We claim that momentum is conserved, yet most moving objects eventually slow d.c .t 45 kpmj0-r3n utaasz2coown and stop. Explz5kaoa -c pr0tt34s.un cm.2jain.

When a person jumps from a tree to the ground, whal 7pw c0oop)+ddno0/n(go( a qt happens to the momentum of the person upon striking p)doq0d/ ( 7wnpon (oglca+o0the ground?

When you release an inflated but untied balloon, why does it fl8sb,sbv h,:. mds 9lyxy across the room?yh9,vm,b:8x ss sbdl.

It is said that in ancient times a rich man with a bag of gold coins froze t 1+1yfmfygdp 1o death while strdgff+ 1pyy11 manded on a frozen lake. Because the ice was frictionless, he could not push himself to shore. What could he have done to save himself had he not been so miserly?

How can a rocket change direction when it is far out i99-enxj tia1 8e denu;n space and is essentially in a9 1e8;je d9-xtaiunen vacuum?

According to Eq. 7–5, the longer the impact time of mwqs6 ,oyvg t*m(9d)yan impulse, the smaller the force can be for the same momentum change, and hence the smaller the deformation of the object on wog*9ts,wy 6) d(myqv mhich 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 witpic u c)jhtixs5si-q+ 6l)1 f7hstand collisions. Today, though, cars are designed to haj+c1xu 7s)i-i)q6 hfl5tsci pve “crumple zones” that collapse upon impact. What is the advantage of this new design?

Why can a batter hit a pitched basebipkc85 e8xj*un2 vz ugnk4c*/all further than a ball tossed in the air by the bgup5nzunx kjki4882v e/c** catter?

Is it possible for an object to receive a larger ndn;oq+h y(rpa ,))5jgv twd.impulse from a small force than fgdn +,r)vqa y; ). wj5tdh(opnrom a large force? Explain.

A light object and a heavy object have eo/3h5gzj + sph74ka.c rro/ ythe same kinetic energy. Which has the greater momentu5 3azopr hjyek/r g hs+7.4/ocm? Explain.

Describe a collision in which all axtmi 4mmevy96cm- c r j))2,ikinetic energy is lost.

At a hydroelectric power plant, water is directed at high speed m/ngg,xni1 c* against turbine blades on an axle that turns an electric generator. For maxim /,1n*c gixgmnum 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 atc+x 5n,rlzj i6xn,jme7y8 .jl xs26kl a 45 $^{\circ} $ angle as shown in Fig. 7–30. What is the direction (a) of the change in momentum of the ball, (b) of the force on the wall?

A Superball is dropped from a height h onto a hard steel plat00al jr7q* c s2j/kdufe (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 0c7/jjrldf2a*s0 ku qball and Earth as our system, during what parts of the process is momentum conserved? (c) Answer part (b) for a piece of putty that falls and sticks to the steel plate.

Why do you tend to lean backward when carrying a heavy load inwqrz5pq73 7nl;7nrr 0ft 1pr :nwmw(u your arms?

Why is the CM of a 1-m length of pc,uf( twr)c9z ipe at its mid-point, whereas this is not true for fwr cc)(t z9,uyour arm or leg?

Show on a diagram how your CM shifts whj srnqu7o/q6 ,gu kc76en you change from a lying position to a sitting positionu6rcgk7os7 u,q6qnj/ .

If only an external force can change the momenthg;*qywuuro1q;eqsx2 : ; -olum of the center of mass of an object, how can the internal force of an engine accelerate agq;-oeq 1*u;yr hu:xws 2oql; car?

A rocket following a parabolic path through the air suddenly explodesn23+azvzv2 -hefvik1 into many pieces. What can you say about the vf 2+vhkez1-a 3vni2z motion of this system of pieces?

