We claim that momentum is conse:la,nfp 6;b/f zew)uzrved, yet most moving objects eventually slow down and sto:nf,z)w 6z/fu e alp;bp. Explain.

When a person jumps f-+5 psam6wya4jmjfr rrn+x5 ;-yoct/ rom a tree to the ground, what happens to the momentum of the person upon striking the groundmoy+ 4mc6an x-r;jprft-wjay5/s r5 +?

When you release an inflated but untied balloon, why d 2 0r49kevxseqm -(azloes it fly across the room9es20 mr qa-v4zk( exl?

It is said that in ancient times a rich man with a bag of gold coins frou tij 8pqb.u .;t(n*x-qo; wjbze to death while stranded on a frozen lake. Because the ice was frictionless, he c; x8j*;boiw..-ut qpn ubqt (jould 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 in space and is es. ;o7uux zkcjw ;4jl,nsentially i,.ul 7xc ;;uwzo4kj jnn a vacuum?

According to Eq. 7–5, the longer the impact time of an impulse, the9o 6ui wjjc)jgj:qgc3, .6kww 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 a)og:9u,j6 c wqjj3j.cw w6gkin automobile collision and reduce the possibility of fracture or death.

Cars used to be built as rigi 7)l+solbags3 d as possible to withstand collisions. Today, though, cars are designed to have “crumple zones” that collapse upon impact. Wha+a3l)b sog 7slt is the advantage of this new design?

Why can a batter hit a pitched basebao,bl d9qz:p ,a(drs;kf4 pxj) ll further than a ball tossed in the air by the baafd zp(k,):;rjbl49 qx d,sp otter?

Is it possible for an object to receive a larger impulse from a small force ghn*/t 2m38(cn j m+4vs.rm4ktxlue pthan from a large force42*xk(ghmt+nmjp3m8.l s/cu4 nvter ? Explain.

A light object and a heavy object have the same kinetic energy f9yv+s,7p.w+e i x47aduekp2xccgi - . Which has the greater momeevp- iy u9ipxw fx+ g,. 7d2+ake7cc4sntum? Explain.

Describe a collision ivtj3a 5scy l45q .ppu y.ak:b0n which all kinetic energy is lost.

At a hydroelectric power plant, water is dirc+0 e az6c2hxiz jq(z(ected at high speed against turbine blades on an axle that turns an electric generator. For maximum power generation, should the turbine blades be designed so that the water is brought to a dead stop, or so that(2c0 azczxz qhe6j i(+ the water rebounds?

A squash ball hits a wall at a/c ;jm uratpe 2yt9r;+g 45ktc 45 $^{\circ} $ angle as shown in Fig. below. What is the direction (a) of the change in momentum of the ball, (b) of the force on the wall?

A Superball is dropped from a height h onto a1i3h7 cq vuj2 bok3(ut hard steel plate (fixed to the Earth), from which it rebounds at very nearly itsi3tubk3h71vq 2cju(o 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 piece of putty that falls and sticks to the steel plate.

Why do you tend to lean backward wvap jm:6t(76 sf.x5g0mip qjzhen carrying a heavy load in your arms?

Why is the CM of a 1-m length of pipe at its mid-point, whereas this is not truqgc4w ic,bogpi)+59 ye for your arm or lgq4p+i9io,cbg ) 5ywceg?

Show on a diagram how your CM shifts *-pjbc*b .+g lfbu /:un sz ed/3wu:ipwhen you change from a lying position to a sitting position.-:uw ibub:ppzegb.3/+u*jl fc* /sd n

If only an external force can change the mg:zx 59c0i xe pz;f)jlomentum of the center of mass of an object, how can the internal force of an engine accelerat;ipl0 9:jx zfecz5xg)e a car?

A rocket following a parabolic path throughxmcuy- ;2bz *s the air suddenly explodes into many pcyu -2 bsx;*zmieces. What can you say about the motion of this system of pieces?

