We claim that momentum is conserved, yetr 7pjw4f 24uk +5d7umjx+xu qh most moving objects eventually slow down and stop. Explain.wrph75d x u 7k2ujf4qxu+m 4+j

When a person jumps aum*o bp.kg5).sk*h4 wa. mrtfrom a tree to the ground, what happens to the momentum of the person ts*4w)mmk5o.gpr. *b .au hak upon striking the ground?

When you release an inq6 el,ezx ,gxudnr o+t; g*i20flated but untied balloon, why does it fly across the room?6; +o0,g,liexgt e z2*drx nqu

It is said that in ay.ruf)gm: :a kke (g(cncient times 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 could he have done to save himself had he ng k(.k:a(:fcm greu) yot been so miserly?

How can a rocket change direction when it is far out in space and is essentia79 -l* *c07qdafgfpd r+biwndlly in a 7+7pbd9d*-f r 0glia*dnq cwfvacuum?

According to Eq. 7–5, the ok)1 cw puq8avn77s 8prhjr-3longer 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 the value of air bags, which are intended to inflate during an automobile collision and reduce the possibility of fracture vu8h- kr)w7psj7 rc8 q1o3anpor death.

Cars used to be built as rigid as possible to withstand cole-7k kuzab a6d;a*e 9flisions. Today, though, cars are designed to have “crumple zones” that collapse upon impact. What is ;ake f a7*da6uzke9b-the advantage of this new design?

Why can a batter hit a pbt5orguq 7(*or6 c*gi s:. eacitched baseball further than a ball tossed in the air by thgo*q rosc6. * e:cau(tr7b5 gie batter?

Is it possible for an object to receive a larger impulse from a small f g5mu;cs1(tdyorce than from a large force? Explai1 (dg; ycsutm5n.

A light object and a heavy object have the same kinetic e sw/d;ro*t6 o9 ef1zb/w/jtibnergy. Which has the greater mj//s r/w owe 9ob6tt;z1d*i bfomentum? Explain.

Describe a collision in 0th fq20t q3 .ypzdht0which all kinetic energy is lost.

At a hydroelectric power plant, water is directed at high spaqnv rn0:x173jgx fcxb ,q2/2*v nrpweed against turbine blades on*xqrv71grc/ vpqx,bjn 0 a2 nx:nf 3w2 an axle that turns an electric generator. For maximum power generation, should the turbine blades be designed so that the water is brought to a dead stop, or so that the water rebounds?

A squash ball hits a wall at a azy ;l6t1,gwd45 $^{\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 h4,z)om p 1ktkz6js+go onto 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 process? (b) If we consider the ball ak6ot mks1 p4,)zjo+g znd Earth as our system, during what parts of the process is momentum conserved? (c) Answer part (b) for a piece of putty that falls and sticks to the steel plate.

Why do you tend to lean backward when carrying a hep i0(ani .3nivavy load in your arms?

Why is the CM of a 1-m length of pipe at its mid-point, whereas this is not c e,4ysu66ymotrue for yo6yseu,cmy6o4 ur arm or leg?

Show on a diagram how your CM shifts when you change 87aesr9 qzg-2ob0 ga wfrom a lying position to a sitting positio0gas zo28- wqeb9r7agn.

If only an external force can change the momentum of the c7anvvg/0v-zvj 6 c j,denter of mass of an objdvn jv6z jg/-0v7 ,cavect, how can the internal force of an engine accelerate a car?

A rocket following a parabolic path through the air smpim 2z 1 niy27-zbc-cuddenly explodes into many pieces. What can you say about the motion of th--z bipc1 7c n2iym2mzis system of pieces?

