We claim that momentum is conserved, yet most moving object2ks *) dugh5 8schl0zrhzi ++ws eventually slow down and hlr h ) k8dc2h+ w+gs*s0u5izzstop. Explain.

When a person jumps from a tree to the ut7nv r)q 3rf,n5 0m.cjvmr5nground, what happens to the momentum of the person upon strik mn v7 qn30ct.u,rjrnfm5)5rving the ground?

When you release an inflated but untied balloon, why does it flyn7 f1,j 2ned)n yww5hu across the roomnu1n 52 wwn),jh7df ey?

It is said that in ancient times a rich man withh b rkfco0;.xy3v*oz1 a bag of gold coins froze to death while stranded on a frozen lake. Because the ice was frictionless, he could not push himself to shore. What could he have done to save himself had he not been so miserlyzbvo1oc krx.f0;3h* y?

How can a rocket change direction when it is far out in space and is /wet )gf2 xh+wessentially in a vacuum?+w /h g2)etwxf

According to Eq. 7–5, the longer the impact tim0b/u g,v 7d-. 49aeg,s2xykdbxaeje 1wt ,aa me 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, e,jd4e1g by-ekmaag.udst , a x7xeab/9 20vw,xplain 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 with5n0:ohni5 v 0lvr 2ayowfg:4k stand collisions. Today, though, cars are designed to have “crumple zones” that collapse upon impact. What is the advantage of this new designwoak20 4 v05:nhlvnr:y o 5ifg?

Why can a batter hit a pitched baseball further than a ball tossf ;b nfe p/u;35hb9snled in the air by th ;n 5sfbn/f9blpe; hu3e batter?

Is it possible for an object to receive a larger impulse from yr w7 3ibhayyb 1mbi3jbutc/3 hl;7wk3t7p.7a small force than from a large foribpa/. hby3clry7ukt;i7 bmjbt7y 37w 3wh31ce? Explain.

A light object and a heavy object have the same kinew 3+ nzcy 63y8,iiypcytic energy. Which has the gren c,3+yw3y68ic yzp yiater momentum? Explain.

Describe a collision in which all kinetic energy im/rpggoks(:fm7qvj (y 5af08s lost.

At a hydroelectric powuw00l* at; kgker plant, water is directed at high speed against turbine blades on an axle that turns an electric generator. For maximum power generation, should the turbine blades be designed so that the water is brought to a dead stop, or so that the water rek0w g;*atlku0bounds?

A squash ball hits a wall at a 4oxyo6 37 2boldgy8sgep7cu-x8 ba. g35 $^{\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 steelkaahex5 g9nojv(,n:p5 w 3l;o plate (fixed to the Earth), from which it rebounds at very nearly its original speed. (a) Is the momentum53e lja :(vohna9pkgw, ;5onx of the ball conserved during any part of this process? (b) If we consider the ball and Earth as our system, during what parts of the process is momentum conserved? (c) Answer part (b) for a piece of putty that falls and sticks to the steel plate.

Why do you tend to lean backward when carrying a heavy load i ,lrofuke q/l3+aw1a-n your arms?

Why is the CM of a 1-m lejy c: u) k2ef yng*7w t);fhdo+8zyj,jngth of pipe at its mid-point, whereas this is not true for your arm or l:2yjfnc,goz 7hut;jfdkw )y *e j)8+ yeg?

Show on a diagram how your yobto uc f;;e9 x)1ju 6(gvhwr2qe43eCM shifts when you change from a lying position to a siwf2 e3)uj; 146 go eo(b9rxqtyuv;hcetting position.

If only an external force can change the momentum of the ce9 d7mcu2z unp2 r numl;e*4bv(nter of mass of an object, how can the internal force of an engine acceleratezvmucbmn4u 9*r lnp22 7u(d ;e a car?

A rocket following a parabolic path through the air suddenly explodes into many e5z5 nk obkk6g3s e-ha6r (7copieces. What can you say about the motionrbce gkn-3 s ekzh6 567okoa5( of this system of pieces?

