We claim that momentum ikns2 y7lbtd 48jlpo 66s conserved, yet most moving objects eventually slow down and stop. Exn64sd7pblo2y 6tlj8 kplain.

When a person jumps from a tree to the ground, what happens to vsrj w0h5-3sbthe momentum of the perwrv0h5j s3 b-sson upon striking the ground?

When you release an inflated but untied bals0gg67 fm.k pzel31; udqbl/9umze . xloon, why does it fly across the roomubzdez xg.. ; um61smgp70f3ll q/ 9ek?

It is said that in ancient times a rich man witrx 6esd - 6tap4id2d1ch a bag of gold coins froze to death while stranded on a frozen lake. Because the ice was friction1-2c6t4 rxeda6i dsdp less, 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 whenh2l 39ovy d sr27:ouzfy;lbb 1yu6i2f it is far out in space and is essentially in a vayyfdb6uboo h92 uv;2 3sr2 z:lil7f1ycuum?

According to Eq. 7–5, the longer the iq ipx)(c1ckii14 e*vlmpact 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 the value of air bags, whic14k)vcx1 ql pce(*iii h are intended to inflate during an automobile collision and reduce the possibility of fracture or death.

Cars used to be built a7xt 1m+ kgclg,s rigid as possible to withstand collisions. Today, though, cars are designed to have “crumple zones” that c, 7cltm+ kg1xgollapse upon impact. What is the advantage of this new design?

Why can a batter hit a pitched baseball fura(lw;2t)(sskvd )vg pther than a ball tossed in the air by the battes ;(gs)pkda)vv l(2 wtr?

Is it possible for an object to receive a larger impulse from a smalagun/xy e6*k4 l force than from4*ye/x6ak gn u a large force? Explain.

A light object and a heavy obhpk 6;;lwhe py1ez.68b zu8 jgject have the same kinetic energy. Which has the greater momep yg81;ekbh668eh zlu;pj w z.ntum? Explain.

Describe a collision in wau g b/e42f.r2j:xjw which all kinetic energy is lost.

At a hydroelectric power plane3,gmkjj4.cev /,eupmx4d5r4zn ; x et, water is directed at high speed against turbine blades on an axle that turns an electric generator. For maximum power generation, should the turbine blades be designed so that the water is brought to a dead ste /egv,4dj34 e.4xuc mp5rejmnkz,x;op, or so that the water rebounds?

A squash ball hits a wallbd 0/)tn.z+wi/v9m0 f ayiizz 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 to the d3qn+tb.qb9c Earth), from which it rebounds at very nn9dcb3 q+tb .qearly 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) Answer part (b) for a piece of putty that falls and sticks to the steel plate.

Why do you tend to lean backward when carrr-dc7s(cgzks 3,4bi9k/ rdb5k g7q h oying a heavy load in your arms?

Why is the CM of a 1-m length of pipe at its mid-point, wherh/ov 3g8*yolu eas this is not true for your arm or levyu h* 8o3ol/gg?

Show on a diagram ho cmjz - -gfxlmm8.ei27iz)xm (w your CM shifts when you change from a lying position to a sitting positionzxf-x2 g( 7-e)zm jlc.mi8m mi.

If only an external force can change the momentum of the center o+)pkn jtsx+a p*8+rgpf mass of an object, how can the internal force of an engine accele+x knp*)p r+8+ja gpstrate a car?

A rocket following a parabolic path through the air suddenly explodes 7*xrb 8-ux 0vh4oz(uqc j-:ay1 lilfvinto many pieces. What can you say about the motion of this systemaorb -7jc*(8- x qvx ul40huv1zilfy : of pieces?

