We claim that momentum is conserved, yet most moving obj;* +vo ,unjffdwbp: ,nects eventually slow down and stof jo wp*,;ufd:vn,b n+p. Explain.

When a person jumps from a tree to the ground, what happens to the momentum oaz (xgzg9*uk. f the person upon striking tga 9 zuxg.zk*(he ground?

When you release an inflated yqi6z7e2 yd9vm2o x7 ebut untied balloon, why does it fly across the room?o2 67ix7vqmd9zy ey2e

It is said that in ancien ;bwtfuwb/1::fzhrj,(w+he *g:;ozyy n u+ya t times a rich man with a bag of gold coins froze to death while stranded on a frozen lake. Because the ice was frictionless, he could not push himself to shore. What could he have done tauru:b;z +,f+:yy/gh( zw ey1*jwfw ht:no;bo save himself had he not been so miserly?

How can a rocket change direction when it is far out in space and is esrao5)-;rnqf q-t57cip) hleg sentially in a vacuur;ich75-qone f r)lgpaq- t) 5m?

According to Eq. 7–5, bpo nffypf ftz,+(tml77 va:y m/xu3d9e0 y): the longer the impact time of an impulse, the smaller the force can be for the sa3m yf:f,ybdpx7y/ z f ( a7:lto0)+pvfun9temme 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. Today, ysx cfwu*7lle9j;4 /-*zn upjthough, cars aplyzs*e;nuc f-x / j*uw9j74lre designed to have “crumple 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 the a-0xnnax;p. vgir by the battgxa0 -;nnvp.x er?

Is it possible for an object76wh 1:y;fvbkml + ybm to receive a larger impulse from a small force than from a large for 1kf6bhbymwy :v7+ ;lmce? Explain.

A light object and a heavy object have the same kinetic energy. Which ha9* 6mrm ,r nojyx(6mkis the gream6(jrix rn m *,kymo96ter momentum? Explain.

Describe a collision in which all kinetic energy/4w wiy 4l(gwl is lost.

At a hydroelectric power plant, water is directed at hig3qecxay a8 h(4h speed against turbine blades on an axle that turns an electric generator. 4h 38 aycea(xqFor maximum power generation, should the turbine blades be designed so that the water is brought to a dead stop, or so that the water rebounds?

A squash ball hits a w dqt8yfn87v)ll a 3m7ball at a 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 a hard steel plate (fixed 1m y*omt 8 o,wixka5.kcpe 42sto the Earth), from which it rebounds at very nearly its original spee2we omo,yaim4t8ks c1k*.x 5pd. (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 when carrying a heavy load ind/9dag-.. r .k u0c +rcczmxb9ild;wk your arms?

Why is the CM of a 1-m length of pipe at its mid-poi wu.63k+ew zjent, whereas this is not true for your arm or legz+kwe u. 3j6we?

Show on a diagram how your CM shifts o jloy tyor 87t+3).lufgd+1hwhen you change from a lying position to a sittro.lh1ft y l7) g8jt+oo3yu+ding position.

If only an external force can change the momentum of the centij guo/4o)37wt)kbk ter of mass of an object, how can the intg)o4uwk tkj7o tb/ 3i)ernal force of an engine accelerate a car?

A rocket following a parap/pb /lb :dh3wvbrz an44e :lki(:pk:bolic path through the air suddenly explodes into many pieces. What/ hd /(rwvl :pae: b34nl4p: bbkiz:pk can you say about the motion of this system of pieces?

  What is the magnitude of the momentum pvkal 9airu(vbw)o7h s 3lis:-5 )pr, 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 skibx6)ehs xk57w er for 20 s. What is the skier’s xb)kseh57wx 6change in velocity?    m/s

  A 0.145-kg baseball pitched at 39 m/s is hit on a hors7ine 15t i wka-;sl9z me*:qkizontal line drive straight back toward the pitcher at 52m/s If the contact time between bai7n9 e-wzk;eai m*kl 1s5q:t st 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 pa;m5a:lbo 0u dcalw)-qckage out horizontally with a speed of 10 m/s Fig. below Cc; lmo a-w lu):aqb5d0alculate 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 magnitude of the velocity of the boat is    m/s

  Calculate the force exerted one dwua98 6r5xgruwde7)fxw *3 a rocket, given that the propelling gases are expelled at a rate of 8d73wfxxuw5 waer *ur )g96ed$1500 \; kg/s$ with a speed of $ 4\times10^{4 } \; m/s$ (at the moment of takeoff). F =    $\times 10^7 \; N$