  What is the magnitude of thfg)g2a l0/x+2z gnca de momentum of a 28-g sparrow flying with a speed of $8.4 \; m/s$    $kg \; m/s$

  A constant friction force of 25 N acts on a 65-kg skier for 20 s. What is t b + dd u*x u3pus,yyhnls8jb3l4;6wk0he skier’s b yx ;b ,dulwn4 l0s3p6+uj8s k3hud*ychange in velocity?    m/s

  A 0.145-kg baseball pitched at 39 m/s is hit oki5 zfun 918ton a horizontal line drive straight back toward the pitcher at 52m/s If the contact time between bat and i u8kn1f 5zt9oball 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-ki v( euti11x2cg package out horizontally with a speed of 10 m/s Fig. be vi ciu11e2(xtlow 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. The magnitude of the velocity of the boat is    m/s

  Calculate the force exeriwx41 f1qpy-s ted on a rocket, given that the propelling gases are expelled at a rate isp-wxyqf411 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 movun 8,u 7mhjqi i9m+(wding 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 a2 1rpzdi y4vi60lnq( alone on alevel frictionless track with a constant speed yizr ( 0v1 nal64pidq2of 18m/s A 5350-kg load,initially at rest, is dropped onto the car. What will be the car’s new speed?    m/s

  A 9300-kg boxcar traveling at dwz7e /23 dc8.fgqrdr$15 \; m/s$ 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 of 100km/h Iek 4 ox( -dvaz/gz7j:xf the air strikes a person at the rate of 40kg/s per square meter and is brought to rest, estimate the force of the z g (d jzoxx:a7/k-4evwind on a person. Assume the person is 1.50 m high and 0.50 m wide. Compare to the typical maximum force of friction $\mu\approx1.0$ between the person and the ground, if the person has a mass of 70 kg.    N
$F_{on person}$  ----待选择----<> $F_{fr}$

  A 3800-kg open railroad car coasts along with a constant spvv:ertl-df rz ;66q, jt6*ghdf4hq+ teed of 8.6m/s on a level track. Snow begins to fall vertically and fills the car at a rate of 3.5kg/min Ignoring friction with the tracks, what is the speed of t-r,z hv erthd;jdq4:6tftg6 v+ qf*6 lhe car after 90.0 min?$\approx$    m/s

  An atomic nucleus initially moving at 420m/s emits an alpab +)gm(f(3kp(l wmz)8rembbha particle in the direction of its velocity, and the remaining nucleus slows to 350m/s If the alpha particle has a mass of 4.0 u and the original nucleus has a mass of 222 u, what speed does the alpha particle have w)(+be)rlz3mgw p( ( abkmbmf8hen it is emitted?    m/s

  A 23-g bullet traveling 230m/s penetrates a 2.0-kg block of wood and emenq z6.vz om ibqo-r)2(hi;5wb0 hin*zrges cleanly at 170m/s If the block is stationary on a frictionless surfacn izvo-bi2 iz bqhn.rh6;oqm ()w5z0 *e when hit, how fast does it move after the bullet emerges?    m/s

  A 975-kg two-stage rocket is travci q.(dagdjz+5r.+r eeling 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 olu 1va57xd1mouter space with a velocity of 115m/s To 5dau m o711xvlalter its course 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- 3hxtj0v30 xujc 7gqf the tee at a speed of 45m/s The golf club was in contact with the ball forgxx-jchut f q0303vj7 $3.5\times10^{-3}$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 o r.sjsqg5z0aeza2tqd c( 262.5m/s and comes to rest in a time interval2c.ao056 qr z2zdq sgsa(2j et of 8.0 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 mass m=0.06kg and speed v=25m/s stnbcg66-tvziv t: ty ;2rikes 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 automo*0)pz yzheo2qd8pntwk t (7+. zyv-yrbile models. Cars are tested by s .8h7y dz+e-ozp0 kn2qytzrp*v)(ytw mashing 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 barrier. $\approx$$a\times10^5$N a =   
(b) Calculate the average deceleration of the car.    m/$s^2$

