We claim that momentum is conserved, yet most moving .wmm.ih 8eph6. x oog*objects eventually slow down i8h gem6m h..p oxow.*and stop. Explain.

When a person jumps from a tree to3iy/cmhyc r g38mrm-, the ground, what happens to the momentum of the pm3 ciry3y,- mc/m8ghrerson upon striking the ground?

When you release an inf ;fo)*8uwhy+-qyl bll1o d r3wlated but untied balloon, why does it fly across the roomwwl)y3 +h*dbou;8 y 1 rqf-oll?

It is said that in ancient times a rich man with6 5bak uhwlr7a7ognzb8 l.*/g a bag of gold coins froze to death while stranded on a frozen lake. Bounza.b/7 56k7g8lg*rablwhecause the ice was frictionless, he could not push himself to shore. What could he have done to save himself had he not been so miserly?

How can a rocket change direction when it 49 qd mmj0;du oxe(d(vis far out in space and is essentially in a vacxedmvu0qo;j ( dm9d(4uum?

According to Eq. 7–5,bs ; zad-yw)(g the longer the impact time of an impulse, the smaller the force can be for the same momentum change, and hence the d(; bg)ayws-z 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 rgq:8lxsr64lc dhz9 0 gigid as possible to withstand collisions. Today, though, cadrcxl94q0l86g:sh zgrs are designed to have “crumple zones” that collapse upon impact. What is the advantage of this new design?

Why can a batter hit a pitched ba.uwa+xezv / j1 /it6oe34rjpj seball further than a ball tossed in the air by +o tp rz/4vjjj. eui63w1/aexthe batter?

Is it possible for an object to receive a larger impu.q6r u3st u4gylse from a small force than from a lar3uqt 6 4syr.ugge force? Explain.

A light object and a -5l-jbe3s8djrc;, i o xw3mgrheavy object have the same kinetic energy. Which has the gr ,;c-3sjeligrorj38bmxw 5d- eater momentum? Explain.

Describe a collision in which all roia( /5suzz9k8uaevx*+y ;d kinetic energy is lost.

At a hydroelectric power plant, water is directed a;)rjj2*a (m jev c:wkbt high speed against turbine blades on an axlj :ajwjb 2kc(ev;m *)re 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 the water rebounds?

A squash ball hits a wall 4 7sihc4t:cdlat 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 to thef k(q m8--zgyuca3 c)g Earth), from which it rebounds at very nearly its original speed. (a) Is the momentum ofyc)ukm(c gq- -8za 3gf 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 ins-h ut8vi6py7 your arms?

Why is the CM of a 1-m length of pipe at its mid-pz e +(go4hu*ae57xzo soint, whereas this is not true for yooeohze+u5*x 7gz a4s( ur arm or leg?

Show on a diagram how your CM shifts wqn7xs .s.aejk .(j/vuzk yr07hen you change from a lying position to a sitting positijeu ky.jqkv/xnsr7a. z (70. son.

If only an external force canfzc/2fqy )/u mx/v4th 7 ysqx/ change the momentum of the center of mass of an object, howyff/ ht2yu q//v/scmq 7) xxz4 can the internal force of an engine accelerate a car?

A rocket following a pal7e.py*wcun:y1xrr j(8 1 ep qrabolic path through the air suddenly explodes into many pieces. What can yy7rqnc .(xpp jley811e w:u *rou say about the motion of this system of pieces?

  What is the magnitude of the momentum of a 28-g sparrow flying with n9p hhnr;4 6uia speed of $8.4 \; m/s$    $kg \; m/s$

  A constant friction force of 25 N acts on a 65-kg skier fofx,l(pyxvp (e,ykdz (3 1cro 1r 20 s. What is the skiecl,xpy,rz 13 v1fdpko (x (ye(r’s change in velocity?    m/s

  A 0.145-kg baseball pitched at 39 m/s is hit on a horizontal line drive / v, elvyhty9b3u .bk-straight back towarlv.tv9byb uh/ 3-k y,ed the pitcher at 52m/s If the contact time between bat and ball is $3\times10^{-3}$s calculate the average force between the ball and bat during contact.    N

