We claim that momentum is conserved, yet most mo- ybqoy(pl(*d mi;9bymgn4l6ving objects eventually slow down andbmil(lmp*9 ; bo-qgy6y4(dyn stop. Explain.

When a person jumps from a tree to the ground, what happens to the kpzeu.+ mxyk58pa y20momentum of the person upon striking the pm02 zx8 keyu5py+ a.kground?

When you release an inflated but untied balloon, why d3 e39y nizlo.hoes it fly across the roomlh 9 3eyiozn3.?

It is said that in ancient times a rich man with a bagx ;mkos3.taq2 me5r fmj9:y x31pc:ti of gold coins froze to death while stranded on a frozen lake. Because the ice was frictionless, he could not push himself to shore. What cot m:;21y s fetj5ak3xq3.:9 xripmco muld 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 essentiacm0d*o( .:aue t.tvja lly d oavet*( j0.ct :m.uain a vacuum?

According to Eq. 7–5, the longer the impact time of an impulse, the smalx m ;p: mloo4n/v01hsakra 4lk7+cf,uler 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 duringm70kp,:ul+ l ;ovaka/1 n mhoscx44fr an automobile collision and reduce the possibility of fracture or death.

Cars used to be built as rigid as possible to withstand collis s,,*qad6 x f*.sezhlcions. Today, though, cars are designed to have “crumple zones” that collapse upon impact. What is the advantage ofdlfe*hs.xcs* z 6q,,a this new design?

Why can a batter hit a pitched baseball further than a bll ud1hw/gl bd95 e19rall tossed in the air by the brhuelg/ 99b1l l15d dwatter?

Is it possible for an object to receive a larger c9tvj5-ih pc;-i r8ji impulse from a small force than from a large force? Expl9pvcicjir 85ij;h- t-ain.

A light object and a heavy object have the same kineticxy 9na-/xk;4:y ++q2c)mlbzc zyty hi w8q ti, energy. Which has the greaterm9 zq lxn-y+zcw)ht:xa2 +tib,cy 4qyi8y k;/ momentum? Explain.

Describe a collision in whi9xhh14c mwqko o:d,88e sc1x*jae.spch all kinetic energy is lost.

At a hydroelectric power plant, water is directed at +d.ckrr9s-xm high speed against turbine blades on an axle that turns an electric generator. For maximum power generation, shok r. cdms9r+x-uld 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 rrsu8wmc((:e9 r(ll mwall 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 plavwewzma x b vo5tl q78o9nlww (3, 3aob(*.du-te (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 thioqo(wdwo w v 3av 5tum. 3*a8zeb9(l7wbl,x-ns process? (b) If we consider the ball and Earth as our system, during what parts of the process is momentum conserved? (c) Answer part (b) for a piece of putty that falls and sticks to the steel plate.

Why do you tend to lean backward when carrying a heavy load in(y)oct.6ot+q t3 7v0 lkdobmz your arms?

Why is the CM of a 1-m length of pipe at its mid-point, wher :d8s*n,;crbaua.cvf eas this is not true for your arm o,8s.;baac vcn rd*u f:r leg?

Show on a diagram how your CM shifts wxmyp / f.b gq-):im5mthen you change from a lying position to a sitt-yx /: q tp)m.fmmg5ibing position.

If only an external force can chfz+rmk: p 6c )lix-e:0j1mdol1j ;5tovdiml 9ange the momentum of the center of mass of an object, how05-l+j c:kotrx:;iv m1)dpmldz1f mj6l eoi9 can the internal force of an engine accelerate a car?

A rocket following a parabolic path throuu:;(03t fikg;xyxb cj gh the air suddenly explodes into many pieces. What can you say about the motion of this system of pb:3;ct ;yk uigj(0 xxfieces?