  What is the magnitude of thfyc.(apu/(+sw2 - *ppvaje hte momentum of a 28-g sparrow flying with a speed of 8.4 m/s sf2th*av. -j (puyp c /(+apwe   $kg\;m/s$

  A constant friction force of 25 N acts on a 65-kg skier for 20 s. What isvhd52: vasi9q3i7z rkd( 9mle the skier’s chald93vi(zaeh25 :r 7 isqk m9dvnge in velocity?    m/s

  A 0.145-kg baseball pitched at 39 m/s is hit on a horizontal line drive stu r k:g;wuhsa*z8hu. /raight back t.a uwuh:;*s r8 zhug/koward the pitcher at 52m/s If the contact time between bat and ball is $3\times10^{-3}$s calculate the average force between the ball and bat during contact.    N

  A child in a boat throws a 6.40-kg packard;5abg1: l opm x2ryal:)hv5ge out horizontally with a speed of 10 m/s Fig. below Calculate the velocity of the boat immediately after, assuming it was initially at rest. The mass of the child is 26.0 kg, and that of the boat is 45.0 kg. Ignore water resist:)a2 px:;lmb 5ry rv5glohd 1aance. The velocity of the boat is    m/s

  Calculate the force exerted on aj/txx(suo2 6 t rocket, given that the propelling gases are expel 2/ oju6xst(txled at a rate of 1500kg/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 breakaway for a toucolg;m/nq k ;/dhdown 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 immediately aq/;;lmkg o/dnfter the tackle?    m/s

  A 12,600-kg railroad car travels alone on alevel frictionless track wz :zqr,l)z1owith a constantz,1oz )w lz:qr speed of 18m/s A 5350-kg load,initially at rest, is dropped onto the car. What will be the car’s new speed?    m/s

  A 9300-kg boxcar traveling at 15m/s strikes a second boxcar at rest. The two sm0h1)p7myc w ptick together and move off with a speed of 6m/s What is the mass of the second carm1 p)mpc0h wy7?    m/s

  During a Chicago storm, winds can whip horiz o8v, t.n 5bg8kv4e:mmfqd3u uontally 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. A,b 4tn.ge dmuv5v :fmq88ouk3ssume 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 railroaq-3lf ; +thwshbe*(aa d car coasts along with a constant speed of 8.6m/s on a level track. Snow begins to fall v sl*ah;wt fq bea-(h3+ertically and fills the car at a rate of 3.5kg/min Ignoring friction with the tracks, what is the speed of the car after 90.0 min?$\approx$    m/s

  An atomic nucleus initially moving at 420m/s emits an alpha pnm7k4 j ;la/tdarticle 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 ; 4m/lndjkta7, what speed does the alpha particle have when it is emitted?    m/s

  A 23-g bullet traveling 230m/;wafo xyszb1 7 *oat,xwdu2 3/s penetrates a 2.0-kg block of wood and emerges cleanly at 170m/s If the block is stationary on a frictionless surface whodx uf*/t7,azyw b as ;o31w2xen hit, how fast does it move after the bullet emerges?    m/s

  A 975-kg two-stage rocket jp6sjh.*hmdxsdf6 p l( 2q.-1jf or6 his traveling at a speed of $5.80\times10^3\mathrm{~m/s}$ with respect to Earth when a pre-designed explosion separates the rocket into two sections of equal mass that then move at a speed of $2.20\times10^3\mathrm{~m/s}$ relative to each other along the original line of motion. Let “A” represent the upper stage (that moves away faster) and “B” represent the lower stage.
(a) What are the speed and direction of each section (relative to Earth) after the explosion? $v'_A$   m/s  ----待选择----away from the Earthtowards the Earth  $v'_B$   m/s  ----待选择----away from the Earthtowards the Earth 
(b) How much energy was supplied by the explosion? [Hint: What is the change in KE as a result of the explosion? $a\times10^8$ a =    J