  A 95-kg halfback moving2 g/-wdecxj68c+ieu72tpg8vf sbl +t 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 alevel frictifo jf9tw) o3g2onless track with a constant speed of 18m/s A 535)93go fj f2two0-kg load,initially at rest, is dropped onto the car. What will be the car’s new speed?    m/s

  A 9300-kg boxcar traveling a oqqqw7wag)v v)kcu;4fq225 nt $15 \; m/s$ 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 /wh b71-fo+p .s sq z8v6rtewnspeeds 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 is 1.50 m high and 0.50 m wide. Compare to then7t6pw1v-s .e8fozhqrw+s/ b 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 coas7. j husw e(2u9r *kd-t5kmhiyts along with a constant speed of 8.6m/s on a level track. Snow begins to fall vertically and fills the car at a rate of 3.5kg/min Ignori-7ukh 5r.sd 2jm yie9*wh (ktung 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 pajailc/ *s f ypq.b zyx.c7ci;xx4 )4s/rticle 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 andcyxc i7ij)s/ clqs.zba4 /fx ;4*yp .x the original nucleus has a mass of 222 u, what speed does the alpha particle have when it is emitted?    m/s

  A 23-g bullet traveling 230m/s penetrates a 2.0-kg block of wood and emerges 4l w 97acl4xwycleanly at 170m/s If the block is stationary on a frictionless surface when hit, how fast does it move after the bull ywxla944w 7lcet emerges?    m/s

  A 975-kg two-stage rockaf 1k7qiduzy-m4l63 eet 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 isrx: ,m(ybl p o3j32yxx traveling in outer space with a velocity of 115m/s 2rmx(, p3oyxl b:3xj yTo 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 0.045k;m-tyczy6 hscr;0; 9nqzsd( kg is hit off the tee at a speed of 45m/s The golf club was in contact with the bal;nd(zcr-hkz msqs6tcy0; ;y9l 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 v-blk w oa2snk;6ig2 2tyml9g* elocity of 8.5m/s and comes to rest in a time interval of 8.0 ms. (a) What is thy 6g*gkiws n2at;ll2 mk9o2b -e 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 wahig nb,7: f cvn3/uxjj:.e 2hall 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 ./a dtoyd /:be 68qrq8mrcg3dthe crashworthiness of new automobile models. Cars are tested by smashing them into fixed, massive barriers at 50km/h (30 mph). A new model of mass 1500 kg takes 0.15 s from the time of impact untilg.d ac8:qd8ye r3 6/dbrt qom/ 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 7rjzgg 0m 3v0erunning at 4m/s to the east and is stopped in 0.75 s by a head-on tackle by a tr0z07gejg3vm ackler 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 ,- bd0qg5sfoo :zk0wj in the +x direction and is given by the g o0w5d :z ,sb-j0gofqkraph 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 jumpkf (9:sjhl ge4 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 standinggf4k (:j se9hl 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 ,gz*lzn/v ea0l* cke4a speed of collides head-on with a 0.220-kg ball at rest. If the ,gl/cv 4z aek*0e*zlncollision 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,(qzx-mk:boelu yt 2d )87aw4x-gob 3 u 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 willbeu- q -)b24:zo yk3 mga(tdwux8ol7x 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-kg puck. v'$_A$ =    m/s ----待选择----eastwest  v'$_B$ =    m/s ----待选择----eastwest 

  Two billiard balls of equal mass under r:4 n)rrx el-ajfs3pqu(x-8 ygo 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 en8-x) q :r(p4j- fayur3lsrxwill 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 with a speed of 2.5m/s 7 krv:hmrlpv* *t g2q(mg:hd.collides head-on with a 0.090-kg ball initially moving away from it at a speed of 1.15m/s Assuming a perfectly mkt d.v(7:h *q ml2r:vp h*grgelastic collision, what are 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 moving with a speed of 8.5m/s cocf9iyh82+b y 4muy ff0llides head-on and elastically with another ball initially at rest. Afterward the incoming softball bounces backward with a speed of 3.7m/s Calculatef m+ffb y8hy0uy ic492
(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 aab5ae* e5zjc7s 71 vpvn amusement park ride collide elastically as one approaches the other directly from th* cvz 15a7vbas7ep5je e rear (Fig. 7–34). Car A has a mass of 450 kg and car B 550 kg, owing to differences in passenger mass. If car A approaches at 4.5m/s and car B is moving at 3.7m/s calculate
(a) their velocities after the collision v'$_A$ =    m/s v'$_B$ =    m/s
(b) the change in momentum of each.$\Delta p_{\mathrm{A}}$$\approx$    kg*m/s $\Delta p_{\mathrm{B}}$$\approx$    kg*m/s