  What is the magnitude of the momentum of a 28-g sparrow flyi49p dpza31h8eb8zz8z -y2gp zu wlg4c-fu : reng with a speed of 8.4 m/u44g18zgw8felu: zh3bez arpz -z9pc p28 -yds    $kg\;m/s$

  A constant friction force of 25 N acts on a 65-kg skier for 20 s. What is t,i1g ybdre.5 uhe skier’s cha,u e1d5grbi y.nge in velocity?    m/s

  A 0.145-kg baseball pitched at 39 m/s is hs.hjz/ 04pu2tsf s1jom 91q ytit on a horizontal line drive straight back toward the4uj. zpm9 j11ysts t/qfs02oh 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 thromwl ,,h w 9ukl+z/jjt1ws a 6.40-kg package 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 wl9l, z1tmjwuj+/ ,hk water resistance. The velocity of the boat is    m/s

  Calculate the force exerted on a rocket, given that-k s1xw:/mbwh the propelling gases are expelled at a ram:xw1 b-k/w shte 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 breakaw wm i( q*rx;a;qdp:5ceynuts 8 3q20sway for a touchdown is tackled from behind. When he was tackled by an 85-kg cornerback running at 5.5m/s in the same direction, what was their nq3a r y:cwq0;2xe5 tids *(msuwq ;p8mutual speed immediately after the tackle?    m/s

  A 12,600-kg railroad car td msp 14 zcv 2he,fnrylv+.9*dravels alone 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 new speed1+,c h .szln9*vr dyve4fdp m2?    m/s

  A 9300-kg boxcar traveling at 15m/s strikes a second bo tc3dh vmub6,rfa2 7,c +m 0v+csneuu4xcar at rest. The two stick together and movee, hr +va30u m+7cctcdnufms2ub 4v,6 off with a speed of 6m/s What is the mass of the second car?    m/s

  During a Chicago storm, winds can whip horizontally at speeds of 100km/h Ifhz-47j+w gymc the air strikes a person at the rate of 40kg/s per square meter and is brought to rescg y4z 7w+mhj-t, 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 speed:i/)p6ke1aq vnhkj d 0 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 ij)n0qev1pd/h:6 kakwith the tracks, what is the speed of the car after 90.0 min?$\approx$    m/s

  An atomic nucleus initially moving at 420m/s emiz rdymnv1 p9 7++.ojdets an alpha particle in the direction of its velocity, and the revrz91.p7d+ o+dejm y nmaining nucleus slows to 350m/s If the alpha particle has a mass of 4.0 u and the original nucleus has a mass of 222 u, what speed does the alpha particle have when it is emitted?    m/s

  A 23-g bullet traveling 230m/s penetrates a 2.0-kg blobsf9, -j dnw3sck of wood and emerges cleanly at 170m/s If the block is stationary on a frictionless surface when hit, how fast doeb-jss9nf ,3wd s it move after the bullet emerges?    m/s

  A 975-kg two-stage rocket is traveling at fi:e ,imba2.v a speed of $5.80\times10^3\mathrm{~m/s}$ with respect to Earth when a pre-designed explosion separates the rocket into two sections of equal mass that then move at a speed of $2.20\times10^3\mathrm{~m/s}$ relative to each other along the original line of motion. Let “A” represent the upper stage (that moves away faster) and “B” represent the lower stage.
(a) What are the speed and direction of each section (relative to Earth) after the explosion? $v'_A$   m/s  ----待选择----away from the Earthtowards the Earth  $v'_B$   m/s  ----待选择----away from the Earthtowards the Earth 
(b) How much energy was supplied by the explosion? [Hint: What is the change in KE as a result of the explosion? $a\times10^8$ a =    J

  A rocket of total mass 3180 kg is traveling in outer spaceu;:6gns 9rpu*1nq; +pixeri i with a velocity of 11:niu;*;n+ r es1riu6x pqgp9 i5m/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 a speed of 45m/s Theaz-g*l;2 8;gyivnib v zxz/ f) xqx7(m golf club wgx xgbn;l mqi/xf(zyiz2 z;)a*v- 87vas 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 vel8 qkll1n5m+o focity of 8.5m/s and comes to rest in a time interval of 8.0 ms. (a) What is the impulse given to the na 1flkm+nol5q8 il?    kg*m/s
(b) What is the average force acting on the nail?    N