  A rocket of total mass 3180 kg is traim ,x xad/q:0s/uo*2 qwrk d(iveling in outer space with a velocity of 115m/s To0rd2k/*q oqm xd(axw/isi: u, 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 teejvre* 1qmp0h 9 at a speed of 45m/s The golf club was i0q1ve9*jm ph rn 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, j0jmximdz m:lg;j 39 tw;4 h+oomk7f of 8.5m/s and comes to rest in a time interval of 8; hj7m+d,:k0zxtwl3jom ifm jm94og ;.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 stri .i, hejkgw61xan6l))fkx +tlkes 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 cgx3sfh;ng/t645 cfko rashworthiness 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 3 gt;4h/snkgx56ffcokg 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 4) 5kewyluzld +:k2m,wm/s to the east and is stopped in 0.75 s by a head-on tackle by a tackler run,l) u ykwlekm: dwz5+2ning 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 v08 owopl54u wa tennis ball (mass 0.060 kg) points in the +x direction and is given by the graph ol45wv uoow8p0 f 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 canl0- ylsxrz 56p a 75-kg person jump 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 positirlylx -sz5 06pon (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 mov z .blg/w4e6c56ypicc uc p(t,ing east (+x direction) with a speed of collides head-on with a 0.220-kg ball at rest. If the collision is perfectly elastic, what will be the speed and direction of each ball after the collision?Let A represent the 0.440-k ,c/6yc tpz56 (uiwg.4celpbcg 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, movmxnn+m d o3dmpakc -:. 2 qtukx3j470bing east with a speed of 3m/s has a head-on collision with a 0.900-kg puck initially at rest. Assuming a perfectly elastic collision, what will be the speed and direction of each object after the collision?Let A represent the 0.450-kg puck, and let B : u2cx30 mkx4 qkn.t3bjd7 +-pmdnma orepresent the 0.900-kg puck. v'$_A$ =    m/s ----待选择----eastwest  v'$_B$ =    m/s ----待选择----eastwest 

  Two billiard balls om phtc +wv./.3g:d jtbf equal 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 positwthmtbv d3c:.+j g/.p ive 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 head-on withx4aj,3 ,vrdrv 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,a4x,3v djvrr the collision?(Let A represent the 0.060-kg tennis ball, and let B represent the 0.090-kg ball.)v'$_A$ =    m/s v'$_B$ =    m/s

  A softball of mass 0.220 kg that is moving with x1+xlo.3fif*n q yf7ia speed of 8.5m/s collides head-on and elastically with another ball initially ato fl.7iix1 xfn+y qf3* rest. Afterward the incoming softball bounces backward with a speed of 3.7m/s Calculate
(a) the velocity of the target ball after the collision    m/s
(b) the mass of the target ball.    kg
(Let A represent the moving softball, and let B represent the ball initially at rest.)

  Two bumper cars in an amu zcg;fdqrs .*1sement park ride collide elastically as one approaches the other directly from the rear (Fig. 7–34). Car A has a mass of 450 kg and car B 550 kg, owing to differences in passenger mass. If car A approaches at 4.5m/s andc*fq s.gd;1r z 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 n17;:f ry4s9p sgeb-mcdews6second ball initially at rest. The second ball moves off with half the original speed of the first ball. ys g9rdfce 7sep b;4n6w1s: m-
(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 6f jmcrd-su-gre; k6.slides down a frictionless incline as shown in Fig. 7–35, and elastically 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 doeu j-dg6;- rrc.skfme6 s 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 dy49cwhwrlp 5e14s xe,p:bi /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 height h otx*5l,fqgn v.qi*0 sr f the pendun.,x q*lt*qsi 0fg5vrlum equal to 2.6 cm. A second projectile causes the the pendulum to swing twice as high, $h_2=5.2\mathrm{cm}$ The second projectile was how many times faster than the first? $v_1$ =    $v_2$ ([color=rgba(0, 0, 0, 0.85)]Round to three decimal places)

  A 28-g rifle bullet traveling 230m/su;1+kk d+mj xu buries itself in a 3.6-kg pendulum hanging on a 2.8-m-long string, which makes the pendulum swing upward in an arc. Determine the vertical and horizonkj1 ;+ +duxmuktal components of the pendulum’s displacement.vertical$\approx$    m horizontal =    m