  A 95-kg fullback is running at 4m/s to the east and is stopped in 0.,xha4mocjcqo82 bu 3 ws;yn5775 s by a head-on tackleycs,735w; c2mqxnu o 8ajhb4o by a tackler running due west. Calculate
(a) the original momentum of the fullback    kg*m/s
(b) the impulse exerted on the fullback    kg*m/s
(c) the impulse exerted on the tackler,    kg*m/s
(d) the average force exerted on the tackler.    N

  Suppose the force acting on a tennis ball (mass t/1 wo.:9osrebe9j+ wqbui7 qofr t210.060 kg) points in the +x direction and is given by the graph of Fig. 7–o +er7buq2ow/s o19rj.1ewqt:fbt i9 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 n9ue ;mrr;jhx +v gby u.(buxvi95y+3can a 75-kg person jump without breaking the lower leg bone of either leg? Ignore air resistance and assume the CM of the person 5yx9+guy be( h+j 39iv ;.rm;bxnuurvmoves a distance of 0.60 m from the standing to the seated position (that is, in breaking the fall). Assume the breaking strength (force per unit area) of bone is $170\times10^6\mathrm{~N/m^2}$ and its smallest cross-sectional area is $2.5\times10^{-4}m^2$ [Hint: Do not try this experimentally.]    m

  A ball of mass 0.440 kg moving east (cyx-)xjj6 +ohxf* xir;i w0n4+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 direc xix- n4j6jr*fo+hi; x)wcx0ytion 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 3mqn+w m*:pj2co /s has a head-on collision with a 0.900-kgpwj mc n:+qo2* 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 represent the 0.900-kg puck. v'$_A$ =    m/s ----待选择----eastwest  v'$_B$ =    m/s ----待选择----eastwest 

  Two billiard balls of equal mass undergo a p6isy)y :9dt ygerfectly 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 y: 9siy6ty)gdspeeds 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, movs5v .-isywny lgw q2ak533b;b ing with a speed of 2.5m/s collides head-on with a 0.090-kg ball initially moving away from it at a speed of 1.15m/s Assuming a perfectly elastic collision, what are the speed and direction of each ball after the collision?(Let A represent the 0.060-kg tennis ball, and let B represent the 0.090-kg bal3s5 25yky b3nli-sbgvaw;q.w l.)v'$_A$ =    m/s v'$_B$ =    m/s

  A softball of mass 0.220 kg that isih+; f t)c75 tblsx3ll moving with a speed of 8.5m/s collides head-on and elastically with another ball initially at rest. Afterwar)l tl c;+f3ihx7l5s btd 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 wgurt0oj 401t+qzn l3 park 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 at0nt0z q go+wtu4 13lrj 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 m z6 9tja3ufc,takes an elastic head-on collision with a second ball initially at rest. The second ball moves off with half the originaf ju6t9 3zt,cal 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 frictionless incli pf4nsus-3u .nne as shown in Fig. 7–35, and elastically strikes another cube at the bottom that is osf4usn.upn 3-nly 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 pub;*b2, q dp:pon0 xvof an object of mass m$_A$ and velocity v$_A$ elastically striking a stationary object of mass head-on. (a) Show that the final velocities v'$_A$ and v'$_B$ are given by$v_{\mathrm{A}}^{\prime}=\left(\frac{m_{\mathrm{A}}-m_{\mathrm{B}}}{m_{\mathrm{A}}+m_{\mathrm{B}}}\right)\nu_{\mathrm{A}},v_{\mathrm{B}}^{\prime}=\left(\frac{2m_{\mathrm{A}}}{m_{\mathrm{A}}+m_{\mathrm{B}}}\right)\nu_{\mathrm{A}}.$(b) What happens in the extreme case when m$_A$ is much smaller than m$_B$ Cite a common example of this. (c) What happens in the extreme case when m$_A$ is much larger than m$_B$ Cite a common example of this. (d) What happens in the case when m$_A$=m$_B$ Cite a common example.