  What is the magnitude of the momentum of a 28-g sparrow flying with a speed of p0i0 z tozl/zt b3sr-)tw2 kdv0: k*tf$8.4 \; m/s$    $kg \; m/s$

  A constant friction force of 25 N acts on a 65-kg skier for 20 s. What nw0 c- i6,y3lgndzea *is the skier’s change in veloccy6 zni - l3e*,0gdnwaity?    m/s

  A 0.145-kg baseball pitched at 39 m/s is hit on a horizontal line drive sh2j:e(o:bh t)fkri:8 + k wywdtraight back toward the pitcher at 52m/s If the contact time between bat and bk ie:2kow :8fh)r(h: dt+wyjball is $3\times10^{-3}$s calculate the average force between the ball and bat during contact.    N

  A child in a boat throws a 6.40-kg package out horizonta 6ke5+g.ehplgf z *( u;pk*bmilly 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 thatepmk;*f +g bigu6k 5pzl(h.* e 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 propelling gal;j 7olbbr w5e.(*x v-aydy nyw, up8(ses are expelyeb(o w5. 8*x,ln-wdrybl;vjua py7( led 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 movinn83 ylb 8pjx) ,pf/s1d bnwzs:g 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 tr1fr7 (p; e6r btizanz4avels 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 will be the car’s new speedfie;6za7bnp z4r 1(r t?    m/s

  A 9300-kg boxcar travel -x1+bsorkq qu6 ciw60ing 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, wu(g w.cx/hmr7(icn6c 6jex 4q inds 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 the person is .6h/ ujm( w(6e7c qgxxcnic4r1.50 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 cougffn)aqmlkne;ds v4go2 7zh.7 m758k e m t1,asts along with a constant speed of 8.6m/s on a level track. Snow begins to fall verticala ;d n7e7 htfkmg4.fskz8n5qm7u )1ve ol2,m gly and fills the car at a rate of 3.5kg/min Ignoring friction with the tracks, what is the speed of the car after 90.0 min?$\approx$    m/s

  An atomic nucleus initially mqo:zw6p -elg6.m/t axgk) vki.* mb9g oving at 420m/s emits an alpha particle in the direction of its velocity, and the remaining nucleus slows to 350m/s If theigq6* gxb w o6pt.l)vemmkgk .-/z:a9 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 penetrates a 2.0-kg bloc6i nbu, gb*7gz/pd0iek of wood and emerges cleanly at 170m/s If th6iz e */g bugpdnb,07ie block is stationary on a frictionless surface when hit, how fast does it move after the bullet emerges?    m/s

  A 975-kg two-stage rocket is traveling at at986y s7;olz)r a qiy0zwsy .c speed of $5.80\times10^3\mathrm{~m/s}$ with respect to Earth when a pre-designed explosion separates the rocket into two sections of equal mass that then move at a speed of $2.20\times10^3\mathrm{~m/s}$ relative to each other along the original line of motion. Let “A” represent the upper stage (that moves away faster) and “B” represent the lower stage.
(a) What are the speed and direction of each section (relative to Earth) after the explosion? $v'_A$   m/s  ----待选择----away from the Earthtowards the Earth  $v'_B$   m/s  ----待选择----away from the Earthtowards the Earth 
(b) How much energy was supplied by the explosion? [Hint: What is the change in KE as a result of the explosion? $a\times10^8$ a =    J

