We claim that momentum is conserved, yet,npo 6d70eq zt most moving objects eventually slow down and stop. Explai np eod,60q7ztn.

When a person jumps from a tree to the ground, what ha:s: k89(lq 6hpoyhscg ppens to the momentum of the person upon str hkpl(8s:qh96sc go: yiking the ground?

When you release an inflated but untied balloon, w3:blk*mjle2b,,zqb t c z6b- a5 pcoo)hy does it fly across the room?bb zco*)56 j2lbaz,,lb 3etko-qmc p :

It is said that in ancient times a rich9iir4ivnu/ l/ g ap0-b 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 could hei/rabgv 9u ip/40inl - have done to save himself had he not been so miserly?

How can a rocket change direction when it is far out in space auy,t4)dcpnqal;;* ( x nbh 66s scyo4end is essentially in a vacuu64h cy q,ds*()n ls6toub nexc;;pya4 m?

According to Eq. 7–5, tope c,qve2ek.j7l bp,1o vazo(z+m0 o hi,e .5he longer the impact time of an impulse, the smaller the force can be for the same momentum change, and hence the smaller the deformation of the object on which the force acts. On this basis, explain ie0km l ,7 e b21ozh(o,pee,c5v.zj o .qpo+avthe 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 possiblehca/pc w y iir2y(1g;5 to withstand collisions. Today, though, cars are designed to have “crumple zones” thci;aw/c hr (52gypiy 1at collapse upon impact. What is the advantage of this new design?

Why can a batter hit a pitched baseball fur 65ve mj;fwfrj70qvp4ther than a ball tossed in the air by thf p7erv6;jvfjm 405qwe batter?

Is it possible for an object to receive a larger impulse from a small force th,-0 y8 92vlqcemde qvpan from a large force? Explaincvey,p0mvd9 8qq-e l 2.

A light object and a heavy objectz ;zl 5g tfe(e(le8om6 have the same kinetic energy. Which has the grea;tlzlm(oege 8z6fe (5ter momentum? Explain.

Describe a collision in which all kinzt(khu8oku0* b r0h-metic energy is lost.

At a hydroelectric powe)ev1wiy m)zt)58voa0y:eyip r 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 soo) av:yywymz 1e0pe8)5)vi ti that the water rebounds?

A squash ball hits a wall at a62 4;p m8s9rbzlzjbf:iz i. yv 45 $^{\circ} $ angle as shown in Fig. below. What is the direction (a) of the change in momentum of the ball, (b) of the force on the wall?

A Superball is dropped from a height h onto a hard steel k; rg(3c f(qiaplate (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 process? (b) If we consiicr3(;faq( kg der 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 wheneyw4sgud23 ii o4l8w 5 carrying a heavy load in your arms?

Why is the CM of a 1-m length of pipe at its mid-point, whereas this is not truq*px.x lc8qo)dbu ,d .e for your ab qxpqxdo* )u,8.d lc.rm or leg?

Show on a diagram how youu9 -oo;ko m-rtr CM shifts when you change from a lying position to a sitting positio mkout9; o-or-n.

If only an external force can change the mo 5+cl llxhv13wmentum of the center of mass of an object, how can the internal force of an engine acclxwv3 hlc5+1lelerate a car?

A rocket following a parabolic path through the air suddenly explodes n9b ctq/-u1kb into many pieces. What can you sab1- 9tnc/bqkuy about the motion of this system of pieces?

  What is the magnitude of the momentum of a 28-g sparrow flying wi )92, xqobxnqbth 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. Whar hc+wu,eg;l l n6hcss.q r7;yb* k+z.t is the skier’s changlhrs ;h,+.;zgkl b*rnc 6s7u+ewqc. ye in velocity?    m/s

  A 0.145-kg baseball pitched at 39 m/s is hit on a s66lnp11h tf/y biih 1horizontal line drive straight back toward thbi/s1li6nty1 16fp hhe pitcher at 52m/s If the contact time between bat and ball is $3\times10^{-3}$s calculate the average force between the ball and bat during contact.    N

  A child in a boat throws a 6.40-kg package out horizontally with a speed of7vr4 i0-ninuc 10 m/s Fig. below Calculate the velocity of the boat immediately after, assuming it was initially at rest. The mass of the child is 26.0 kg, and that of the boat is 45.0 kg. unv4r07i n- icIgnore water resistance. The magnitude of the velocity of the boat is    m/s

