We claim that momentum is conserved, yet most moving objects eventually qva1w ia6-avy)4:vpa slow down 4a:1p6vi v-awqavy )a and stop. Explain.

When a person jumps from a tree to the ground, what h67bx(om7c t dgappens to the momentum of the person upon striking the d67btcoxg7m( ground?

When you release an inflatedowgpj6t,)h (3zrf.q d but untied balloon, why does it fly across the roomftjg. p,rzo wh 6d)3(q?

It is said that in ancient tij+s7r4mxu7i4p: eu ok mes a rich man with a bag of gold coins froze to death while stranded on a frozen lake. Because the ice was frictionless, he could not push himself to shore. What could7e srkjmu+i:xou44 p 7 he have done to save himself had he not been so miserly?

How can a rocket change direction when it is fa-lem g.ei*c -br out in space and is essentially ini-eg .l*e-cmb a vacuum?

According to Eq. 7–5, the longer the impact time of an impulse,dzg pt 8e1lhx56.li 8e4og0fb the smaller the force can be for the same momentum change, and hence the smaller the deformation of the object on which the force acts. On this basis, explain the value of air bags, which are intended to inflate during an autodez g0.bhetpf4g51 6lox 8i8lmobile collision and reduce the possibility of fracture or death.

Cars used to be built as rigid as possible to withstand collisions. Today /wefcolum x)r*q(29j7rlm6b, though, cars are designed to have “crumple fm j/wclr2umbeqr76 l * 9o(x)zones” that collapse upon impact. What is the advantage of this new design?

Why can a batter hit a pitched baseball furtg:vo v k*2g9p(frnxce kj2v9l)5 z,:tjejqm-her than a ball tossed in the air by the bgg2r x5kc(mjvle:2j qvve 9*,)op tkfn : 9-jzatter?

Is it possible for an object to receive a larger impulse from9h.fvdas(.2kwxz i ;o9 dsiywi ,9)xx a small force than io 9xhyad99)ii;swwkzfxs .,xv.d(2 from a large force? Explain.

A light object and a heavy object have the same kinetic enex4ot3o91- u1kqao njm rgy. Which has the greater momentum? j9t 1nuakqxo4 oo1-m3Explain.

Describe a collision in which all kinetict pl)e)j-o+k o energy is lost.

At a hydroelectric power 5g h1mbzl5)-lu.eka,a ms3mll p g(t+ 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 b ml +ms- (z1u)p ak,gag3.l5etlm hlb5rought to a dead stop, or so that the water rebounds?

A squash ball hits a wall at a 4m.oalsei9m o:+2(ym-jj wiaf,4+t u p 5 $^{\circ} $ angle as shown in Fig. 7–30. 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 stesu+2 i+ xwtl0nel plate (fixed to the Earth), from which it rebounds at very nearly its original speed. (a) Is the momentum of the ball conserved durx+w niu+0stl 2ing 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 carr ncih; w::6 alw0o8uiyzij;1l8 cg2iuying a heavy load in your arms?

Why is the CM of a 1-m length of pipe att rr)nfl1 vz/qolw . di+4iu3/ its mid-point, whereas this is not true for your arm or legw1lfvr n+r/dziq/34liot u. )?

Show on a diagram how your CM shifts when you change from a lying p5zei..8c)9*lc3rdc0p o*m x waulbuv osition to a sitting positc.we u3x p.zr9l 5ialdo*)u80vmcb* cion.

If only an external force can change the momx-7cpkdd )i)albuq :p w.y6 :sentum of the center of mass of an object, how can the internal force oq -6) su: ld:7cwpx).p kiyadbf an engine accelerate a car?

A rocket following a paraboys* 1r njxd1b4 ;4g3 tga.fqpglic path through the air suddenly explodes into many pieces. What can yoj x;dgnbgp1 yg41. *atf3 r4squ say about the motion of this system of pieces?

  What is the magnitude of the 569x 7ivxxkii,m;k wf2qo;jvmomentum of a 28-g sparrow flying with a speed of 8.4 m/s w ikx 26m f ovj;q5xii;7vk9x,   $kg\;m/s$

  A constant friction force of 25 N acts on a 65-kg skier for 20 s. Whab-fop q)t 7v zy 4ay.vhr,k/u0t is the skier’s change in veltz rky -) u7hq 0a/4vf.boyvp,ocity?    m/s