  A child in a boat throws brd7m7m:xtp m.l( ,xvd e ,y.mi1i:haa 6.40-kg package out horizontally with a speed of 10 m/s Fig. below Calculate the velocity of the boat immediately after, assuming it was initially at rest. The mass of the child is 26.0 kg, and that of the boat is 45.0 kg. Ignore water resistanc1pm(.idvahmt l : by.7exmxr,i : dm7,e. The magnitude of the velocity of the boat is    m/s

  Calculate the force exerted on a rocket, givem ;.mx69rbos lsbpt+f)xi j2;sa. 2 vln that the propelling gases are expea mb9) v.p2rl b;m; xssj.+2lo6xstfilled 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 movayyn:58wwji) ing 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 railroadf(* b8zl hmrv/4cmz3 s car travels alone on alevel frictionless track with a constant speed of 18m/s A 5350-kg load,initially at rest, is dropped onto the car. What ml/zr8mc svh(b* 43 zfwill be the car’s new speed?    m/s

  A 9300-kg boxcar tra+n 6wq gw, k1bf.l,s.bsdf hm(veling 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 stok/gd*oh5, uv3y)z g parm, winds can whip 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 thpok y*/3v,gg 5a)zdh ue 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 alook fzsdwl6qkn +s j:)th 6nb18a*et; -ng 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 Ignoring friction with the tracks, whsst8t )k6*+lk-1fd nq6waoz; : hbjenat is the speed of the car after 90.0 min?$\approx$    m/s

  An atomic nucleus initially moving at 420m/s emits an alpha particle o bp p oan51b,v3+5oynin the direction of its velocityn+, bopv5a53ny1bp oo, 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 pmybb)mbk(q l56gx+ 7x 5ky(acenetrates a 2.0-kg block of wood and emerges cleanly at 170m/s If the block is stationary on a frictionless surface when hit, how fast does it move after the bullet5)lkb xk myq7b(my a6xg 5(c+b emerges?    m/s

  A 975-kg two-stage rocket d(ltd;cxq byyh1+ozk, +r*e - 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 outer1w)vz (de9hxl2.gn)4pq gvi +4i jjbm space with a velocity of 115m/s To alter its g+.dwpnb )gq em2iji1j vz4h49(xvl) 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 0.3 bp5obd lskb,/ tqx;+045 kg is hit off the tee at a speed of 45m/s The golf club was in cobd,3l/t+k;qp o bbx5sntact 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 velochta :kj nk1q*;ity of 8.5m/s and comes to rest in a time interval of 8.0 ms. (a) What t1a*nh;:k k jqis 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 srn,xp ew j4u.- grl7a5wu ;3oppeed v=25m/s strikes a wall at a 45 $^{\circ} $ angle and rebounds with the same speed at 45 $^{\circ} $ (Fig. 7–32). What is the impulse (magnitude and direction) given to the ball?   kg*m/s to the  ----待选择----leftright 

  You are the design en/4 ,2olpcl t4 ;vefmfc s 4ka(g(oz4wcgineer in charge of the crashworthiness of new automobile models. Cars are tested by smashing them into fixed, massive barriers at o4va /pesz (,mfk;g44lt o2fccw4 c(l50km/h (30 mph). A new model of mass 1500 kg takes 0.15 s from the time of impact until it is brought to rest. (a) Calculate the average force exerted on the car by the barrier. $\approx$$a\times10^5$N a =   
(b) Calculate the average deceleration of the car.    m/$s^2$

  A 95-kg fullback is running at 4m/s to the east and is stopped in 0.75 s by a he y,h1z j lqoussn*3f2l(jr:l ;ad-on tackle by a tackler running dol rsnl*:,1hjj 23q;uyf(z l sue 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) point4n7zwc-f 4zmdl c+k 2js in the +x direction and is given by the graph of Fig. 7–33 as a functio+k4zj cw4-cndlf7 m2 zn 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 withk k11d:l6yfn wout breaking the lower leg bone of either leg? Ignore air resistance and assume the CM of the person moves a distance of 0.60 m from the standing to the seated position (that is, in breaking the fall). Assume the brea1 k6w dlnk:1yfking strength (force per unit area) of bone is $170\times10^6\mathrm{~N/m^2}$ and its smallest cross-sectional area is $2.5\times10^{-4}m^2$ [Hint: Do not try this experimentally.]    m

