We claim that momentum is conserved, yet mo+ bpext.p+b1k st moving objects eventually slow down and sto + t.bek1bp+pxp. Explain.

When a person jumps from a tree to the ground, what happkq oe ,h2(s*zpens to the momentum of the person upon strikinq(koze ,hs* p2g the ground?

When you release an inflated but untied balloon, why does it fly across the du9mk2xquv : 3roomm9u 2qvx:uk3 d?

It is said that in ancient tsi o;mh bk 5fpva1o xb)(mgc+c4s*.d-5mp0 ksimes a rich man with a bag of gold coins froze to death while stranded on a frozen lake. Because the ichm kgsp;ixbs. cm4 v- 5d )o0 kamc+p1bf5*o(se 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 fpizj:6xp:- l kar out in space and is essentially in a k ip-:: ljpxz6vacuum?

According to Eq. 7–5, the longer the impact time o /6 i: cxq(hf(per)z iid;qi s3;mwu3zf an impulse, the smaller the force u(f x6qi;hi)zmzr3pi w; q (ies :cd3/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 or death.

Cars used to be built as rigid as possible to withstand collisions. Todavcx igl+2xh0u1 3/+ig yb-lzzy, though, cars are designed to have “c h-cg+3vl lx1 zuzyi2+i/xgb0rumple zones” that collapse upon impact. What is the advantage of this new design?

Why can a batter hit a pitched baseball further than a ball tossed in th) uqv)v9)/95zml 0dtna1uyletm q; uze air by the dua5 m)y1)zqt9)luv;/qmt0 uzn l9vebatter?

Is it possible for an object to receive a larg. jfifh,r2g/ yer impulse from a small force than from a large force? Ex /,fryji2g f.hplain.

A light object and a heavy object have the same kinee;5)dtjaf7 6 n elw,gwtic energy. Which has the greater momentunj6egew5fl )a,;7wtdm? Explain.

Describe a collision in w3 em3pov)jzfx g65ei/ w;pl-n hich all kinetic energy is lost.

At a hydroelectric power plant, 1jczdply1p0*(hqgz/1hb so ; 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 g1 1j/qdhhlc1pb0y*oz;sz( p, or so that the water rebounds?

A squash ball hits a wall at l 3 cx9.2vpessdg18 fw/str 5ga 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 a9b) z+ a8pdddxh97 wo 4*o9 w0s wskfs2om3pksteel 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 and Earth as our system, during what parts of the process is momentum conserved? (c) Answer part (b) for a piecwpd s* os k8 9f)mw+z4h9s k2b9d 3xodpa7a0owe of putty that falls and sticks to the steel plate.

Why do you tend to lean backward when carrying,6j;zs l 7m.rq;azoxs a heavy load in your arms?

Why is the CM of a 1-m length 6yim.cb3oj:io r ag74 of pipe at its mid-point, whereas this is not true for c4 :b3o7ajy.gr m6oiiyour arm or leg?

Show on a diagram how your CM shifts when you change9.jnf ob,i .oz from a lying position to a sitting position i.bj.f,z n9oo.

If only an external force can c8,vh pyhbx8-*q,a utz hange the momentum of the center of mass of an object, how can the internal force of aba8 ,zh8ytq v* pxu,-hn engine accelerate a car?

A rocket following a parabolic path through the air suddenly explodes intrjoxx ,r4u,a bg+ 4zw+o many pieces. What can you say about the motion 4rzb++axx 4rgj,w u,o of this system of pieces?