  A 0.145-kg baseball pitched j8/ofpvi (zmjvs bk)5sc 06p0at 39 m/s is hit on a horizontal line drive straight back toward the pitcher at 52m/s If the contact timei/pj5o 06s0cvkmbp (j) zfvs 8 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 horizvb+rm-, gf-b,xtiss/ l gx+f*ontally 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 thalbif,f/xbvx+ s-rgt ,s*-gm +t of the boat is 45.0 kg. Ignore water resistance. The velocity of the boat is    m/s

  Calculate the force exerted on a rocket, given that the propellingnr8mrw.r*u z)8 cual( gases are expelled at a rate of 1500r .wl*)r ur8muacz (n8kg/s with a speed of $ 4\times10^{4 }$ (at the moment of takeoff).$a\times10^7$ N a =   

  A 95-kg halfback moving at 4.1m/s on an apparent breaka 6l9yw+jl/c6pjvx;w8ie fi6b way for a touchdown is tackled from behind. When he was tackled by an 85-kg cornerback running at 5.5m/s in the same direction, what was their mutual speed immediate i/6;9 8wlfv+yji xlb6je6 cwply after the tackle?    m/s

  A 12,600-kg railroad car travels alone on alevely,h-3 w;ami cb frictionless track with a constant speed of 18myma-c,b;hwi 3/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 15m/s strikes a second boxcaxr g l.:hm0id:r at rest. The two stick together and move off with a speed of 6m/x.md:i:l g0 rhs What is the mass of the second car?    m/s

  During a Chicago storm, windo .rce 5uz1bq4s can whip horizontally at speeds of 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 an1 5uqc b.oerz4d 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 sg )rpcs5p+:b along with a constant speed of 8.6m/s on a level track. Snow begins to fall vertically and fills the car at a rate of 3.5kg/min Ignoring friction with the tracks, what is the speed of tp+)gbsc5 p s:rhe car after 90.0 min?$\approx$    m/s

  An atomic nucleus inkk e8m.2o 4vbm dly9t6itially moving at 420m/s emits an alpha particle in the direction of its velocity, and the remaining nucleus slows to 350m/s If the alpha particle has a mass2v8o . 9mkmk4td6eb ly 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(wbx.wz obk 83fh k374sodam / cleanly at 170m/s If the block 3oo 4bm .8fzb/7hasxw(kw d3k 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 speed o0oaoc; k d9p;af $5.80\times10^3\mathrm{~m/s}$ 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 s0n wgz1z p.amd22vm1traveling in outer space with a velocity of 115m/s To a21p snvmmz g201 z.wdalter 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 the tee at a speed of 45m/s The 0 ,jcup /o/r8d z) asmlx;tvt5golf club was in contact with the ba vrculpoa)/jz5/8stm,0 d; txll 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 ve8l kevy)/k 4yllocity of 8.5m/s and comes to rest in a time intervyle y8k)l v4k/al 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 strikes a wall at a 4/d+rk4g m ya/f5 $^{\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 chargern1pp u1edz0;n+0e ceo7if g/ 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 1500 kg takes 0.15 s from the time of impact until it is brought to rest. (a) Calculate the averag ;ze ieg repu70df10o+1n/pnce 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 0.7*+wjgmr*y k 2u5 s by a head-on tackle by a tackler runnik*u m+wyr *jg2ng due west. Calculate
(a) the original momentum of the fullback    kg*m/s
(b) the impulse exerted on the fullback    kg*m/s
(c) the impulse exerted on the tackler,    kg*m/s
(d) the average force exerted on the tackler.    N

  Suppose the force acting on a tennis ball (mass 0.060 kg) points in tu4 +4cxgtz; huhe +x direction and is given by the graph of Fig. 7–33 as a function of time. Use graphical methods to estx uh4z;4+ugtc imate
(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 j1gf;w9/dy4vas*mj: x i ++qoiq( zp bwump without breaking the lower leg bone of either leg? Ignore air resistance and assume the CM of the person moves a distance of 0.60 m from the standing to the seated position (that is, in breaking the fall). Assume the breaking strengthqi1d m +bw(afp;gow*4x/vi j z:ys9+q (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 direction) with a speed of collidey *9g eaud(gnx4aan, tzq2 9z.s head-on with y.,zgxa2 9*ne4( gnuaaqz9 tda 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-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 o5 lxs0wx;si(tz unn dn lq*e46s y/)h(efu6 (af 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 auy5 (alfhs q *6/t sel;nn(iesxwz)x6d(u4n0nd 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 perfectly elastictpegq:lcr ob q:6dn4; 0 gkksc(*mh7; head-on collision. If one ball’s initial speed was 2m/s a6;4gd(q; or lcnkgbqhp:c 7 0:ms* ktend the other’s was 3m/s in the opposite direction, what will be their speeds after the collision?(Let A represent the ball moving at 2.00 m/s, and call that direction the positive direction.Let B represent the ball moving at 3.00 m/s in the opposite direction. ) v'$_A$ =    m/s v'$_B$ =    m/s

