We claim that momentum is conserved,0rlrzqmyhv+, 1wjo adrg- 3u )fb6w 58 yet most moving objects eventually slow down and stop. E z8h3fy16bldw)vm5 ,o-r rq 0uwr+ajgxplain.

When a person jumps from a tree to the rjc.v -pte(/2y l/eadground, what happens to the momentum of the person upon stj-cd(l2/aee ./tpry v riking the ground?

When you release an inflated but untied balloon, w1xod yzk,+; rceyzp+y dn+ 2s9hy does it fly across the room? y 9cz d+y2ke++o1zxs dr;,pny

It is said that in ancient ti.8q )mbvvt7 p2pmgga0b 3c7dames a rich man with a bag of gold coins froze to death while stranded on a frozen lake. Because the ice was frictionless, he could not push himself to shore. Wha)t2mbgb7d vqpa.pv 8 gmc70a3t 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 essentiah 2d v vl+q(wmxh 8xsr8v3-8sjllywx+ r8 dl82 (xvs vhs-3m8qvjh in a vacuum?

According to Eq. 7–5, the longer tgb/ 75(kvss npo-3i4 ay m0irlhe impact time of an impulse, the smaller the force can be for the same momentum change, and henc l3v74(gn /io i 5bkpmy-0sasre 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. Today*3w-is-s-tx z a)m +0vlbfr wb, though, cars are designed to have “crumple zones” thatti -zrw)+ bmas0b *lxfv3 ws-- collapse upon impact. What is the advantage of this new design?

Why can a batter hit a pitched baseball further than a mp9*jc df;cy8w v1 :u etah51yball tossed in the air by the batter? 1ey:d;aj9p1*yu h 8 5wtvcfcm

Is it possible for an object to receive ae6fpp2 ;yxgj 0 larger impulse from a small force than fr6jfy0pe ;pxg2 om a large force? Explain.

A light object and a heavy object ha u(fdezy(g5z :ve the same kinetic energy. Which has the greater mome(d zf(zuy5g e:ntum? Explain.

Describe a collision inck zn-1x0t.djsoi0gqms. x9 nw7iloe18d2 8y which all kinetic energy is lost.

At a hydroelectric power plant, wax(r1cwfh+ epi5uj64 fter 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 watfr5x6fi jc4e u+(1pwh er is brought to a dead stop, or so that the water rebounds?

A squash ball hits a wall at a 4dw (3c0twb sa(5 $^{\circ} $ angle as shown in Fig. below. What is the direction (a) of the change in momentum of the ball, (b) of the force on the wall?

A Superball is dropped from a height h onto a hard steel plate (fixed tzg f rqbg8wjm3jybu;w 5:.k *7u5 f/qlf6( rfyo the Earth), from which it rebounds at very nearly its original speed. (a/ qgqfu6rfg .byjw8j7b(w:uf zml 5k5ry3 f;*) 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 when cuoew:g02c/ p xarrying a heavy load in your arms?

Why is the CM of a 1-m length of pipe at its mid-point2ozth 27wr m9i, whereas this is not true for your armoiz 2rh7t 29wm or leg?

Show on a diagram how your CM shifts vxq*/c6 t2c5hnufum t 8--vd 8d,orn bwhen you change from a lying position to a sitting podm6/ 8utv-td2nuqnx ro- 5cf*hv c8, bsition.

If only an external force ca7*(y2 )5sv xxme vaakcn change the momentum of the center of mass of an object, how can the internal force of an engine acca() vx75y* msecxav k2elerate a car?

A rocket following a parabolic path through the aic* -fw-u;yl xqr suddenly explodes into many pieces. What can you say about the motion of this *fxuw-l-q;y csystem of pieces?