  A rocket of total mass 3180 kg is traveling in outer space with a velocityd w1sa:nyci,5 of 115m/s To alter its co:,s1y ain5d wcurse 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 0.045 kg is hit off the tec:*uej/1l fo7sq08t y ozo or1e at a speed of 45m/s The golf club was in contact with the ball for tco8*1efqzu0o s7o1r y o/:jl$3.5\times10^{-3}$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 velocit bv),bojk 2 .wj-pa;di i8zq.ry of 8.5m/s and comes to rest in a time interval of 8.0 mi,v p2obwjbdajqz- 8 )i.;.rk s. (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=0.06kg and speed v=25m/s strikes a w(rqzat1a jua w+z(t:h r7ce)1all 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 c 5w4- ,np3 rpxwt.mzatharge of the 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 zpr xpm4-. t, ta3w5wnof 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 svkj :kq) 35anltopped in 0.75 s by a head-on tackle by a tackler running duv : ql3akk5nj)e 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 (maptu+c:r8 nh b,.r8;jgp/noqzdd0j/ hss 0.060 kg) points in the +x direction and is given by the graph of rp8hdb z;d uj+rqpt.jg:onn/ ,8h /0cFig. 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 ca;cn:a -em :n* f;jf v9nyrxhg-n a 75-kg person jump without breaking the lower leg bone of either leg? Ignore air resistance and assume the CM of the person moves a distance of 0.60 m from the sy;egmjf: - 9naxrh; v*cnn:f-tanding to the seated position (that is, in breaking the fall). Assume the breaking strength (force per unit area) of bone is $170\times10^6\mathrm{~N/m^2}$ and its smallest cross-sectional area is $2.5\times10^{-4}m^2$ [Hint: Do not try this experimentally.]    m

  A ball of mass 0.440 kg moving east (+x direction) with a speed of *v2j,) ry;paf kirfwk* t+g2o 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 colpa w+kt2r2;kr*j f*fiv,o)g ylision?Let A represent the 0.440-kg ball, and B represent the 0.220-kg ball. $v'_A$    m/s  ----待选择----eastwest  $v'_B$    m/s  ----待选择----eastwest 

  A 0.450-kg ice puck, moving east with a speed of 3m/s has a he- g m(g6ugn7zxad-on collision with a 0.900-kg puck initially at rest. Assuming a perfectly elastic collision, what will be the speed and direction of each object after the collision?Let A represent the 0.450-kg puck, and let B represent the 0.900-kg p7gg-zg(mxn 6uuck. 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 collirshj-hsl as/9)p2f4msion. If one ball’s initial speed was 2m/s and the other’s was 3m/s in the opposit fpam shslsj/4r2-9 )he 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, movin7,dvxy d w ate*9xzjxn8t; 7,kg with a speed of 2.5m/s collides head-on with a 0.090-kg ball initially moving away from it at a speed of ,jz yvx7 xtnd*;7kt9ae, 8 xdw1.15m/s Assuming 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 with a speed of 8.5mumt2w +4l7*x z-mxc26a t vbfn/s collides head-on and elastically with another ball initially at rest. Afterward the incoming softball bounces backward with a speed of 3.77nb2amx*l-mx+cuzt2f v6wt 4m/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/sx y9m yn-(u;xc9 kvtk. p3lt elastically as one approaches the other directly from the rear (Fig. 7–34). Car A has a mass of 450 kg and car B 550 kg, owing to differences in ;9 9 lkk yy/xu.ntv(msctxp3- 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 t 8euvse4hot++9p i5e makes an elastic head-on collision with a second ball initially at rest. The second ball moves ofso9tp4tuehe+5 ve 8 i+f 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 shoe c5/ xsdt36yk/v;bv f )hdow 406nflgwn in Fig. 7–35, and elastically strikes another cube at the bottom that is only one-half its mass. If the incline is 30 cm high and the table is 90 cm off the floor, where does eachglc4/wxsn t ef6 vfdkyod0)hv6 5b3;/ cube land? [Hint: Both leave the incline moving horizontally.]$\Delta x_{m}$$\approx$    m $\Delta x_{M}$$\approx$    m

ake the general cases)oz5 xb 0op(g of an object 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 experiment, projuudr 93usxg+8b+cp( jean w (9ectile 1 results in a maximum height h of the pendulum equal to 2.6 cm. A second projectilecu3e jgn u( dp+w a(brux99+s8 causes the the pendulum to swing twice as high, $h_2=5.2\mathrm{cm}$ The second projectile was how many times faster than the first? $v_1$ =    $v_2$ ([color=rgba(0, 0, 0, 0.85)]Round to three decimal places)