  Calculate the force exerted ouo 4r)w4 cjh,rn a rocket, given that the propelling gases are expelled at a rate ofrj 4ur4)chow, $1500 \; kg/s$ with a speed of $ 4\times10^{4 } \; m/s$ (at the moment of takeoff). F =    $\times 10^7 \; N$

  A 95-kg halfback moving azbg5rvc h; fjf9j+9j7 t $4.1 \; m/s$ on an apparent breakaway for a touchdown is tackled from behind. When he was tackled by an 85-kg cornerback running at $5.5 \; m/s$ in the same direction, what was their mutual speed immediately after the tackle?    $m/s$

  A 12,600-kg railroad car travels alone on alevel frictionless track with a v;1ypeg /p2b)f,tx2mf wwd(2kt2 owx constant speed of 18m/s A 5350-kg load,initially at rest, is dropped onto the car. Whap2mx2w)1twt/gff2vk dxw, 2eb y; op(t will be the car’s new speed?    m/s

  A 9300-kg boxcar traz+ u,i bw1a: u*/t 1xqnernnr8)(paseveling at $15 \; m/s$ strikes a second boxcar at rest. The two stick together and move off with a speed of $6 \; m/s$ What is the mass of the second car?    $m/s$

  During a Chicago storm, winds can whip horizontally at3og9xlze61-by.o gy x speeds of 100km/h If the air strikes a person at the rate of 40kg/s per square meter and 61gol - gy9x.o3b exyzis brought to rest, estimate the force of the wind on a person. Assume the person is 1.50 m high and 0.50 m wide. 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 cjyq9q+w2zx ms0 e ex):oasts 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/min0)+2q :e9xsm qzjywex Ignoring friction with the tracks, what is the speed of the car after 90.0 min?$\approx$    m/s

  An atomic nucleus initially moving 9otjhy 4:hwo 0at 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 mass of 4.0 u and the original noho: 9wy0 j4thucleus 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 wo )zt-73.hcf y+)l/ae,mzub i8j75 zjbo dhxwpod and emerges cleanly at 170m/s If the block is stationary) 7bzh l7j83myzo5 jxp)+ ec if,ua .bd/wz-ht 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 speed8ccz zonhs64y79 goq* 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 hy c5* yu- hzuupnalb3+cf/ +0is traveling in outer space with a velocity of 115+ cyp 5ubh+hy3a uz* nf0c/lu-m/s To alter 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 edj g/wqq-9d8ish9 (c a speed of 45m/s The golf club (is 89cwq/ edq9-jd hgwas in 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 and) (ba p5nam84juxfqa0 comes to rest in a time interval of 4)quja(fpabm a5 8 0nx8.0 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 speeph7 n*j8*5jell2)e vp x1u o -oxadku6d v=25m/s strikes a wall at a 45 $^{\circ} $ angle and rebounds with the same speed at 45 $^{\circ} $ (Fig. 7–32). What is the impulse (magnitude and direction) given to the ball?   kg*m/s to the  ----待选择----leftright 

  You are the design engineer in charge of the crash6ua.3d ekxh +,+dhg /w1zbbhnworthiness of new automobile models. Cars are tested by smashing them into fixed, massive barriers at 50km/h (30 mph). A new modbkuxbza/n d+hh1weh 6, d3.+gel 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 4p7s iryrz9j: ;m/s to the east and is stopped in 0.75 s by a head-on tackle by a tackler running duesijrp9:y ; zr7 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 to fz9qo2bt;c4z1b5k d1zsif /ennis ball (mass 0.060 kg) points in the +x direction and is given by the graph of Fig. 7–33 as a function of time. Use graphical 59of b4qdkz1zo2b sc/f1 itz; 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 person jump w07zzdw q/+ *afxszi7 iithout 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 strength (force pz qx7 d7fs/wa+0zizi*er 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 di-ospte:o ec)bzkwuik. 23*q 5 rection) with a speed of collides head-on with a 0.220-kg ball at rest. If the collision isi ksb*p-teu3wo:2c) 5kq e.zo 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 of 3m/s has a head-on -6ls itun5 0/yw+ebfqcollision with a 0.900-kg puck initially at rest. Assuming a perfectly elastic collision, what will be the speed and direction of each object after the collision?Let A represent the 0.450-kg puck, and let B represent the 0.900-kg pucel+/ us605tbqi- y nfwk. 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 elastic head-on collis9p , 310carhasmu(*i1bnr e42j okt4arfrvh:ion. 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 thrki rs0jc,4f( 21rua *hb h1 9orv:ne3ptm aa4at 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 withmj1:)83b txb d,f 9os2gk tedg 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?(L t3dbm ,dxf1 8esko)2g:jbtg 9et A represent the 0.060-kg tennis ball, and let B represent the 0.090-kg ball.)v'$_A$ =    m/s v'$_B$ =    m/s

