram how your CM shifts when you change from a lying positionm5: b bbhht.-snb/vy6 to a sitt ts5h -6bbb.bm/ :nhyving position.

If only an external force can change the momenwq72mviq 7 gwc9,,jlx tum of the center of mass of an object, how can the in77g92jv cwl, qiw,xm qternal force of an engine accelerate a car?

A rocket following a parabolic path through the air suddenly exra.dy iir06b/plodes into many pieces. What can you say about the motion of this systirbdr60.yi a/em of pieces?

  What is the magnitude of the momentum of a 28-7 +1mzjjwzl,+ ik ap7yg sparrow flying with a speed of $8.4 \; m/s$    $kg \; m/s$

  A constant friction force of 25 N acts on a 65-kg skier for 20 s. What isx /-bjb9n f8ytv9p 0qyt/;rhx the skier’s change in veloj0;ptqn9 x hb8yy v9/-fxr b/tcity?    m/s

  A 0.145-kg baseball pitched at 39 m/s is hit on a horizontal l,0o .rd0ah xm+*4wv*ce)al9 ro dsrfiine drive straight back t xoof*drm)h 9ec,d va+rl.a 4rw*s0i0 oward the pitcher at 52m/s If 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 ot05i7yh is-vj(vfk yf0 z 3/qlut horizontally 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.hvj zyt(fqy-3 l/fi7 0vks50i Ignore water resistance. The magnitude of the velocity of the boat is    m/s

  Calculate the force wqyt j3 g22e1fc7v4qrxq:ty5 t76okf.n/u fzexerted on a rocket, given that the propelling gases are expelledkx y1z tv4guq3 tcfef/6.nqw7r 2 qj7ot:y5 2f 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 movi2i y gfs3. 0 kb.d1 luyhlqft2q.i8bl5ng 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 trav zyzdn 4tgsd6e(za m6400ad,vels alone on alevel frictionless track with a constant speed of 18m/s A 5350-kg load,initially at rest, is dropped onto the car. What will be the car’s new speed? zyadn( 0zd4evzdgm60 46a,st    m/s

  A 9300-kg boxcar traveling2b l*6 z2b dd5zoo5qr1v *utg p1g4frg 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 qpzdo l t+v h;0g n,xvw72x6,aof 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. Comparh0+ plqvon7ag,t; 2,xzw6x dve 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:l pl*hqoqmf: , *7:9 en/puqz;rnifb.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 tracks, what is the speed of the car afte:qmq efqp ;/l9p rh: ,uz*on7*inl bf:r 90.0 min?$\approx$    m/s

  An atomic nucleus initially moving at 420m/s emits anp4.b0yo,a f26o f3 radlmjuv/ alpha particle in the direction of its velocity, and the f,.bmf4l6ayua3/ do v2r j p0oremaining 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 emy,g py 34qh 5hth(bx +k/j;ijaerges cleanly at 170m/s If the 4i,a qy 3k; tyh(x j+ghh/bj5pblock is stationary on a frictionless surface when hit, how fast does it move after the bullet emerges?    m/s

  A 975-kg two-stage rocket is traveling at a spea/0 xh q- l49y8fbvvhoed 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 maw-u0 k 8hbkidwij-o.8 ss 3180 kg is traveling in outer space with a velocity of 115m/s To alter its coursejow.b kwi08 -i8-dukh 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 ofv* zz,3( 6hctu fu,dcuf the tee at a speed of 45m/s The golf club was in contact with the bz duuvu6zfc *(,,ct3hall 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 o )erhre2. mcp: im1,ac m.06;ebwe jjnf 8.5m/s and comes to rest in a time interval of 8h .ipace)n.werj1 2r6m 0bjmmc:;e, e.0 ms. (a) What is the impulse given to the nail?    kg*m/s
(b) What is the average force acting on the nail?    N

  A tennis ball of massx)i(pi6td,;tu6e a z k m=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 engineer in charge of the crashworthiness of new automobil1enr1z 4q ym8ap;26qma8ody, kjc9a ze 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 exertdrm1a4z aj8 ,96y8n;y1ke zomq2qpaced 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 stoj oz5tfioww b(m 44- l8ax,.copped in 0.75 s by a head-on tackle by a tackler running due woj4m4 bi .(lta-,f8 cwwxo oz5est. 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 3-mxyg iu1ddf9yw7h ()uhrj7kg) points in the +x direction and is given by the graph of Fig. 7–33 as a function of time. Use graphical me9i myu x3(1y7 j-ddg)w7hurhf thods 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 j. d*p5dec)pkjump 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 ppdjc.*5d e)kbreaking 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 (v,ab6 v4n:h qoy d2hf 5yc-:zp+x direction) with a speed of collides head-on with a 0.220-kg ball at rest. If the collision is perfectly elastic, what will be the speed and direction of each ball after the collision?Let A represent the 0.440-kg ball, and B represent the 0.220-kfhq a4y do-h:bpn6 c5vv2z,:yg 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 wis.,:a)t; )0hive f3hsl limff lp41 ck,ik 9hrth a speed 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-kg puck, and let B reprecf lslip4)ml 3avhr0f,;)9f:ik eht,h ik1. ssent 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 und1mpd-uktgnt/ el28 a 0ergo 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, whdep2k1t/a l- u0gt8m nat will be their speeds after the collision?(Let A represent the ball moving at 2.00 m/s, and call that direction the positive direction.Let B represent the ball moving at 3.00 m/s in the opposite direction. ) v'$_A$ =    m/s v'$_B$ =    m/s