  A 0.060-kg tennis ball, moving with a speed of 2.5m/s collides headcwm (ho9tl-,o ;bwyu+xwroyxk.;3e - -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.w.xykw3eytoo,lx;ouh+;-(c w 9-r b m060-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 a6jurnf-ydymxq w5,7* speed of 8.5m/s collides head-on and elastically with another ball initially at rest. Afterward the incoming softball*j-qny uf wr,7x y6md5 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 rifk / clj ctkygf( mjz,ouq:p 8,;lc5;8dl-h9e de collide elastically as one approaches the other dirl;e8 cpq, ukzd 89th:comjl, ffg/ k(l5 ;jcy-ectly from the rear (Fig. 7–34). Car A has a mass of 450 kg and car B 550 kg, owing to differences in passenger mass. If car A approaches at 4.5m/s and car B is moving at 3.7m/s calculate
(a) their velocities after the collision v'$_A$ =    m/s v'$_B$ =    m/s
(b) the change in momentum of each.$\Delta p_{\mathrm{A}}$$\approx$    kg*m/s $\Delta p_{\mathrm{B}}$$\approx$    kg*m/s

  A 0.280-kg croquet ball makes an elastic head-on collision with a secon y vthn(e,w,l05wd .4buzf 7uvd ball initially at rest. The second ball moves off with half the original speed of the uf5(ww4vly n,dtv,ubh.0z 7 e 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 incline as sho : iw+ojla1xk6wn in Fig. 7–35, and elastically strikes another cubo jkl:aw1 6ix+e at the bottom that is only one-half its mass. If the incline is 30 cm high and the table is 90 cm off the floor, where does each cube land? [Hint: Both leave the incline moving horizontally.]$\Delta x_{m}$$\approx$    m $\Delta x_{M}$$\approx$    m

ake the general case of an obj9j ctq ;* ksx/.ui(ju ex1.0w1kurugaect 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 4 p9*n1ksiz-uv 7ptw9tz4 wzwresults in a maximum height h of the pendulum equal to 2.6 cm. A second projectil7 w 4zpupkwn*4-zs1vz9wt 9ite 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-kcc: s060 r qtac zm b6yn33kd6p:brw,ag pendulum hanging onc drqc3n wb0 :3try: ,66b caskam06pz a 2.8-m-long string, which makes the pendulum swing upward in an arc. Determine the vertical and horizontal components of the pendulum’s displacement.vertical$\approx$    m horizontal =    m

(a) Derive a formula f1ljeaw;e7 3tqor 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 rest, into two pieces, one(i4srrm,: g:qy9uc me: k,oqe of which has 1.5 times the mass of the other. If 7500 J were released in the explosion, how much kineti eq9ms(:u ,y:mirckr:g4 qoe ,c energy did each piece acquire? (Let A represent the heavier particle, and B represent the lighter particle. ) KE'$_A$ =    J KE$_B$ =    J

  A 920-kg sports car collides into the rear end of a 2300-kg SUV st,bqsr+ 34 frynol+m4 wopped at a red light. The bumpers lock,,qf ro4 n34s+bmylrw+ the brakes are locked, and the two cars skid forward 2.8 m before stopping. The police officer, knowing that the coefficient of kinetic friction between tires and road is 0.80, calculates the speed of the sports car at impact. What was that speed?(Let A represent the sports car, and B represent the SUV) $\approx$    m/s

  A ball is dropped from a height of 1.50 m and rebosf 0hoz90w .0ajmwxhhh p716je c+ ;yaunds to a height of 1.20 m. Approximately how many rebounds will thhf ;0.x17w9pjoa0 hz6hsejy a ch0+w me ball make before losing 90% of its energy?   