  A 0.280-kg croquet ball makes an elastic head-on collision with a sec8d-0fl fj;df k lnr9 bxn5c9 fq(p5h-zond ball initially at rest. The sec dlp-r qx-dh9fc85nj(l9fkfb5 ;n0zfond 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 down a frictionless incline as shown i.p9 jrrjqpm 38n Fig. 7–35, and ela.rjp39qr jm p8stically 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 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 m4z5f.fgd o,bow6n;tk ass 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 os/8hljxcp6baqt;i r rv*)e/*f the pendulum equal to 2.6 cm.jselxhtva q)/ 6rpc r**/i;b8 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 t h;i2 wtlq-*n phtucz(l2l75iraveling 230m/s buries itself in a 3.6-kg pendulum hanging on a 2.8-m-long string, which makes the pendulum swing upward in an arc. Determine the vertical and horizontal components of the ptlh uzc2 l2wnq 5iit- (*;7lhpendulum’s displacement.vertical$\approx$    m horizontal =    m

(a) Derive a formula for the fraction of kinetic energy lost, ig2y0a(am)sp. 8tcoi $(\Delta\mathrm{KE/KE})$ 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 +(mlf/p5udcb-0y gjs5f 4h 5s9of rnr, into two 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 d5j 4(9+rfoyds5bh r-fc 5un lgp0/mfsid 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.;,m:t o-tgb2tieb 9j- ahz wv into the rear end of a 2300-kg SUV stopped at a red light. The bumpers lock, the brakes are locked, and the two cars skid forward 2.8 m before stopping. The police officer, knowing that the coefficient of kinetic friction between tires and road is 0.80, calculates the speed of the sports car at impact. What was that speed?(Let A represent the sports car, and B re 2zt m;hgt ,eaw-v-o9i:b b.jtpresent the SUV) $\approx$    m/s

  A ball is dropped from a height of 1.50 m and rebounds to a height of 1.12u s9rvoh ,ey0 odxo120 m. Approximately how many rebounds will the ball make before losi02o1dxhv9 eso 1y ,ruong 90% of its energy?   

A measure of inelasticity in a head-on collision of two objectsgqbk9h,yc:,(t celnrvg-rg1 wc.n * 2 is the coefficient of restitution, e, defin twnl, c,nh:vg*2ceg g q.c1k-(ryrb9ed 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 twow 8*km5h4 xpj 1xz8uzb pieces, 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 reassem *5xj ph1mw4kz z88xbubled 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 collidex n x/h2z zz84+31kg6adefg bmta8rw. s head-on with a 10.0-2hbzr3 azanmf+d4/e8 t k 8g.zw gxx61kg object moving in the -x direction at 4m/s Find the final velocity of each mass if:
(a) the objects stick together;   m/s
(b) the collision is elastic; v'$_A$ =    m/s v'$_B$ =    m/s
(c) the 15.0-kg object is at rest after the collision;   m/s ----待选择----not reasonable reasonable 
(d) the 10.0-kg object is at rest after the collision;   m/s ----待选择----not reasonable reasonable 
(e) the 15.0-kg object has a velocity of 4m/s in the -x direction after the collision. .   m/s ----待选择----not reasonable reasonable 
Are the results in (c), (d), and (e) “reasonable”? Explain
( Let A represent the 15.0-kg object, and let B represent the 10.0-kg object.)