  A ball of mass 0.440 kg moving east (+x direction) with a speed of collidr(y -zy12lw7e 2owra, ju jn3qes head-on with a 0.220-kg ball at re ,r j1zw3q- noj2(r7yuwal2yest. If the collision is perfectly elastic, what will be the speed and direction of each ball after the collision?Let A represent the 0.440-kg ball, and B represent the 0.220-kg ball. $v'_A$    m/s  ----待选择----eastwest  $v'_B$    m/s  ----待选择----eastwest 

  A 0.450-kg ice puck, moving east wtpxqyzojh,1 a 9+8zn 1ith 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 repre9 p8z1,xq 1aj+ yhotznsent 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 o /e /ivse*mw z4g,*fzmass undergo a perfectly elastic head-on collision. If one ball’s initial speed was 2m/s and the other’s was 3m/s in the opposite direction, what will be their speeds after the collision?(Let A represent 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//me s/zv,4o*fzwi g*es in the opposite direction. ) v'$_A$ =    m/s v'$_B$ =    m/s

  A 0.060-kg tennis ball, moving with a speed o e--il6rh a2bh1. gkb (vaov+r;gr xt7f 2.5m/s collides head-on with a 0.090-kg ball initially moving away from it at a speed of 1.15m/s Assum+7xa i boer(vvg;hkrr--2h6 .a tbg1ling a perfectly elastic 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 withqs b;x81 3qsexf+i ;as6soq,riib/ o- a speed of 8.5m/s collides head-on and elastically with ano;ssifsqo-xr 8q13oax/+e;,i bq bi s6ther ball initially at rest. Afterward the incoming softball bounces backward with a speed of 3.7m/s Calculate
(a) the velocity of the target ball after the collision    m/s
(b) the mass of the target ball.    kg
(Let A represent the moving softball, and let B represent the ball initially at rest.)

  Two bumper cars in an amusement par ba:rdw+yq1f* zi5px0lp5b8b k ride collide elastically as one approaches the other directly from the rear (Fig. 7–34). Car A has a mass of 450 kg and car B+x 1r:bbp q0ib5 8apz*w dl5fy 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 seczwrgf3 lg.tbb 6 z/4cb 7zm3+vond ball initially at rest. The second ball mz3bt7lg4bzgz+6.c b f/rmwv 3 oves 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 cuf j52z f4j3acjbe slides down a frictionless incline as shown in Fig. 7–35, and elastically strikes another cube at thf53jaf jj4c z2e 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 objectc2b d1z pg*nq9gbw0d5oh2b 3p of mass m$_A$ and velocity v$_A$ elastically striking a stationary object of mass head-on. (a) Show that the final velocities v'$_A$ and v'$_B$ are given by$v_{\mathrm{A}}^{\prime}=\left(\frac{m_{\mathrm{A}}-m_{\mathrm{B}}}{m_{\mathrm{A}}+m_{\mathrm{B}}}\right)\nu_{\mathrm{A}},v_{\mathrm{B}}^{\prime}=\left(\frac{2m_{\mathrm{A}}}{m_{\mathrm{A}}+m_{\mathrm{B}}}\right)\nu_{\mathrm{A}}.$(b) What happens in the extreme case when m$_A$ is much smaller than m$_B$ Cite a common example of this. (c) What happens in the extreme case when m$_A$ is much larger than m$_B$ Cite a common example of this. (d) What happens in the case when m$_A$=m$_B$ Cite a common example.

