We claim that momentum is conserved, yet most moving objects event8nh1+2x/yll go fs+qoually slow down and stop. Expoq/ogy+flh81xn2s l +lain.

When a person jumps from a tree to the ground, what happens -/jyft89g oxi to the momentum of the pe9 /fjio xtg-y8rson upon striking the ground?

When you release an inflated but untied balloon, why does it fly 55yxteava 0*c/fzlj 1across the roomex150 zyat lv5a* cj/f?

It is said that in ancient times a rich man with a bag of gold coins froze k:wk/k-5pn0u n 2 0 vtf0wvd,pfuzd*lto death while stranded on a frozen lake. Because the ice was frictionlln0knuf2u dd* p/ k-0 0:z vtwkfvw,p5ess, 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 is far out in space and is essentiallyu) xpt/qjuv7x:ude 0:7;pbf c in a vacuum) u7b:tpc/v dpju0u7 :ex;xqf?

According to Eq. 7–5, the longer the impact m:i q (a7tkk.mipcit7 73fw5mvzb9w4 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, which are intended to inflate during an automobbitzkwp4t5:7 v mkq.9mwacf7 i(73imile collision and reduce the possibility of fracture or death.

Cars used to be built a/:i7 8k4x/vq:gi r cw.axzwlqs rigid as possible to withstand collisions. Today, though, cars are designed to have “crumple zones” t/q7/.k : awwq 8icl:4xgxrzivhat collapse upon impact. What is the advantage of this new design?

Why can a batter hit a pitch*+ 6c mpehgq3lcii15p ed baseball further than a ball tossed in the air by the bateilcp6p+q* img 5hc31ter?

Is it possible for an object to receive a larger impulse n dhwt;+ck(jw(-*lfo from a small force than from a large force? Expla+do(wj-kl;tf *(hnw cin.

A light object and a heavy object have theo.tnlc+a p/x6r 4op5 k2g5kuy same kinetic energy. Which has the greater momentum? Eypkg6 5+ pak.co run/4t5xo2lxplain.

Describe a collision in which all kinetic energy wz 9-lez mbwd 8; xox(.mmhq75is lost.

At a hydroelectric power plant, water is did(iihv3f ny*a)vhd.ui q q77qsk f,,5rected at high speed against turbine blades on an axle that turns an electric generator. For max,vunki.i57s7( ad hyq*v ,)3hf dqfqiimum 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 4-w 1w1a cwk+ch5 $^{\circ} $ angle as shown in Fig. 7–30. 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 yg5d3ty- ekt/3hj4mzv n o :7tplate (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) Answer part (b) for a piece of putty that falls and sticks to the:httky7 o jy/tv 45g3de m3-zn steel plate.

Why do you tend to lean backward when carryie+ ri4h8cme7)eateh /ng a heavy load in your arms?

Why is the CM of a 1-m length of pipe at its mid-2c 3(rpx fgs5nx h/ie1point, whereas this is not true for your arm or l1 2i xrcpxgs5e/hn3f( eg?

Show on a diagram how your CM shifts when you change from a lying position twjaw9 hx oj4p)e-e5v4 o a sitting 5evw p4ex)a9-hw 4joj position.

If only an external force can change the momentum of the center of mas /0kvi0vlwqk4d*2zrts of an object, how can k/l0qr0 kv2vwt 4zdi*the internal force of an engine accelerate a car?

A rocket following a paraboliww:ir3 qf)0vm af5t mzocil,w2 y41 *ic path through the air suddenly explodes into many piewm:2tw yc if)z,5 v3w1 riflomqa04i*ces. What can you say about the motion of this system of pieces?

  What is the magnitude of the momentu41wg q 9e)ykspm of a 28-g sparrow flying with a speed of 8.4 m4k)wgp9esy q 1/s    $kg\;m/s$

  A constant friction force of 25 N acts o- r t3qtbx 6qvx7xhy/0j:ym+un a 65-kg skier for 20 s. What is the sk xux0hrb:j ttxy+vq qm7y/3-6 ier’s change in velocity?    m/s

  A 0.145-kg baseball pitched at x0v1zep;i n- 5gjqxb539 m/s is hit on a horizontal line drive straight 5 ipz- b xn0xejgvq;51back toward 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 a 6.40-kg package out;p(qaq dps+/ nbda1w/ horizontally with a speed of 10 m/s Fig /da/+s( n p1a;pbwqqd. 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 resistance. The velocity of the boat is    m/s