  A tennis ball of mass m=0.06kg an,jho yv63p;f s6/uvz nx +csf4d speed 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 crashworthiness of new auto*i qh4.7thh t:v5pi zimobile models. Cars are tested by smashing them into fixed, massive barriers at 50km/h (30 mph). A new model of mass 1500 kg takes 0.15 s from the time of impact until it is brought to rest. (a) Calculate the average force exerted on the car by the barzhh: 7 .iv* tt5hqii4prier. $\approx$$a\times10^5$N a =   
(b) Calculate the average deceleration of the car.    m/$s^2$

  A 95-kg fullback is running at 4m/s to the east and is stopped in 07qaf45fwwjwyz i 4;*p .75 s by a head-o4w* ifw7z5y4 ; pwajqfn 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 tenni , kmyaq9a-(jo9 iqpajr9(h c;s ball (mass 0.060 kg) points in the +x direction and is given by the grapkoaj-cj 9(,a( iq9r9m;y hqaph 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 n;,x8ur.lq gf 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 position (that is, in breaking the fall). Assume8, q.gfrx;nul 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) wie, pe*cicaoz2l4 ga. oi0i)0z yv-5 afth a speed of collides head-on with a 0.220-kg ball at rest. Ila ciaae00zef ,o5z.2v) gii4 *-pcyof the collision is perfectly elastic, what will be the speed and direction of each ball after the collision?Let A represent the 0.440-kg ball, and B represent the 0.220-kg ball. $v'_A$    m/s  ----待选择----eastwest  $v'_B$    m/s  ----待选择----eastwest 

  A 0.450-kg ice puck, moving east with a speed of 3m/s has a w 7);j8w;;ps hl g +ewkm,fsnvhead-on collision with a 0.900-kg puck initially at rest. Assuming a perfectly elastic collision, what will ;; mesfp)+sw 8;j7h kngl,wvwbe the speed and direction of each object after the collision?Let A represent the 0.450-kg puck, and let B represent the 0.900-kg puck. v'$_A$ =    m/s ----待选择----eastwest  v'$_B$ =    m/s ----待选择----eastwest 

  Two billiard balls of equal mass undergo a perfv rfe0ld1*g1:zo g2 yzectly 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 directio:zfv dzl 10gyr1 e*g2on.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 with3if4 ggv 6 h,g1(kdye 2o q./zmziosl7 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 iz qg2mol4svh kg.7ey 1/z( i36fd ,og0.060-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 d xka6l2y,q-. 4ub hnskg that is moving with a speed of 8.5m/s collides head-on and elastica -dx2, sn4klyhauq6. blly with another ball initially at 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 amusemwnkwl f1x f470 m)sgzbyg * mte373ye+ent 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 s41lmb)f7 e73+ tnw w3yyx *egk 0mzfgcar B 550 kg, owing to differences in passenger mass. If car A approaches at 4.5m/s and car B is moving at 3.7m/s calculate
(a) their velocities after the collision v'$_A$ =    m/s v'$_B$ =    m/s
(b) the change in momentum of each.$\Delta p_{\mathrm{A}}$$\approx$    kg*m/s $\Delta p_{\mathrm{B}}$$\approx$    kg*m/s

  A 0.280-kg croquet ball makes an elastic head-on collision with di* q1tq36 jhaa second ball initially at rest. The second ball moves off with half the oriq63jh* dati 1qginal speed of the first ball.
(a) What is the mass of the second ball?    kg
(b) What fraction of the original kinetic energy $(\Delta\mathrm{kE/KE})$ gets transferred to the second ball?   

  In a physics lab, a cube slides down a frictionless76.iu:a mw;fv wbu0x n incline as shown in Fig. 7–35, and elastically strikes another cube at the bottom that is only onxwau.m vn;ib70wf :6ue-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 *5e47 t(ke0is oohrmw of 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 inqk(n0evia6 nsff(x, 0 a maximum height h of the pendulum equal to 2.6 cm. A second projectile causes the the pendulu(f fkqx06 (a0en,nvs im 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 buriegnc4*y2qkx fik*dm 2lu/d e94s itself in a 3.6-kg pendulum hanging on a 2.8-m-l k*kdug44yd eqx/f2 i9*mn2 clong string, which makes the pendulum swing upward in an arc. Determine the vertical and horizontal components of the pendulum’s displacement.vertical$\approx$    m horizontal =    m