  What is the magnitude of the momentum of aexlxjxez6u+z+.s+ +s ,rk 7e j 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 skier2es0v vm5 qysldo1i49 for 20 s. What is the skier’s change1y 5m4lov qv 02d9essi in velocity?    m/s

  A 0.145-kg baseball pitched at 39 m/s is hit on a horizontal line drive straight6 8u;nvt(clkwnvd*(m back toward the pitcher at 52m/s If the contact time between bat and bc*n 8vl ;mt(d wu6(nkvall 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 horizontally with a 8 v zc)lwxp* af-;q;ay4 bce4ispeed of 10 m/s Fig. below Calculate the velocity of the boat immediately after, a4 p*y8ib-l 4vwq ; c;a)fzxceassuming 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 propelling gases2z3v7 hyey2v)hb fg)n are expelled at nh3f yv) 2y2z)vhbe g7a 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 moving atujeo, ,h j;3 edc1c,bf $4.1 \; m/s$ on an apparent breakaway for a touchdown is tackled from behind. When he was tackled by an 85-kg cornerback running at $5.5 \; m/s$ in the same direction, what was their mutual speed immediately after the tackle?    $m/s$

  A 12,600-kg railroad car travels alone on aleyh3b ,z l+citb 0s18ecvel frictionless track with a constant speed of 18m/s A 5350-kg lzib 1l+0cb3,s 8hy tecoad,initially at rest, is dropped onto the car. What will be the car’s new speed?    m/s

  A 9300-kg boxcar traveling a k q ratraonu+(myh*;128ed;gsq p(b4t $15 \; m/s$ strikes a second boxcar at rest. The two stick together and move off with a speed of $6 \; m/s$ What is the mass of the second car?    $m/s$

  During a Chicago storm, winds can whip horizontally at speeds of 100km/h If ti9ct.eon6gz :b9h w+ khe we6. t9co9g :kz +hnbiair strikes a person at the rate of 40kg/s per square meter and is brought to rest, estimate the force of the wind on a person. Assume the person is 1.50 m high and 0.50 m wide. Compare to 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 witigjv);-+.e2 :o ekdzgc;ew c ch 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 tra2ec:gc jkv ceze;- i+odw)g; .cks, what is the speed of the car after 90.0 min?$\approx$    m/s

  An atomic nucleus initially moving at 420m/s emits an alpha particle in the 5.r 3z gvbf(mrdirection of its velocity, and the remaining nucleus slows to 350m/s If the alpha partfb5 (mvgr3r. zicle 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 block o.nk o,8k -w64 pky pu(qydb9mkf wood and emerges cleanly at 170m/s If the block is stationary on a frictionless surface when hit, how fast does it movkkw ,poq-8.pkbnmky9du ( 6y4 e after the bullet emerges?    m/s