  Calculate the force exerted on a rocket, given that the propelling9aqff yu9l 9w9 gases are expelled at a rate of 1500kgl99a qf9w fyu9/s with a speed of $ 4\times10^{4 }$ (at the moment of takeoff).$a\times10^7$ N a =   

  A 95-kg halfback mov* tam 3-romd6fing at 4.1m/s on an apparent breakaway for a touchdown is tackled from beh *fmt3rm-ad6o ind. When he was tackled by an 85-kg cornerback running at 5.5m/s in the same direction, what was their mutual speed immediately after the tackle?    m/s

  A 12,600-kg railroad car travels alone on alev-bx6a*;8 n 1 yulyli; jg)lxufel 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 spe j1x l)8g *y;-6ubuxain;lfyled?    m/s

  A 9300-kg boxcar traveling at 15m ,2j-i jd gijj so7a:9zhn+9yd/s strikes a second boxcar at rest. The two stick together and move off with a speed of 6m/d 9 hjig: j97y a+no-i,dsj2zjs What is the mass of the second car?    m/s

  During a Chicago storm, winds can whip horizontally at speeds of 1(cxrt t)1y6k8mo4lurwmohz p8u*x7;00km/h If the air strikes a person at the rate of 40kg/s per square meter and is brought to rest, estit 6 l8( 4m)cxt*o 7whp z1yr;muuxko8rmate 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 railrojbda1);9.oi d0ffw jbr963y +nejmtg ad car coasts along with a constant speed of 8.6m/s on a level track. Snow begins to fall vertically and fills the car at a rate of 3.5kg/min Ignoring friction with the tracks, whfjtg9 31fd.n;96j o0m)yaibdbj +rewat 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 in thi)rm y asthw6 j:czj,r5h/*9ie direction of its velocity, and the:5ai, ct hhi/jry s* w6z)j9rm 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/du:zc,)r7 b qdb8r1gss penetrates a 2.0-kg block of wood and emerges cleanly at 170m/s Ifz7rdcbr) 8g ,db1q su: the 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 a sfvs jfg(ir)u+r m*fx al;5. 8fpeed 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 s 4rk:xfgv7i 6outer space with a velocity of 115m/s To alter its course6igs 7xkvf4r : 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 p6*t,alfw . 5 ybjkr/cbhuo)gyx9 4m/the tee at a speed of 45m/s The golf club was in cocw/ophykjux t9ybb54 a* f),g m r6.l/ntact with the ball for $3.5\times10^{-3}$s Find (a) the impulse imparted to the golf ball,    kg*m/s
(b) the average force exerted on the ball by the golf club.    N

  A 12-kg hammer strikes a nail at a velocity of 8.5m/s and comes to rest v)do+j or*24izy-yd:d,ra 2ln jx o(q in a time interval oyq dior(42*ol+ a r2jz:nxjy, dv-o)df 8.0 ms. (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 str s2rga raz)mqwlx s;+,e+z,0rikes 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 charge of the crashworthiness of new 4lkwn/o 3;g v+4tywrkautomobile models. Cars are tested by smashing them into fixed, massive lkr ;yvgtnw4wk o4/+3barriers 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 by a heu5enutg; pe.w2opvlm ) l znor/;6 8c:ad-on tackle by a tackler running )/ p;enptnzugolle; o6 :25.r8mcuvwdue 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 3endnrgs2r :+ (mass 0.060 kg) points in the +x direction and is given by the graph of F re :sngdn+32rig. 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 persomugu9afit .+:n.*ia*qxq2a;j2 zw ey n 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 standing toq.9y2z*gtia:naa fq+ej .2x* u;mwu i 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 collg1*-v zxi,d 9(h 3fhbdmg23 mofhpwa7 ides head-on with a 0.220-kg ball at hdm3, *1bf wg p397d -vaighh2 mxf(ozrest. 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 with j zcpdce 4hh30ny12*9 kc r0dfa speed of 3m/s has a head-on collision with a 0.900-kg puck initially at rest. Assuming a perfectly elastic c31nc0rfhe0 k cj hcdpy492d*zollision, 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 collisz+ mju;bepmcd.;ra 29ion. 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/s in the opposite direc+ uma2.djmcp;ez9b;r tion. ) v'$_A$ =    m/s v'$_B$ =    m/s