  A 28-g rifle bullet traveling 230m/s buries itself in awqmadn3u ):i--ie -e v wo61ce 3.6-kg pendulum hanging on a 2.8-m-long string, which makqe: a-n1dow-wie6vm)cu3 -e ies the pendulum swing upward in an arc. Determine the vertical and horizontal components of the pendulum’s displacement.vertical$\approx$    m horizontal =    m

(a) Derive a formula for the fraction of kinetic ehcrtcic, haj (,2k3vh6j :fp3nergy lost, $(\Delta\mathrm{KE/KE})$ for the ballistic pendulum collision of Example 7–10. (b) Evaluate for m=14g and M=380g

  An internal explosion breaks an object, initially at rest, intn xxlq;+hl3vi5 bq, j6o 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 thh bxi+qnx5q;3,jv6 l le heavier particle, and B represent the lighter particle. ) KE'$_A$ =    J KE$_B$ =    J

  A 920-kg sports car collides into the rear end olo ely)v6u9:t31 cg bvf 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 coefficieny36ce vl19: ) outbgvlt 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 fromm ezn js29o;/h a height of 1.50 m and rebounds to a height of 1.20 m. Approximately hohn2m 9j;zse/ ow many rebounds will the ball make before losing 90% of its energy?   

A measure of inelasticity in a head+i-g q(qy9lzc0thfo i38bcm--on collision of two objects is the coefficient of restitution, e,0zct-i83qil+y- 9 qm c(bofhg 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 n-z (q 6d)d.(4 6jplpeabjcydinto two 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 reassembled block is set on a rough-surfaced table, and thd plq dj6ncj p(zy)(4eb-.6ade fuse is lit. When the firecracker explodes, the two blocks separate and slide apart. What is the ratio of distances each block travels? ----待选择----1/91/101/81/6 

  A 15.0-kg object moving in the +x direction at 5.5m/s collides p9 tnt0 :ssg0z,tsnx y,(lcx4head-on with a 10.0-kg object moving in the -x dt04s:szct 9tnyl, g 0n xxs,(pirection 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 nucr (j, r+hsfzp1leus, an electron, and a neutrino. The electron and neutrino are emitted at righs+f1r pr ,zh(jt 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 mq,i3bo4n 3b1k tpyr l)ass $m_\mathrm{A}=0.400$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 betuy2 wu(i my8:yween two objects of equal mass, each having initial speed the two move off together with speed v/3 What was the angle betwe :8i m(uy2yyuwen their initial directions?    $^{\circ} $

  Two billiard balls of equal mass move at right angles and meet at3x iwy) 3o6urp the origin of an xy coordinate system. Ball A is moving upward along the y axis at 2m/s and ball B i3xu3)yorwp 6is moving to the right along the x axis with speed 3.7m/s After the collision, assumed elastic, ball B is moving along the positive y axis (Fig. 7–37). What is the final direction of ball A and what are their two speeds? direction of ball A is  ----待选择----x directionx direction v'$_A$ =    m/s v'$_B$ =    m/s

  A neon atom (m=20u) may lexbu(;(l6tdt 1wj/kes a perfectly elastic collision with another atom at rest. After the impact, the neon a(lybu;(6t1 t dwx/eljtom 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 z)rm2y6*xuvi * qx 8wfelastic collision with another atom at rest. After the impact, the neon atom travels away at a 55.w*6)qmvx xru8*y 2fiz 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. 7z+;43f,sgzetjsvy n dvr /53a–38. Specify relativ;szjz4y+ vrtf3a3vdsgen5 /, e to the left-hand 1.00-kg mass.    m

