We claim that momentum is conserved, yet most moving objects eventxlyi,l 13o wy/e:q,xrually slow down and stop. Explain.:3/oyl y1qx,e lrw ,xi

When a person jumps from a tree to the ground,a3z; kyb7e vr, what happens to the momentum of the person uponz3 kba;e7v,ry striking the ground?

When you release an inflateaadm6 wb 57oe.p /y:wkd but untied balloon, why does it fly across the room/ 7 5akwdowe.apy:m6 b?

It is said that in ancient times a rich man with a bag of gojsxuxq uj: +h +0**yltyasfcb6.t l- ,ld 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 himsel*0,jy-uf tashcx 6bu yj+qs+tx. l *:lf had he not been so miserly?

How can a rocket change direction when it is far out in spacey ,zs: 0u5kfae and is essentially in y5ez k:u ,0afsa vacuum?

According to Eq. 7–5, the longer the impact time of an impulse, the smaller tf 8pz3e vh5kh9he force can be for the same momentum change, and hence thfzhph3 ke9 v85e smaller the deformation of the object on which the force acts. On this basis, explain the value of air bags, which are intended to inflate during an automobile collision and reduce the possibility of fracture or death.

Cars used to be built as rigid as possible to withstand c6cpr0xk 2 d ajkjsw2,;ollisions. Today, though, cars are designed to have “crumple zones” that collapse upon impact. What is the advantage of this n20,rk kdspax;c2j jw6ew design?

Why can a batter hit a pitched basea6m:i7f 4uaq bdq ,i47,gtgyxij+cz) ball further than a ball tossed in the air by the batter:xcaf4q iitjgzb7m,)7dyia 4 u6gq,+?

Is it possible for an object to receive a larger impulse from a small force thss. j6*tvn: m:kuphj-p 9ge j4an from a large forn:6.4 t pkjjj- m phvseu*s9g:ce? Explain.

A light object and a heavy object have the same kinet0zrrb t9,2da5fvuf; vic energy. Which has the greater mv;tza 0r uv,r b5ffd29omentum? Explain.

Describe a collision in which all kinetic energy i)jt/bl;qs hto d2u*/as lost.

At a hydroelectric power plant, water is directed at high speed ag 2mlk2 yvqu+qhd )ef.-ainst 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 wa.u qm2qkdlh v)y+fe 2-ter rebounds?

A squash ball hits a 3t5*r6r b fsztc)u1cio:8)a yrew h:vwall at 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 ow /9qxuj 2pv/a*j2wdo nto a hard steel plate (fixed to the Earth), from which it rebounds at very nearly its original speed. (a) Is the momentum of the ball conserved during any part of this prwp*qx2d /2w aj/ujvo9ocess? (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 wp9t72vkj x0 kphen carrying a heavy load in your arms?

Why is the CM of a 1- ,q d*0 nsp3kt4lc;rt 3vy3fjfm length of pipe at its mid-point, whereas this is not true for your arm or 3ttc ,fpy0;n4jv d3lqrsfk3 *leg?

Show on a diagram how your CM shifts when you change from a l 2kwly:kb79 nfying position to a sittingkly:w9 2fb nk7 position.

If only an external force can change the momentum of the center ohg qquf9m1 a35f mass of an object, how can the internal force of an engine accq3u5f9a ghmq1 elerate a car?

A rocket following a parabolicrhdwnt :+5a 5e path through the air suddenly explodes into many pieces. What can you say about the 5hw d:en t+5armotion of this system of pieces?

  What is the magnitude of the momentum of a 28-g sparrow fl(a2d;jd5j/ gtot k*j * t.xonkying with a speed of $8.4 \; m/s$    $kg \; m/s$

  A constant friction force o5vm,er7hq: hpf 25 N acts on a 65-kg skier for 20 s. What is the skier’s change in5h:,7qv rpehm velocity?    m/s

  A 0.145-kg baseball pitched at 39 m/s is hit on a horizontal line drive 9woo fr apc1, fod+)*wstraight back toward the pitcher at 52m/s aw1d+9rc oop,fow )f *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 owj fvk:qp *;x)d)-ij cut 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 masipcvd-;wq fj kx* ):)js 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 exerted on a rocket, given that the propelling gases are e+.s+dbe3r8i0f nv ubnxpelled at a ratdnf0 e3s + b+bivur8n.e 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 movizfk,j5+tf oir p +0en*ng 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 q4: 8/ it:gow0;hos rbbcy )ivalone 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 ne /:o8iogy t;vcqbi 0w b4:srh)w speed?    m/s