  In a ballistic pendurc7)6krolk;6)q l3 yl ;r yyqolum experiment, projectile 1 results in a maximum height h of the pendulum equal to 2.6 cm. A second projectile causes th;l)ry7oqqo)y rkl 3r6lc; 6yke 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 tra pdkm7v-jaj85w3s4r qveling 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. D8pkj- d5vjaq sm7wr34etermine the vertical and horizontal components of the pendulum’s displacement.vertical$\approx$    m horizontal =    m

(a) Derive a formula for the fractiomhumvpz hy1l(p :+c41 n 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, i ow6b/a:;sheinitially at rest, 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 did each piece acquirsa: wei 6b;oh/e? (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 2300oqm+j; 2ylm7b-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 i2o m7qmb+l;j ympact. 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 heighf;d:t x x;,q/xrn.9o44ze ccbkojg3vt of 1.20 m. Approximately how many rebounds will the ball make;xe v4;z:4/fbqx. drc,9g3 ctx okjon before losing 90% of its energy?   

A measure of inelasticity in a head-on collision of two objectnj)dsg49tl4kl l e;2p9c q is2s is the coefficient of94jsk2lpsncd) qt;e 4 l9l 2ig restitution, e, defined as$e=\frac{\nu_\mathrm{A}^{\prime}-\nu_\mathrm{B}^{\prime}}{\nu_\mathrm{B}-\nu_\mathrm{A}},$
where $\nu_\mathrm{A}^{\prime}-\nu_\mathrm{B}^{\prime}$ is the relative velocity of the two objects after the collision and $\nu_\mathrm{B}-\nu_\mathrm{A}$ is their relative velocity before it.
(a) Show that e=1 for a perfectly elastic collision, and e=0 for a completely inelastic collision.
(b) A simple method for measuring the coefficient of restitution for an object colliding with a very hard surface like steel is to drop the object onto a heavy steel plate, as shown in Fig. 7–36. Determine a formula for e in terms of the original height h and the maximum height h’ reached after one collision.

  A wooden block is cut into two pieces, one with three times the mass of ty;b8td;95pctrjy1u+q 4 rkm j0i /i7wk8g ohnhe 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 reassembled block is set on a rough-surfaced table, and the fuse is lit. When the firecracker explodes, the two blocks separateyo i8+dtk1ycntgkrw70/ j ;h4 rb59;8uj qmpi 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 ai ua r(8e.yqlq: :ab -ow5voz6 10.0-kg obv(u6rqya-5zo :il w. oq e8a:bject 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 second nucleus, an he) rh)dd jz)c9is f48electron, and a neutrino. The electron and neutrino are emitted at right angles and have9h ersi)8 hd4 )dz)fcj 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 mas4feoxzqyr,)q z1 56t js $m_\mathrm{A}=0.400$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 be1b8,gkorg(bcx5 j t p3tween two objects of equal mass, each having initial speed the two move off together with speed v/3 What wa 8jrpco kb53,xb(tg1g s the angle between their initial directions?    $^{\circ} $

  Two billiard balls of equal mass move at right angles and meet af3gcv+ z :p4x kdbn6:;m: dqsxt 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? dirx:::z b3sv;f 4npd d+k6xmcqgection of ball A is  ----待选择----x directionx direction v'$_A$ =    m/s v'$_B$ =    m/s

  A neon atom (m=20u) makes a perfectly elastic collision with another atom l - gw1;8x9u)oyav8zs 9c9d4yh qhnfgat rest. After the impact, the neon atom travels awhyagouxzh q8;49 ) v1dngyf c-w89s9lay 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) m8.lu1btw/ gk qakes a perfectly elastic collision with another atom at rest. After the impact, the neon atom travels away at a 55.6 lubg1k/.tw8q $^{\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 m:aw310lft78lm s xne eass of the three-mass system shown in Fig. 7–38. Specify relative to the f0a n187e:lm3s lexwt left-hand 1.00-kg mass.    m

  The distance between k(7ojfd n0ps nqy86 ,da carbon atom ($m_{\mathrm{C}}=12\mathrm{u}$) and an oxygen atom ($m_{\mathrm{O}}=16\mathrm{u}$) in the CO molecule is $1.13\times10^{-10}$m How far from the carbon atom is the center of mass of the molecule?    $\times10^{-11}$m