(a) Derive a formula for the fraction of kinetic energyie3sk;q +c34puzz m u) 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 twpgb* x,zrqg x:rd;)3qc v(1 zxo pieces, one of which has 1.5 times the mass of the other. If 7500 J were released inx *, rgbx()v;:3 z1 rqdpzcgxq 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 end of a 2300-kg SUV stopped at acgv:skv 6 f0::rds3kk red light. The bumpers lock, the brakes are locked, ang:kvvd: rk k63f: 0scsd 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 z6bq-va1 9cfkand rebounds to a height of 1.20 m. Approximate9zq 61-v cabkfly how many rebounds will the ball make before losing 90% of its energy?   

A measure of inelasticity in a head-on collision of two 7(:*koiyl umao *qe -j7.ncch objects is the coefficient of restitution, e, definedi(jy 7oo*ean-cu:h c*qk 7l.m 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, o:aq0n4 /g1yzhno 0d pton0.6ju7h wkhne 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 reassemblezj0aohu 1dqthpwh0 ny4760k n . g:/nod 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 movin9a5 kmh)s7g 7xas-,t*umaane g in the +x direction at 5.5m/s collides head-on with a 10.0-kg object moving in the -x dia st9 sna-*) kaae7hgmm7u5 ,xrection at 4m/s Find the final velocity of each mass if:
(a) the objects stick together;   m/s
(b) the collision is elastic; v'$_A$ =    m/s v'$_B$ =    m/s
(c) the 15.0-kg object is at rest after the collision;   m/s ----待选择----not reasonable reasonable 
(d) the 10.0-kg object is at rest after the collision;   m/s ----待选择----not reasonable reasonable 
(e) the 15.0-kg object has a velocity of 4m/s in the -x direction after the collision. .   m/s ----待选择----not reasonable reasonable 
Are the results in (c), (d), and (e) “reasonable”? Explain
( Let A represent the 15.0-kg object, and let B represent the 10.0-kg object.)

  A radioactive nucleus at rew*xt ;- t 9do:fxh x3fmql/e(kst decays into a second nucleus, an electron, and a neutrino. The electron and neutrino are-w3xqx tt(m9fkx;/lod fh: *e 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 mass4q sh*1 ak rxr1x*oj0e $m_\mathrm{A}=0.400$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 biflck:k:8 gsn,6* xlo etween two objects of equal mass, each having initial speed the two move off togetherkn sf oill:*6:8g kc,x with speed v/3 What was the angle between their initial directions?    $^{\circ} $

  Two billiard balls of eq 5cv,; 5ist8g+bowxf9) c- alfuj0usbg3dgu, ual mass move at right angles and meet at the origin of an xy coordinate system. Ball A is moving upcv583;siag o+,-dcuu5g9)b 0 fts,l uwgjxbfward 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. 7–37). 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 collision with anof-m/2qs 9bts kther atom at rest. After the impact, the neon atom trtf/29 -qmsk sbavels 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 h1m0jc1y/:k; h x)jzx1aay enym hz;1 elastic collision with another atom at rest. After the impact, the neon atom travels away atm)ana10xe y :1cm khzj;/yhxy;1zhj1 a 55.6 $^{\circ} $ angle from its original direction and the unknown atom travels away at a -50 $^{\circ} $ angle. What is the mass (in u) of the unknown atom? [Hint: You can use the law of sines.](Let A represent the incoming neon atom, and B represent the target atom) $m_B$   u

  Find the center of mass of the three-mass system shown in Fi(jis+cov8s(k g. 7–38. Specify relative to the left-hand (jv8iokssc ( +1.00-kg mass.    m

  The distance between a carbon a uqax 4qvlmqs(* u-d90cxe- ,ltom ($m_{\mathrm{C}}=12\mathrm{u}$) 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 behinde(0;1 km(kecblit df+06v 3w:b+j njlwqvcg / the front of the car. How far from the front of the car will the CM be when two people sit in the front seat 2.80 m from the front of the car, and three people sit in the back seat 3.90 m from the front? Assume t6v0kw3(e b(icfn lb+q mcjw1d:vje / kgl+t0; hat each person has a mass of 70.0 kg.    m