  What is the magnitude of the uavs 1afe986u momentum of a 28-g sparrow flying with a speed of $8.4 \; m/s$    $kg \; m/s$

  A constant friction force of 25 N acts on a 65-kg skier fo/xc q4ndnbxcpg j9n:9 w8.ib0 r 20 s. What is the skier.in 4 q/ bb8ncdjpgx0c9:xnw9’s change in velocity?    m/s

  A 0.145-kg baseball pitched at 39 m/s is hit on a horizontal line drive strat5 e f7n -x- u+4vhukp krfdza-pcu27+ight back toward the pitcher at 52m/s If the contauxhk kau+tnc- +5f7 -d4zpf72r u -pvect time between bat and ball is $3\times10^{-3}$s calculate the average force between the ball and bat during contact.    N

  A child in a boat throws a 6.40-kg package out horin)6gcrs, r)p yzontally with a speed of 10 m/s Fig. below Calculate the velocity of the boat immediately ay,r)6)grsnc p fter, 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 magnitude of the velocity of the boat is    m/s

  Calculate the force exerted on a rocket, given th+-dxjc*5ojrp+t ;m0ni mrfhe:vni 0 3at the propelling gases are expelled v c35fd0:xr+p rt-nei ;o inmjm j0h*+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 moving at 4lb: d (4k-syxmcl p;u$4.1 \; m/s$ 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 travel )guiozmxp3h5 :q2(fbs alone on alevel frictionless track with a constant speed of 18m/s A 5350-kg load,initially at rest, is dropped onto the car. pi53 hg)(moxbz2q :fu What will be the car’s new speed?    m/s

  A 9300-kg boxcar traveling 9rda5m iw:yd20dmsx6xcfeq; ; x j5+sat $15 \; m/s$ 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 whipi1qj:7 r:d( 5*kbmgvl0kj btj horizontally at speeds of 100km/h If the air strikes a person at the rate of 40kg/s per square meter and is brought to rest, estimate the force of the wind on a person. Assume the person :tgj rbvkb(d0j7 qli:1kmj5* 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 of 8.6m/s ondc7c u1amqwrho:q: u/5rqho/,7 ;id s a level track. Snow begins to fall vertically and fills the car at a rate of 3.5kg/min Ignoring friction with the tracks, what is the speed of the car aft:/cc doh;d u/w 1u,r 75oqsrq7:hmiaq er 90.0 min?$\approx$    m/s

  An atomic nucleus initially mo+7pzu n.,mok9lw .pog ving at 420m/s emits an alpha particle in the directionm+p g.pl9 7uok, o.wzn of its velocity, and the remaining nucleus slows to 350m/s If the alpha particle has a mass of 4.0 u and the original nucleus has a mass of 222 u, what speed does the alpha particle have when it is emitted?    m/s

  A 23-g bullet traveling 230m/s penetr8s- ytp1b( qazates 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 doa(zyp- b q8st1es it move after the bullet emerges?    m/s

  A 975-kg two-stage rocket is traveling at ap;jtu0lx* x8nyd o+* f 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 matybbgp9ux 82x 0is :4nss 3180 kg is traveling in outer space with a velocity of 115m/s To alter its course by 35.0 nu xt42bbgsi:08x p y9$^{\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 odcv p4wiku 7 9vub5zh2jt*fuax73o;bz) +ag3ff the tee at a speed of 45m/s The golf club was in contact3jovbuu kv b475u + t2z;ch gza9f adipx*w)73 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 comeeuus5sf7+o*n)ox 1,zv) qwy as to rest in a time interval of 8.0 ms. (a) What is the impulse given to o*5uas f xw1)zq,e7s onv )+yuthe 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 strikeij 7f+u4v+b-c4 m*k3skn mk v5 rq7ocx5fijk- s 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 charln+g 8-k-vnjwj ,on8k ge of the crashworthiness of new automobile models. Cars are tested by smashing them into fixed, massive barriers at 50km/h (30 mph)vlk8g+kjn -,8on-n j w. 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 89h*oy(c azd9gqsge;ffd-h pts, z y88 h i.-bto the east and is stopped in 0.75 s by a head-on tackle by a tackler running due west. Calculas8,8yg bads qhp gd ff-ez.9h*zt (;i y8-hoc9te
(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 *:s s)63p lemt t/qpfytennis ball (mass 0.060 kg) points in the +x direction and is given by es )q/pm 6:*fttpy3 lsthe graph 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 75-kg person jump without breakiny:pd iguil+v7 *y nhfh ,3xy*s1b-079 ulmpxng 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 standinux*pb3gx hs7y y,- fip :hn*lnl+dmi71u0y9vg 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 (,1aym 5r4 hgr../ b7lbvlwmnw +x direction) with a speed of collides head-on with a 0.220-kg ball at rest. If the collision is perfectly elastic, what will be the speed and direction of each ball after the covr mn1/7 hwb5rwb lym. 4l,g.allision?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, g y5gs hpe v6f:hc00 bz8rzz y0;4l*32dblzwv moving east with a speed of 3m/s has a head-on collision with a 0.900-kg puck initially at rest. Assuming a perfectly elastic collision, what will be the speed and direction of each object after the collision?Let A represent the 0.450-kg puck, and let B represent the 0.900-kgvbz6v 2z w:g85cf y0lbypser30*;zhgl0 hdz4 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 perff,0k6zp i;aja o7ztad a32gf79rmb xcf ;.bo /ectly elastic head-on collision. If one ball’s initial speed was 2m/s and the other’s was 3m/s in the opposite direction,ot76b; /m.azc xr gaazofkf2j ,p0b 73ia9;d f 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 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 k*4tt av.lqn4with a speed of 2.5m/s collides head-on with a 0.090-kg ball initially moving away from it at a speed of 1.15m/s Assuming a perfectly elastic collision, what a.tnltkvq4a 4*re the speed and direction of each ball after the collision?(Let A represent the 0.060-kg tennis ball, and let B represent the 0.090-kg ball.)v'$_A$ =    m/s v'$_B$ =    m/s