  What is the magnitude of the momentum vh tjm+g9/,u)qdn qledz1/ oy0:o7 ho 1t)kqwof a 28-g sparrow flying with a speed of 8.4 m/1+70) d /otqu ,my 9njtzhlkqvh:e)ooqg1d/ws    $kg\;m/s$

  A constant friction force ofu( + 6uqhblh /j4udrl g8x8*to 25 N acts on a 65-kg skier for 20 s. What is the skier’s change in ve/ho uh*d8u6t(4 b+jxq8grlullocity?    m/s

  A 0.145-kg baseball pitched at 39 m/s is hitz)j(/g gi sl7sh7pa -aa -;hhu7vjsm2 on a horizontal line drive straight back toward the pitcher at 52m/s If the contact time between b 2)i s az sjsa-;7hm/7hlgua(g-jhv p7at 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 horizon d8vm z0w77gkx1wk zh7tally with a speed of 10 m/s Fig. belowdgmvz0zkh w7k7 w 78x1 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 resistance. The velocity of the boat is    m/s

  Calculate the force exerted on a rocket, givenntlq:v yg,(ku8/h z1 e that the propelling gases are expelled at a rate of 1500kg/s wv8uq1 g /(t,ykh:ez nlith 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 toucry);fi(pfjio8 l. p s(hdown is tackled from behind. When he was tackled by an 85-kg cornerback running ati)f( ;sy.j( fprl8pio 5.5m/s in the same direction, what was their mutual speed immediately after the tackle?    m/s

  A 12,600-kg railroad car travels alone onq*ym,yv me.d0c ttfa7:4 gf n: alevel frictionless track with a constant speed of 18m/s A 5350-kg load,initially at rest, is drom q,tna4my0f* e f7d:gc:vt .ypped onto the car. What will be the car’s new speed?    m/s

  A 9300-kg boxcar traveling at 15m/s strikes a seconn+gcq+lfi*7u c 8j :fkd boxcar at rest. The two stick together and move off with aifu8f*n+c 7lgk+:jqc 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 y+em(,pj 5m 8,lypw5izofc7s/h If the air strikes a person at the rate of 40kg/s per square meter and is brought to rest, estimate the force of the wind on a person. Assume the p8ez,(oyc+ym p5 pf5ji7swl,m erson 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 coast8a*s +n 0ijibas along with a constant speed of 8.6m/s on a level track. Snow begins to fall vertically and fills theban+ii0j *8a s 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 movie s)54-b+xxnqhmf vj qi 5-2pji4 t;xjng at 420m/s emits an alpha particle in the direction of its velocity, and the remaining h)4-5ji; 2vtx5eq j b+f-nmxqj i4psx 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 penete09 l dxamak u3:kp8r;rr r5e7rates a 2.0-kg block of wood and emerges cleanly at 170m/s If the block is stationary on a frictionless surface when hit, how fast does it move ;rdk9 kx8el05prma rar73u e: after the bullet emerges?    m/s

  A 975-kg two-stage rocket is traveling at a speed gkron+qw.n;(o:h8mc g,zi7j 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 space with a veloczv/ xy.h r*q1city of 115m/xqr1 *h/y.zv cs 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 The golf 5)rohigjo.v7 club was in contact with 5 g7ovh .oijr)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 jg ;y4pcw(;4ogppl 6cvelocity of 8.5m/s and comes to rest in a time interval of 8.0 ms. (al6pcw jo;;cy p4( 4pgg) 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 striwgapfy: /b 13ekes 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 crashwomtr f.h-gsjnf cd76/+.srb2p rthiness of new automobile models. Cars are tested by smashing them into fixed, massivegm.p7rtrcjb+2hf d6 f sn/-.s 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 barrier. $\approx$$a\times10^5$N a =   
(b) Calculate the average deceleration of the car.    m/$s^2$

  A 95-kg fullback is running at 4m/s to the east and is stopped in 0.75 s by/.t*- flhctzb a head-on tackle by a tackler running due west. Ccbtz t *hlf/-.alculate
(a) the original momentum of the fullback    kg*m/s
(b) the impulse exerted on the fullback    kg*m/s
(c) the impulse exerted on the tackler,    kg*m/s
(d) the average force exerted on the tackler.    N

  Suppose the force acting on a tennis ball2no .r*ruwnka4:cu7 v (mass 0.060 kg) points in the +x direction and is given by the graph oow 4 *c .au27nnvr:kruf Fig. 7–33 as a function of time. Use graphical methods to estimate
(a) the total impulse given the ball    N*s
(b) the velocity of the ball after being struck, assuming the ball is being served so it is nearly at rest initially.    m/s