  A square uniform raft, 18 m by 18 m, of ma) fhwc7.i8 y)2m oawihss 6800 kg, is used as a ferryboat. If three cars, each of mass 1200 kg, occupy its NE, SE, and SW corners, determine the CM of the loaded fer i) o.8i)hcmwf 2yw7ahryboat.$X_{CM}$ =    m $Y_{CM}$ =    m

  Three cubes, of sides avo8-a89 l,c1p+jtbf mn-g6ieqcr0 w a -/mev $l_0$,$2l_0$, 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 hassg)+feokh5-zn 7i ta;xmg8z : a load of identical cases of tomato paste (see Fig. 7–40), each of which is a cube of length l. Find the center of gravity in the horizontal plane, so that the crane operator can picge-7kh;sxio+t8z f5 )mz:gan k 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 ofoim/zri1 d+3 a 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 positi+zmo i di1ar/3on of the center of mass of the plate? [Hint: Try subtraction.]   R

  Assume that your proportions are the s 9l (fys+ 4yodd*kwc3kame as those in Table 7–1, and calculate the m sld4w 3fd yy(9+cko*kass of one of your legs.    kg

  Determine the CM of an outstretched armt p/ xue)v; zv tmb2os047pmz+ using Table 7–1.   % of the person's height along the line from the shoulder to the hand

  Use Table 7–1 to calculate the position ofcy 7 +;pbjtxcvbed1( * the CM of an arm bent at a right angle. Assume that the person y cpj +bev cbxd;*1t7(is 155 cm tall. $X_{CM}$ =    cm $Y_{CM}$ =    cm

When a high jumper is in a position such that his arms and legs are hanging vert:uc d29( oboy,ucyq / qen3ii2ically, and his trunk and head are horizontal, calculate how far belob9un :o (yic,i2 eud32cyoqq/ w 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 pa4bg c-1tk7 f$5.98\times10^{24}$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 apap gdhws 5qikg83ez* i(ix)m 9(rt 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 kgy ec(aoyc4 cf/*6jm *fjsig; 1 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, spijc; / 4*com(1s*jf 6c egyafiynning, 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 uni cvny3 y;0hnjb*b,wi +form 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 y+,0n3bicnwb* y v;hjin 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?    d    d

  (a) Suppose that in Example 7–14 p zl8 n5 p5:u6ey+0objl6czam (Fig. 7–29), $m_{II}$=3$m_{I}$ Where then would $m_{II}$ land?    d(Round to two decimal places)
(b) What if $m_{I}$=3$m_{II}$    d

A helium balloon and its gondola, of mass M, are in the air and stationaryn:nnafxlg) )dfpm ,5a* 3umi0 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 the passengam ,f5pfm nx0:un l3ni)ad*)ger stops?

  An 0.145-kg baseball pitche2l x;u; qzf3 3g,v23opaexxt 7 w3yzcbd horizontally at strikes a bat and is popped strai;cu7a3xo vzfxgteqp23 xwlbz33 ,2 y; ght up to a height of 55.6 m. If the contact time is 1.4 ms, calculate the average force on the ball during the contact.    $^{\circ} $

  A rocket of mass m to3k3 a -lyqi ,8h8nachraveling with speed $v_0$ along the x axis suddenly shoots out fuel, equal to one-third of its mass, parallel to the y axis (perpendicular to the rocket as seen from the ground) with speed 2$v_0$ Give the components of the final velocity of the rocket.$P_x$: v'$_x$=    $v_0$
$P_y$: v'$_y$=    $v_0$

A novice pool player is faced with the corner pocket shot shown in Fig. 7-aaw :x1m m y1/ 7yhwo+hmp*dwh; ;jwz–43. Relative dimensions are also shown. Should the player be worried about th m+1dwo*jm/wxp -;h ya7wwh1az y:m h;is being a “scratch shot,” in which the cue ball will also fall into a pocket? Give details.