  A radioactive nucleus at rest decays into a seconhdqj9f+ n 2iy)d nucleus, an electron, and a neutrino. q9)fd+n y h2ijThe 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 mass*yjq76fls) i sy1qon ( $m_\mathrm{A}=0.400$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 coll:3);qlv7ct g n.iai 9(1bletyd*dx oj ision between two objects of equal mass, each having initial speed the two move off togetht9 a7;q ybgi)oli* 3vxd.l( n:jtdce1 er with speed v/3 What was the angle between their initial directions?    $^{\circ} $

  Two billiard balls of equal mass move at right angles :5ed4 j0e7x jy0ti txhand meet at the origin of an xy coordinate system. Ball A is moving upward along the y axis at 2m/s and ball B is moving to the right along the x axis with speed 3.7m/s After the collision, assumed 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 isx7 4x:jhe jdye500tti  ----待选择----x directionx direction v'$_A$ =    m/s v'$_B$ =    m/s

  A neon atom (m=20u) makes a perfectly9xc2 53ky/5i x1engf3 bp ndbp elastic collision with another atom at rest. After the impa3db i fyxbpxnek5c53g1n/9 2 pct, the neon atom travels away at a 55.6 $^{\circ} $ angle from its original direction and the unknown atom travels away at a -50 $^{\circ} $ angle. What is the mass (in u) of the unknown atom? [Hint: You can use the law of sines.](Let A represent the incoming neon atom, and B represent the target atom) $m_B$   u

  A neon atom (m=20u) makes a perfectly ela5d35m jvukeb+ rfc e),stic collision with another atom at rest. Af,)jdkf eb3vemc5ru 5+ter 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 sys2-k slfnvie 1skf89f9tem shown in Fig. 7–38. Specify relative to the left-hand 1.00-99k s n1vlk8-f2f sfeikg mass.    m

  The distance between a l5wy7 w ldb(/kcarbon atom ($m_{\mathrm{C}}=12\mathrm{u}$) and an oxygen atom ($m_{\mathrm{O}}=16\mathrm{u}$) in the CO molecule is $1.13\times10^{-10}$m How far from the carbon atom is the center of mass of the molecule?    $\times10^{-11}$m

  The CM of an empty 1mh :icap:m6f )8y9itgg s(p3r050-kg 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 people sit in the back seat 3.90 m from the front? Assume that each persons9 r::pp(tcfm3yag g 8m6)hii has a mass of 70.0 kg.    m

  A square uniform raft, 18 m by 18 m,2qm aa (9zj,hfo,k2x x of mass 6800 kg, is used as a ferryboat. If three cars, each of mass 1200 kg, occupy its NE, SE, and SW co9x qa,mk (o2zjh2x, afrners, determine the CM of the loaded ferryboat.$X_{CM}$ =    m $Y_{CM}$ =    m

  Three cubes, of sidescugx; yr,m5-y8i-imy7b 1 acb $l_0$,$2l_0$, 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 hasqj3(z,uk+u ku0i m, ri )m3n6n8qgozh a load of identical cases of tomato paste (see Fig. 7–40), each of which is a cube of length l. Find the center of gravity in the horizontal plane, so that the crane operator can pick up krz,3u 8u,0z( j)ko q3+ unmi qmghn6ithe load without tipping it.$X_{CM}$ =    l $Y_{CM}$ =    l

  A uniform circular plate of radius 2R has a circular hole of radius R cut ia 7igq46wc s4out of 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 poiiwaq4g76s 4csition 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, a: n8jto .y ao(.s6xypend calculate the mass y p8y:6.oso(jtxe. n aof one of your legs.    kg

  Determine the CM of an6)vj vdfyc .8e 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 ajj +zvi2 mjt k47ymf*)n arm bent at a right angle. As +2yjm7 i jk4zfmjv)t*sume that the person is 155 cm tall. $X_{CM}$ =    cm $Y_{CM}$ =    cm

When a high jumper is in a position such that his armpi6zjsnk1 wopt5bom1:a2c7. s and legs are hanging vertically, and his trunk and head are horizontal, calculate how far below the torso’s median line thbsp6 koo5m .zp 12aw :ji7n1tce CM will be. Will this CM be outside the body? Use Table 7–1.

The masses of the Earth an 7jp;dro6omd2d 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 mbc* gg7itauavt (;i:m8 *ngm;an 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 uniformfgo o-v.l -tc tu7b16s cylindrical head of mass 2.00 kg and a diameter 0.0800 m mounted on a uniform cylindrical handle of7-. bgot1s-ovcl f6ut 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 ul1r gleq)6/p cylindrical head of mass 2.00 kg and a diameter 0.0800 m mounted on a uniform cylindrical handle of mass 0.500 kg and length 0.240 m, as shown in Figqur ) lpe6l1g/. 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 (j8(. ; pks wkd;7ojkbvFig. 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 i yxn5 0bhw /brk; az(q idh-ko9/;: io.b,nwhmass M, are in the air and stationary with respect to the ground. A passenger, o;i-n/k5bi9 :x;boaohnwhkzbh y/ i,d0 r(wq.f mass m, then climbs out and slides down a rope with speed measured with respect to the balloon. With what speed and direction (relative to Earth) does the balloon then move? What happens if the passenger stops?