A measure of inelasticity in a head-on collision );gk( )yy m;*gazlrnhof two objects is the coefficieggm l( z)k*;;any)yr hnt of 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 pndm mw nnky;2cp1xy : z/c5y69ieces, 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 separate and slide apart. What is the rati5dk6/n wmy1ycp:9x n;n 2czym o 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 collides head-on ezt f.-+cky68 mruedb lqb .0;0aesi+ with a 10.0-kg object moving in the -x direction at 4m/s Find the final0+ 0t .ms6lb8zuecyq de. abri+-e; fk 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, anqu/k, ; ngc;vxt.qz+l electron, and a neutrino. The electron and neutrino are exg.c kq; n/t;quv,lz+mitted 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 kbevr *y1isb 4rhdv:l/+t),rss $m_\mathrm{A}=0.400$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 coo 2 juljz*;/ng;s kqa4llision between two objects of equal mass, each having initial speed the two move off as4kq;z n;2*ojl /gujtogether with speed v/3 What was the angle between their initial directions?    $^{\circ} $

  Two billiard balls of e xdhr u(du9e7091cf thqual 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 with speed 3.7m/s After the collision, assumed elastic, ball B is moving along the positive y axis (Fig. 7–377d d(uuht9cf h9 re1x0). 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 p5(ii iwxp;k hj +y8h69 *;aasa-jpmsperfectly elastic collision with another atom at rest. After the impact, the neon atom travels away 6;i;mjxs*iakh a-w p8p apsjy+59i( h 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 pfqz2wxg-:g q f tn2f27erfectly elastic collision with another atom at rest. After the impact,2xw tf 27:gg-z qq2nff 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 shoqvl,l)brlh x7(-d .rvo-ox k6 wn in Fig. 7–38. Specify relative to the ll o,lx)v rdqk (7vxh-l-6. boreft-hand 1.00-kg mass.    m

  The distance between a catys/ohi o;oiq3 ob 022rbon atom ($m_{\mathrm{C}}=12\mathrm{u}$) and an oxygen atom ($m_{\mathrm{O}}=16\mathrm{u}$) in the CO molecule is $1.13\times10^{-10}$m How far from the carbon atom is the center of mass of the molecule?    $\times10^{-11}$m

  The CM of an empty 1050-kg car is 2.50 m behind the fw j7dapk)u 6k i*rg49uront of the car. How far from the front of the car will the CM be when two people sit inkigauj9 w*u7 krp6d )4 the front seat 2.80 m from the front of the car, and three people sit in the back seat 3.90 m from the front? Assume that each person has a mass of 70.0 kg.    m

  A square uniform raft, 18 m by 18 m, of mass 6800 kg,ct)bp2ph) lr7dxj fi39)/zwm 9*ubdl 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 ferr* )z2dt pf3j hlr9pcl) diwb/bx7u) 9myboat.$X_{CM}$ =    m $Y_{CM}$ =    m

  Three cubes, of sides ,f pmv8mb+/i qxs/ k2y$l_0$,$2l_0$, 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 pfw;mkl c9 ta ykv3wx7n 7:+4clvus* 0laste (see Fig. 7–swk;u97f cml 07a :tck4 lwyn3* vv+xl40), each of which is a cube of length l. Find the center of gravity in the horizontal plane, so that the crane operator can pick up the load without tipping it.$X_{CM}$ =    l $Y_{CM}$ =    l

  A uniform circular plate of radius 2R has a circular hole of radius hdkdt3vy0a( uv s(c94(ng96j k:oo rvorh5t 5R cut out of it. The center of the smaller circle is a distance 0.80R from the center C of the larger circle, Fig. 7–415hgtr 0vu ( khrv (sotv6(aj9 k9:d no4y53ocd. What is the position of the center of mass of the plate? [Hint: Try subtraction.]   R

  Assume that your proportions are 7)+c0cha;4iczt )ncsp ro6hathe same as those in Table 7–1, and calculate the mass of one o + cicsz; n aoc)ptr76)0hcah4f your legs.    kg

  Determine the CM of an outstretched arm using Tab h0vfn( iqzkrqnc:yn0,) hp:4 le 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 5(hnwxee3p+(h6 mtck z :3(enbx9arsright angle. Assume that the person is 155 ka:neehrx+6t hw (cm593sb( pz3 (nxe cm tall. $X_{CM}$ =    cm $Y_{CM}$ =    cm

When a high jumper is in a position such that his arms and legs9/qrz wl0u;qpm)n r2)re)z dl are hanging vertically, anq d/mlr;qrn )0 we)lu2rzzp9)d his trunk and head are horizontal, calculate how far below the torso’s median line the CM will be. Will this CM be outside the body? Use Table 7–1.

The masses of the Earcyw)q qqh 0n00th 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 man stand ugm1etiz 62-a 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 cylhn(zv72 k6 gijindrical head of mass 2.00 kg and a diameter 0.0800 m mounted on a uniform cylindrical hah(6v7 nizk2jg ndle 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 trajectory?    cm

  A mallet consists of a 0u-.8 f sf*0v l2 gbdocdjrqh4uniform 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 botd* jcqu8v0.d -or0h2f bsf 4lgtom of the handle is the point that will follow a parabolic trajectory?    d    d

  (a) Suppose that in Example 7–14 (Fig. 7–29)8rz8 ts (hhilnu) mxz ,-g,,tp, $m_{II}$=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 aig i yfzjfy8nbj2925v/r 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 th 2yif/z9fyj5v2jg nb8 en move? What happens if the passenger stops?