  A 975-kg two-stage rocket is traveling at a speed of vzqpa1 kk8jgw)m6 + :x$5.80\times10^3\mathrm{~m/s}$ 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 k 6wlv2( .u5mj1(qa/ yifeg hyhg is traveling in outer space with a velocity of 115m/s To alter its 6g mq. (lhevu2 yy a/(hfj5i1wcourse 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 tee asp :mcte1 f50x3aqqw0fx /z t6t a speed of 45m/s The golf club wa/c5qz1tqs0: eatf w 3mxx60fp s in 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 velocity of 8.5m/s an/hpho;o .1dmc d comes to rest in a time interval of 8.0 ms. (ac h;mp.d1oo/h) 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=0.06gqc(xd7fnbik m.zz +gkea8 7 ji)5;2ckg 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 charge ofwapm2.j0vph ;e -er3 j*ith3w the crashworthiness of new automobile models. Cars are tested by smashing them into fixed, massive barriers at 500vjihpe-h3tw.pj ;e rma *3w2km/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 ng 8jkk,;znf t,+b 7nxy.d dh3to the east and is stopped in 0.75 s by a head-on tackle by a tackler running due d n ,g 3, ;dht7z8nkkyxfjnb.+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 (0kc;xpj 7vek;(m 0aypmass 0.060 kg) points in the +x direction and is given ; p7vkjp0eym akxc;(0 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 jump without breaking the lo8d2i *iaw.eez wer leg bone of either leg? Ig2i*id. we ea8znore air resistance and assume the CM of the person moves a distance of 0.60 m from the standing to the seated position (that is, in breaking the fall). Assume the 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- 5rl.xui toq7) with a speed of collides head-on with a 0.220-kg ball at rest. If the collision is p q i5-ru7xl.toerfectly 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 a speed of 3m/s has a head-on collisio-eqgwr +v8ca 9n 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 0.450c8a+9qewg-r v-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-o e 21hbeihfg8* a988gm hdoye q:gd/-cn collision. If one ball’s initial speed was 2m/s and the other’s was 3m/s in the opposite direction, what will be their speeds after the collision?(Let A represent the ball moving at 2.00 m/s, and call that direction the positive direction.Let B represent the ball moving at 3.00 m/s in the opposite directhye2gb:g1-ic8q98 d/foe a eg h8m*dhion. ) 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 wivu05b,n7a tbn+( w,or0gprq i 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 each ball after the collision?(Letbart( w 0,,go5vu+ 0p7nnrbiq 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 th.x.mxrwf,n0 m.k-h bd at is moving with a speed of 8.5m/s collides head-on and elastically with another ball initially at rest. Afterward the incoming softbh.x b m-x.0mdnr, .fkwall bounces backward with a speed of 3.7m/s Calculate
(a) the velocity of the target ball after the collision    m/s
(b) the mass of the target ball.    kg
(Let A represent the moving softball, and let B represent the ball initially at rest.)

  Two bumper cars in an amusement park ride collide elasticarrel +qac ph -7. (m45svijnu)lly 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 passenger mass. If car A approaches at 4.5m/s and car B i.ius4m( p-jqv+n7 e a)5 rrlchs 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 h taz2 rqi/(yg/ufr++ dead-on collision with a second ball initially at rest. T2qa u/+z/ (tir +rdfgyhe second ball moves off with half the original speed of the first ball.
(a) What is the mass of the second ball?    kg
(b) What fraction of the original kinetic energy $(\Delta\mathrm{kE/KE})$ gets transferred to the second ball?   

  In a physics lab, a cube slides down a frictionless ig0vb*0mn6o mw 3(rw apce-i s1ncline as shown 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 thsg0 wi3p1 *ovem m6a-0(bwc rne 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 objetpyv zl+hvr))h.m 6b(ct 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, projectile 1 resu 0.2hqgbz apmlb1 ,n r-pp0d(glts in a maximum height h of the pendulum equal to 2.6 cm. A second projectile cah 1(npg2ard g0bb-mpz l.p,q0uses 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 afg3j 2d(p;1rhp cbw +h 3.6-kg pendulum hanging on a 2.8-m-long string, which makes the pendulum swing upward in an arc. Dete 3p j+d(2gbfp1hrwc;h rmine the vertical and horizontal components of the pendulum’s displacement.vertical$\approx$    m horizontal =    m

(a) Derive a formula for the dk3r.j15r; zih)dt fyg3p6kofraction of kinetic energy lost, $(\Delta\mathrm{KE/KE})$ for the ballistic pendulum collision of Example 7–10. (b) Evaluate for m=14g and M=380g

  An internal explosion breaks an object, initially at rest, into two piecesf1-8yl,wkupxg f tqfw.k h/:b3f p70j, 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 r,7lfw y 8:qjp0fwfu1. ptxfb 3h/kgk-epresent the lighter particle. ) KE'$_A$ =    J KE$_B$ =    J

  A 920-kg sports car collides into the rear j ukhnxf+(p/n(8mv16 gz*rnn end of a 2300-kg SUV stopped at a red light. The bumpers lock, the brakes are locked, and the two cars skid forward 2.8 m before stopping. The police officer, knowing that the coefficient of kinetic friction between tires and road is 0.80, calculates the speed of the sports car at img8 +nxprn(nhu v (f1* 6jznkm/pact. What was that speed?(Let A represent the sports car, and B represent the SUV) $\approx$    m/s

  A ball is dropped from a height of 1.50 m and rebounds to a height of 1.20 m. 0kkj7:mihac6xwct 7d 37bn v *Approximately how many rebounds will the ball make before losing 90% of its energ:djbm7 wc*kt 6 n0k3 7i7xahvcy?   