  From what maximum height can a 75-kg person jum91g me3q9p) q-h+ xhg+sp 4ajs+eqjhkp without breaking the lower leg b1h 9hjm+ aeq+gqe-sgqs 9 k3jh4p +p)xone 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 per unit area) of bone is $170\times10^6\mathrm{~N/m^2}$ and its smallest cross-sectional area is $2.5\times10^{-4}m^2$ [Hint: Do not try this experimentally.]    m

  A ball of mass 0.440 kg moving east (+x direction) with a speed of colwv mq21gd 4(gblides head-on with a 0.220-kg ball a2gdmbqw4v1 g (t rest. If the collision is perfectly elastic, what will be the speed and direction of each ball after the collision?Let A represent the 0.440-kg ball, and B represent the 0.220-kg ball. $v'_A$    m/s  ----待选择----eastwest  $v'_B$    m/s  ----待选择----eastwest 

  A 0.450-kg ice puck, moving east with a speed of 3m/s has dfq(hgrh(;l 2 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 repres(dlr 2gf( ;qhhent 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 mass9+z zp 93*9mczxok mqa(h 4x,hztfpw9.ewmf0 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 thefz+0mf9 z9pt,wmmeqox* xhw. ahz 39p c(94zk ball moving at 2.00 m/s, and call that direction the positive direction.Let B represent the ball moving at 3.00 m/s in the opposite direction. ) v'$_A$ =    m/s v'$_B$ =    m/s

  A 0.060-kg tennis ball, moving with a speed of 2.5m/s collides heq el-*bkj.j0dmvvh5xx -:v:s ad-on with a 0.090-kg ball initially moving away from it at a speed of 1.15m/s Assuming a perfectly elastic collision, what are the speed and direction of each ball after the collision?(Let A represent the 0.060-kg tennis j5dskjv :v0*-m -.qlx:v bxehball, 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 wi0kk 3hf-hl,moke,y 9uiyjo3(th a speed of 8.5m/s collides head-on and elastically with another ball initially at rest. Afterward the incoming sok k(hfh,om,9oyy3 3ei j -k0luftball 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 amuse6zh lt8)8e eldment park ride collide elastically as one approaches the other directly from the rear (Fi8zd) 6eh tlel8g. 7–34). Car A has a mass of 450 kg and car B 550 kg, owing to differences in passenger mass. If car A approaches at 4.5m/s and car B is moving at 3.7m/s calculate
(a) their velocities after the collision v'$_A$ =    m/s v'$_B$ =    m/s
(b) the change in momentum of each.$\Delta p_{\mathrm{A}}$$\approx$    kg*m/s $\Delta p_{\mathrm{B}}$$\approx$    kg*m/s

  A 0.280-kg croquet ball m; l 1yo4knfp6ef no7.makes an elastic head-on collision with a second ball initially at rest. The second ball moves off with half the original speed of .e;n6fln o7o4y m1fpkthe first ball.
(a) What is the mass of the second ball?    kg
(b) What fraction of the original kinetic energy $(\Delta\mathrm{kE/KE})$ gets transferred to the second ball?   

  In a physics lab, a cube slides down a frictionless incdb2x5m 8kgv6yc3h 2i iline 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 o5dkhiymvb cxg i32628 ff 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 h m1);zmyn we(ydmajv 4fz)t/72 4ppian 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 omu2- 77o::4io ipr5 -ygosdg b- jjqfgf the pendulum equal to 2.6 cm. A second projectile causes the the pendulum to swing ti:2fdb5i:--so jp- 7oqygum r g7gjo4wice 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-pc qj4 nwch)v9;-m b qgs+iv,43.j vuxkg pendulum hanging on a 2.8-m-long string, which makes the pendulum swing upward in an arc. Determine the verq3 .s4i v,9njjgc p4v mhc-xu)b+v qw;tical and horizontal components of the pendulum’s displacement.vertical$\approx$    m horizontal =    m