(a) Derive a formula for the fraction o s.*tph jqt:0cf kinetic energy lost, $(\Delta\mathrm{KE/KE})$ for the ballistic pendulum collision of Example 7–10. (b) Evaluate for m=14g and M=380g

  An internal explosion breaks an object, initially at rest, into two pieces, onej )q0 +omk4bj/vsu4 ua of which has 1.5 times the mass of the other. If 7500 J were relev4qk/ joajus40+b um)ased 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 collil/dsvg*dv)6:r)2uxf ;y xw 2yo8tolf des into the rear end of a 2300-kg SUV stopped at a red light. The bumpers lock, the brakes are locked, and the two cars sk 2rv;)8du/g : o*lxxwystf ldfy26) ovid forward 2.8 m before stopping. The police officer, knowing that the coefficient of kinetic friction between tires and road is 0.80, calculates the speed of the sports car at impact. What was that speed?(Let A represent the sports car, and B represent the SUV) $\approx$    m/s

  A ball is dropped from a height of 1.50 m and rebounds to1s18f u0 ;p dfbxzo)dn a height of 1.20 m. Approximately how many rebounds will the ball make before losid1 1s;bu)fpo 0d xz8nfng 90% of its energy?   

A measure of inelasticity in aw wai3s3s uyq67b(vjequ.phng + -t4: head-on collision of two objects is the coefficient of rest3( wjgiq h3qsn a- u4ep.ytv+6w7: ubsitution, 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 ma;tudw-,i tdt.x6 ne 8m /ndv(5ddnp2nss of the other. A depression is made in both faces of the cut, so that a firec n6dnp2 wttn/dim tx v,d (u-den;d58.racker 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 colli094xgv.msyk n,7pvne i jy13odes head-on with a 10.0-kg object moving in the -x directioe3n, m.op ivng40y9ksj7xy1v n 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 rest decays into a second nucleus, an electron, a hr( 00sbigp7z,fznx pb40w(m nd a neutrino. The electron and neutrino are emitted at right angles and have momen( fzbrx4p07i,s0z nbh p0g wm(ta 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 m.3ak9a pudp g2ass $m_\mathrm{A}=0.400$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 object(b1agws( zay (s42+i wvvwwh: s of equal mass, each having initial speed the two move off together with speed v/3 What was the angle between their initial directions2:(vgswhsawyav 4i1 + (w(zb w?    $^{\circ} $

  Two billiard balls of equal mass move at righx;r au26 f+ dpdl)xw*tt angles and meet at the origin of an xy coordinate system. Ball A is moving upward along the y axis at 2m/s and ball B is moving to the right along the x axis with speed 3.7m/s After the collision, assumed el+*wr2u6p dfxxt)la ;dastic, 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 e(q8 t r8x;wa,wf+ncy8krlp;clw84rzfr3 x,v lastic collision with another atom at rest. w nz,8 rtxvwalfq+pk84 f(;;l,8rw3 cxry 8rcAfter 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

  A neon atom (m=20u) makes a perfectly elastic collision with anfxx;lovgkh4 ::x p (z;other atom at rest. After the impact,;l xokf:4p:zg (x ;xvh the neon atom travels away at a 55.6 $^{\circ} $ angle from its original direction and the unknown atom travels away at a -50 $^{\circ} $ angle. What is the mass (in u) of the unknown atom? [Hint: You can use the law of sines.](Let A represent the incoming neon atom, and B represent the target atom) $m_B$   u

  Find the center of mass of the three-mass system shown in Fig.r/ job y6ui2:u 7–38. Specify relative to the left-hand jio2uru/by :61.00-kg mass.    m

  The distance between a .i9 ce8mcwsfj :,wq6m v5bd3gcarbon 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 20wlsk8ztvf b3r/ y7:ff 6 dwspfe)v63.50 m behind the front of the car. How far from the front of the car will the CM be when two people sit in the front seat 2.80 m from the front of the car, and three people sit in the backwy3k:p/ wt 6f svf836fr)7v zelsfdb0 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 6807nsa v0m4ljt 1fw-)(vtlh+md0 kg, is used as a ferryboat. If three l)10 vdt+hf nmj7-vw(4atmls cars, each of mass 1200 kg, occupy its NE, SE, and SW corners, determine the CM of the loaded ferryboat.$X_{CM}$ =    m $Y_{CM}$ =    m

