We claim that momentum is conserved, yet most moving objects eventuash6cb. ;kh s dn 3;q4osc9p2nklly slow down and stop. Expsh9qn2 cp;sko;shncbkd46.3lain.

When a person jumps from a tree to the ground, what happens to the momentum i5kc0)ancxs.fn m. 0jof the person upon striking tc axijnk m..sf)cn 005he ground?

When you release an inflated but untied balloon, wha 2c4sx(ult a/3xmk:iy does it fly across the rooma umlc/xx a42i( s:t3k?

It is said that in ancient times a rich man with a bag of gold ch3crrfri:,8k :b(w ywoins 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 to save himselfyrr:h8c,b kw3 :(rw if had he not been so miserly?

How can a rocket change direction when ifbe 4cev dmjj-5j0r 0)t is far out in space and is essentially in a4 0jb) ferd-0 cjv5ejm vacuum?

According to Eq. 7–5, the longer twegypkps0 :+6 he impact time of an impulse, the smaller the force can be for the same momentum change, and hence the smaller the deformation of the object on which the force acts. On this basis, explain :0pg y+k6eswpthe 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 r/:jk7 x.7wlqyp0lon )4 kdtm as rigid as possible to withstand collisions. Today, though, cars are designed to have “crumple zones” that collapse upon impact. What is the advantage of this new design?d40t:yro7kln /)j qpk.wm7x l

Why can a batter hit a pitche f6*uzot :hra ;a+6)w* yynvua7fl:kd d baseball further than a ball tossed in the air by they: akh; a+6u7dyao :6utf* z nvlwrf*) batter?

Is it possible for an object to receive a larger impulss4zoe+h ,ighrsn/e,-cle ,x * 6 it1lge from a small force than from aclh+h ,e-igigs ,4o /xl1 zr,es*ent6 large force? Explain.

A light object and a heavy object have the same kinetefck25zy) 92 w /zkifpic energy. Which has the greatercfew5i/)f 29 kkz yp2z momentum? Explain.

Describe a collision in qe1*gz9tae )n which all kinetic energy is lost.

At a hydroelectric power plant, water is directed at high spe1a ,jl+ 61vm uaxy izp690h4s iqe6ttaed against turbine blades on an axle th6xut6j a6q l1sm aa9 iyvep4,zit1 h0+at 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 at a 45o fc/xbs h*xz 2zcp**y6cl 8-o $^{\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 plaala: ta(p)mby jnlx0( 6xs; awe o1k56te (fixed to the Earth), from which it rebounds at very nearly its original speed. (a) Is the momentum of the ball conserved during any part of this process? (b) If we consider the ball and Earth as our system, during what parts of the process is momentum conserved? (c) Answekm1;0jt5n a:6paes((by)a wlx 6lxao r part (b) for a piece of putty that falls and sticks to the steel plate.

Why do you tend to lean backward when carry5 gq7ixjd04sping a heavy load in your arms?

Why is the CM of a 1-m length of pipe at its mid-point, /axpqsxlccki-4g;2bq ( i.m fq4ue . /whereas this is not true fa/cxqieqg u4i(c;mfxk l .p/. -2s4q bor your arm or leg?

Show on a diagram how your CM shifts when you change from a lyinw2 5, neh)zigmg position to a sitting peg h5) zi,mw2nosition.

If only an external force can chang0hj qthe:8q2 zega*,me the momentum of the center of mass of an objec08jthqg2a,* :heze qmt, how can the internal force of an engine accelerate a car?

A rocket following a para1 (mt1 )nze ts)-w a5657 m.gaz,uyfxgcz fetpbolic path through the air suddenly explodes into many pieces. What c7fzt5x t51gagw , fmazys)n e(1e6tc) uz m-.pan you say about the motion of this system of pieces?