  What is the magnitude of the momentum of a 28-g sparrow flying(l)-1x5 zxkv:whu xv sd)iy* f with a speed of $8.4 \; m/s$    $kg \; m/s$

  A constant friction force of 25 N actjk7pnb ,+1fjr7k8 bxes on a 65-kg skier for 20 s. What is the skier’s changk,exk 1 fbpjrj87 +bn7e in velocity?    m/s

  A 0.145-kg baseball pitched at 39 m/s is hit onw1/v2d(k -lf2m pc3qie1 boaz a horizontal line drive straight back toward the pql zm2 we o- 1aif(c3p2vkdb/1itcher 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 throwp/f- 2gh6 jzr6+in skts 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.i jr ft+h26n-k/s gz6p0 kg. Ignore water resistance. The magnitude of the velocity of the boat is    m/s

  Calculate the force exerted on a rocket, given that the propegbd,teisb0 sqjqp;.k: 8o2)t lling gases are expetot.,8i;bebd: js )gsp0 kqq2lled at a rate of $1500 \; kg/s$ with a speed of $ 4\times10^{4 } \; m/s$ (at the moment of takeoff). F =    $\times 10^7 \; N$

  A 95-kg halfback movi6o0fht8us 1 09xln cgda93hbu ng at $4.1 \; m/s$ on an apparent breakaway for a touchdown is tackled from behind. When he was tackled by an 85-kg cornerback running at $5.5 \; m/s$ in the same direction, what was their mutual speed immediately after the tackle?    $m/s$

  A 12,600-kg railroad car travels alone on ajm(a(p 9pi j9flevel frictionless track with a constant speed of 18m/s Aija(m(9j pf p9 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 travelingv do+r 2ak1gy-r)td.d at $15 \; m/s$ strikes a second boxcar at rest. The two stick together and move off with a speed of $6 \; m/s$ What is the mass of the second car?    $m/s$

  During a Chicago storm, winds can whip horizontally at speeds of 100k.qz cb( 2v8de ,hew77z0zha mrm/h If the air strikes a person at the rate of 40kg/s per square meter and is brought to rest, estimate hz2,0h8qb( m77zwz r .aed cevthe 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 cond2d l z94jtia2stant speed of 8.6m/s on a level track. Snow begins to fall vertically anit lz24d d9aj2d 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 particle3sb* 1v-surs p 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 1*u 3rbssv-ps 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 ad*3ht-/ko)wo wb 7po e 2.0-kg block of wood and emerges cleanly at 170m/s If thekwod3p -bw*h/o ) 7eot block is stationary on a frictionless surface when hit, how fast does it move after the bullet emerges?    m/s

  A 975-kg two-stage rocrkvg .s.,ds6te(.v/vkacf4o ket is 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 traveling in outer space with a velocity oxw0rdc- vf (j/f 115m/s To alter its course (/vx-0fw rcjdby 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/sqxr9 ewf,h2v (t3*0om yg,cgr The golf club was in co3x w(oh ef gt,vm*2 90qyrr,gcntact with the ball for $3.5\times10^{-3}$s Find (a) the impulse imparted to the golf ball,    kg*m/s
(b) the average force exerted on the ball by the golf club.    N

  A 12-kg hammer strikes a nail at a velocity of 8.5m/s and comes to rest oshh52t1ge(j t3c+h 5awar/ gin a time interval of 8.0 ms. (a) Wh1ha/ga 5 (3 hwe5chr2+tsjogtat 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 strikes a wak/8 om5uypy2u4f ftwg (i2pd)ll 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 autyu.le0(s. 2 tjau d.u*5t qltcomobile models. Cars are tested by smashing them into fixed, massive barriers at 50km/h (30 mph). A new model of mauu.l a*t u52tlq (.tds.0jecyss 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 : y+y).dfdfd0 ips8h /wh0ax athe east and is stopped in 0.75 s by a head-on tackle by a tacklpy 0xf) 8+d:w . dyisdh/hafa0er running due west. Calculate
(a) the original momentum of the fullback    kg*m/s
(b) the impulse exerted on the fullback    kg*m/s
(c) the impulse exerted on the tackler,    kg*m/s
(d) the average force exerted on the tackler.    N