  A 9300-kg boxcar traver7pge sx 6n(e9ling 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 horizontall-0etcqr5j mbnv+vd :u (3 9qigy at speeds of 100km/h If the air strikes a person at the rate of 40kg/s per square meter and is brouqdtrej:(9 inb+v g0vcmq35-u ght to rest, estimate the force of the wind on a person. Assume the person is 1.50 m high and 0.50 m wide. Compare to the typical maximum force of friction $\mu\approx1.0$ between the person and the ground, if the person has a mass of 70 kg.    N
$F_{on person}$  ----待选择----<> $F_{fr}$

  A 3800-kg open railroad car coasts along with a constant sc4,s z isv.,hbaebod l+5rk+)peed 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, e ab)ihkzlsc,. b o4s5+dvr+, what is the speed of the car after 90.0 min?$\approx$    m/s

  An atomic nucleus initially moving at 4: ro- l)htte/s20m/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 mass of 4.0 u and the original nucleus has a mass of 222 u, what speed do)/lhr toe:-tses the alpha particle have when it is emitted?    m/s

  A 23-g bullet travelin6im /fczu f2l(g 230m/s penetrates a 2.0-kg block of wood and emerges cleanly at 170m/s If the block is stationary on a frictionless surface l(mff62 uzc/ iwhen hit, how fast does it move after the bullet emerges?    m/s

  A 975-kg two-stage rocket is traveling at +/b;lo ns fep7a 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 ggr(,*) kg tnz.npxqlw o8o+9 outer space with a velocity of 115m/s To alter its cn)tgngl(.8+9gx *r ,wqkoz op ourse 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 4eg8x /9tzkx9mx + h+mc5m/s The golf club was i9k+ xhxz m/+c9e tmx8gn contact with the ball for $3.5\times10^{-3}$s Find (a) the impulse imparted to the golf ball,    kg*m/s
(b) the average force exerted on the ball by the golf club.    N

  A 12-kg hammer strikes a nail at a velocity of 8.5m/s ag 48nw+gwfg o4nd comes to rest in a time interval of 8.0 ms. (a) What is the impulse given to the nail? nw 448g wogg+f   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 wal7/nq-sbq;ub/ f) ofj hl 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 engi6i 0wf*m mp sd- +jhcn/k0fxh.neer in charge of the crashworthiness of new automobile models. Cars are tested by smashing them into fixed, massive barrier fm/+h wk 6-*sh0.cfpxnji0mds 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 run n1w:xoocb+d( ning at 4m/s to the east and is stopped in 0.75 s by a head-on n d:ox(1wbo+c tackle 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 0.060 nnbft5z9:pj6 kg) points in the +x direction and is give9 tbnp fn6:j5zn by the graph of Fig. 7–33 as a function of time. Use graphical methods to estimate
(a) the total impulse given the ball    N*s
(b) the velocity of the ball after being struck, assuming the ball is being served so it is nearly at rest initially.    m/s

  From what maximum height can a 75-kg persfixgj 2 b8uyxwd/-iw y (vf/.(on jump without breaking the lower leg bone of either leg? Ignore air resistance and assume the CM of the person moves a distance i 82f(fg/yvj ubi -x.wx(/d ywof 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 (+x direction) with a speed,v0ty ;vg1z5 (v epkme of collides head-on with a 0.220-kg ball at rest. If the collision is perfectly elastic, what will be the speed and direce;1mvepyg,( tz5v vk0tion 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,,eua dojn qi3+t.b f34 moving east with a speed of 3m/s has a head-on collision with a 0.900jabtq.,+ eio n433d fu-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 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 equ4 0h;dnt6ajd dal mass undergo a perfectly elastic head-on collision. If one ball’s initial speed was 2m/s and the other’s was 3m/s in the opposite direction, what will be their speeds after the collision?(Let A represent the ball moving at 2.00 m/s, and call that direction the positive direction.Let B represent the ball moving at 3.00t0dn4;ah 6ddj m/s in the opposite direction. ) v'$_A$ =    m/s v'$_B$ =    m/s