  In a ballistic pendulum experiment, projectile 1 results in a fr82agpkwuh:n-vkro x 1,z 9 z av(k99maximum height h of the pendulurf okk9xkh-nz:(v1p2 , wav9rza9g8u m equal to 2.6 cm. A second projectile causes the the pendulum to swing twice as high, $h_2=5.2\mathrm{cm}$ The second projectile was how many times faster than the first? $v_1$ =    $v_2$ ([color=rgba(0, 0, 0, 0.85)]Round to three decimal places)

  A 28-g rifle bullet traveling 230m/s buries itself in a 3.xx39 d6jme 3tmp0pkl bbt47q -6-kg pendulum hanging on a 2.8-m-long string, which makes the pendulum swing upward in an arc. Determine the vertical and horizontalqx9b t- de76 3b0px4pk3lmmjt components of the pendulum’s displacement.vertical$\approx$    m horizontal =    m

(a) Derive a formula for the fra qq4boya3a38 6vl a,oyfvq;q:ction 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 rest, into two piecds9:alw qqa 8nwanj(oa60+ 2d 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 pie8woaaan 2ldd jaq: n6w(qs+ 90ce acquire? (Let A represent the heavier particle, and B represent the lighter particle. ) KE'$_A$ =    J KE$_B$ =    J

  A 920-kg sports car collides i f i -t4z2-etfipui1rlf7xznlo4s+ql .ui3)2 nto 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 car at impact. What was that speed?(Let A represent thex4n-.ti2z4lflu zi2q+p-r 7 1t )o sleiiuff 3 sports car, and B represent the SUV) $\approx$    m/s

  A ball is dropped from a height of 1.50 m and rebound qviyrecm3:7e y0kou z78p:h+s to a height of 1.20 m. Approximately how many rebounds wikp : 7zyi03re:vqmy7+ c8 ouehll the ball make before losing 90% of its energy?   

A measure of inelasticity in a head-on collis2)00mbuyrh x /nps olgv8am gx2,3syyp g,-t 3ion of two objects is the coefficient of r /0 g,sopggyunlt 82smmbhr y,)y0xa3vpx-23 estitution, 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 mass wu.ubp - oeks)t-fu b8.p2mnfh2 n+.gof the other. A depressiofekgmp t-).b8u+n ns.opfuw2h -.bu 2n is made in both faces of the cut, so that a firecracker can be placed in it with the block reassembled. The reassembled block is set on a rough-surfaced table, and the fuse is lit. When the firecracker explodes, the two blocks separate and slide apart. What is the ratio of distances each block travels? ----待选择----1/91/101/81/6 

  A 15.0-kg object moving in the +x directioniy6-v(c-d kmlb:a v d5rbk)+k at 5.5m/s collides head-on with a 10.0-kg object moving in the -x direction at 4m/s Find th: dbv-m65a l vry-c+kikd k)(be final velocity of each mass if:
(a) the objects stick together;   m/s
(b) the collision is elastic; v'$_A$ =    m/s v'$_B$ =    m/s
(c) the 15.0-kg object is at rest after the collision;   m/s ----待选择----not reasonable reasonable 
(d) the 10.0-kg object is at rest after the collision;   m/s ----待选择----not reasonable reasonable 
(e) the 15.0-kg object has a velocity of 4m/s in the -x direction after the collision. .   m/s ----待选择----not reasonable reasonable 
Are the results in (c), (d), and (e) “reasonable”? Explain
( Let A represent the 15.0-kg object, and let B represent the 10.0-kg object.)

  A radioactive nucleus at rest decays into a second nucleus, an elec bw swmb:9xm*s/,ji 5xtron, and a neutrino. The electron and neutriwx5ms9*j msi,bbwx /: no 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 ma oib+q pc :0b2p/t4rrqss $m_\mathrm{A}=0.400$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 inelastiiwv3)ii0q w3jny 5 2uhc collision between two objects of equal mass, each having initial speed the two3 hnw5w)3yqv jii20i u move off together with speed v/3 What was the angle between their initial directions?    $^{\circ} $

  Two billiard balls of equal mass move at right angles and meet at the origin oxnh x2*gub4 : ,6ovegwxt(rojm ,yj1+f an xy coordinate system. Ball A is moving upward a,j(4m+r2gonjbv6oyte :*,x1x wu xghlong the y axis at 2m/s and ball B is moving to the right along the x axis with speed 3.7m/s After the collision, assumed elastic, ball B is moving along the positive y axis (Fig. 7–37). What is the final direction of ball A and what are 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 b bz 7t:beva7-perfectly elastic collision with another atom at rest. After the impact, the neon atom travels awa7e7bb-btz va :y at a 55.6 $^{\circ} $ angle from its original direction and the unknown atom travels away at a -50 $^{\circ} $ angle. What is the mass (in u) of the unknown atom? [Hint: You can use the law of sines.](Let A represent the incoming neon atom, and B represent the target atom) $m_B$   u