  A softball of mass 0.220 kg that is moving with a speed of +xhw ma5 klc438.5m/s collides head-on and elastically with another ball initially at rest. Afterward the incoming softball bounces backward with a speedx+hcmk5 3aw 4l 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 approaches m b5- j+1sto5six* foithe 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 bs+tf5-ioio *sj m1x5A 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 co/i)7tb0+ xtczb*g rl tllision with a second ball initially at rest. The second ball moves off with half the og/b )7tb c tx0+tz*ilrriginal 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 cub10oi d0u 2;lp 9ia/nsgax pf;p)ljh5le slides down a frictionless incline as shown in Fig. 7–35, and elastically strikes anotf p0n2ai5gai uo9 pll/0;h ld s1p;)xjher 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 an object of 6zrcx5umzbf81s0n loy i 8 ;(rmass 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 a- 0x 2sezpqj(maximum height h of the pendulum equal to 2.6 cm. A second projx0 (ps2z qae-jectile 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 pendulum hangii9 c;w+v62ei352d fljrdqjeeqh) e5 sng on a 2.8-m-long string, which makes the pendulum swing upward in an arc. Determine the vertical and horizontal compo)q9j5w5f2+hvce;rji2i q ee ed s3ld6nents of the pendulum’s displacement.vertical$\approx$    m horizontal =    m

(a) Derive a formula for the fractba v*xlk*- ac9ion 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 brewae(av8 :/y-w l5* mvl u)h t.nyvsp.naks an object, initially at rest, into two pieces, one of which has 1.5 times the mass of the other. If 7500 J were released in the explosion, how much kinetic energy did each piece acquire? (Let A represent the heavier particle, and Bp*wyv)asn ve ynl t5 alu8h-:m.v/(.w represent the lighter particle. ) KE'$_A$ =    J KE$_B$ =    J

  A 920-kg sports car collides into the rear end 44h)s nph0:kadnh(e vof 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 th 04hk4p):evhsnd( anh at 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 rebounds to a heigbtavyk i5n 8/,ht of 1.20 m. Approximately how many rebounds will the ball makea n,iyvk /tb58 before losing 90% of its energy?   

A measure of inelasticity in a head-on collision of two wm; 1z bme-ml.objects is the coefficient of remzbmmle.w1- ;stitution, 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, onmch3 t-s/bc p)e 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 reassemp/ch)-tsb3m c bled. 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 collten ;b-o -yk2;oxnl nfrd98b:ides head-on with a 10.0-kg object moving in the -x direction at 4m/s Fibynk2o;nxtdrl:n9;-b -oef8 nd the final velocity of each mass if:
(a) the objects stick together;   m/s
(b) the collision is elastic; v'$_A$ =    m/s v'$_B$ =    m/s
(c) the 15.0-kg object is at rest after the collision;   m/s ----待选择----not reasonable reasonable 
(d) the 10.0-kg object is at rest after the collision;   m/s ----待选择----not reasonable reasonable 
(e) the 15.0-kg object has a velocity of 4m/s in the -x direction after the collision. .   m/s ----待选择----not reasonable reasonable 
Are the results in (c), (d), and (e) “reasonable”? Explain
( Let A represent the 15.0-kg object, and let B represent the 10.0-kg object.)

  A radioactive nucleus at rest decays into a second s. *ub f+cug89spte:inucleus, an electron, and a neutriecus i*b+f t :98sg.puno. The electron and neutrino are emitted at right angles and have momenta of $9.30\times10^{-23}kg\cdot m/s$ and $5.40\times10^{-23}\mathrm{~kg}\cdot\mathrm{m/s}$ respectively. What are the magnitude and direction of the momentum of the second (recoiling) nucleus?    $ \times10^{-22}$    $^{\circ} $ from the momentum of the electron

  An eagle ($m_{\mathrm{A}}=4.3\mathrm{kg}$) moving with speed $\nu_\mathrm{A}=7.8\mathrm{~m/s}$ is on a collision course with a second eagle ($m_{\mathrm{B}}=5.6\mathrm{kg}$) moving at $\nu_{\mathrm{B}}=10.2\mathrm{m/s}$ in a direction perpendicular to the first. After they collide, they hold onto one another. In what direction, and with what speed, are they moving after the collision? v =    m/s $\theta$ =    $^{\circ} $ rel. to eagle  ----待选择----AB 