  A 0.060-kg tennis bal+ p98-pt9rcauktzxy( i vm7k5 l, moving 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 l-7+ticrmkktz (p 5u98apvyx9 et 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 wit svwp7r8y6x+ ph a speed of 8.5m/s collides head-on and elastically with another ball initially at rest. Afterward the incoming softball bouncep vsr 67yx8+pws 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 as one approac6:y ricn38pmo (l/rlkhes 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 massio lr6r(yp:mn k/cl83. 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 wiu )8xc utzi5igem.5 ;g7,fz dkth a second ball initially at rest. The second ball moves off with half the original speed of the first balle78c txgu gfi5 du)5; zz.,mik.
(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 shown in Fig. e+fcwxdisuh i9 vnrk(9(l-8(xtv 8-* yv nu7 x7–35, and elasticallyu+(df ui 88v xwcvs(xi9(r 9v -thynnlke7*x- strikes another cube at the bottom that is only one-half its mass. If the incline is 30 cm high and the table is 90 cm off the floor, where does each cube land? [Hint: Both leave the incline moving horizontally.]$\Delta x_{m}$$\approx$    m $\Delta x_{M}$$\approx$    m

ake the general case of hxsg6 i7u+a/l 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 maximum hef: hfsse3w)2y 0 e5rlxight h of the pendulum eqywfe3) rlsfx e5s0 h2:ual 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 3.6-kg pendului9t:m/o vtbo vyt.d hq)7k7,ym hanging on 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 displacemed v9ot/otk.)7hi:7tm qyvyb , nt.vertical$\approx$    m horizontal =    m

(a) Derive a formula for the6;6cn; s ivgbxs r;zp3 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 anf m6pb :huy,n) object, initially at rest, into two pieces, one of which has 1.5 times the mass of the oth p ),unhy6fb:mer. If 7500 J were released in the explosion, how much kinetic energy did each piece acquire? (Let A represent the heavier particle, and B represent the lighter particle. ) KE'$_A$ =    J KE$_B$ =    J

  A 920-kg sports car collides into the rear en1wcs0lju/:k6vw y + fcd 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 spelsfjyu k0 /cvw:+ 61wced of the sports car at impact. What was that speed?(Let A represent the sports car, and B represent the SUV) $\approx$    m/s

  A ball is dropped from a height of 1.50 m and rebounds to a height mb/ e 6ooyx6j2of 1.20 m. Approximately how many rebounds will the bam6 o/xyjbe2 o6ll make before losing 90% of its energy?   

A measure of inelasticity in a head-on collision of two objects is ;nzrik -8nbh)bh wo( a2,t;gz the coefficie ia-tbn,hg b o);28 wzhzrnk;(nt 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 pieces, one with three times the mass of thd* k+ xlbdc8eyx)c:2ve other. A deprl+2ddvc )e8bxk xc*:y ession 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 direction at 5.5m/s c3czn 09f5vde3v iwi v 3fldr+;ollides head-on with a 10.0-kg object moving in the -x direction at 4m/s Find the fe v5 nici v0z33wvd; l93rfd+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 electron, and a8/d- lm3 k(hvb zwidi1 neutrino. The electron and neutrino idv-kz1 h3 ( dim/lbw8are 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 mapd7hp9yz10ps 2r7,g . nw izuyss $m_\mathrm{A}=0.400$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 collisu; 6ajq6ggp;f2cbrd fmd57p )ion between two objects of equal mass, each having initial speed the two move off together with spe6m57 gdpaq j;p;c2f)f g6 dubred 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 or jpbx(yln,;u yqr m )+v8on20xigin 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.bj v8xoql )x0 2rnm u+ny;yp(, 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 perfed2d9)i6f0s cpkwpw :s09br g+vzl l+ tctly elastic collision with another atom at rest. After the impact, the neon atom travels away at a 55.6 zpk 06 0+l s9i:p9wwfd lsrcv) 2dbg+t$^{\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 6gg7oai3i1be es a perfectly elastic collision with another atom at rest. After the impact, the neon atom travels awaya bggi 6i7e13o 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 syste :umh(lmu - 0u(n5buunhhx a8,jpz2 *ob-(lrtm shown in Fig. 7–38. Specify relative to the left-hand 1 run ,*-hm(0 xphulhaluon5 8tjumb:(-2buz (.00-kg mass.    m