  Three cubes, of sides ,b6bqy8j:js) yi/j s vc.5ivt$l_0$,$2l_0$, 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 oeqs 3kzwjv.o9av ) f-sx5m()jf 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 pick up the load we5j )w3s q jaok9vm-zxfs.(v) ithout tipping it.$X_{CM}$ =    l $Y_{CM}$ =    l

  A uniform circular plate of radiud2 .i )rhdaza0s 2R has a circular hole of radius R cut out of it. The center of the s0dad hr )2ai.zmaller 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 plate? [Hint: Try subtraction.]   R

  Assume that your proportions are the same as those in Ta g(vcbujncc:6(zm7 l-ble 7–1, and calculate the mass ojul:7( 6ccvg- mbczn (f one of your legs.    kg

  Determine the CM of and+2 inacjj .r5 sr(6 lm ql0(b1zh,4cu jdeh:w outstretched arm using Table 7–1.   % of the person's height along the line from the shoulder to the hand

  Use Table 7–1 to calculate the position of the CM of an arm bent at a(h ii28s 8rgmmn;b0/i r oq/yp right angle. Assume that the person is m b/ipsqn0y8r(h ig/o8i rm2;155 cm tall. $X_{CM}$ =    cm $Y_{CM}$ =    cm

When a high jumper is in a position such that his armsr1 dv-b1smo ieemf4( 6 and legs are hanging vertically, and his trunk and head are horizontal, calculate how far below the torso’s median line the CM will bimb rd1sf4m (v-1ee o6e. Will this CM be outside the body? Use Table 7–1.

The masses of the Ear97dvu7x gvbgjr1z 81hth and Moon are $5.98\times10^{24}$kg and $7.35\times10^{22}$kg respectively, and their centers are separated by $3.84\times10^{8}$m (a) Where is the CM of this system located? (b) What can you say about the motion of the Earth–Moon system about the Sun, and of the Earth and Moon separately about the Sun?

  A 55-kg woman and an 80-kg man stand 10.0 jqr so3iyi(k;,l+ .w-gqpd( um apart on frictionless ice.
(a) How far from the woman is their CM?    m from the woman
(b) If each holds one end of a rope, and the man pulls on the rope so that he moves 2.5 m, how far from the woman will he be now?    m
(c) How far will the man have moved when he collides with the woman? He has moved    m from his original position

  A mallet consists of a uniform cylindrical head ofdvaug5 bt-(c bh3p.o5 mass 2.00 kg and a diameter 0.0800 m mounted on a uniform cylindrical handle of mass 0.500 kg and length 0p5g bdb c 5-o(u.3atvh.240 m, as shown in Fig. 7–42. If this mallet is tossed, spinning, into the air, how far above the bottom of the handle is the point that will follow a parabolic trajectory?    cm

  A mallet consists of a uniform cylindrical head of mass 2.00 kguavmt; i ;7a3l 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 that will follow a parabolic trajectol3;;mua iv7 atry?    d    d

  (a) Suppose that in Example ;(4rq feq*+kzfj)syk u0ho,r 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 gondola, of mass M, are in the a32*zkiiscwv4 (qu . vpir 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 balloons k4.qp zcvu2i w(*3vi then move? What happens if the passenger stops?

  An 0.145-kg baseball pitched horizontally at strikes qpf:2xknwht8 85jx 92xq+iwae4yot 1 a bat and is popped straight up to a hei jhfwk+q1itwx9xaqxn4 5y 8o8 tp2e2:ght 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 travelingwv3 -d449jbkg i6hjg2 v*tbat 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 q43 t)c ibr8rxlz1pcm* fl07sthe corner pocket shot shown in Fig. 7–43. Relative dimensions are also shown. Should the player be worried about this being a 3*c src7 l0 l4z8bxftim1qrp )“scratch shot,” in which the cue ball will also fall into a pocket? Give details.