  Suppose the force acting on a tennis ball (mass 0.060 kg) points in tpml f o -oq.zxu.) s2d36ph,xkhe +x direction and is given by the graph of Fig. 7–33 as a funct u-zxqohod3p.f6,x.sm2 p)k lion 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 mx ))u jmfx-(ydwy*w/,d s.mn 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 sta u)m jy.f-wm/)syd(wx dm,x*nnding 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 spe slrqlexo9 m rs7za2.i(z4c3 9ed of collides head-on with a 0.220-kg ball at rest. If the collision is perfectly elastic7z932iz srrlcqsex. am4 o (l9, what will be the speed and direction of each ball after the collision?Let A represent the 0.440-kg ball, and B represent the 0.220-kg ball. $v'_A$    m/s  ----待选择----eastwest  $v'_B$    m/s  ----待选择----eastwest 

  A 0.450-kg ice puck, moving east with a speed of 3m/s has a head-on collis6p-cb huhff zixzc5.fp ,j(s:u ()1rlion 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,hlc,1z 5pifxrpsu:f). zbhf (cu 6- j( 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 perfectly elastic head-on zae0t-rj+evxq0lur f 6 r014bcollision. If one ball’s initial speed was 2m/s and the other’s was 3m/s in the opposite direction, what will be their speeds after the collision?(Let A represent the ball moving at 2.00 m/s, and call that direction the positive direction.Let B represent the ball mrq10rae 00 fxrebtvz6ju4-l +oving 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.p3wa;pe9xsov9 t* 4 iz5m/s collides head-on with a 0.090-kg ball initially moving away from it at a speed of 1.15m/s Assuming a perfectly elastic collision, what are the speed and direction of each ball after the collision?(Let A represent the 0tp3w9ax9; zei4ps* vo .060-kg tennis ball, and let B represent the 0.090-kg ball.)v'$_A$ =    m/s v'$_B$ =    m/s

  A softball of mass 0.220 kg that is moving with a speed of 8.5m/s collidwyf(g,, t6dx mjhn 8uxmn6t9. es head-on and elastically with another ball initially at rest. Afterward the incoming softball bounces backward with a speed otx fm(8tjnwn6,h um .x,9ygd6f 3.7m/s Calculate
(a) the velocity of the target ball after the collision    m/s
(b) the mass of the target ball.    kg
(Let A represent the moving softball, and let B represent the ball initially at rest.)

  Two bumper cars in an amusement park ride collide elastically al 6+6mep 8h -xhxm.arbn ysf-pd go7.cc2v+ r:s one approaches the other directly from the rear (Fig. 7–34). Car A has a mass of 450 kg and car blc ympmh +7-ec2rs.6n:+ 6x8ga vo-h.fd xrpB 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 a9b9dq jc-mt s0n elastic head-on collision with a second ball initially at rest. The secondjb9 - qst9cdm0 ball moves off with half the original 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 dn*jk4;7) kv aofra1k7n2 u0w k0 kjsqmown a frictionless incline as shown in Fig. 7–35, and elastically strikes another cube at tkq7k2mkasoka u kfn4 0; 0wrnj1 j*)v7he bottom that is only one-half its mass. If the incline is 30 cm high and the table is 90 cm off the floor, where does each cube land? [Hint: Both leave the incline moving horizontally.]$\Delta x_{m}$$\approx$    m $\Delta x_{M}$$\approx$    m

ake the general case of an object of ma1e)-cl s *gqgkss 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 ewbhnvsou i4bb1b- *dd7o 1:5 txperiment, projectile 1 results in a maximum height h of the pendulum 17vd14dnoobb hu5sb: wt ib-*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/s buries itself in a 3.6-kg peoztsz. ; -3l*0pjbucz xg vd(2ndulum hanging on a 2.8-m-long string, which makes the pendulum swing upward in an arc. Determine the vertical and horizontal components of the pendulum’s displacement.veg*o (. dvzcl2tszx;uj pz0 -3brtical$\approx$    m horizontal =    m