  A 0.060-kg tennis ball, moving with a speed of 2.5m/s collides hea4g+lj0n9 e 6sjtwt7y od-on with a 0.090-kg ball initially moving away from it at a speed of 1.15m/s Assuming a perfe tjgo 7yn4e lj9+sw06tctly elastic collision, what are the speed and direction of each ball after the collision?(Let A represent the 0.060-kg tennis ball, and let B represent the 0.090-kg ball.)v'$_A$ =    m/s v'$_B$ =    m/s

  A softball of mass 0.220 kg that xv 9al)6rz7 fx1wqa i:9dbq 9qis moving with a speed of 8.5m/s collides head-on and elastically with another ball init9x 91 )6v7:i q9lfdbqwza rqxaially 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 park ride collide elastically ;7tbhl6yutmyrf8g:4a jiu ) 7as one approaches the other directly from the rear (Fig. 7–34). Car A 8lr64f a u :yty7umbt)7hjgi ;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 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 collisiowz+ *a kai*s:z tv-wz5n with a second ball initially at rest. The second ball moves i +w*:st zzk*avzaw5-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 d joa9lw9qx mt-dj/2:frictionless incline as shown in Fig. 7–35, and elastically strikes another cube at the bodt- 2w:d9xa9 l/mjjqo ttom 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 object 4 mi8s cyfw99eof mass m$_A$ and velocity v$_A$ elastically striking a stationary object of mass head-on. (a) Show that the final velocities v'$_A$ and v'$_B$ are given by$v_{\mathrm{A}}^{\prime}=\left(\frac{m_{\mathrm{A}}-m_{\mathrm{B}}}{m_{\mathrm{A}}+m_{\mathrm{B}}}\right)\nu_{\mathrm{A}},v_{\mathrm{B}}^{\prime}=\left(\frac{2m_{\mathrm{A}}}{m_{\mathrm{A}}+m_{\mathrm{B}}}\right)\nu_{\mathrm{A}}.$(b) What happens in the extreme case when m$_A$ is much smaller than m$_B$ Cite a common example of this. (c) What happens in the extreme case when m$_A$ is much larger than m$_B$ Cite a common example of this. (d) What happens in the case when m$_A$=m$_B$ Cite a common example.

  In a ballistic pendulum experiment, projectile 1 results in a 1v6y nrrv.m 2e4/xjdbmaximum height h of the pendulum equal to 2.6 cm. A second projectile causes dre6mvyjxn 41/v b2r. the the pendulum to swing twice as high, $h_2=5.2\mathrm{cm}$ The second projectile was how many times faster than the first? $v_1$ =    $v_2$ ([color=rgba(0, 0, 0, 0.85)]Round to three decimal places)

  A 28-g rifle bullet traveling 230m/s buries itself in a 3.6-kg pendulum hanging d2;xicw r /x/c t0g;ufb+i j7jon a 2.8-m-long string, which makes the pendulum swing upward in an arc. Determine the vertical and horizo icd7w/0gc+x;uirxtjj 2 f;b/ntal components of the pendulum’s displacement.vertical$\approx$    m horizontal =    m

(a) Derive a formula fol(qrw5a:pwa 6w+pb8t wkl) n2r the fraction 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 an object, initially at res0itjh- mun qi4k)/t 8xt, into 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? (Let A represent the heaviej kh)ii-0 4/nmtqtx8ur particle, and B represent the lighter particle. ) KE'$_A$ =    J KE$_B$ =    J

  A 920-kg sports car collides into the rea963kjvqm smd6av/weqey )5w0wkt+y (r end of a 2300-kg SUV stopped at a red light. The bumpers lock, the brakes are +vje w)m sk6(ym5avt6q09w/ey3d wq klocked, 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 aw1eo d3,l f*n f chp:i8n(nar8nd rebounds to a height of 1.20 m. Approximately how many(pnf8wl3onn:*f ah edcir 1,8 rebounds will the ball make before losing 90% of its energy?   