  A 140-kg astronaut (including space suit) acquirescq y 80-p(6jcucmu sd. a speed of 2.5m/s by pushing off with his legs from an 1800-kg spaceqmcyp( du8-cc06 j.su 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 ,3p 5j..uwylg3 iroh yother 80 kg, are initially at rest in outer space. They then push each other apart. How far apart are they when thoywjrl.p5 u.y3g3,i he lighter astronaut has moved 12 m?    m

  A ball of mass m makes a head-on elastic collision with a second balw.j-1-84de nq zju kg0mrm 7;nng cxu*l*fr0il (at rest) and rebounds in the opposite direction withz ec nuu-rqj-*j1gn;0wmm8irl n .74x0dkf *g a speed equal to one-fourth its original speed. What is the mass of the second ball? $m_B$ =    $m_A$(Round to two decimal places)

  You have been hired as an expert witness in a court case involving an automeyq:p 1 ft3mp)obile 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 measured to be 0.60. Show that the driver of car A e1pm)t3qf y:p was exceeding the 55-mph (90km/h) speed limit before applying the brakes.    mi/h

A golf ball rolls ofmzsx5f83t jv-ndj1sasen8 t9 bt 9-9xf the top of a flight of concrete steps of total vertical 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 collision9e1xnj89 bstaf8-nt9 vjsxd z tsm3 -5s 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 intlrf,//efyljf;,1in bo a 1.40-kg block of wood at rest directly above it. If the bullet has a mass of 29.0 g and a speed of 510m/s how high will the block rise after the bullet bf nl/ib,l1,fr y/jf ;eecomes embedded in it?    m

  A 25-g bullet strikes and becomes embedded in a 1.35-kg block of wood4nkredk( ipl1is01c * 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 i4k1ieslnr0kd 1c(*p 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 of o 5 j xd+e-k3y(4lkfea;jpk- cmass 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 other, now exchange seats. How far and in what direction 3pe ; -o(5d j+lxyc afkj4-kkewill 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 abou-dwuikull,93zd/3fzxs1io 2ie3 i2 qt $ 1\times10^{ 8}$kg struck the Earth ($m_E$=$6 \times10^{ 24}$kg) with a speed of about 15km/s and came to rest in the Earth.
(a) What was the Earth’s recoil speed?    $ \times10^{-13 }$m/s
(b) What fraction of the meteor’s kinetic energy was transformed to kinetic energy of the Earth?    $ \times10^{ -17}$
(c) By how much did the Earth’s kinetic energy change as a result of this collision?    J

  An object at rest is suddenly broken apart into6; )*b6 gfefic um3 mneg ,br.:wqxvz; two fragments by an explosion. One fragment acquires twice the kinetic energy of the other. What is the ratio of their masses;eux;ff6zb:mg3c)nbev w mgqi* r,. 6?   

  The force on a bullet26lidz+dn k0gal5 1r 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 masses vp mnkh w y.2y8t+g.fv-r(r m6$m_A$ = 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 radioactivug2/; dhj0tj jely into an alpha particle and a smaller nucleus. What will be the speed of this recoih ;jd0utgjj2/ ling nucleus if the speed of the alpha particle is $ 3.8\times10^{5 }$m/s Assume the recoiling nucleus has a mass 57 times greater than that of the alpha particle.    m/s

  A 0.25-kg skeet (clay target) is firedvoo 6 fw+w)r6c4z* hq(l wabv- at an angle of 30 $^{\circ} $ to the horizon with a speed of 25m/s (Fig. 7–45). When it reaches the maximum height, it is hit from below by a 15-g pellet traveling vertically upward at a speed of 200m/s The pellet is embedded in the skeet.
(a) How much higher did the skeet go up?    m
(b) How much extra distance, $\Delta{x}$ does the skeet travel because of the collision? $\approx$   

  A block of mass m=2.2kg slides down a 30.0-) gc- nzeiha2v1ph 9jbz+3va $^{\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 t3c i494eh:czo8( yaslray0c mo rebound from M, slide up the incline, stop,mcy :ioy0czeahc43(94a s lr8 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 shoj;qra;i pp+ 9ews the planet Saturn moving in the negative x direction at its orbital speed (with respect to ;eipp9;a r+ jqthe 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