  A softball of mass 0.220 kg that is movingo+a r 170: )lk bi,gaalh;gjlr with a speed of 8.5m/s collides head-on and elastically with another ball1l:go alarjb h 0,);+ali r7kg 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 amusement park ride collide elastically as ov axk x6vd+t;,ne approaches the other directly from the rear (+x6dv,ktxa v;Fig. 7–34). Car A has a mass of 450 kg and car B 550 kg, owing to differences in passenger mass. If car A approaches at 4.5m/s 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 wilwc tp+( hc0lg2wc -lec/; t,dv-zap8th a second ball initially at rest. The second ball moves off with /8wcd0 ltt -;clvzew+ 2 cplg(h- apc,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 slide.wrcjk2xz.; ml 3oq ;5zin5ous down a frictionless incline as shown in Fig. 7–35, and elastically strikes another cube at the bottom that is only one-half its mass. If the incline is 30 cm high and the table is 90 cm off the floor, where does each cube lrqwzoi3;k5. ln o2czj x um;5.and? [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 masb; 8nv30 ;vxtg0 -k)fawnzq ths 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 ifehcxa0 - vn32*sn)zheight h of the pendulum equal to 2.6 cm. A second projectile causes the the pendulum to swing twice afn i0c)3 en*a- hsxvz2s 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 bdx( qnnt00r( 4tqmq0puries itself in a 3.6-kg pendulum hanging onn0pd0q4r( mxtqtq0n ( 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.vertical$\approx$    m horizontal =    m

(a) Derive a formula l;6qaz )wl y*ofor the fraction of kinetic energy lost, $(\Delta\mathrm{KE/KE})$ for the ballistic pendulum collision of Example 7–10. (b) Evaluate for m=14g and M=380g

  An internal explosion breaks an object, initially at rest,-byuuz1eczwn07r- 0d into two pieces, one of which has 1.5 timbwcz-nd-ze1u0 r7 uy0es 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. ) KE'$_A$ =    J KE$_B$ =    J

  A 920-kg sports car collides into the rear end of a 2300-kg SUV sto sn;/i;qirgphog8 *m 5 shv9b3pped at a red light. The bumpers lock, the brakes are locked, and the two cars skid forward 2.8 m before stopping. The polo*vgs3sb 58/h;i rn ;hqpmg9 iice 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 rebounwq1a7dt4l/ar c8h bc 1ds to a height of 1.20 m. Approximately how many rebounds will the ball make before locdh 1lbacw 8 r74qt/a1sing 90% of its energy?   

A measure of inelasticity in a head-on (pk;*6 p btavwcollision of two objects is the coefficient of restitu*k; pv p6bawt(tion, 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 ikugw ,yup87j, nto two pieces, one with three times the mass of the other. A depression is made in both faces gp ywju,u7, 8kof 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 ifw mk ;ch4t:q1n the +x direction at 5.5m/s collides head-on with a 10.0-kg object moving in the -x direction at 4m/s Find h 14mwqk:tcf; 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 dergoj w)qz8;(b4o.wkno z* yz:cays into a second nucleus, an electron, and a neutrinq. nz* gjb) r4 kzw8y;o:w(zooo. 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 mkewd11jy d xzd,4m4r2ass $m_\mathrm{A}=0.400$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 collisi 61xqmtgxr fb-k-3c0t on between two objects of equal mass, each having initial speed the -br6ktqcfx 0 3 1-mtxgtwo move off together with speed v/3 What was the angle between their initial directions?    $^{\circ} $