  A 0.060-kg tennis ball, moving with a speed of 2.5m/s collides hea8s*v( ez9j9k bwbbpu 0d-on with a 0.090-kg bbu09bjz b(9vw kpe8s *all initially moving away from it at a speed of 1.15m/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 vcv xrp*y(jtxq e8zu (7z+/l /8.5m/s collides head-on and elastically with another ball initially at rest. Afterward the incoming softball bounces backward with a speed /z rx*/ez (+yupxv7l tvcqj( 8of 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 cow 3q6 6dj s ee1s+b b;9cum:)jkkftf:rllide elastically as one approaches the other directly from the rear (Fig. 7–34).:dkj6ssec mt f9uwjr1); bkf: q e+3b6 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 el3hfazk,/d4i m41h 9knavz k4gg)d9rv astic head-on collision with a second ball initially at rest. The secok19h )rm 44gv9ighdd v3,aa /n4zk kfznd ball moves off with half the original speed of the first ball.
(a) What is the mass of the second ball?    kg
(b) What fraction of the original kinetic energy $(\Delta\mathrm{kE/KE})$ gets transferred to the second ball?   

  In a physics lab, a cubifzi1 -v6 7b15lop esme slides down a frictionless incline as shown in Fig. 7–35, and elastically strikes another cfipi761v 1b m-e l5szoube at the bottom that is only one-half its mass. If the incline is 30 cm high and the table is 90 cm off the floor, where does each cube land? [Hint: Both leave the incline moving horizontally.]$\Delta x_{m}$$\approx$    m $\Delta x_{M}$$\approx$    m

ake the general case of an object of mass.vgp -*)xcj :fs r;koals-nt - 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 experimeno2q k0bnw *c2at, projectile 1 results in a maximum height h of the pendulum equacb2ko*q0 wa n2l 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 230m/s buk zh icj7f6z-ot.k8r *ries itself in a 3.6-kg pendulum hanging on a 2.8-m-long string, which makes the pendufohtij.zk-*rk c8 z67lum 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 energy miv72 rgvi.ep(.n0 zhlost, $(\Delta\mathrm{KE/KE})$ for the ballistic pendulum collision of Example 7–10. (b) Evaluate for m=14g and M=380g

  An internal explosion breaks an object,4/-:n 9tgz*,5inesvm smd; :suj zt3d)annng initially at rest, into two pieces, one of which has 1.5 times the mn: zn)v/jtdmmnust4 za9is 3d- ;n*ngge s5,:ass of the other. If 7500 J were released in the explosion, how much kinetic energy did each piece acquire? (Let A represent the heavier particle, and B represent the lighter particle. ) KE'$_A$ =    J KE$_B$ =    J

  A 920-kg sports car collides into the rear end of a 2300-kg SUV stoppbi6w07ebm .pqc 21vrjtbg6x+ed at a red light. The bumpers lock, the brakes are locked, and the two cars skid forward 2.8 m before stopping. The police officer, knowing that the coefficient of kinetic friction between tires and road is 0.80, calculates the speed of the sports car at impact. What was that speed?(Le +w jtp6 mbc.vbb60 i72xeqg1rt 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 height of 1.20qx (6 uzltb8-s m. Approximately how many rebounds will the ball make before losing 90% of its ener8z-t xul(6sq bgy?   

A measure of inelasticity 5o qw ,budn/1:+df9b o;/rsadn9qf g pin a head-on collision of two objects is the coefficient of rest udgn,fswd/q; b5qbond+/9fr:p 9 1oaitution, 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 thre0+fc ni l51:l2a fgm rfp3f*eye times the mass of the other. A depression is made in both faces of the cu5f f3ngml*afe i f21y+p0:lc rt, so that a firecracker can be placed in it with the block reassembled. The reassembled block is set on a rough-surfaced table, and the fuse is lit. When the firecracker explodes, the two blocks separate and slide apart. What is the ratio of distances each block travels? ----待选择----1/91/101/81/6 

  A 15.0-kg object moving in the +x direction at 5.5m/i-ixgl) ./* nkbt+/ wmfw :fxws collides head-on with a 10.0-kg object moving in the -x direction at 4m/s Find the final velocity of each mangl /).kb /m f+x-:tx*wi wfwiss 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 dx*ltia. sf n)xx n-9nxxb2n.8ecays into a second nucleus, an electron, and a neutrino. The electron and neutrino ar)fx-2 xs*nxx.nnltxbi 8 . a9ne emitted at right angles and have momenta of $9.30\times10^{-23}kg\cdot m/s$ and $5.40\times10^{-23}\mathrm{~kg}\cdot\mathrm{m/s}$ respectively. What are the magnitude and direction of the momentum of the second (recoiling) nucleus?    $ \times10^{-22}$    $^{\circ} $ from the momentum of the electron