  An 0.145-kg baseball pitched horizontalltbc8;u a7 grdj(k1 qo-y at strikes a bat and is popped straight up to a g1odu(t8-q k7jcab ;rheight 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 traveling /+rtdye -/ipbup6ext:lf- l/ 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 zgbf(jj4 ,ka q4;mjl7 faced with the corner pocket shot shown in Fig. 7–43. Relative dimensions are also shown. Should the player be worried about t74zq4jj(mj,;f l bagk his being a “scratch shot,” in which the cue ball will also fall into a pocket? Give details.

  A 140-kg astronaut (including space suit) r2vbljo j ty2r-7xf0n)tx 8x;acquires a speed of 2.5m/s by pushing off with his legs frolf t rr yjoxv7-2x0jn2bx;t8) m 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 initially at e ly ir*fi,f o*ie.(ah66j2 xdrest in outer space. They then push each other apart. How far apart are they when the lighter astronaut has moved 12 m?yea r*2, i*fiihjl exf( d6.6o    m

  A ball of mass m makes a head-on elastic h6v hx(1yjtuyx, w3pw eg4-+o collision with a second ball (at rest) and rebounds in the opposite direction with a speed equal to one-fourth its original speed. What is the mass of the se xogw- y p3h1,vwju(yt4 +ex6hcond ball? $m_B$ =    $m_A$(Round to two decimal places)

  You have been hired as an expert witness in a court case involving an aut.lu fg)(uni k7omobile accident. The accident involved car A of mass 1900 kg which crashed into stationary car B of mass 1100 kg. The driver of car A applied his brakes 15 m before he crashed into car B. After the collision, car A slid 18 m while car B slid 30 m. The coefficient of kinetic friction between the locked wheels and the road was measured to be 0.60. Show that the d(u.)kilngf7 u river of car A was exceeding the 55-mph (90km/h) speed limit before applying the brakes.    mi/h

A golf ball rolls off thewuf 76pd/ 0ym5s ln,uz top of a flight of concrete steps of total vertical height,f5 p sz7 6ymulwu0nd/ 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 when the ball reaches the bottom of the stairs?

  A bullet is fired vertically into a 1.40-kg block of wood ai a:m)qqdh+4 mc tqnzhc0 -v03t rest directly above it. If the bullet has a mass of 29.0 g and a speed of 510m/s how - iq c3)vn0 dc0am4+:hthzqqmhigh will the block rise after the bullet becomes embedded in it?    m

  A 25-g bullet strikes and becomes embedded in a 1.35-kg block of w z09y-ud1p ewjood placed on a hori9 z0u1ej pywd-zontal 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?    m/s

  Two people, one of mass 75 kg and the other of mas4yvst6n60 2e n,efr sms 60 kg, sit 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 boen 0nr e6t f6sv,42mysat 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 ihl7mtqx33h k*o 0br5was 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 sudqef)l 5l5 uaf,denly broken apart into two fragments by an explosion. One fragment acquires twice the kinetic 5,fl5 qa) fuelenergy of the other. What is the ratio of their masses?   

  The force on a bullet is given by tge9pooge++gupo*z5 g 8h rzo2b3; . qrhe 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 3uj5n-0tha2ity: j ovj8z7o n$m_A$ = 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 radi5*n e rkd,mn4 jmctmzs r096z0oactively into an alpha particle and a smaller nucleus. What will be the speed of this recoiling nuc d0cz,t zsr n569 *memrkjn4m0leus 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 targfkegzzj;6 jdf6j+9.v et) 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=2.2kge o. q30.gqq rs 7ov7db3:mlc/z qt7kb slides down 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 is the upper limit on ma2d ynk)4bv58anzx, 5,hvsu9oq dn:r jss m if it is to rebound from M, slide up the incl89 q4ds ,ha:jnvub5vkr,2xnoy5 d zn)ine, 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 thezr 0kak(u ,wm1 planet Saturn moving in the negative x direction at its orbital speed (with respect to the Su0(kzku a1 mr,wn) 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