  The distance between a carbonxv0 t2u7xz6 /aj oy*zq 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 front of the car. How far f1)p+j p3 3pqkwlno*v qrom 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 each person has a mass okjw3q1 +3qp* p povl)nf 70.0 kg.    m

  A square uniform raft, 18 m by 18 m, of mass 6800 kg, is used as a ferryboat.vf1j z l1.jak3* z)cvc If three cars, each of mass 1200 kg, occupy its NE, SE, and SW corners, determine tjcv.*1jl 3)cz zkf a1vhe CM of the loaded ferryboat.$X_{CM}$ =    m $Y_{CM}$ =    m

  Three cubes, of sides z acjewl*4rv 8.hq/qj9er: m( $l_0$,$2l_0$, 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 identicfu/fe 6uzwq ky1e*12y al cases of tomato paste (see Fig. 7–40), each of which is a cube of length l. Find the center ofqw*/6 1fe1fzu uyy2ke 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 xea *jyf.je5w5 w.x3g mev-p:of radius 2R has a circular hole of radius R cut out of it. The center of the smaller circle is a distance 0.80R from the center C of the larger circle, Fig. 7–41. What is the position of the center of mass of the pla*-5.wj:35x mw. xafejveypeg te? [Hint: Try subtraction.]   R

  Assume that your proportions are the same as those in Table 7–1, and calfx hppzg/6 8;cculate thgpc;68/f phz xe mass of one of your legs.    kg

  Determine the CM of an outstretched arm usi3qesh .o;z.blng 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 bentpqbyn6v6 xn2 4 at a right angle. Assume that the per4pxn626qvbn y son is 155 cm tall. $X_{CM}$ =    cm $Y_{CM}$ =    cm

When a high jumper is in a position such that his arms andedb z8y+-qa/. ixol8++zbd2hinl ps ) legs are hanging vertically, and his trunk and he ni qhib dpa+l++sd8x l8./-zy2b)ezoad are horizontal, calculate how far below the torso’s median line the CM will be. Will this CM be outside the body? Use Table 7–1.

The masses of the Earth and Moon are /0nt16yg1wetgfhy s ,qn5( ui$5.98\times10^{24}$kg and $7.35\times10^{22}$kg respectively, and their centers are separated by $3.84\times10^{8}$m (a) Where is the CM of this system located? (b) What can you say about the motion of the Earth–Moon system about the Sun, and of the Earth and Moon separately about the Sun?

  A 55-kg woman and an 80-kg man stand 10.0 m apax3mjov by(j8o:r-ck .a*sm. irt 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 azs0shv j-3 a .jpj2q+spe bsfl4wl4 k(p)m a:,nd a diameter 0.0800 m mounted on a uniform cylindrical handle of mass 0.500 kg and length 0.240 f3s-el:wmjpk p .sa a04,h jvjs q4) lb+z2s(pm, 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 uniform cylindrical head of mass 2.00 ebid3kh 89kgse , 1q4o,bi/ dkeat*e)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 toss4,eod ebq,ted1/b9gike8 *ki sk) 3ahed, 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 7–14 (Fig. 76.6 kgv4eeh7tr l9l 0tpt7bs w–29), $m_{II}$=3$m_{I}$ Where then would $m_{II}$ land?    d(Round to two decimal places)
(b) What if $m_{I}$=3$m_{II}$    d

A helium balloon and its gondola, of mass M, are in the air and s8o,uh , qzpe6:efv+njtationary with respect to the ground. A passenger, of mass m, then climbs out and slides down a rope with speed measuh+ef8 v6o zp e,:jq,unred 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 horizontalivt,k+1hb id05 xcsu 4ly 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 uh,i ki+t 50scxb dv14during the contact.    $^{\circ} $

  A rocket of mass m traveling with 7h 5z.:tzc xurspeed $v_0$ 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 sho d1e nal6 vn2+xxdl)e)e)l;t-o5am rat shown in Fig. 7–43. Rel lenr)62ma ;v) dl) x5exe1+ oadtn-laative dimensions are also shown. Should the player be worried about this being a “scratch shot,” in which the cue ball will also fall into a pocket? Give details.