  An eagle ($m_{\mathrm{A}}=4.3\mathrm{kg}$) moving with speed $\nu_\mathrm{A}=7.8\mathrm{~m/s}$ is on a collision course with a second eagle ($m_{\mathrm{B}}=5.6\mathrm{kg}$) moving at $\nu_{\mathrm{B}}=10.2\mathrm{m/s}$ in a direction perpendicular to the first. After they collide, they hold onto one another. In what direction, and with what speed, are they moving after the collision? v =    m/s $\theta$ =    $^{\circ} $ rel. to eagle  ----待选择----AB 

  Billiard ball A of mas5 2k, v9kw*q :t,nt4r y)x9+vy.zi xcwakhvbs s $m_\mathrm{A}=0.400$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*v e4t+wyue/vdiy4wa1z59e0 mjp mq8 of equal mass, each having initial speed the two move off together with speed m*4 u 5mwwdqepy04zt9+e8 jviy/v e1av/3 What was the angle between their initial directions?    $^{\circ} $

  Two billiard balls of equal masmht m l7i.n2 w8s(v2bi; /mvyps move at right angles 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 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 ballm (2mlni7 2;i8stvwmvbh .yp / 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 wit xno+k0sdsmku7:z-er25uf7 c h another atom at rest. After the impact, the neon atom travels a n7dsr 7u:zc u+omsxk-fk05e 2way 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 another atom at resr;pxdk;.u wspht +*,rt. Afp.d ;, rhr; spwux+t*kter the impact, the neon atom travels away at a 55.6 $^{\circ} $ angle from its original direction and the unknown atom travels away at a -50 $^{\circ} $ angle. What is the mass (in u) of the unknown atom? [Hint: You can use the law of sines.](Let A represent the incoming neon atom, and B represent the target atom) $m_B$   u

  Find the center of mass z+qj+e3 na-jhe) pyxt o.1ov8of the three-mass system shown in Fig. 7–38. Specify relative to the left-hand 1.00-kg massvp j-3ae+y1j +xhzo. 8tq)eon.    m

  The distance between a carbon v:pdete;:h 5m 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 behlxu7 q3tb19b9qmh,npder 2(+n+ xevnind the front of the car. How far from the front of the car will the CM be when two people sit in the front tl+b9r3n qhpx+unv dqbex9n 21em7(,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 maywxk we9g0bwz**)4lyss 6800 kg, is used as a ferryboat. If three cars, each of mass 1200 kg, occupy its NE, SE*z eglyw9)kx0b w 4*yw, and SW corners, determine the CM of the loaded ferryboat.$X_{CM}$ =    m $Y_{CM}$ =    m

  Three cubes, of sides;yy-h:-y l bbp $l_0$,$2l_0$, 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 cbg:l0: m;vzwq ases of tomato paste (see Fig. 7–40), each of which is a cube of length l. Find the center of gravity in the horizontal plane, so that the crane operator can pick up the load without tippin0: qzv;lgw: bmg it.$X_{CM}$ =    l $Y_{CM}$ =    l

  A uniform circular plate ofa .ue c(ffd2o- 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 circle, Fig. 7–41. What is the position of the center of mass of the plate? [Hint: Try subtraction(-of 2efcdau ..]   R

  Assume that your proportions are the same as those in Table 7–1, and calculate +,, ng kaf9us3kanh,z the mass 3ankhsku+, 9gnza, f ,of one of your legs.    kg

  Determine the CM of an outstretched arm using Tt;fi y,la o*0v3mlumki02rx-ckj j7;able 7–1.   % of the person's height along the line from the shoulder to the hand

  Use Table 7–1 to calculate thxw)+zck vnu-)x b/n0ue position of the CM of an arm bent at a right angle. Assume that the person is 155 c))kwzux +n uc -nxb/0vm tall. $X_{CM}$ =    cm $Y_{CM}$ =    cm

When a high jumper is in a position such that his arms and legs are hanging vert6wg0eu h isa))ically, and his trunk and head are horizontal, calculate ah)i6weus)g0how far below the torso’s median line the CM will be. Will this CM be outside the body? Use Table 7–1.