  What is the magnitude of the momentc 8t:p f4tb7jgum 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 for 2kba0a*7 4yy g o-wxhr20 s. What is the skier’2argy*y w0h ox47b-k as change in velocity?    m/s

  A 0.145-kg baseball pitched at 39 m/s is hit on a ho7 5 dzaqv o8dys2sk7-orizontal line drive straight back toward the pitcher at 52m/s If the contac7ysqadv5zk8 o72sd- ot 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 packi 3xxsyj*1- rv+s t1lqage out horizontally with a speed of 10 m/s Fig. below Calculate the velocity of the boat rss11-vyj *qxltx+i 3 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 on a rocket, given that the prolvde)7g +/cpo pelling gases are exp cop) /g+d7levelled 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 movyq1 s-ir e,9jddnc4w4 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 railroad car travqus3a4r6jw66 awwv y -els alone on alevel frictionless track with a constantsjqwy6r6va u 3w a-w46 speed of 18m/s A 5350-kg load,initially at rest, is dropped onto the car. What will be the car’s new speed?    m/s

  A 9300-kg boxcar traveliuhrb2)rt kf-a6k wd;-2*j7:3uliuew 5 brg vjng at $15 \; m/s$ strikes a second boxcar at rest. The two stick together and move off with a speed of $6 \; m/s$ What is the mass of the second car?    $m/s$

  During a Chicago storm, winds can whip horizontally ltgpk/f+2 f3m at speeds of 100km/h If the air strikes a person at the rate of 40kg/s per squapg ft/+kfm32lre 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 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 + pvhk*d2-a-1 dgr uetwith a constant speed of 8.6m/s on a level track. Snow begins to fall vertically and fills the car at a rate oe*u1rhk avgd-p+d - 2tf 3.5kg/min Ignoring friction with the tracks, what is the speed of the car after 90.0 min?$\approx$    m/s

  An atomic nucleus initially moving at 420m/s e 8xg +u hr/lt)ay86 spfewjs27mits an alpha particle in the direction of its velocity, and the remaining nucleus slows to 350m/s If the alpha particle has a mass of 4.0 u and the original nucleus has a mass of 222)8p+x y/f 6js8rltg72uahesw u, what speed does the alpha particle have when it is emitted?    m/s

  A 23-g bullet traveling 23m3*mvxu(m )q fi m0ru3j8rt3a0m/s penetrates 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 afq*mm rx03)umv(m jf8 i3rta3 uter the bullet emerges?    m/s

  A 975-kg two-stage rocket 8b/y4dh l ty,pis 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 i j4ht50cn, oeus traveling in outer space with a velocity of 115m/s To alter its course by 35.4nc u5j,to0e h0 $^{\circ} $, its rockets can be fired briefly in a direction perpendicular to its original motion. If the rocket gases are expelled at a speed of 1750m/s how much mass must be expelled?    kg

  A golf ball of mass 0.045 kg is hit off the tee at a speed oi v39ua* 9v;jcij;+ih4uvwg p f 45m/s The golf club was inivv +;ap;iw9ui gucjhjv4* 3 9 contact 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 velk.2wer hmasjs(rwz k 74,))t*xd3 hm oocity of 8.5m/s and comes to rest in a time interval of 8.0 ms4t r7j,x)3 khe* wzs )as.2mdhowr(km. (a) What is the impulse given to the nail?    kg*m/s
(b) What is the average force acting on the nail?    N

  A tennis ball of mass m=0.06dzix3uaxd d y f09k*)3kg and speed 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 engineer in 4dx hvr5lc q*4charge of the crashworthiness of new automobile models. Cars are tested by smashing them into fixed, massive ba*4d vx5lrcqh 4rriers at 50km/h (30 mph). A new model of mass 1500 kg takes 0.15 s from the time of impact until it is brought to rest. (a) Calculate the average force exerted on the car by the barrier. $\approx$$a\times10^5$N a =   
(b) Calculate the average deceleration of the car.    m/$s^2$

  A 95-kg fullback is running at 4m/s to the east and is stopped in 0.75 s b0frruiyt 9uy9 k,x/ i7y a head-on tackle by a tackler running due i,kf 0y /ur9ixtru7y 9west. Calculate
(a) the original momentum of the fullback    kg*m/s
(b) the impulse exerted on the fullback    kg*m/s
(c) the impulse exerted on the tackler,    kg*m/s
(d) the average force exerted on the tackler.    N

  Suppose the force acting on a tennis ball (mass 0.060 kg) points in the +x diqxd(5ast+l w 3q,tu5f3,e npl rection and is giv5,let +(3t u, q3wxfas nqd5plen by the 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 j96 vfby kz. od;ra3czdc,n 0d9ump without breaking the lower leg bone of either leg? Ignore air resistance and assume the CM of the person ; d 9 r. bd9k,vcnzc0daozy36fmoves a distance of 0.60 m from the standing to the seated position (that is, in breaking the fall). Assume the breaking strength (force per unit area) of bone is $170\times10^6\mathrm{~N/m^2}$ and its smallest cross-sectional area is $2.5\times10^{-4}m^2$ [Hint: Do not try this experimentally.]    m