A measure of inelasticith k8s)k.maud/ /fskj4eqi.; ry in a head-on collision of two objects is the coefficient of r/rk8.d4)khs/ s.akfmiue q;jestitution, 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 t5b1 g2g( rip .mwxv1sfimes 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 the fuse is lit. When the firecracker explodes, the two blocks xv1(2ri1bg pgfm.5s wseparate 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 5.5 hcl rp7rt2-l+e vr t1nv+4hv;m/s collides head-on with a 10.0-kg objectv+rt; rhp-vtr +le 2c7hnl1v4 moving in the -x direction at 4m/s Find the final velocity of each mass if:
(a) the objects stick together;   m/s
(b) the collision is elastic; v'$_A$ =    m/s v'$_B$ =    m/s
(c) the 15.0-kg object is at rest after the collision;   m/s ----待选择----not reasonable reasonable 
(d) the 10.0-kg object is at rest after the collision;   m/s ----待选择----not reasonable reasonable 
(e) the 15.0-kg object has a velocity of 4m/s in the -x direction after the collision. .   m/s ----待选择----not reasonable reasonable 
Are the results in (c), (d), and (e) “reasonable”? Explain
( Let A represent the 15.0-kg object, and let B represent the 10.0-kg object.)

  A radioactive nucleus at rest decays into a second nucleus,y1fa+tvg.3z l 5 1hvf.j pw;lz an electron, and a neutrino. The electron and neutr13. zl1.hwgvfz5 jp+ytf lva; ino are emitted at right angles and have momenta of $9.30\times10^{-23}kg\cdot m/s$ and $5.40\times10^{-23}\mathrm{~kg}\cdot\mathrm{m/s}$ respectively. What are the magnitude and direction of the momentum of the second (recoiling) nucleus?    $ \times10^{-22}$    $^{\circ} $ from the momentum of the electron

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

  Billiard ball A of massx89sbvu gxw 98 $m_\mathrm{A}=0.400$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 mass, each2a+w5y w( 8olb ,)i ;xvftpvxl having initial speed the two move off together with speed v/3 What was the angle between their ivv,8 x alt(wio5bply;2xw)f+nitial directions?    $^{\circ} $

  Two billiard balls of equal mass move at right angl b o*s7h;lnmo;w-ex *tc)api :es 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 directio bal)7o: ;tx;con* ehpm* -swin 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 perfectly elastic collision with anow,9ocs x+/ msi 6xb+6g npd6uzther atom at rest. After the impact, 6o b+ix+6c, 6 xuspng/m9dwz sthe neon atom travels away at a 55.6 $^{\circ} $ angle from its original direction and the unknown atom travels away at a -50 $^{\circ} $ angle. What is the mass (in u) of the unknown atom? [Hint: You can use the law of sines.](Let A represent the incoming neon atom, and B represent the target atom) $m_B$   u

  A neon atom (m=20u) makes a perfectly elastic covm5 xpc5ibk )4llision with another atom at rest. After thxvmb)i 4 55pcke 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 t 8wp:g9frceyd*+4r ,p3ck qwd he three-mass system shown in Fig. 7–38. Specify relative to the left-hand 1.00-kg massweck9, d4pc+gfdw3q*r:y p8r.    m

  The distance between.0ywim(p vo,y a carbon atom ($m_{\mathrm{C}}=12\mathrm{u}$) and an oxygen atom ($m_{\mathrm{O}}=16\mathrm{u}$) in the CO molecule is $1.13\times10^{-10}$m How far from the carbon atom is the center of mass of the molecule?    $\times10^{-11}$m