  Two billiard balls of equal mass move at right angles and meet at the origin7zl e++ 0qppbl11trxs of an xy coordinate system. Ball A is moving upward alo1e 0 z+ x1t+plrl7sbpqng 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 y*.gyd 1sie6we *h6atcollision with another atom at rest. After the impact, the neon atygi*aye h e.tw661s *dom 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 elasud+o ii3 p3e1stic collision with another atom at rest. Aft+usio 13idpe3 er the impact, the neon atom travels away at a 55.6 $^{\circ} $ angle from its original direction and the unknown atom travels away at a -50 $^{\circ} $ angle. What is the mass (in u) of the unknown atom? [Hint: You can use the law of sines.](Let A represent the incoming neon atom, and B represent the target atom) $m_B$   u

  Find the center of mass of the three-mass system shown in Fig.13fvs i3 *w7jgb cpq) 7x,gmxp 7–38. Specify relative to the left-f) isp gp,3 3m7wbxxv1q7gcj *hand 1.00-kg mass.    m

  The distance between a carbon atomfy-m;8 cim8pl ($m_{\mathrm{C}}=12\mathrm{u}$) 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 iit;r9w b0ktdb g zp x6:yh8j62s 2.50 m behind the front of the car. How far from the front of the car will the CM be when two p b 9bktdi hrwtyx06;z2:j8p6g eople sit in the front seat 2.80 m from the front of the car, and three people sit in the back seat 3.90 m from the front? Assume that each person has a mass of 70.0 kg.    m

  A square uniform raft, 18 m by 18 m, of mass 68v0f jz, ji 5:rv)t hpsjih+v/800 kg, is used as a ferryboat. If three cars, each of mass 1200 kg, occupy its NE, SE, and SW corners, deteri+pjh,jf t vi hjv/0r 8v:s5z)mine the CM of the loaded ferryboat.$X_{CM}$ =    m $Y_{CM}$ =    m

  Three cubes, of sides )d /jz, hc1 0l +csusc8xv8yxm:ezcn ($l_0$,$2l_0$, 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 07ousy ja:hk.g: vx8t 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 thattg8:suox k:aj7 0h.yv the crane operator can pick up the load without tipping it.$X_{CM}$ =    l $Y_{CM}$ =    l

  A uniform circular plate of radius 2R has a circular hole of9o,s;bvzp1 e n radius R cut out of it. The center of the smaller circle is a distance 0.80R from the center C of the larger circlbp;,zs9n1o e ve, Fig. 7–41. What is the position of the center of mass of the plate? [Hint: Try subtraction.]   R

  Assume that your proy: fiyg -0azg1portions are the same as those in Table 7–1, and calculate the -z1f gi0a:gyymass of one of your legs.    kg

  Determine the CM of an outst;8gtlj70pzy o)egdk 9retched 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 r xi3uv 78vb8e2au:exu yy2 t;of the CM of an arm bent at a right angle. Assume that the person is 15v8it 3u:reayx8ub27 2y e;u xv5 cm tall. $X_{CM}$ =    cm $Y_{CM}$ =    cm

When a high jumper is in a position such that ongla u/ or/208gi)uwy ld78whis arms and legs are hanging verticalr2 gng /oy/80l wow8)7audu lily, and his trunk and head 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 Earth and M t+*m4 dmyv 8,xy4-llc7wa isfoon 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 hn hbbs0rc321 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 8ra/nuy)awb) u */x mstm8ehiok73n: 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 tossedt7b/horu e)ia8asy /8 x*u):nk wm 3mn, 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 kg and a diameter a/k2 7k lstkr30.0800 m mounted on a uniform cylindrical handle of m/ a7kksk2rt3l ass 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–a l++8( nkxwwv29), $m_{II}$=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 .tfq jp.a8rp4c9 ve2tthe air and stationary with respect to the ground. A passenger, of mass m, then climbs out and slides down a rope with speed measured with respect to the balloon. With what speed and direction (relative to Earth) does the balloon then mot4r.a.9ecq pjpv82ftve? What happens if the passenger stops?