  The CM of an empty 1050-kg car is 2.50 m bef1 g3s.vo6vkchind the front of the car. How far from the front of thgsvckfv1 .3o6 e 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 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 kggt/ +nu1 9/.pabrmz n0bbe, a ferryboat. If thnu/m, +/ n09 bzgketbaprb.g1ree cars, each of mass 1200 kg, occupy its NE, SE, and SW corners, determine the CM of the loaded ferryboat.$X_{CM}$ =    m $Y_{CM}$ =    m

  Three cubes, of sidesoz* ie bp7q0*w $l_0$,$2l_0$, 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 o ,v plz2yos6)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 cranos 26vp )zo,lye operator can pick up the load without tipping it.$X_{CM}$ =    l $Y_{CM}$ =    l

  A uniform circular plate of radius 2R has a bu 9e 3;myn e2m,m//gj7alg ahcircular hole of radius R cut out of it. The center of the smaller circle is a distance 0.80R frol/ gu g2/mam j myne7hba,3;e9m the center C of the larger circle, Fig. 7–41. What is the position of the center of mass of the plate? [Hint: Try subtraction.]   R

  Assume that your proportions are the same as those in Table 7–1, and cs1bcojy5/ rz 8alculate t/rozc 5j8sy1b he mass of one of your legs.    kg

  Determine the CM of an outstretofqm7pknx .mrud-;*bj68ad u4 ciz)3 ched arm using Table 7–1.   % of the person's height along the line from the shoulder to the hand

  Use Table 7–1 to calculate the position of the CM of an arm bent at a*dg;ocj * rc;f right angle. Assume ;jfco gr d;c**that the person is 155 cm tall. $X_{CM}$ =    cm $Y_{CM}$ =    cm

When a high jumper is in a position s48 2 fmzhw(kaz hvw:c9uch that his arms and legs are hanging vertically, 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. c9z wwh 4(: fak2hm8zv

The masses of the Eac k5.:z( fe0cueu l+llrth and Moon are $5.98\times10^{24}$kg and $7.35\times10^{22}$kg respectively, and their centers are separated by $3.84\times10^{8}$m (a) Where is the CM of this system located? (b) What can you say about the motion of the Earth–Moon system about the Sun, and of the Earth and Moon separately about the Sun?

  A 55-kg woman and an 80-kg man stand 10.0 m apart on fyb+w :7l;o lza mlyd5.rictionless 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 un4exm)bh*gz3x iform 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 bx3mg*zh)x4 ein Fig. 7–42. If this mallet is tossed, spinning, into the air, how far above the bottom of the handle is the point that will follow a parabolic trajectory?    cm

  A mallet consists of a uniform cylindrical head of mass 2.00 kg and a diameter 0 mdnh43xe+5yn tgn/fnf7 y2q5.0800 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 tos/xt4 yd5nf57h+g q3y f enn2mnsed, 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 Exa3az;o-d e)/ g1rp zrfnbhr5ak25 k) gomple 7–14 (Fig. 7–29), $m_{II}$=3$m_{I}$ Where then would $m_{II}$ land?    d(Round to two decimal places)
(b) What if $m_{I}$=3$m_{II}$    d

A helium balloon and its gondola, of mass M, are in the air and station7dwsaun/93 6s bj rwjw-k- .eeary 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 direc-.k7ewr/9webu3j s -w n6a dsjtion (relative to Earth) does the balloon then move? What happens if the passenger stops?

  An 0.145-kg baseball pitched horizontally at strikes a bat and is popp u:+thylwmu) coq :k+1ed straight up to a height of 55.6 m. If the contact time is 1.4 ms, calculate the average force on thu):w+ qum+t1l: kyoc he ball during the contact.    $^{\circ} $

  A rocket of mass m tjbto8n2yze vfg 697u(g,ukvkm+ip8 lga,2 0y raveling 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 ih omnff/ (jv3vd72 mj1tbzds y4,q +z*s faced with the corner pocket shot shown in Fig. 7–43. Relative dimensions are also shown. Should the player be worried about this being a “scratch shot,” in which the cue ball will also fall in ob(4f jt zj+vq1df/z2m3v*7 d,my hsnto a pocket? Give details.