  The CM of an empty 1050-kg car is 2.50 m behindh aq;,+2 4hzvkwmb ji6 the front of the car. How far from the front of the car will the CM be when two peopw ;h4k,h2z6m+vaqbj ile 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, j w6u r;:k6cawis used as a ferryboat. If three cars, each of mass 1200 kg, occupy its NE, SE, and SW coa6ucr6; j w:wkrners, determine the CM of the loaded ferryboat.$X_{CM}$ =    m $Y_{CM}$ =    m

  Three cubes, of sides : yq.c84kwq sziu7.ix$l_0$,$2l_0$, 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 cases of tomato paior4*u rbor 2,+q-y1 y no-h1z t*bocju0n.q zste (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 withbu+n1 rbqjzzy0uc.o *n-i2o *- 1yh,qrrto 4 oout tipping it.$X_{CM}$ =    l $Y_{CM}$ =    l

  A uniform circular plai3y+w9yfdzzvg 2i5 ph+ - t-ovte of radius 2R has a circular hole of radius R cut out of it. The center of the s-fh vydowpy gtzz23ivi + 9-+5maller 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.]   R

  Assume that your prop -hoh( 70x0pehfx 8lr 4dy;creortions are the same as those in Table 7–1, and calculate the mass of one ofr8d fh xx clh(r-4yp0o;0e 7eh your legs.    kg

  Determine the CM of an outstretched arm using Ta /gyzpoa 38 7h/fhc,pable 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 ofoz+z : iu9iz)lyg)p/ o an arm bent at a right angle. Assume th iouo/z) yp9+lz:z i)gat the person is 155 cm tall. $X_{CM}$ =    cm $Y_{CM}$ =    cm

When a high jumper is in a position such that his arm onaubg:u,/4 4-j:wrjn uhf o1s and legs are hanging vertically, and his tro:4h-jo4 u/ w,:a1u ujnfn rbgunk and head are horizontal, calculate how far below the torso’s median line the CM will be. Will this CM be outside the body? Use Table 7–1.

The masses of the Earth and Mo2mgu s.cw ukdvg9/2 6,f*anheon 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 /fk k**ivilk u lnd+l79if-1y80-kg man 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 mass 2.00 kg an gwy4q2e5u) sft;v7pxd a diameter 0.0800 m mounted on a uniform cylindrical handle of mass 0.500 kg and length 0.240ytg4u7vxs p)52q f ;ew 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 head of mass 2.00 kg and a diametew87h-*u h )tva ) abqnssy+5rdr 0.0800 m mounted y)tqaha nv5b +uhw7 *8)s rs-don 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 7–14 (Fig6 ec(r)tp o7md amyp91:6wedc. 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 lwpktg 718la/ar*dl/ryy b myhlp3j2e(h/7/ , are in the air and stationary with respect to the ground. A passenger, of mass m, then climbs out and slides down a rope with speed measured with respect to the balloon. With what speed and direction (relative to Earth) la y/p/h a8 7et(ymk/*hl 2rjgylb7r1/dpwl3does the balloon then move? What happens if the passenger stops?

  An 0.145-kg baseball pitched horizontally at strikes a bat and ism.-hwcf;.16c:xw w8fa a bt tq popped straight up to a heig- ahtc:q;mfca. w1tw w8 bxf6.ht of 55.6 m. If the contact time is 1.4 ms, calculate the average force on the ball during the contact.    $^{\circ} $

  A rocket of mass m traveling wit gvd6jb(oe.m 1h 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 pocket shot shown )+ltmumh6 o+sn)* *;nye6ekown9d a a 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 aa; awmke*tsd) n6nu9)yh6 o o+*en+ml pocket? Give details.