  The distance between a carbon atomsiu6 geei 9/5n u,)4fknac ip6 ($m_{\mathrm{C}}=12\mathrm{u}$) 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 2.5 dkq(s*wj4( be0 m behind the front of the car. How far from the front of the car will the CM be when t4qjsd(wek b (*wo 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 ag nyj)yl(t+pa3b q z 5sr ;t2vj*z+cc)s a ferryboat. If three cars, each of mass 1200 kg, occupy its Nct5 yn3 +2q zg*pjb;ljvtayc z)s(r)+ E, SE, and SW corners, determine the CM of the loaded ferryboat.$X_{CM}$ =    m $Y_{CM}$ =    m

  Three cubes, of sidesd+gm sc wui:w+t. 1s*z $l_0$,$2l_0$, 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 /pblbj4h3d,m6wyvm gtn (m*/wi;zg 2has 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 gra /gw 2,gwpv6myj/h (d3 m;4izbb*mtnlvity 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 p1hiy*mpx 3; rg,x xopa,l.h z/rm +g(rlate of radius 2R has a circular hole of radius R cut out of it. The center of the smaller circle is a distance 0.80R from the center C of the larger circlexgixror (l ;.*zp,ph/1x am+3h,rmy g , Fig. 7–41. What is the position of the center of mass of the plate? [Hint: Try subtraction.]   R

  Assume that your proportions ju8 j x77fri4ra 5vjcy3h/w+eare the same as those in Table 7–1, and calculate the mass of cyx7ji4+ r ver 87/5juh3fwa jone of your legs.    kg

  Determine the CM of an outstretched arm using Table 7–1. r;xz8al1y2sj   % 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 right ,u8(yv gis-g :cszg5x9(gw ahx 2 (hviangle. Assume that the person is 155 cm talca wgghs52-g,xx8(g( s:z9uvi y(i vhl. $X_{CM}$ =    cm $Y_{CM}$ =    cm

When a high jumper is in a position such that his arms and leg4af 41)ozeoj rb/p.nx9z f7nd s 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?orz4 an n)o71zdpeb9j 4x/. ff Use Table 7–1.

The masses of the Earth (:vqp:1dxbb, l hfy7y6fe*fv m/ao(sand 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 vze;hd 0lb), tman stand 10.0 m apart on frictionless ice.
(a) How far from the woman is their CM?    m from the woman
(b) If each holds one end of a rope, and the man pulls on the rope so that he moves 2.5 m, how far from the woman will he be now?    m
(c) How far will the man have moved when he collides with the woman? He has moved    m from his original position

  A mallet consists of a uniform cylindrical head of m,14bh bd8gf o:gia 1nuass 2.00 kg and a diameter 0.0800 m mounted on a uniform cylindrical handle of mass 0.500 kgg i,4h:nb1 ubgdo1af8 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 an yfqfbu));n tr ek8x4y.)ki8 uniform 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 Fig. 7–42. If this mallet is tossed, spn 8 xy)eq.k 8))ufb4rk;fiytninning, 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 5qi4/:qsrsb i–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 :; fyb4 n hh 5tnk0fdw.gwk.1uM, are in the air and stationary with respect to the ground. A passenger, of mass m, then climbs out and sli0 4 k;ftuh.wn5w:bndhf y.kg1des 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 sh;hgm5h(ne ,e trikes a bat and is popped straight up to a height of 55.6 m. If thg(e , hhm;5hnee contact time is 1.4 ms, calculate the average force on the ball during the contact.    $^{\circ} $

  A rocket of mass m traveling )3 jtwnzfqk8 x6 8u8p/zbvqw, with speed $v_0$ along the x axis suddenly shoots out fuel, equal to one-third of its mass, parallel to the y axis (perpendicular to the rocket as seen from the ground) with speed 2$v_0$ Give the components of the final velocity of the rocket.$P_x$: v'$_x$=    $v_0$
$P_y$: v'$_y$=    $v_0$

A novice pool player is faced with the corner pocklqjmp4isqu:w-)tl nq a2)5h:/)h m avet 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 into a pocket? Give detail:nav -lm)q 4/j5s2)h whq uaq: i)tlmps.