(a) Derive a formula for the fraction of kinetic f7yky 4ae64l hbuz28 tenergy 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 tw nxyx)1m5j:y avk ost91bm4ik0 n )b.eo 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 represent the lighter particle. vni)oejmm5:b na 0x y9tkx .ys14)k1b) KE'$_A$ =    J KE$_B$ =    J

  A 920-kg sports car collides into the rear end of a 230 hdcisa4 /lm yf9:4,pm0-kg SUV stopped at a red light. The bumpers lock, the brakes are locked, and the two cars skid forward 2.8 m before stopping. The police officer, knowing that the csam ,h4cdyp4/m :f9li oefficient 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 xgwm;-)ic:a8 , x s3bpladb .cm. Approximately how many rebounds will the ball make before losing 90% ofcml),8awa g:x3id - bsp.b;xc its energy?   

A measure of inelasticity in a head-on collision of twovpfn up3o28960sw zcc objects is the coefficient of restitutiovn0p 9pcoscf32zw6u 8n, 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 in gzy3k us89*zcto two pieces, one with three times the mass of the other. A depression is made in both face8gk3 zc9u*yz ss of the cut, so that a firecracker can be placed in it with the block reassembled. The reassembled block is set on a rough-surfaced table, and the fuse is lit. When the firecracker explodes, the two blocks separate and slide apart. What is the ratio of distances each block travels? ----待选择----1/91/101/81/6 

  A 15.0-kg object moving in the +x direction at 5.5m/s collides head-on with ahifz)yr1n6 y0 10.0-kg object moving in the -x direction at 4m/s Find the final velocity f1 h0z)6yin ryof 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, andvf8+cj6 let4 c a neutrino. The electron and neutrino are emitted at right angles and have mome4v f+e8lc 6tcjnta 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 masfxlqi 3.rxwb -8;f v+rgyz)3vs $m_\mathrm{A}=0.400$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 ma(bfs / :5iq: vugf6ihp2 q(5oykw a3jpss, each having initial speed the two move off together with speed v/3 Wh( 2(/5 g:fhi ksbof6qu q:jp3ay5 wvipat was the angle between their initial directions?    $^{\circ} $

  Two billiard balls of equal mass move at right angles3o z : 1hczjr*ac ze5-czqmp)1r46yfs 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 ri4z136hq:czza c-e1orzr f psj5 my* )cght 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 perfee cf.h xn,g0e+jeh-6tctly elastic collision with another atom at rest. After the impact, the neon atomjth+ e0,ce-x6 g.hen f travels away at a 55.6 $^{\circ} $ angle from its original direction and the unknown atom travels away at a -50 $^{\circ} $ angle. What is the mass (in u) of the unknown atom? [Hint: You can use the law of sines.](Let A represent the incoming neon atom, and B represent the target atom) $m_B$   u

  A neon atom (m=20u) makes a perfectly elastic collision with another atom*w pczq9n7hq52 9,kmx rlh51zydw+ mm at rest. 9nhyp+l 529r k cmdx,1mwhwq z*5mzq7After the impact, the neon atom travels away at a 55.6 $^{\circ} $ angle from its original direction and the unknown atom travels away at a -50 $^{\circ} $ angle. What is the mass (in u) of the unknown atom? [Hint: You can use the law of sines.](Let A represent the incoming neon atom, and B represent the target atom) $m_B$   u

  Find the center of mass jb wgn43e p zv*a :v/x-ax8ae8of the three-mass system shown in Fig. 7–38. Specify relative to the left-hand 1.00-kg vwxgzej:e-4x a8/b *3 a8 vapnmass.    m

  The distance between a carbon atonf2s)znf85 q cjyn3t1 m ($m_{\mathrm{C}}=12\mathrm{u}$) 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-kgmo*yvnb-j 8ukw+ e rpzg( f9mb4 t6; pa8vw,i4 car is 2.50 m behind the front of the car. How far from the front of the car will the CM be when two people sit in the front seat 2.80 m from the front of the car, and three peo b(wvn 6*j4 wmo,guva 8y - f;89mzepbitkp4+rple sit in the back seat 3.90 m from the front? Assume that each person has a mass of 70.0 kg.    m