  A 140-kg astronaut (includinga)ky :sn7nu4 f space suit) acquires a speed of 2.5m/s by pushing off with hik4fu asn:)y7ns legs from an 1800-kg space capsule.
(a) What is the change in speed of the space capsule?    m/s
(b) If the push lasts 0.40 s, what is the average force exerted on the astronaut by the space capsule? As the reference frame, use the position of the space capsule before the push.    N

  Two astronauts, one of mass 6i-yg *w./mju- vux w*h0 kg and the other 80 kg, are initially at rest in outer space. They then push each other apart. How far apart are they when the liu- wug -x v*hwmy/i.*jghter astronaut has moved 12 m?    m

  A ball of mass m makes a head-on elastic collision with a second bal0gtf dkeof:1 wsgm7+ 0l (at rest) and rebounds in the opposite directd0fg kf0+sgow7:1 e mtion 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 g-o;ix lmp en)/l)5v ecase involving 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 A slid 18 m while car B slid 30 m. The coefficient of kinetic friction between the locked wheels and the road was measur/ -g ix o)m)pe;velnl5ed to be 0.60. Show that the driver of car A was exceeding the 55-mph (90km/h) speed limit before applying the brakes.    mi/h

A golf ball rolls off the top of a flight of concrete steps of 70yg jq1 5akh dtld2c4total vertical height 4.00 m. The ball hits four times on the way down, each time striking the horizontal part of a different step 1.0 m lower. If all collisions are perfectly elastic, what is the bounce dt 5yj 4ha10lc 2qd7kgheight 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 axv m,6k 3s b*wf0cbh2ft rest directly above it. Ik0w fc,v*bh b6s2xm3f f the bullet has a mass of 29.0 g and a speed of 510m/s 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 block of wood plac k0a/w/p,f)) p blwzkyed on a horizontal surface just in front of the gun. If the coefficient of kinetic friction between tw a 0/k)fpy) zw,/pblkhe 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 .v2nbah,;nt:h7j6xqf7 (wi m31z + sikxuyrp 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 apart from each other, now exchange seats. How far and in what direction will the boat move? The boat wiu3apn7zwm7n 2,sih:( x q1;j vfy rik6h.+xbtll move    towards the initial position of the 75 kg person(Round to two decimal places)

  A meteor whose mass was about zf:rl7s/gcf/ $ 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 fragments by an emrp o4,5abx-v o pa9(hxplosion. One fragment acquires twice the kinetic energy of the other. What is t-5(4ar mxvo,p 9pobh ahe ratio of their masses?   

  The force on a bullet is given by the formula F = 580-(zv7 z63s+e ix7jll1 tc $1.8 \times10^{ 5}$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 u9c 9e(aoygax1h)qu /$m_A$ = 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 decr99r)yelw(h idy,* xvays radioactively into an alpha particle and a smaller ndhe, v rlw9*( y)xiy9rucleus. 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) i( e:rodv7kv 5) eg22lk)prpios fired at an angle of 30 $^{\circ} $ to the horizon with a speed of 25m/s (Fig. 7–45). When it reaches the maximum height, it is hit from below by a 15-g pellet traveling vertically upward at a speed of 200m/s The pellet is embedded in the skeet.
(a) How much higher did the skeet go up?    m
(b) How much extra distance, $\Delta{x}$ does the skeet travel because of the collision? $\approx$   

  A block of mass m=2.2kg slides down a 30.j0 wmspz-t j2d+oym;5 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. +we:7u9v)ubp lf1atp +xeh f07–46), what is the upper limit on mass m if it is to rebound from M, slide up the incline, stop, slide d)lfv xw1fepb+ at:9euup0+ h 7own the incline, and collide with M again?    kg (Let A represent mass m, and B represent mass M.)

  The gravitational slin18eu5z v0eeqogshot effect. Figure 7–47 shows the planet Saturn moving in the negative x direction at its orbital speed (with respect to the Sun) of 9.6k8e1 evoz0euq5 m/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