(a) Derive a formula for the fraction oa.f hyu9-vfxk9t ;,etnbq8c ,/o+ wck f 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 twotcj*zlf a:148k iva 5 -r5olsz 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 B repr*5fc-5:klslt4irza a8z1 o vj esent the lighter particle. ) KE'$_A$ =    J KE$_B$ =    J

  A 920-kg sports car collides w coxq02c-6u: uph 9qbinto the rear end of a 2300-kg SUV stopped at a red light. The bumpers lock, the brakes are locked, and the two cars skid forward 2.8 m before stopping9co2u qc6bp-qhxu 0w:. 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 to a height of 1.20 m. Apu,r 1b,(ybucgc 1ug,(bbu,ry proximately how many rebounds will the ball make before losing 90% of its energy?   

A measure of inelasticity in a d7 l**v ugpxf1 4x9cejhead-on collision of two objects is the coefficient of restitution, g7cvxxd 4pl*uf1e*j9e, 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 piecescsip1n8,9 za vgvctf+m1z s61, one with three times the mass of the other. A depression is made in both faces of the cut, so that a firecracker can be placed in it with the block reassembled. The rm8f ztc6a 1vzi1v1css gn, +9peassembled 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 th*h6.bix f f:c/ao,9u6xmksj me +x direction at 5.5m/s collides head-on with a 10.0-kg object moving in the -x direction aom:xaufsj/6 x c i,.b km*f96ht 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, ank ( 1nfyo +6sm-f01iymy -i/icp0adfvd a neutri+1kvd/n0i-oyyc (0f- s y mfi6a fmp1ino. 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 m.*;emg pms2s7q c vf,fass $m_\mathrm{A}=0.400$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, ejv(/ap)ga jsms +90vbzc z k94ach having initial speed the two move off together with speed v/3 What was the angle between their inija4jk( 9a9 v)+mg bcz/zvs0sptial directions?    $^{\circ} $

  Two billiard balls of equal mass move at right angles and mee toz ij9:gx p/grgrg7o5 q,+:et at the origin of an xy coordinate system. Ball A is moving ugoi7gror q ggz/j et9,x+p5::pward 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 another atom a pvqx0 c0j1stgm;3h o9t rest. After the impaj hc0oqmg 0px913 ;vtsct, 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 per;0 awirlad m15fectly elastic collision with another atom at rest. After the impact, the neon atom travels away ;1i5lw d mra0aat 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. 7–38.98 py3mryq sza/sq+u 4bfyn;+ a3klt- Specify relative to the left-hand 1.00-kg m ;ym 34f8 rk+zlustqynaaqp3s+9by/- ass.    m

  The distance between a carbon atom x bdi/sr x 1m05zld03z($m_{\mathrm{C}}=12\mathrm{u}$) and an oxygen atom ($m_{\mathrm{O}}=16\mathrm{u}$) in the CO molecule is $1.13\times10^{-10}$m How far from the carbon atom is the center of mass of the molecule?    $\times10^{-11}$m

  The CM of an empty 1050-kg car is 2.50 m behind the front of the car. How far fr r13zm1 kc,pi)fwr. alom 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? i,1f)rw1. zpl mckar3 Assume that each person has a mass of 70.0 kg.    m

  A square uniform raft, 18 m by 18 m, of mass 2) idt(ydv5sera1jf4 o7/wx e6800 kg, is used as a ferryboat. If three cars, each of mass 1200 kg, occupy its NE, SE, and SW corners, determine the CM of54jxeareof7( /1 wsiy2tv)d d the loaded ferryboat.$X_{CM}$ =    m $Y_{CM}$ =    m

  Three cubes, of sides ,a1wpmw e guzhv/s 65($l_0$,$2l_0$, and $3l_0$ are placed next to one another (in contact) with their centers along a straight line and the $l=2l_{0}$ cube in the center (Fig. 7–39). What is the position, along this line, of the CM of this system? Assume the cubes are made of the same uniform material. $X_{CM}$ =    $l_0$ from the  ----待选择----leftright  edge of the smallest cube