  A 140-kg astronaut (ikd)fqx8b t +8bncluding space suit) acquires a speed of 2.5m/s by pushing off with his lx 8k) 8bd+qftbegs 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, arefcb r yxzkh.69mb7n48 initially at rest in outer space. They then push each other apart. How far apart are they when th nfkbzy78 4m.h9rbc6xe lighter astronaut has moved 12 m?    m

  A ball of mass m makes a head-on elastic collision with a second ball (atl+/-shwn 8xlhnvm,y-l4 f e y4 rest) and rebounds in the opposite direction with a speed equal to one-fourth its v helw+y-4,sn xy/fh n4-l 8lmoriginal 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 invo vp.2tfjq1 ci;lving an automobile accident. The accident involved car A of mass 1900 kg which crashed into stationary car B of mass 1100 kg. The driver of car A applied his brakes 15 m before he crashed into car B. After the collision, car A slid 18 m while car B slid 30 m. The coefficient of kinetic friction between the locked wheels and the road was measuredjq.v1cp; fit 2 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 ste2xkzqr i7k8*9ns w;zj oja- 6dps of total vertical height 4.00 m. The ball hits four times on the way down, each time striking the xn 6 ;za zw ki-7o9r28ksjqdj*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 blqiw+xludi + -9ock of wood at rest directly above it. If the bullet+ xd wq+iu9il- has a mass of 29.0 g and a speed of 510m/s how high will the block rise after the bullet becomes embedded in it?    m

  A 25-g bullet strikes and becomes embedded in a 1.35-kg blhnf 09;sn d;tjock of wood placed on a horizontal surface just in front of the gun. If the coefficient of kinetic frictioj0;t f9 nndh;sn 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 mas/qu thwcc::a x0i*vouvebu98 *0a5pt s 60 kg, sit in a rowboat of mass 80 kg. With :/w5eh 0ub *auo*xviqcpttc89 avu0: the boat initially at rest, the two people, who have been sitting at opposite ends of the boat 3.2 m apart from each other, now exchange seats. How far and in what direction will the boat move? The boat will move    towards the initial position of the 75 kg person(Round to two decimal places)

  A meteor whose mass igieon,( 2iz0bc acytpp68j96d( aj;was about $ 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 sudden7e58 qekki4j xly broken apart into two fragments by an explosion. One fix5k e 84q7jekragment acquires twice the kinetic energy of the other. What is the ratio of their masses?   

  The force on a bullenav*nqd9v+-v :7vlfjh m*kz+ t 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 massesc.zxq2dxs,5 atum;fy:q +*/s e ,vjeq $m_A$ = 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 atoe g auz*t:u38 rest decays radioactively into an alpha particle and a smaller nucleus. What will be the speed of this recoiling nucleus if the speed of tz*ogut38 : euahe alpha particle is $ 3.8\times10^{5 }$m/s Assume the recoiling nucleus has a mass 57 times greater than that of the alpha particle.    m/s

  A 0.25-kg skeet (clay target) is fired at anwtys*j2h 6 mps+t+-f m 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 downm*q4 de2kt9c9t5 ,nvq5zlfop 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. 7–4z j6 25,qt0d(yorqcqp5fderj n84 /km6), what is the upper limit on mass m if it is to rebound from M, slide up the incline, stop, slidt( ej qmfddry c/o qjzp4q05,2 85kn6re down the incline, and collide with M again?    kg (Let A represent mass m, and B represent mass M.)

  The gravitational slingshot effect aju-i )g.yd 8pohv3 fw7f wfy+4739b pilf3gx. Figure 7–47 shows the planet Saturn moving in the negatiwd+gf8 bpfyjh3 9 7.i34folvfa -7 gx uwp)iy3ve 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