  A 140-kg astronaut (including space suit) acquires a speed ea6ui+n w9c,: um1 humof 2.5m/s by pushing off with his legs from an 1800-kg spaai+:16un cwmm,9euuh ce 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 ohq 1,+e0) m x4q)jtgve, wnr3o4c kxxwther 80 kg, are initially at rest in outer space. They tow cqk0rgn,44 ,)hx xe+tmwq x1vj3e)hen push each other apart. How far apart are they when the lighter astronaut has moved 12 m?    m

  A ball of mass m makes a head-on elastictjewzv; - zt25i.rxy7 collision with a second ball (at rest) and reb;we i-z2tzv.j5xt7r younds 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 involving an nc(dw5k. n eu6automobile 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. Shwcnud( n .k5e6ow 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 thy islle++8 5yop 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 horizontal part of a different step 1.y5il8shy +l +e0 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 at rest directly abpu: i/sr7r6 cv;yz v-s25fyroove it. If the bullet has a mass of 29.0 g and a speed of 510m/su zs:fr 57ys-porv/ic vy;r 26 how high 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 blocmj4 +pcaa ) 9rc:ez,ad(u3l)kw qnkj+ k of wood placed on a horizontal surface just in front of the gun. If the coefficient of kinetic friction between the block and the surface is 0.25, and the impact drives the block a distance of 9.5 m before it comes to rest, what was the muzzle speed o):ajnea4a+u,d3) w qml9(kpz+rkj c cf the bullet?    m/s

  Two people, one of mass -v5adrt,slo6eh f, t275 kg and the other of mass 60 kg, sit in a rowboat of mass 80 kg. With the boat initially at rest, the two people, who have been sitting at opposite ends of the boat 3.2 m apar dr5 a2,o tl,tfvhe6-st 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 aboutt 0s5q8u vw q2oj858t 9rqvvmm $ 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 fragment9v;au:m. stm 7i omea,s by an explosion. One fragment acquires twice the kinetic energy of the other. um :mis,; aov9taem7. What is the ratio of their masses?   

  The force on a bullet r/7z biwrt/xx+s -7-ou cmbz7is given by the formula F = 580-( $1.8 \times10^{ 5}$t) over the time interval t=0 to t = $3.0 \times10^{-3 }$s In this formula, t is in seconds and F is in newtons.
(a) Plot a graph of F vs. t for t=0 to t=3.0ms
(b) Estimate, using graphical methods, the impulse given the bullet.    N*s
(c) If the bullet achieves a speed of 220m/s as a result of this impulse, given to it in the barrel of a gun, what must its mass be?    kg

  Two balls, of masses qtrtri z1tagq+ne; m- jl;os+ ;m+ /.a$m_A$ = 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 into an alpha part31gee n9zhigw kg) /( xhre780d d1mraicle and a smaller nu9z3r7(me/kri1heda)gg xe1 wdg 0n8hcleus. What will be the speed of this recoiling nucleus if the speed of the alpha particle is $ 3.8\times10^{5 }$m/s Assume the recoiling nucleus has a mass 57 times greater than that of the alpha particle.    m/s

  A 0.25-kg skeet (clay target) is firedrvg-qo a 1cdnf.y6o. 81wsu;a 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 sl8-rwl ieul0 qarpw;e7 f6evy9( w1ul-ides 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 limv v yfx,2a mbypagf9aoc52.:6 it on mass m if it is to rebound from M, slide up the incline, stop, slide down the incline, andv a vfo22:pmfca95xagy, y .b6 collide with M again?    kg (Let A represent mass m, and B represent mass M.)

  The gravitational slingshot effect. Figure 7–47 shows t;fc /9zncs alwx)pt k-8 r+3mshe planet Saturn moving in the negative x direction at its orbital speed (with rew-rsc 3a; /ft9pmxkn8s+ zlc)spect 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