  Billiard ball A of mass4-,q xnxun/omad ,5hu r3)l mw $m_\mathrm{A}=0.400$kg moving with speed $\nu_\mathrm{A}=1.80$m/s strikes ball B, initially at rest, of mass $m_\mathrm{B}=0.500$kg As a result of the collision, ball A is deflected off at an angle of 30.0 $^{\circ} $ with a speed $\nu_\mathrm{A}^{\prime}=1.10$m/s (a) Taking the x axis to be the original direction of motion of ball A, write down the equations expressing the conservation of momentum for the components in the x and y directions separately. (b) Solve these equations for the speed v'$_B$ and angle $\theta_{\mathrm{B}}$ of ball B. Do not assume the collision is elastic. $\theta_{\mathrm{B}}$ =    $^{\circ} $ v'$_B$ =    m/s

  After a completely inelastic collision between two objects of equal mass, each hj+t4a ge,mx1uv 6 ;c alk)s-oiaving initial speed the two move off together with speed v/3 What was the angle between their initial sk+4ox,1;u)gcv li6jea amt- directions?    $^{\circ} $

  Two billiard balls of equal mass move at right ,6 5wt7(vghao pu 4naaangles 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 4a n,wpuhag6to v57 a(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 perfectly elastic collisiohc oi,;lm 6.v)lcyqd *) a2curn with another atom at rest. After the impact, )2v 6c;rcy q*,dmolh.) ciaulthe neon atom travels away at a 55.6 $^{\circ} $ angle from its original direction and the unknown atom travels away at a -50 $^{\circ} $ angle. What is the mass (in u) of the unknown atom? [Hint: You can use the law of sines.](Let A represent the incoming neon atom, and B represent the target atom) $m_B$   u

  A neon atom (m=20u) makes a perfectly elastic collision with another atkw2(c5/mp -or i g;ajzom at rest. Aftera(cm2 p5g izow;/k- rj 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 sy9 9bp5xrb1iuuju jg3 3stem shown in Fig. 7–38. Specify relative to the left-hand 1.00-kg mass.53uju3b91pu9irbjg x    m

  The distance between yymil, bk 1g2)a carbon 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 iox s- ;o+.mdzfs 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 -o;s xzd +mfo.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 ;w0o 1h ijga)okg, 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 )1jo wg ;ha0oiloaded ferryboat.$X_{CM}$ =    m $Y_{CM}$ =    m

  Three cubes, of side6(( qi 5pxn0cjorrg 7ns $l_0$,$2l_0$, 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 loa;/rwt m+p06g ff yu0wmd of identical cases of tomato paste (see Fig. 7–40), each of which is a cube of length l. Findwtpur/ m y g00;mff+w6 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 R cut out o:pe/ jstvjoz6 mp39 b)f it. The center of the smaller circle is a distance 0.80R from the center C:p9e6j to)b szv/jp3 m 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 t*,n 86 pgwyr ;uvg7ksvhe same as those in Table 7–1, and calculate the mass of one of yrg6n7gu*vkpwv , ;ys8our legs.    kg

  Determine the CM of an outstretched arm u y 5hj 4uut1as i-g4/tu2c6wnyhd1 )t;tw, zlrsing 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 right ang:y ln8)2iz(ugusxs 4u/r(g*x(idsa l le. Assume that the person iuuzg(: lysni)rl (x u8s 4/da2x gs*i(s 155 cm tall. $X_{CM}$ =    cm $Y_{CM}$ =    cm

When a high jumper is in a position such7 .(7xf oomymj that his arms and legs are hanging vertically, and his trunk and head are horizontal, calculate how fm(.y 7fo7mxoj ar 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 Moo)w)msm j(p,kzn 4e 7wn)2ndfpn 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-kgxrkc ax :;d)g6j 3j)jr man stand 10.0 m apart on frictionless ice.
(a) How far from the woman is their CM?    m from the woman
(b) If each holds one end of a rope, and the man pulls on the rope so that he moves 2.5 m, how far from the woman will he be now?    m
(c) How far will the man have moved when he collides with the woman? He has moved    m from his original position

  A mallet consists of a uniform cylindrical heabf ztr( 3r69msd of mass 2.00 kg and a diameter 0.0800 m mounted on a uniform cylindrical handle of mass 0.500 kg and length 0.240 m, as shown in Fig. 7–42. If this mallet is tossed, spinning, into the air, how far above the bottom of the handle is the point thabtr( s3f9r6z mt will follow a parabolic trajectory?    cm

  A mallet consists of a uniform cylindrical head of mass 2.00 kg and a diameter :f- wka4srsa)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, intfa:s-s)w 4r kao 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 Exam asath.r*+id r);kz nh-8sh2ve gw()ople 7–14 (Fig. 7–29), $m_{II}$=3$m_{I}$ Where then would $m_{II}$ land?    d(Round to two decimal places)
(b) What if $m_{I}$=3$m_{II}$    d

A helium balloon and its gondo4,xqhypd ; ;r0ok+iso la, of mass M, are in the air 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 happens if xyqhk0o;d ip+o r;,4s the passenger stops?