  A (lightweight) pallet has a load of identical cases of tomato paste (see Fig. 7wd2f8qb- 5rydpe-9 un xsau;:–40), each of which is a cube opde5anyu 9wu xd2;8qfrb :-s- f length l. Find the center of gravity in the horizontal plane, so that the crane operator can pick up the load without tipping it.$X_{CM}$ =    l $Y_{CM}$ =    l

  A uniform circular plate of radius 2R has a cirhu (mlsxgs y4r6d5s,bf j:8 ;s mud(z.cular hole of radius R cut out of d xu;sf(,ldh(m4:m rj6u sbyz.58s sg it. The center of the smaller circle is a distance 0.80R from the center C of the larger circle, Fig. 7–41. What is the position of the center of mass of the plate? [Hint: Try subtraction.]   R

  Assume that your proportt .s5ym3k ly5 lm +bbe,teg7r1ions are the same as those in Table 7–1, and calculate the mag,e13k bm l+s7ym t5b.lyr5e tss of one of your legs.    kg

  Determine the CM of an outstretchc.4 fns3e n dm1rdc.3)pbt3ebed 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 ;e.lj*g vjq+qd5x3mp the position of the CM of an arm bent at a right angle. Assume that the ;*+3 l5v.xdmgq j jeqpperson is 155 cm tall. $X_{CM}$ =    cm $Y_{CM}$ =    cm

When a high jumper is in a position such that his arms an:w iy1i -tpm10kstu+ id legs are hanging vertically, and his trunk and head are horizontal, calculate how far below the torso’s mep 0it+mt iu1i:kys1w- dian line the CM will be. Will this CM be outside the body? Use Table 7–1.

The masses of the Ea3eamj0tktb0m1v1 4p f rth 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 m apart on frictionleeq d54 yar26wk vvg25rp5vgn+ss 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 cyo( if+c/mn:hwt- ubb9 ot5k f0lindrical head of mass 2.00 kg and a diameter 0.0800 m mounted on a uniform cylindrical handle of mass 0.500 kg and length 0.240 m, as shown in Fig. 7–42. If this mallet is tossed, spinning, into the air, how far above the bottom of the handle is the poi hn :5(f/-i0bkbo9ufowt mtc+nt that will follow a parabolic trajectory?    cm

  A mallet consists of a uniform cylindrical head of mass 2.00 kg and yrevytx:x1fx3 c+9km6tr )9e a diameter 0.0800 m mounted on a uniform cylink1rxy)3x:v9 tmt6 r+9cx e yefdrical 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 trajectory?    d    d

  (a) Suppose that in Example 7–14 (Fiqnb593mb 91qzvop b5ng. 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 stat.ck(c .y( 0v p, nrzj0inww5awionary with respect to the ground. A passenger, of mass m, then climbs out and slides down a rope with 0. v.c,kaw(nnwc0z ywp5(r i jspeed measured with respect to the balloon. With what speed and direction (relative to Earth) does the balloon then move? What happens if the passenger stops?

  An 0.145-kg baseball pr+5hl cx7wj 3ditched horizontally at strikes a bat and is popped straight up to a height of 55.6 m. If the contact time is 1.4 ms, calculate the average force on the ball during the colc3 hdrjw x7+5ntact.    $^{\circ} $

  A rocket of mass m tqr/mkalto0o 6t,n 0t -l :a9hvraveling 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 f xht: )k3pfu)y :7ww*i5df5w(lcndl maced with the corner pocket shot shown in Fig. 7–43. Relative dimensions are also shown. Should the player be worried about this being a “scratch shot,” in which the cue ball will also fall into3 55(:xlw tww)fh d)uf*l:knicpy7 dm a pocket? Give details.