  A neon atom (m=20u) makes a perfectly elastic collision with anotheci:n( t e8rp37k/d0ghuk 6gi ;,bl)hpf 9mjkdr atom at respjlprdk)h69tmhe b7i0k;f /g8i3cu:,g(k ndt. After the impact, the neon atom travels away at a 55.6 $^{\circ} $ angle from its original direction and the unknown atom travels away at a -50 $^{\circ} $ angle. What is the mass (in u) of the unknown atom? [Hint: You can use the law of sines.](Let A represent the incoming neon atom, and B represent the target atom) $m_B$   u

  Find the center of mass of the three-mass system shown in Fig. 7–38. S / d(0anp(ateepecify relati(de tn/ aeap0(ve to the left-hand 1.00-kg mass.    m

  The distance between a carbojph.b hidsc8 *t9 ;1zan 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 iz vuo5 s*3yv/q(dt0xts 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 2.8z5xt/ 0tquso v(d*y3v 0 m from the front of the car, and three people sit in the back seat 3.90 m from the front? Assume that each person has a mass of 70.0 kg.    m

  A square uniform raft, 18 m b k,4tb z1,fxa 37vehj.zeng8cy 18 m, of mass 6800 kg, is used as a ferryboat. If three cars, each of mass 1200 kg, occupy its NE, SE, and SW corners, determine the CM of the loaded fer7xec,3 jntzg v b afze1.,k4h8ryboat.$X_{CM}$ =    m $Y_{CM}$ =    m

  Three cubes, of side,x sb4 rw-ix gq-f3ipozabavy7h7 +06 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 has a load of identical cases of tomato paste tjqq+oc2k x t7-jv-t*(see Fig. 7–40), each of which is a cube of length l. Find the center of gravity in the horizontal plane, so that the crane operator cax+t 27c *ovtt--j qkqjn pick up the load without tipping it.$X_{CM}$ =    l $Y_{CM}$ =    l

  A uniform circular plat2mz y-2 eqsr9ie of radius 2R has a circular hole of radius R cut out of it. The center of the smaller circlz mei22s -9ryqe is a distance 0.80R from the center C of the larger circle, Fig. 7–41. What is the position of the center of mass of the plate? [Hint: Try subtraction.]   R

  Assume that your proportions are the same as those in Table 7–1, and ca3ulb0no-b6o: q hgjg8lculate the mass ogb 36n o:8-ub gho0jqlf one of your legs.    kg

  Determine the CM of an ouy,77kv-f8eb) :8dw lypshv yststretched 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 bent at a vs-.sbdy(ob /;g(ygrright angle. Assb ysy;(dgrv o -/gs(b.ume that the person is 155 cm tall. $X_{CM}$ =    cm $Y_{CM}$ =    cm

When a high jumper is in a pc z*1 *pieg5/6akxnvn osition such that his arms and legs are hanging vertically, and his trunk and head are horizontal, calculate how far below the */ a6x p5knvicnz1ge*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 Moo2 n,avgc /1 : kz,:lnaizdsod1n 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 h4 f6sgqmwnf)7z3-s 8j )g izv10.0 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 andfjb1yip fy0+ 1b;u pp57uv2nh 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 parabolic trajecp 107p hpbj5f2iuubyn ;v +yf1tory?    cm

  A mallet consists of a uniform cylindd+x,:enxnhe , rical 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 t h:,n+x ,nedxehe air, how far above the bottom of the handle is the point that will follow a parabolic trajectory?    d    d

  (a) Suppose that in Example 7–14 (F uz(ewgg4.-,oub6 vfrig. 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 axll4w q-w(d - +m q(uttniwn41ir and stationary with respect to the ground. A passenger, of mass m, then climbs out and slides down a rope with speed measured with respect to the balloon. With what speed and direction (relative to Earth) does the balloon then move? What halq wxnt( 1twlnd (-ui+q4-4 wmppens if the passenger stops?