  An 0.145-kg baseball pitched horizontally at strikes a bat and is poppqxwkm i +c5+c.r ql;+ied straight up to a height of 55.6 m. If the contact time is 1.4 ms, calculate the lixwiqm+c+cr;k+. 5q average force on the ball during the contact.    $^{\circ} $

  A rocket of mass m th 92y*sbfkl l3raveling 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 corn(,(o1,zq xwb5 9ra: rgi fnlloer pocket shot shown in Fig. 7–43. Relative dime bxiflqrzn:r ( w5,go9 ol(a1,nsions 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 pushinud3vqk21t2 x6k 4)hfcennv.q g off with his l 6nf c 2td2xuk.n1vve3h4kq)q egs 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 thgk;* crf+0b/a2qc2o 7 h+pqi/g oqcb ie other 80 kg, are initially at rest in outer space. They then push each other apart. How far apart are they when th/bqi/c h2 ob+7q+pg *oq;fgc2ik0rcae lighter astronaut has moved 12 m?    m

  A ball of mass m makes a head-on elastic collision with a second ball (aqw.e0-ebnv 0ajg1 tb6t rest) av1e 6jqnwg b0.0-baetnd rebounds in the opposite direction 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 cf ut4+ bvfhcamf..87s1t p3fw ourt 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 b.au3w.v18m ft tsc+p7ff4fb hefore 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 vertical yvj i5s+mg))u height 4.00 m. The ball hits four times on the way down, each time striking the horizontal part of a different step 1.0 m lower. If all collisions are perfectly elastic, what is the bouji)5ys)gmu v +nce 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 woe-zp)4h ,mxaz 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 be-4h)x m,az ezpcomes embedded in it?    m

  A 25-g bullet strikes and kk5 mtve+s 8.8d amk:zbecomes embedded in a 1.35-kg block of wood placed on a horizontal surface just in+.8m sk az:km5 tk8edv 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 bullet?    m/s

  Two people, one of mass 75 kg and the other of mass 60 kg, sit in a rowboat s h 4rrv*ajcwv3i-.c (of mass 80 kg. With the boat initially at rest, the two people, who have been sitting at opposite ends of the boat 3.2 m apart from each otvw(3-4j.sch*rv i acrher, 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 ab qrdof2w0q;vga 51yijzvoc(1:i.7 xrout $ 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 exprk)oj3a0 tskjmp+2x e (zhv ,/losion. One fragment acquires twice the kinetic energy of tz pjk ,02(k3o vtesrjha)+/mxhe other. What is the ratio of their masses?   

  The force on a bullet is given by the formula F = 580lmzg63t:; ehof1 x ,puvv86i7nbpz6h -( $1.8 \times10^{ 5}$t) over the time interval t=0 to t = $3.0 \times10^{-3 }$s In this formula, t is in seconds and F is in newtons.
(a) Plot a graph of F vs. t for t=0 to t=3.0ms
(b) Estimate, using graphical methods, the impulse given the bullet.    N*s
(c) If the bullet achieves a speed of 220m/s as a result of this impulse, given to it in the barrel of a gun, what must its mass be?    kg

  Two balls, of masses npjgbry0i,esjv 0d9fa. 1f.1$m_A$ = 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 radioactivl g+,mhxa9/wlap6qflrof4 vv8( b -4j ely into an alpha particle and a smaller nucleus. What will be 9 lr4 vxa/om, l+6q(8wfjvbh-pafgl4the 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 to)hnyn zqqty 0htvs 184) 9r/varget) 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 dl,uyo8wf,ek v: x 5xufm)b)yds-jw 95own 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 theml +hum :g.1v uo0i*na upper limit on mass m if it is to rebound from M, slide up the incline, stoia0nlmo: h.u1ugv *m +p, 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 7–47 showq3*aoqhfe5 z bsq 4-v;s the planet Saturn moving in the negative x direction at its orahfz* qveq3bqs4 - 5;obital 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