  A 140-kg astronaut (including space suit) acquires a speed6qw5zy. xek vj+ gyz)m)az*g7 of 2.5m/s by pushing off wk7v.z)y)z x jg qegyw5*6z+amith his legs from an 1800-kg space capsule.
(a) What is the change in speed of the space capsule?    m/s
(b) If the push lasts 0.40 s, what is the average force exerted on the astronaut by the space capsule? As the reference frame, use the position of the space capsule before the push.    N

  Two astronauts, one of mass 60 kg and the other 8i53pm(y cf 8la0 kg, are initially at rest in outer space. They then push each other apart. How far apart are they when (mpfic3ya8l 5the lighter astronaut has moved 12 m?    m

  A ball of mass m makes t9-s jig;v,qw a head-on elastic collision with a second ball (at rest) aw- is, vt9gq;jnd rebounds in the opposite direction with 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 aomhjq0urp7m/2a -6s3f wlb4 involving an automobile accident. The accident involved car A of mass 6ua 0 sj /bmoqm4 7alw2rh-3pf1900 kg which crashed into stationary car B of mass 1100 kg. The driver of car A applied his brakes 15 m before he crashed into car B. After the collision, car A slid 18 m while car B slid 30 m. The coefficient of kinetic friction between the locked wheels and the road was measured to be 0.60. Show that the driver of car A 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 total8 0fspn 7rj14smpwx3p vertical height 4.00 m. The ball hits four times on the way down, each time striking the h4jwr3msp 80np7 s x1fporizontal 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-kgzq((kb6oo.; wuo1 ldn83jbv b 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 afte8b6. d o1vkoubj;wq( (oz3nl br the bullet becomes embedded in it?    m

  A 25-g bullet strikes and becomes embedded in a 1.35-kg block of woodij-.0dv*l:hdnqs -0 fw/ anla 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, a *saj0qnin 0-lf whvd: a-/.dlnd 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 otheri q)-bl()o0vq fo n,fl 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 vqfo-,b0 )qloil f)(n 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 wasi 1q 9lxn:f5e6m rzt-d i19q4spo;inb 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 brokiv;a09ax aaccc1 +mx/en apart into two fragments by an explosion. One fragment acquires twice the kinetic energy of the other. What is the ratio of their massx190aa;cxai/ acvc+m es?   

  The force on a bullet is given by t98vr iy9e/:txtl q59gyih83r * :zepbv wpcf0he 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 masseswqn.2imhdz;p6e 0 jn : $m_A$ = 40g and $m_B$ = 60g are suspended as shown in Fig. 7–44. The lighter ball is pulled away to a 60$^{\circ} $ angle with the vertical and released.
(a) What is the velocity of the lighter ball before impact?$\approx$    m/s
(b) What is the velocity of each ball after the elastic collision?v'$_A$ $\approx$    m/s v'$_B$ $\approx$    m/s(Round to two decimal places)
(c) What will be the maximum height of each ball after the elastic collision?    m

  An atomic nucleus at rest decays radioactively intoi.vjly.ny;a(sc rc y,o.bu1 ib rjd 2 i/tq*+( an alpha particle and a smaller nucleus. What will be the speed of this recoiling nu b+ n/(trisil(jy yc uqv..bidj1.y2oc*;a , rcleus if the speed of the alpha particle is $ 3.8\times10^{5 }$m/s Assume the recoiling nucleus has a mass 57 times greater than that of the alpha particle.    m/s

  A 0.25-kg skeet (clay target) is fired at an angle of 30 m7r6oopuqw.mzj -ozbcs) d8b7 , t;h: $^{\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 shkbj6 qbi-7m 0lides 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 upqvn9 iq6 :/jmeper limit on mass m if it is to rebound from M, slide up the incline, stop, slide down the incline, and collide with Mq9 vqij :m/en6 again?    kg (Let A represent mass m, and B represent mass M.)

  The gravitational slingshot effect. Figure 7–47 shows the p ;hde f4jjr/j)lanet Saturn moving in the negative x direction at its orbital speed (with respect to the Sun) of 9.6d4)jh/j f ;jerkm/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