  An 0.145-kg baseball pitched hbaow 5a axep .ny zij)bc7/:.:orizontally at strikes a bat and is popped straight up to a height of 55.6 m. If the contact time is 1.4 ms, calculate the average force on the ball during the con bwipz7y.a:5.jxa: e/obn)ca tact.    $^{\circ} $

  A rocket of mass m travelinnhn-+sl e8w*f g with speed $v_0$ along the x axis suddenly shoots out fuel, equal to one-third of its mass, parallel to the y axis (perpendicular to the rocket as seen from the ground) with speed 2$v_0$ Give the components of the final velocity of the rocket.$P_x$: v'$_x$=    $v_0$
$P_y$: v'$_y$=    $v_0$

A novice pool player is faced with the corner pocket shot shown in Fig. 7–43./erxjsq +9q b: Relative dimensions are also shown. Should the player be worried about this being a “scratch shot,” in which the cue ball wq rb+s:x /eqj9ill also fall into a pocket? Give details.

  A 140-kg astronaut (including space sui +ifg759yc* ot kbh.ne cdfd**t) acquires a speed of 2.5m/s by pushing off with his legs from an 1800-kg space c*d n5e9b+ cit7.hd gff*co*ykapsule.
(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 oty1x+ /rcdgi -zher 80 kg, are initially at rest in outer space. T1i-dz/+ yxc grhey 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 1llg( t7 l aip50x64m (quqkbl:dhu4h with a second ball (at rest) and rebounds in the opposite direction with a speed equal to ont4 p0 b(l7gihkx a6u ql m4l:lqd1h5(ue-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 involgnc; 4 o38 n m. o4o,qynqdt*s25gveluving 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 beforsmdqqg;n*ucgnon 5348otv.2 le o4y,e 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 o1z -ge/ru (udflalz3a,i/w2l f concrete steps of total vertical height 4.00 m. The ball hiz,gwal/ul li12/-d 3a ezf(urts 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 when the ball reaches the bottom of the stairs?

  A bullet is fired vertically into a 1.40-kg block of wotx9e,pa s tuo/9xd9p0 od 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 becomes embedded in it? s90dt oue9,x a/9pptx    m

  A 25-g bullet strikes and becommy lr+y2 rm0eo, qw)i:8vlq s:il-e1ees 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, what was t+l m01mvl y:e:s ,q irlqwroi2y)e8e-he muzzle speed of the bullet?    m/s

  Two people, one of mass 75 kg and the oth). o8bdnxc-rw upe0a 3x*a5wvhq g;p ;er of mass 60 kg, sit in a rowboat of mass 80 kg. With the boat initially at rest, the two people, who have been sitting at opposite ends of the boat 3.2 3.u ado;r)axqxpwv0cg pb5-e8w ;h*n 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 s-:nap -eo /lp$ 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 v)9mz+9mt r knapart into two fragments by an explosion. One fragment acquires twice the kinetic energyv9rn9 tm )zmk+ of the other. What is the ratio of their masses?   

  The force on a bullet is given by the fo7ei6n:. vzr+ulix6j i);x il urmula 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 massesk/oi6 1i(8cj ju g vhy;+s9grt $m_A$ = 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 de ;gffks9q wgv1 5vo*(e(mjr69ack,e e cays radioactively into an alpha particle and a smaller nucleus. ;c6(r fmgejkv9,ev915qkgf w ae*so(What will be the 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 targakh;+tp) a n+vet) is fired at an angle 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 30.0yp.l- s/asu3o $^{\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 ona (-0y mxgt,fx mass m if it is to rebound from M, slide up the incline, stop, slide down the i xy0,(gtfax-m ncline, and collide with M again?    kg (Let A represent mass m, and B represent mass M.)

  The gravitational slingshot effect. Figure +hlcnx)mux4) p7 p,gm7–47 shows the planet Saturn moving in the negative x direction at its orbital speed (with respect tm,)7mn)4 +ppugl xchx o 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