The masses of the Earth an/ ped6h.lumbx4w6ag /zy4l- w d 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 frictionless ice.a pzspj95k:kqnc 4 s4 qj*c0u+
(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 mass 2.qh2j/y gtj r/hczr,+6 00 kg and a diameter 0.0800 m mounted on a uniforjh6 zhr2/+j/grt q y,cm 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 trajectory?    cm

  A mallet consists of a uxzhg kl22h+ni*n1 h4tniform cylindrical head of mass 2.00 kg and a diameter 0.08002g4 i* hxtz hhl+2nnk1 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 trajectory?    d    d

  (a) Suppose that in Example 7–1 zihwyjx3*y f 3 yis5d315wf9./sd fjk4 (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 stationary wit4u a mg (e9n(v4,zm.qd3pxf ewh respect to the ground. A passenger, of mass m, then climbs ougzeunemq(w, v4pa4 x f(.m 39dt 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 hog/0i y6l 4lx2wr m gkru9/j2kbrizontally at strikes a bat and is popped straight up to a height of 55 /206 uwx2likylg9k4b/jgrmr .6 m. If the contact time is 1.4 ms, calculate the average force on the ball during the contact.    $^{\circ} $

  A rocket of mass m traveling wd 2z/9 ya,dfk4rou/thv4w4q,fb aik ,ith 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 playerx* :5gxoa2aismz/ am 7 is faced with the corner pocket shot shown in Fig. 7–43. Relative dimensions are also shown. Should the player be aoz52maisx *7:g/ xmaworried about this being a “scratch shot,” in which the cue ball will also fall into a pocket? Give details.

  A 140-kg astronaut (includingiz.7vxc ,b+* 4m/rrrzkb.on b space suit) acquires a speed of 2.5m/s by pushing off with his legs fr7ib vmr4/ nz,x.bzcb k.r+r* oom 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* +k/trpu-neykd9fh3 +- g no9*rgwi q rest in outer spacqnr/ *nhkkpue9g+* -3igfr+-y 9o twde. They then 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 elastic collisionnn7 ghkqd msaz *477n) with a second ball (at rest) and rebounds in the opposite direction with a speed equal to onnk g77ndh n a4mz)*7sqe-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 .y;l)ogk:u0kaq k,q dan expert witness in a court case involving an automobile accident. The accident involved car A of mass 1900 kg which crashed into stationary c.uqy:klk) a ko0,q ;gdar 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 topq5w;wq1pd ,thfvk* h ov+e zmcqv;bw,:y,1h4 of a flight of concrete steps of total vertical height 4.0hqb wy ,p:4vwk;vw hqq1t;+f zeo5d1, hvmc*,0 m. The ball hits four times on the way down, each time striking the horizontal part of a different step 1.0 m lower. If all collisions are perfectly elastic, what is the bounce height on the fourth bounce when the ball reaches the bottom of the stairs?

  A bullet is fired vertically into a 1.40-kg block of wood at rv f 6cq/wa,hu3est directly above it. If the bullet has a mass of 29.0 g and a speed of 510m/s3h6q caf/ u,vw how high will the block rise after the bullet becomes embedded in it?    m

  A 25-g bullet strikes and2yzl vu m8zcf;ti93 s4u,i-z7;fq zie becomes embedded in a 1.35-kg block of wood placed on a horizontal surface just in i v,7uf;t e;zzylq fi3m2s-cz48izu9front of the gun. If the coefficient of kinetic friction between the block and the surface is 0.25, and the impact drives the block a distance of 9.5 m before it comes to rest, what was the muzzle speed of the bullet?    m/s

  Two people, one of mass 75 kg and the other of mass 60 kg, sit in a rowboat of zdu ix+*4ndj9 3/a cbfmass 80 kg. With the boat initially at rest, the 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 boat3dxb9d+n /aji* zfc4u move? The boat will move    towards the initial position of the 75 kg person(Round to two decimal places)

  A meteor whose mass was aboe +-qyj(-ikz ia(*5mp a q.bvnut $ 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 e zfgp;12p+gxinto two fragments by an explosion. One fragment acquires twice the kinetic energy of the other. What is the ratio of thegxp2f 1z;pe+ gir masses?   

  The force on a bullet is given by the form*w ;h8cqvh j zsb i77pg,tp:f/h6bdf0ula 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 4dsl;2.o djr j$m_A$ = 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 particle aeo*:ra 7tynulx7 bia7 jg5z18 nd a smaller nucleus. What will be the sab 7azr o:el5tjy* 1gx8i u7n7peed 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 fired at an angle ofjntv v+ t3h)i;-,tx ia 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 30.paj 3+cb23 igywil-xf8dbvg)8(q 5; k /dizsc 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 b i;slr i cl;*e:dup2mzd73d; is the upper limit on mass m if it is to rebound from M, slide up the inclind bz7 m;*s2;3ul;eiddlip rc:e, stop, slide down the incline, and collide with M again?    kg (Let A represent mass m, and B represent mass M.)

  The gravitational slingshot effect. Figure 7–47 shows the planet Saturn moq 0f.l,pz3fne30vx a0xbs7 t uving in the negative x direction at its orbital speed (w3tx.7z0 bex0 flau v0p3,nqs fith 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