  An 0.145-kg baseball pitched huy7hf xb8q(vbi66d1h orizontally at strikes a bat and is popped straight up to a height of 55.6 mh b1hf6(i 8qy7vbx6d u. If the contact time is 1.4 ms, calculate the average force on the ball during the contact.    $^{\circ} $

  A rocket of mass m traveling withw eul b8-;dm)x 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. 7–4*el5* )vpil/v, e--mp emv jzg3. Relative dimensions are also shown. Should the player be worried about this being a “scratch shot,” in which the cue v p/ jv *-*eip5,lmzl eg-e)vmball will also fall into a pocket? Give details.

  A 140-kg astronaut (incwijej7 7dc f:hl/)5y cluding space suit) acquires a speed of 2.5m/s by pushing off wh5c:fy /ecwil)77 j jdith his legs from 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 the other 80 kg, are initiwc6 czqja:;vn ddy51,ally at rest in outer space. They then push each other apart. How far apart are they when the lighter astronautawjy,cd cn1:z5qvd6; has moved 12 m?    m

  A ball of mass m makes a head-on elastic cole+lz)*8ipe ky q 0tbc(lision with a second ball (at rest) and rebounds in the opposite dir *eizq8+ 0ekc )pblty(ection 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 involkn ;5ar11jhi+ow om8dving 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 appliedodhwj; amkrn 1+1 85io his brakes 15 m before he crashed into car B. After the collision, car A slid 18 m while car B slid 30 m. The coefficient of kinetic friction between the locked wheels and the road was measured to be 0.60. Show that the driver of car A was exceeding the 55-mph (90km/h) speed limit before applying the brakes.    mi/h

A golf ball rolls off the top of a flight of concrete steps of total v3xx: ob0qkkh:0m0kotk4 nw *vertical height 4.00 m. The ball hits four times on the way down, each time striking the horizontakm:v t*x0 hokn04k3 oxwqb:0k l 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 6+rzt)c6 nca na 1.40-kg block of wood 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 caz66ct nn+ r)after the bullet becomes embedded in it?    m

  A 25-g bullet strikes and becr zk1wo2ry i+/omes 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 the muzzle speed of the bulle/o1kry ir+ zw2t?    m/s

  Two people, one of mass 75 kg and the other of mass 60 kg, sit in a rowboat ofi +uqwg l(nt8gj04 il7 mass 80 kg. With the boat initially at rest, the two people,gtg 8il0( +w4lq7n uji 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 abouqej35/n sb q/qt $ 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 zjouuk3 cuu4 w.kjt/. 4nk9:v explosion. One fragment acquires twice the kinetic eneuk kc/9vjk .oztuu3 :jn4uw4.rgy of the other. What is the ratio of their masses?   

  The force on a bulletpu4qq(j)z 00mgv+x zf is 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 masses7fk-) n*iy lzezlnkz5.ido7( $m_A$ = 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 dc3m5l(z yibv,*fq0m radioactively into an alpha particle and a smaller nucleus. What will be the speed of this recoi 3m(cblf,*idvyzmq5 0 ling 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 ta9i -j7j6,isqfuty 4bdrget) 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=2.2kg2 lsvftms1p:5 j-a gl) slides down 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. 7z d,veestd2 o7,ncs; -–46), what is the upper limit on mass m if it is to rebound from M, slide up the incline, stop, slide down the incline, and collide with M aga7v,cdze2o -es,;sn dtin?    kg (Let A represent mass m, and B represent mass M.)

  The gravitational slingshot effect. Figure 7–47 shows th/rqs.sb kj 25ge planet Saturn moving in the negative x direction at its orbital speersjb5/g. 2ksqd (with respect to the Sun) of 9.6km/s The mass of Saturn is $5.69 \times10^{ 26}$kg A spacecraft with mass 825 kg approaches Saturn. When far from Saturn, it moves in the direction at 10.4km/s The gravitational attraction of Saturn (a conservative force) acting on the spacecraft causes it to swing around the planet (orbit shown as dashed line) and head off in the opposite direction. Estimate the final speed of the spacecraft after it is far enough away to be considered free of Saturn’s gravitational pull.    km/s