  A square uniform raft, 18 m by 18 m, of mass 6800 kg, is used as a ferryb5;i6bp y5wha-1yz tf hoat. If three cars, each of mass 1200 kg, occupy its NE, SE, and SW corners, determine the CM of thw;ib ay1yzth 5hf65-p e loaded ferryboat.$X_{CM}$ =    m $Y_{CM}$ =    m

  Three cubes, of side joa(h5 e9*9s:.mu. qvgionubs $l_0$,$2l_0$, 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 hvmit6s cj1ccx/ exu 35)v(n4of tomato paste (see Fig. 7–40), each of which )v/c 1i 5cnjsmch u(6v xte3x4is a cube of 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,ci/6w s 2nu+ pwipsc2 a circular hole of radius R cut out of it. The center of the smaller circle is a distance 0.80R from the 2s pc+s,wwn2/i6uipc 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 Table 7–1, and calculx qd2w3ht.x* wate the mass of one of yourqwh *2tdwx. 3x legs.    kg

  Determine the CM of anaxh ,07sfz ca75ef k6s 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 bentvcf5+ vgo e1r/ at a right angle. Assumegfvv/+ co 51er that the person is 155 cm tall. $X_{CM}$ =    cm $Y_{CM}$ =    cm

When a high jumper is in a position such that hdzej6 ;2dx9h: j;aext)lq 6yhis arms and legs are hanging vertically, and his trunk and headh 9xjet)xj26z ;d deqa:l h;y6 are horizontal, calculate how far below the torso’s median line the CM will be. Will this CM be outside the body? Use Table 7–1.

The masses of the Earthfr9a-fn 9no 1in9)k mf 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 8gvxnxcdw: b fbl,*j2a:*i/5q0-kg man stand 10.0 m apart on frictionless ice.
(a) How far from the woman is their CM?    m from the woman
(b) If each holds one end of a rope, and the man pulls on the rope so that he moves 2.5 m, how far from the woman will he be now?    m
(c) How far will the man have moved when he collides with the woman? He has moved    m from his original position

  A mallet consists of a uniform cylindrical head of mass 2.00 kg and a dia4u q ,umhi8z :sk*cwe)meter 0.0800 m mounted on a unic mu 8u,hqk:zwe)s4*i form 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 trajectory?    cm

  A mallet consists of a uniform cylindrical head of mass 2. )x.de vuuy5l,lde3w3x9. db v00 kg and a diameter 0.0800 m mounted on dwy)d.ue3xv . vlu5b3ldx9e, 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 trajectory?    d    d

  (a) Suppose that in Example 7–14 (Fig. 7–29), 3ez. edc7fdbnf/q:*fx4lf/i03 j ea f$m_{II}$=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 g- 0j9( cii2umeqi2fz zondola, of mass M, are in the air and stationary with respect to the ground. A passenger, of mass m, then climbs out and slides down a rope with speed measured with respect to the balloon. With what speed and direction (relative to Earth) does tmf2iizciqj -e 20 9(uzhe balloon then move? What happens if the passenger stops?

  An 0.145-kg baseball pitched horizontally at strikes a bate1p5sk5 r*sf z and is popped straight up tr* 1sp5 zks5efo 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 trv9s9nyvvh 9t +aveling 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 withjylx99g, 8*burheq 6y the corner pocket shot shown in Fig. 7–43. Relative dimensions are also shown. Shor 89gex 9lh*bj6 uyqy,uld the player be worried about this being a “scratch shot,” in which the cue ball will also fall into a pocket? Give details.