  A ball of mass 0.440 kg moving east (+x direction) withe .b*rhzrn5r v8tq0g; 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 collision?Let A represent the 0.440-kg ball, and B represent;qn.*brz 5grvh r8et0 the 0.220-kg ball. $v'_A$    m/s  ----待选择----eastwest  $v'_B$    m/s  ----待选择----eastwest 

  A 0.450-kg ice puck, moving east with a speed of 3m/s has a u (ub6ak6j35 wurk49vnqdp o8 head-on collision witqbu vk 86wdn39 ru4kj(a p5o6uh 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-kg puck. v'$_A$ =    m/s ----待选择----eastwest  v'$_B$ =    m/s ----待选择----eastwest 

  Two billiard balls of equal mass undergo a perfectly elastic head-on collisin6zv5epaiayh3x6wu ok8+ d5 , on. If one ball’s initial speed was 2m/s and the other’s was 3m/s in the opposit6yid+8 zkeo6aua,w 5 hn53pvxe 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/s in the opposite direction. ) v'$_A$ =    m/s v'$_B$ =    m/s

  A 0.060-kg tennis ball, moving with a speed of 2.5m/s collides head-on wilo p21oz(w3;fnrp q 20z1 ct:a:fnwlp th a 0.090-kg ball initially moving away from it at a speed of 1.15m/s Assuming a perfectly elastic collision, what are the speed and direction of eachp ( 1:npc1;ro3ptwflon0a wlzz:2f2q 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 withsl ftg vw0x)a9aul 9)j6rr6og+wo nz)n 9e,5 y a speed of 8.5m/s collides head-on and elastically with another ball initially at rest. Afterward the incoming softball bo0yo9 rfs99 nw v)e+ljrt)az wlgx a )6g5nou,6unces 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 one approachr.3 jhe)ggcc2ga5/ nl es the other directl c )2hr5la/gjc3egn.gy from the 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 collisio jgjy* iy /rz4+ec; gf:*sm-msn with a second ball initially at rest. The second ball moves off with half+-jgsy ;ijzf*cr4sg mm/y e:* 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 cu xz;da9h;b ;fjbe slides down a frictionless incline as shown in Fig. 7–35, and elastically strikes another cube at the bottom that is only one-half if;;bdh9j;xz ats 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 objecuou4nph;,)i+wtq d8 z t of mass m$_A$ and velocity v$_A$ elastically striking a stationary object of mass head-on. (a) Show that the final velocities v'$_A$ and v'$_B$ are given by$v_{\mathrm{A}}^{\prime}=\left(\frac{m_{\mathrm{A}}-m_{\mathrm{B}}}{m_{\mathrm{A}}+m_{\mathrm{B}}}\right)\nu_{\mathrm{A}},v_{\mathrm{B}}^{\prime}=\left(\frac{2m_{\mathrm{A}}}{m_{\mathrm{A}}+m_{\mathrm{B}}}\right)\nu_{\mathrm{A}}.$(b) What happens in the extreme case when m$_A$ is much smaller than m$_B$ Cite a common example of this. (c) What happens in the extreme case when m$_A$ is much larger than m$_B$ Cite a common example of this. (d) What happens in the case when m$_A$=m$_B$ Cite a common example.

  In a ballistic pendulum exper8p f9oitbr1jym6 (y 3yiment, projectile 1 results in a maximum height h of the pendulu(jr y18mb3 6op9i ytfym equal to 2.6 cm. A second projectile causes the the pendulum to swing twice as high, $h_2=5.2\mathrm{cm}$ The second projectile was how many times faster than the first? $v_1$ =    $v_2$ ([color=rgba(0, 0, 0, 0.85)]Round to three decimal places)

  A 28-g rifle bullet traveling 230msx-4y1h7 1j7sym j ssx/,0zqorwm r8 g/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 pendulum’s displacement.ves0rr1 y78zg mjsyosw , x/hm1 74j-xqsrtical$\approx$    m horizontal =    m