  An 0.145-kg baseball pitched horizontally at strikes a bat and is poppedo,.e i*- dmqbe8ro ac6 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 contacto*bd.eeq6o-rc8a mi ,.    $^{\circ} $

  A rocket of mass m traveling with spwxkinl 61hj 4 yy(obx.0q.d4peed $v_0$ 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 hvsgg+i1yqd;f7li7ze c5, . gc 8 y6mwfaced 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 m ye w57qg g.1c+sch6z yglv7i ;df8,ialso fall into a pocket? Give details.

  A 140-kg astronaut (including space suit) acquires a sp9nk6on6nfe . (l oso.aeed of 2.5m/s by pushing off with his legs from an 1800-kg space capsule.ko o6nf9.an6 ( esnlo.
(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, tm7nn8 wl6+e5cwk am *u,t/mrare initially at rest in outer space. They then push each other apart. How far apart a,8crwk/w6enn5mu t+tm*l7a m re they when the lighter astronaut has moved 12 m?    m

  A ball of mass m makes az.+z vzzj.:2 0kwzpks head-on elastic collision with a second ball (at rest) and rebounds in the opposite direction wiz+kvzpz.z k 2 .s0w:jzth 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 a6na,;c sxp9i nn automobile accident. The accident involved car A of mass 1900 kg which crashed into stationary car B of mass 1100 kg. The driver of car A applied his brakes 15 m before he crashed into car B. After the collision, car A slid 18 m while car B slid 30 m. T; xnpi9cnas 6,he coefficient of kinetic friction between the locked wheels and the road was measured to be 0.60. Show that the driver of car A was exceeding the 55-mph (90km/h) speed limit before applying the brakes.    mi/h

A golf ball rolls off the top of a flight of concrete steps of total vertical f twb)q.2 9x 6-hqxanxheight 4.00anx .w9hb 6ftq )2q-xx 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 when the ball reaches the bottom of the stairs?

  A bullet is fired vertically into a/ fqy.tdm gh,f(o*s-s 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 becomes embedded in itof f ,-*q/h.ssdgm(yt?    m

  A 25-g bullet strikes and becomes embedded in a 1.35-kg block ofux(* s fky),tm4 jdik. 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 rest, what was the muzzle speed of the bullet? xi .f4j,ksu d()mk* yt   m/s

  Two people, one of ma. :fv hny9mj* fqu,fg)d(tak-p2r g ;hss 75 kg and the other of mass 60 kg, sit in a rowboat of mass 80 kg. With the boat initially at rest, the two people, who have been sitting at oppositfv;r.u-mn:*g g9jfhk tady2f(q, )p he 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 wask * fyu;zjr8u, 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 twobfv( zz kf7m4 b :om2uhcm.;1o fragments by an explosion. One fragment acquires twice the kinetic energy of the other. What is them(2:f1f 7bkzozcvm;m4o.u h b ratio of their masses?   

  The force on a bulle31mdlaoib fh86) am42j uv;slt 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 ;y deh-hl; 00w /zamxt sh*q31 yzik5v$m_A$ = 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 decaysbk5 a6;-.o ce.vnp. x+tk yjeamc3s;d radioactively into an alpha particle and a smaller nucleus. What will be the speed of this recoiling o -56a t+v pmbjxy3;nsek.;cea .dck .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 95j7guy( aio. lurj7 rangle 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 dow*,e;3gz 6 n+ae kwdlcvn a 30.0 $^{\circ} $ incline which is 3.60 m high. At the bottom, it strikes a block of mass M=7kg which is at rest on a horizontal surface, Fig. 7–46. (Assume a smooth transition at the bottom of the incline.) If the collision is elastic, and friction can be ignored, determine
(a) the speeds of the two blocks after the collision,v'$_A$ =    m/s v'$_B$ =    m/s
(b) how far back up the incline the smaller mass will go. $\approx$   (Round to the nearest integer) (Let A represent mass m, and B represent mass M.)

  In Problem 79 (Fig. 7–46), what i+xp1ov 4f.tl un/oal c+re)u6s the upper limit on mass m if it is to rebound from M, slide up the incline, stop, slide dowetoap nl+ocr1v.u 6/)u+l x4f n 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 Saturn movif4 fe3pz2dyq-pz8 -hy ng in the negative x direction at its orbita-h- z2zyef84dyqp f3 pl 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