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

  A wooden block is cut into two pieces, one with three times the mat*i ;evi+tnbmkb n/lk0y o;:5y2n ra 1ss 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 reassemb/0ymib:rt*ytil2e kvo 1n+n b ;;5ankled 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 moving in the +x directivpa mo/(alk3-on at 5.5m/s collides head-on with a 10.0-kg object moving in the -x direcaam /k3(ov-lption 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 at6x ackdkiua dujxru/. f3-)62 rest decays into a second nucleus, an electron, and a neutrino. The electron and neutrino ai rkj62c-k)fd 3.xuud aau6x/re 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 ma ; -msr+gnc;wwss $m_\mathrm{A}=0.400$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 inelasti0f+ ;x z wjt jfnh1k(6ypfd;/qc collision between two objects of equal mass, each having initial speed the two move off jdqjh0w pkz1x;(6+;f/yfftn together with speed v/3 What was the angle between their initial directions?    $^{\circ} $

  Two billiard balls of equ huhtu.bso0 hgs57s,:al mass move at right 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 w ,huhsg0htsuo 5 s.b7:ith 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 aq q)tp-jeh-; su) ,hro perfectly elastic collision with another atom at rest. After the impact,)r-q; -ojp)tehuqs ,h 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) mak r9o:2+u jf qs+h6yz-l0gyzfzes a perfectly elastic collision with another atom at rest. After the impact, the neon atoo+l:9+0hj z 62fyfygsr-zzu q m 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. 7–3gs8l ly6.5t tsix;,lm8. Specify relative to the left-hand 1.00-i t xmgy8 lllt;5,.s6skg mass.    m

  The distance between a carbon athfj55 x( qava/niwcm5j0 m,.tom ($m_{\mathrm{C}}=12\mathrm{u}$) and an oxygen atom ($m_{\mathrm{O}}=16\mathrm{u}$) in the CO molecule is $1.13\times10^{-10}$m How far from the carbon atom is the center of mass of the molecule?    $\times10^{-11}$m

  The CM of an empty 1050-kg car is 2.50 m behind the front of t-c*tqz8 ihy8jj59bh z he 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 front? Assume that each5qyihzj j*z8b9c-8t h person has a mass of 70.0 kg.    m

  A square uniform raft, 18 m by 18 m, of mas)pman*9a2e6qsc,uhl( e no 7 us 6800 kg, is used as a ferryboat. If three cars, each of mass 1200 kg, occupy its NE, SE, and SW ceuus ,*9nm(h loe76c) pnqa2aorners, determine the CM of the loaded ferryboat.$X_{CM}$ =    m $Y_{CM}$ =    m

  Three cubes, of sides vsyc78;xt /qfb*wj 8td* j3lm $l_0$,$2l_0$, 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 o7x(; *jw gfx6mlepf 0zoja4v7fds h-e1i +u *rf tomato paste (see Fig. 7–40), each of which is a cube of length lzexawv i j71;p es*ou0(lmjgh74fd+6xf-* f r. 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 circe5-y ;9oifskjv-w2hcular 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 mi ;e c-wjyk29- svfoh5ass of the plate? [Hint: Try subtraction.]   R

  Assume that your proportions are the same as those in Table 7–1, andr-l4m) ucd6sx calculate the mass of one of your l)c4mrxd- s 6ulegs.    kg

  Determine the CM of an outstre(3w bege ., tmebhstpz-hs1* :tched 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 arqinc0 7 f x+lxqu1s;;em bent at a right angle. Assume that t+e70cxs fqn1ui;x lq;he person is 155 cm tall. $X_{CM}$ =    cm $Y_{CM}$ =    cm

When a high jumper is in a position such that his arms and legs are hai3vc;-mz3 )jeen ewl ;nging vertically, and his trunk and head are horizontal, calculate how mjve 3n3 z;)ei;w-lcefar 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 Eai tq+*; i2d9o6pncpdtrth and Moon are $5.98\times10^{24}$kg and $7.35\times10^{22}$kg respectively, and their centers are separated by $3.84\times10^{8}$m (a) Where is the CM of this system located? (b) What can you say about the motion of the Earth–Moon system about the Sun, and of the Earth and Moon separately about the Sun?