(a) Derive a formula for the fraction of kinetic energy lost.;f:p;v fyi 8-9cic0 qmttbb v, $(\Delta\mathrm{KE/KE})$ for the ballistic pendulum collision of Example 7–10. (b) Evaluate for m=14g and M=380g

  An internal explosion breaks an objectqw29+* e7;pq; niin uyss2gw/kx6edo , initially 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 acquire? (Let A represent the heavier particle, and B represent the l2qs u/ * qsnwy;g2xdknp+oi ;6we9e 7iighter particle. ) KE'$_A$ =    J KE$_B$ =    J

  A 920-kg sports car cc0nln 2, hhk*jollides into the rear end of a 2300-kg SUV stopped at a red light. The bumpers lock, the brakes are 0h,jh*c nnlk2locked, 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 represent the SUV) $\approx$    m/s

  A ball is dropped fr- ,*bvxhsi4 dvom a height of 1.50 m and rebounds to a height of 1.20 m. Approximately how many rebounds will the b, ix -dbvvhs*4all make before losing 90% of its energy?   

A measure of inelasticity in a head-on collision of two ohq 2 mvf6 nu9u7w r(gd:ua3to1bjects is the coefficient 7munfu (ag3r6w 2t u: 9ohd1qvof 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 -anx fe)8 5d8bytcq )gtimes 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 reassembled block is set on a ro xt)e -ay58cqf)dng8 bugh-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 cola4,vv7fj/f o3noe ( yhd9nlq)lides head-on with a 10.0-kg object moving in the -xoedyaqn,)h(4 /9vfn l f3vo7j 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 electrono- t(z(el66cd uay n*x, and a neutrino. The electron and neutrino are emitted at right angles and have momentan(x(-6a tl ouy6 *dzce 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 mass6+p0g;h y k -q(dkcbwu $m_\mathrm{A}=0.400$kg moving with speed $\nu_\mathrm{A}=1.80$m/s strikes ball B, initially at rest, of mass $m_\mathrm{B}=0.500$kg As a result of the collision, ball A is deflected off at an angle of 30.0 $^{\circ} $ with a speed $\nu_\mathrm{A}^{\prime}=1.10$m/s (a) Taking the x axis to be the original direction of motion of ball A, write down the equations expressing the conservation of momentum for the components in the x and y directions separately. (b) Solve these equations for the speed v'$_B$ and angle $\theta_{\mathrm{B}}$ of ball B. Do not assume the collision is elastic. $\theta_{\mathrm{B}}$ =    $^{\circ} $ v'$_B$ =    m/s

  After a completely inelastic collision between two objects of equal mcg8m.u fl-p. rass, each having initial speed the two move off together with speed v/3 What was the angle between tf- rp mg.c8.luheir initial directions?    $^{\circ} $

  Two billiard balls of equal mass move at right angles o9htik3*de2u jjzm1 4 and meet at the origin of an xy coordinate system. Ball A is moving upward along the y axis at 2m/s and ball B is moving to the right along the x axis with speed*4 i2jhd e9umtjz3o1k 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 perfect+-vnv wz vx.pjt,p + 6eiwlityo7 +1u5zo1,clly elastic collision with another atom at rest. After the impact, the neip+ +,c t+7v.yewu56 ,ltow-1pvlxi1jv no zzon 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 elastic collision with a/-yl z x.jgde*eq(p1d nother atom at rest. After tql1j/g.* p- ey(zdxde he 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. 7–mif29.l /np tu wsd:2mv0 b(ow38. Specify relative to the left29v:2.im nmb/olw sf0(w utpd-hand 1.00-kg mass.    m

  The distance between a ca c+9f(ffnb+l di w65lkrbon 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 behind the fr: c+j9qd/ahegy3-t5 s9gucsmont of the car. How far frome/uhcaq-+y:95td j g3sgcm 9s 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 person has a mass of 70.0 kg.    m

  A square uniform raft, 18 m by 18 m, of mass 6800 kg, is used a )czxuct*9nz,u )gfvryr0qw(7,0 ikbs a ferryboat. If three cars, each of mass 1200 kg, occupy its NE, SE, and SW corners, determi rw9n0tv*uzz0)gucq7 ), yrfb x(cki ,ne the CM of the loaded ferryboat.$X_{CM}$ =    m $Y_{CM}$ =    m