  A 140-kg astronaut (including space suit) acquires a speed of 2.5m/s by pushing zs+6hg 6amhn+ hcz:)h off with his legs from ascmhhh +h6z +6 gzn)a:n 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 initiall (8e gv+q9ijnzy at rest in outer space. They iqz+8ne vj(g 9then push each other apart. How far apart are they when the lighter astronaut has moved 12 m?    m

  A ball of mass m makes a head-on elastic collision with a secos30 /z*ct 9 jtbof9pmeshr( i4nd ball (at rest) and rebounds in the opposite direction b4h 0 *izor9 ms/3fst9tj(cpewith 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 an/2rsx jw1(quz.d2 oi w- yqq+ 1mdx yx.w-b*gs an expert 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 th2--briud1qjx.x woqgw1m2 ( wqs.x/ y+y *nzde 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 conqt6. g 1 t:n(p2 djga7l3,cr8ub6j lu xu)wfcocrete steps of total vertical height 4.00 m.l3b6ct:ugt.cr,7g x2(f6 upwljd)n oqa j u8 1 The ball hits four times on the way down, each time striking the horizontal part of a different step 1.0 m lower. If all collisions are perfectly elastic, what is the bounce height on the fourth bounce when the ball reaches the bottom of the stairs?

  A bullet is fired vertically into a 1.40-kg block of wood at rest directly above t0d.ybvol/6t it. If the bullet has a mass of 29.0 g and a speed of 510m/s how high w/vto 6t0db.y lill the block rise after the bullet becomes embedded in it?    m

  A 25-g bullet strikes and becomes embedded in a 1.35-kgojy(h.3um;h xdl4 69 c.qlhzc 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 resq lux6 4h( ocdj.;zhm9hc3ly .t, what was the muzzle speed of the bullet?    m/s

  Two people, one of mass 75 kg and thed7y1v k+ 11 )yxzgxcjl other 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 m apart frgj1)y1x 1lkdz+x c7vyom 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 abokx 7apn t0et o 3b5m-/q9s-ydzut $ 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 suddenkrv1h01s6*xrnkiu0i ly broken apart into two fragments by an explosion. One fragment acquires twice the kinetic energy of the other. What is the ranxu *1irk6rshv k0i10tio of their masses?   

  The force on a bullet is given by the formula F = 580-k se742t wxi 7ut1ur*z( $1.8 \times10^{ 5}$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 masses0 m1san, zl2jl bb 0z8xq;x;zw $m_A$ = 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 reb8w whpp83jd 0st decays radioactively into an alpha particle and a smaller nucleus. What will be the speed of this recoiling nucleus if the speed of the alpha particle is jw8h3dpp wb80 $ 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 fi c)h9j4(kno2rk0 gz( c +dngyared 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 d6:j6chh i: uqt 7obx9iown a 30.0 $^{\circ} $ incline which is 3.60 m high. At the bottom, it strikes a block of mass M=7kg which is at rest on a horizontal surface, Fig. 7–46. (Assume a smooth transition at the bottom of the incline.) If the collision is elastic, and friction can be ignored, determine
(a) the speeds of the two blocks after the collision,v'$_A$ =    m/s v'$_B$ =    m/s
(b) how far back up the incline the smaller mass will go. $\approx$   (Round to the nearest integer) (Let A represent mass m, and B represent mass M.)

  In Problem 79 (Fig. 7–46), what is the upper limit on mass m if it is +k0s x 4r/bkzvd5rd 0nto rebound from M, s54 rzs/ k0dn0k b+xdrvlide up the incline, stop, slide down the incline, and collide with M again?    kg (Let A represent mass m, and B represent mass M.)

  The gravitational slingshot effect. Figure 7–mg i.xl h sku3xzldg.59h.g; u5nr,-o47 shows the planet Saturn moving in th .,-lu;9 i zlnm535gk sr.dx xouh.hgge negative x direction at its orbital speed (with respect to the Sun) of 9.6km/s The mass of Saturn is $5.69 \times10^{ 26}$kg A spacecraft with mass 825 kg approaches Saturn. When far from Saturn, it moves in the direction at 10.4km/s The gravitational attraction of Saturn (a conservative force) acting on the spacecraft causes it to swing around the planet (orbit shown as dashed line) and head off in the opposite direction. Estimate the final speed of the spacecraft after it is far enough away to be considered free of Saturn’s gravitational pull.    km/s