  A 55-kg woman and an 80-kg ra, meq8p 9l*xman 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 uniform cylindrical head of mass 2.00 kg and a dki7:ierytro (t f1en50dt2j0iameter 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 (7i2frtjk 0tt n1e05do:er iyr, how far above the bottom of the handle is the point that will follow a parabolic trajectory?    cm

  A mallet consists of a unifors.jgrvy 54wu: m 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. 7–4wy4v ru:sjg .52. 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 m;2rovcrlf.jdj 3: 0y.h5q kx7–14 (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 v n+y/1 1w3 eioksrl)xmass M, are in the air and stationary with respect to the ground. A passenger, of mass m, then climbs out and slidexi1vr/)e 3lwnoyk+1 ss down a rope with speed measured with respect to the balloon. With what speed and direction (relative to Earth) does the balloon then move? What happens if the passenger stops?

  An 0.145-kg baseball pitched horizontally at strikes a bat and is poppedhy wi0ay;dt79 straight up to a height of 55.6 m. If the contact time is 1.4 ms, calculate ;09hti ydy w7athe average force on the ball during the contact.    $^{\circ} $

  A rocket of mass m traveling w -s*xh vec8j5jith 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 wyzvw)-3p 4 rt x8trs; rag:(qrith 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 whir4x- ) wqtyv:r3;zar s(r 8gptch the cue ball will also fall into a pocket? Give details.

  A 140-kg astronaut (including q mckoj0/4eu*-1q *f: ihnzovspace suit) acquires a speed of 2.5m/s by pushing off with his legs from:o4vh/mz1*k cn-o*eq0iq f u j an 1800-kg space capsule.
(a) What is the change in speed of the space capsule?    m/s
(b) If the push lasts 0.40 s, what is the average force exerted on the astronaut by the space capsule? As the reference frame, use the position of the space capsule before the push.    N

  Two astronauts, one of mass 60 kg and th7p (shckn :1xme other 80 kg, are initially at rest in outer space. They then push each other apart. How far apart are they when the lighter astronaut has moved 12hs7cp n1mk:x ( m?    m

  A ball of mass m makes a head-on elastic cr-qvny*czoz2.2pmlw-i 2xs./ y ts e 3ollision with a second ball (at rest) and rebounds in the opposite direction with a speed equal to one-foq r otpc* z/-mv.ws2izx .eyy232l n-surth 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 experufecp 02g2n +qt witness in a court case involving an automobile accident. The accident involved car A of mass 1900 kg which crashed into stationary car B of mass 1100 kg. The driver of car A applied his brakes 15 m before he crashed 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 mea+guneq20 2 pcfsured 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 concrec )3n6go.ejy8rkc g0ete 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 collisions are perfec86e3y0g ).ogn j ckcretly 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 o/j32q095rxgsy (k+y gkaft igf wood at rest directly above it. If the bullet has ak rj9(3g ftq0ig s25yxyak/g+ mass 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 becsn ;xkk 7a5(ocomes 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 resx;7ank(c o k5st, 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 in a roto18 ; p,n5qg,j7n0dyprb8l5 bnv azz wboat 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 bdanp zy ; z857j,vtn815nr pg0l,obq 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 aboutzt,c;9w0(s0xr; t ,h rgfueyu $ 1\times10^{ 8}$kg struck the Earth ($m_E$=$6 \times10^{ 24}$kg) with a speed of about 15km/s and came to rest in the Earth.
(a) What was the Earth’s recoil speed?    $ \times10^{-13 }$m/s
(b) What fraction of the meteor’s kinetic energy was transformed to kinetic energy of the Earth?    $ \times10^{ -17}$
(c) By how much did the Earth’s kinetic energy change as a result of this collision?    J

  An object at rest is suddenly broken apart into two fragments by an explosion. O i+//kuc6:vb(p vpiuv ne fragment acquires twice the kinetic energy of the other. What i/ v:vpc6k/ivup +b(i us the ratio of their masses?   

  The force on a bullet is given by th0t 1fso5wvri-dh5cbm0r0 jve8(dy7 xe 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 iu0qg pc un 5nlf0 x9:et*kio+v4a e/2$m_A$ = 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 parti4i+q gcm(i6 ceu p3a)rcle and a smaller nucleus. What will be the speed of this reco3 cm) ci +(qaiue46rgpiling 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 andht-xakqd:t 6hl 4gkeel(:,y z(g ;k1wyf k 6*gle 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 q,yh6u4x;29va yf :d jvfit )edown 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 te7f0w+beofn szgm)1j /j ,t +a1 /leojx gx6+che upper limit on mass m if it is to rebound from M, slide up the incline,oj/ em7+e t6fjz1s1,+ aw) + go xncb0egfjxl/ stop, slide down the incline, and collide with M again?    kg (Let A represent mass m, and B represent mass M.)

  The gravitational slingsh *bp29((t fgju2qtqkzfnb6u * ot effect. Figure 7–47 shows the planet Saturn moving in the negative x direction at its orbital speed (with respect to the Sun) of 9.6km/s The mass*(bkfb2*u q9pnz(g6jf2t uqt 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