  Three cubes, of sides;n ypoo(. ycjb- ,-upu $l_0$,$2l_0$, 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 case8mp3gwtu+ y9 ds of tomato paste (see Fig. 7–40), each of which is pmd9 u3+wt8gya cube of length l. Find the center of gravity in the horizontal plane, so that the crane operator can pick up the load without tipping it.$X_{CM}$ =    l $Y_{CM}$ =    l

  A uniform circular plate of radius 2R has a circular hole of radius R cut out crwd(vfs k q- ey33s22nq4ki.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 nkdq w2svy-42i fsq3rk.c e3(the position of the center of mass of the plate? [Hint: Try subtraction.]   R

  Assume that your proportions are the same as thos k:.3 r8snzy yx1ay)dre in Table 7–1, and calculate the mass of one of your legs1y8) r. k 3sryndyxz:a.    kg

  Determine the CM of an outstretched arm usi:uet,bf 3,xjh ng 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 bs88)j 21 ouewj gqdxa.ent at a right angle. Aqu )s28 wjo.age1d8jxssume that the person is 155 cm tall. $X_{CM}$ =    cm $Y_{CM}$ =    cm

When a high jumper is in a pos ;,v2/ ut9ddmxu/ melyition such 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 em;vul2xt/y/udd9 ,m CM will be. Will this CM be outside the body? Use Table 7–1.

The masses of the Earth af 6w:9dd6u,/ btyyavckn* o+hnd 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 frict5llef/ g.:(rijft .becwr z+yj: a66-o /inupionless 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 ofefz j bv7fm4m/u8f/a 2:r4wsg mass 2.00 kg and a diameter 0.0800 m mounted on a uniform cylindrical handle of mass 0.500 kg and 4s78 vb/gejzmmf:/u 4fw2ar f length 0.240 m, as shown in Fig. 7–42. If this mallet is tossed, spinning, into the air, how far above the bottom of the handle is the point that will follow a parabolic trajectory?    cm

  A mallet consists of a uniform cylindrical hea +c05w-lx cfkzvw(p p)8tw1yfd of mass 2.00 kg and a diameter 0.0800 m mounted on a uniform cylindrical handle of mass 0.500 kg and length 0.240 m, as shown in Fig. 7–42. If this mallet is tossed, spinning, into the air, how far above the bottom of the handle is the point that will follow a parabolic plwty+1f5)ck (-zw pwfv 80x ctrajectory?    d    d

  (a) Suppose that in Exas kki+ tc52o+tmple 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 masvaob6 5ft9j txgr;x;(a8 oof2 s M, are in the air and stationary with tjfoto; fr bvx26g8aax;(o59respect 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 move? What happens if the passenger stops?

  An 0.145-kg baseball pitched horizontally at strikes a bat and is popped straqn 2;h y dxrydp :xi+:(7tjsc9ight up to a height of 55.6 m. If the contact time is 1.4 ms, calculas d+t;x:(:nqd y i7xcyhpr 29jte the average force on the ball during the contact.    $^{\circ} $

  A rocket of mass m traveling with spedjfyn0)1a + 1xehrff;ed $v_0$ along the x axis suddenly shoots out fuel, equal to one-third of its mass, parallel to the y axis (perpendicular to the rocket as seen from the ground) with speed 2$v_0$ Give the components of the final velocity of the rocket.$P_x$: v'$_x$=    $v_0$
$P_y$: v'$_y$=    $v_0$

A novice pool player is faced lrh+(rur/yflnxkhpa( ey9;: 9y i;0x with the corner pocket shot shown in Fig. 7–43. Relative dimensions are also shown. Should the player be w(f/ky;xl (+ hyryuxl90n9pe ; :a hrriorried about this being a “scratch shot,” in which the cue ball will also fall into a pocket? Give details.