  A 140-kg astronaut (n+)+icyt;cd4 cf v.r7/jvjwpincluding space suit) acquires a speed of 2.5m/s by pushing off with his legs pw nc4 +c djf+ r/v7cy)tjiv;.from an 1800-kg space capsule.
(a) What is the change in speed of the space capsule?    m/s
(b) If the push lasts 0.40 s, what is the average force exerted on the astronaut by the space capsule? As the reference frame, use the position of the space capsule before the push.    N

  Two astronauts, one of mass 60 kg and the other 80 kg, are initiall u19r:n 0p xobwepz14ny at rest in outer space. They then push each other apart. How far apart are they when ther :x0 wun4epnzo 9b11p lighter astronaut has moved 12 m?    m

  A ball of mass m makes a head-on elastic collision with a u5 44qq sasz2psecond ball (at rest) and rebounds in the opposite direction with a speed equal to one-fourth its original speed. Whqp2 4zq5u4 sasat 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 involv 2q3ouy07qzm-zn zv/vte2 (wuing an automobile accident. The accident involved car A of mass 1900 kg which crashed into stationary car B of mass 110vtw7 q(oe2v q3/ u0-m2yuzzz n0 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 was exceeding the 55-mph (90km/h) speed limit before applying the brakes.    mi/h

A golf ball rolls off the a( sja0 -oinln9.er7e top of a flight of concrete steps of total vertical height 4.00 m. The ball hits four times on the way downnas.n0a(7ej-ie olr9 , each time striking the horizontal part of a different step 1.0 m lower. If all collisions are perfectly elastic, what is the bounce height on the fourth bounce when the ball reaches the bottom of the stairs?

  A bullet is fired vertically into a 1.40-kg block of wood at rest d-1vgt 5miahq /5lx0bs irectly above it. If the bullet tqv 0gm55- bila1/hxs 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 strikesodj8ti526 tt(y 5ro q.hef (jc and becomes embedded in a 1.35-kg block of wood placed on a horizontal surface just in front of the gun. If the coefficient of kinetic friction between the block and the surface is 0.25, and the impact drives the block a distance of 9.5 m before it comes to res c6 5o2(ery o5(htq.tijf8 jdtt, 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 (8ycb 9yznycb k2;kw3 in a rowboat of mass 80 kg. With the boat initially at rest, the two people, who have been sitting at opposite ends of the boat 3.2 m apart from each other, noy( yw c;932cz bkbykn8w 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 vp*m/ qnj*ifpa97hv) w3 9rlkwas 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 suddenly broken apart into twu;: h kj:lq(zgo fragments by an explosion. One fragmejkuzqh; (l::gnt acquires twice the kinetic energy of the other. What is the ratio of their masses?   

  The force on a bullet is given by the formula py3wr2 p tcx1.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 massessbd7sscz6 * y +(ni6yeu n*j0j $m_A$ = 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 radioactively into an alpha particle and a srv( bh4 f3aj) kvj3o+dmaller nucleus. Whav3bf+(k4j )r ajhd3o vt will be the 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 target) is fired at an angle 27ogvpev+s2a w7 za(t2 c scrx(c 7u*eof 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.k3mkm* p)a4cfvio9 v bvl- 3e/0 $^{\circ} $ incline which is 3.60 m high. At the bottom, it strikes a block of mass M=7kg which is at rest on a horizontal surface, Fig. 7–46. (Assume a smooth transition at the bottom of the incline.) If the collision is elastic, and friction can be ignored, determine
(a) the speeds of the two blocks after the collision,v'$_A$ =    m/s v'$_B$ =    m/s
(b) how far back up the incline the smaller mass will go. $\approx$   (Round to the nearest integer) (Let A represent mass m, and B represent mass M.)

  In Problem 79 (Fig. 7–46), what is the upper limit on mass m if it is to rkn;c.) zra 0 qg-vi,p*dbw,pvebound from M, sv q ,-)apc*,zkd.wn;rgv0b pi lide up the incline, stop, slide down the incline, and collide with M again?    kg (Let A represent mass m, and B represent mass M.)

  The gravitational slingshot effect. Figure 7–47 shows the planet ns**gab1 ar 3xSaturn moving in the negative x direction at its orbital speed (with respect to the Sun) of 9.6km/s The1 *3*xg nbasar 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