  A 140-kg astronaut (ijr dal1w4 z+0kncluding space suit) acquires a speed of 2.5m/s by pushing off with his legs from an 1800-kg sp4k+wr 0ja1d zlace 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 0zr wp);ne j+wrd4 jb5kg, are initially at rest in outer space. They then push each other apart. How far apart are4wrej;50+rpdjz b wn) they when the lighter astronaut has moved 12 m?    m

  A ball of mass m makes a head-on elastic collision with a se1 k5c (;af5,1hilfsgst/ tfpm cond ball (at rest) and rebounds in the opposite direction with a speed equal to one-fourth its original speed. What is the mass of tc1f(tmp, la/5hs ;sk1 tifg 5fhe 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 automobiswzo7vw5( sstib )2p x c4 30bg.4eqktle 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 7izsbv(p40xtwb csko w325g).te 4 qshis 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 top of a flight of concrete steps of total vertica b4thx,m7 m*wal height 4.00 m. The ball hits four times on the way down, each time striking the horizontal part of a different step 1.0 m lower. If all collisions are perfectly elastic, what is the bounce height on the fourth bounce t xb,wa4m h7*mwhen the ball reaches the bottom of the stairs?

  A bullet is fired vertically into a 1.40-kg block of wood ats)tg kp a)8plz /rk6*6s/uira 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 b r z)*s/s6papa8l)kk6/ gt iruecomes embedded in it?    m

  A 25-g bullet strikes z9j tp/ad w+t/qoc3xw l2:y2t 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 0.2t3 p/wc2dlj29qzxtwa oy/t+: 5, 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 t8yo-it8vg1e b he other of mass 60 kg, sit in a rowboat of mass 80 kg. With the boat initially at rest, the two people, who have bt1voeb 8ig8- yeen 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 was ax;rv77y3r jg5wnpb8:v zsyf 0bout $ 1\times10^{ 8}$kg struck the Earth ($m_E$=$6 \times10^{ 24}$kg) with a speed of about 15km/s and came to rest in the Earth.
(a) What was the Earth’s recoil speed?    $ \times10^{-13 }$m/s
(b) What fraction of the meteor’s kinetic energy was transformed to kinetic energy of the Earth?    $ \times10^{ -17}$
(c) By how much did the Earth’s kinetic energy change as a result of this collision?    J

  An object at rest is suddenly broken apart into two fragments by an explosgh4pb -n:.4midrz 3ee ion. One fragment acquires twice the kinetic energy of the other. What ie 3e4-pi:dhbm 4gz.rns the ratio of their masses?   

  The force on a bullet is given by the formula F = 5rfli8e s1 ,;nu80-( $1.8 \times10^{ 5}$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 massespc jc6(qanltc 315e 7c $m_A$ = 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 radioactivfy3n :c6nz4o 6h,f:ea5x n, wdh)qkub ely into an alpha particle and a smaller nucleus. What will be the speed of this recoiling nucleus if the speed of the alphw3xu f,nafnq6ez ,:dh):cb on4k6 y 5ha 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 tm 2*r+9u w bigyjxoh3:arget) is fired at an angle of 30 $^{\circ} $ to the horizon with a speed of 25m/s (Fig. 7–45). When it reaches the maximum height, it is hit from below by a 15-g pellet traveling vertically upward at a speed of 200m/s The pellet is embedded in the skeet.
(a) How much higher did the skeet go up?    m
(b) How much extra distance, $\Delta{x}$ does the skeet travel because of the collision? $\approx$   

  A block of mass m=2.2kg slides dtgp(a7jd6xy 8own a 30.0 $^{\circ} $ incline which is 3.60 m high. At the bottom, it strikes a block of mass M=7kg which is at rest on a horizontal surface, Fig. 7–46. (Assume a smooth transition at the bottom of the incline.) If the collision is elastic, and friction can be ignored, determine
(a) the speeds of the two blocks after the collision,v'$_A$ =    m/s v'$_B$ =    m/s
(b) how far back up the incline the smaller mass will go. $\approx$   (Round to the nearest integer) (Let A represent mass m, and B represent mass M.)

  In Problem 79 (Fig. 7–46), wo:b20.w2ahs i/ gw+s ,tiwz eehat is the upper limit on mass m if it is to rebound from M, slide up0hsb szew,et awo 2i 2w:+./ig 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 slingsm9zf:cko -a0 qg-gjyp )u8sb+hot effect. Figure 7–47 shows the planet Saturn moving in the negative x direction at -gcgm kjzb qypa9sfuo: +0) -8its 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