  A 140-kg astronaut (including.e)4tnc l ep(z space suit) acquires a speed of 2.5m/s by pushing off with his leg.z(nl 4pe)e cts from an 1800-kg space capsule.
(a) What is the change in speed of the space capsule?    m/s
(b) If the push lasts 0.40 s, what is the average force exerted on the astronaut by the space capsule? As the reference frame, use the position of the space capsule before the push.    N

  Two astronauts, one of mass 60 kg and the other 80 kg, are initially at rest in vr2.c k1zfc:kouter space. They then push each other apart. How fc. kvc1:2fzk rar apart are they when the lighter astronaut has moved 12 m?    m

  A ball of mass m makes a head-on elastic collisio1s/:lissf 3gcn with a second ball (at rest) and rebounds in the opposite direction with a speed equal to one-fourth its original speed. Whatl g3c:i/f1ss s 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 xhm1 8 .8b *e+ p:ttekak7bs3ppsb3wm an 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 Abaepp1ktx3 b:sw sk8t7.8 h mpb+*me 3 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 tstr+)q y dv0 //p:saieop of a flight of concrete steps of total vertical height 4.00 m. The ball hits four times on the way down, each time striking the hori/ +vipsysa/: 0dqert )zontal 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 1.4-l8h9oi , weu 8di/k28 ugmzxs0-kg block of wood at rest directly above it. If the bullet has a mass of 29.0 g and a speed ox u,sku8l8h/8m92 e oiz-iwgdf 510m/s how high will the block rise after the bullet becomes embedded in it?    m

  A 25-g bullet strikes and becomes embedded f xd,qp/av,5 zin a 1.35-kg block of wood placed on a horizontal surface just in front of the gun. If the c d,,q/p 5vafxzoefficient 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 of6hmmvsj6i mn ju92 s2/ mass 60 kg, sit in a rowboat of mass 80 kg. With the boat initially at rest, tv uhjs92s/mi26nmm j6he two people, who have been sitting at opposite ends of the boat 3.2 m apart from each other, now exchange seats. How far and in what direction will the boat move? The boat will move    towards the initial position of the 75 kg person(Round to two decimal places)

  A meteor whose mass was aboul8 8rdrkukbz7.n.mw9 t $ 1\times10^{ 8}$kg struck the Earth ($m_E$=$6 \times10^{ 24}$kg) with a speed of about 15km/s and came to rest in the Earth.
(a) What was the Earth’s recoil speed?    $ \times10^{-13 }$m/s
(b) What fraction of the meteor’s kinetic energy was transformed to kinetic energy of the Earth?    $ \times10^{ -17}$
(c) By how much did the Earth’s kinetic energy change as a result of this collision?    J

  An object at rest is suddenly broken apart into two z+rr5s4wx +o x:c3bc lfragments by an explosion. One fragment acquiblw x5c3c o4s+z :rrx+res twice the kinetic energy of the other. What is the ratio of their masses?   

  The force on a bullet is given by the formula F = dt/hfxkp+ . 6j580-( $1.8 \times10^{ 5}$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 ygr.gx6dc3 06i ror h8$m_A$ = 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 radioactiv84xs kkj-q5u,cms/p nely into an alpha particle and a smaller nucleus. What will be the speed of this recoiling nucleus if the speed of thmq5k/uk scj 4-nx,sp8e 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 firezu 6yrw1dp*mkf,34yj9 vywg. d at an angle of 30 $^{\circ} $ to the horizon with a speed of 25m/s (Fig. 7–45). When it reaches the maximum height, it is hit from below by a 15-g pellet traveling vertically upward at a speed of 200m/s The pellet is embedded in the skeet.
(a) How much higher did the skeet go up?    m
(b) How much extra distance, $\Delta{x}$ does the skeet travel because of the collision? $\approx$   

  A block of mass m=2.2kg slides down a +c a k) fm6q8:m4ixymx5) nroz30.0 $^{\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 og 9q4txckjj6o4)v/ lgn mass m if it is to rebound from M, slide up the incline, stop, slide downo /xjgc 46qt gj)vk49l 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 moms+8e7ntv(m:vv6h5 z mp oo6w ving in tomn:5evo (m87ts6p z hmw6vv+he negative x direction at its orbital speed (with respect to the Sun) of 9.6km/s The mass of Saturn is $5.69 \times10^{ 26}$kg A spacecraft with mass 825 kg approaches Saturn. When far from Saturn, it moves in the direction at 10.4km/s The gravitational attraction of Saturn (a conservative force) acting on the spacecraft causes it to swing around the planet (orbit shown as dashed line) and head off in the opposite direction. Estimate the final speed of the spacecraft after it is far enough away to be considered free of Saturn’s gravitational pull.    km/s