We claim that momentum is conserved, yet most movingjjn+ muhb,t4ie. b:h r hljfp0c)m-9* objects eventually slow down and stop. Extmj l jhm+: hb-*cn. f ehpubr)09j,i4plain.

When a person jumps from a tree to the ground, what happens to the momentumubwl;c9prkz47y 2 c4 7aka -je of the person upon ;a yualcb4p42j 9rk7zewk7 c-striking the ground?

When you release an inflm: 2qlb g7,fwjfq4z.jated but untied balloon, why does it fly across the room?zlq.mwf:,q4f2jj g7 b

It is said that in ancient times a rich mm2,e*cj3f sbp an with a bag of gold coins froze to death while stranded on a frozen lake. Because the ice was frictionless, he could not push himself to sh3jse pf bcm2,*ore. What could he have done to save himself had he not been so miserly?

How can a rocket change direq eq0mn)fx 5,lction when it is far out in space and is essentially5ef,0)qlm nqx in a vacuum?

According to Eq. 7–5, the longer the impact time oro n q+ia9 *7uz8komc-f an impulse, the smaller the force can be for the same momentum change, and hence the smaller the deformation of the object 9kunoqi orma *-87c z+on which the force acts. On this basis, explain the value of air bags, which are intended to inflate during an automobile collision and reduce the possibility of fracture or death.

Cars used to be built as rigid as possible to w5.l/rjjq.gz osh-/rad37 igl i ity9 2ithstand collisions. Today, though, cars are designed to have “cr/q7hs . 3t izo/igar jl2l j-gidy9.5rumple zones” that collapse upon impact. What is the advantage of this new design?

Why can a batter hit a pitched baseball furt,m2mthub :o33g : uowl2. itaaher than a ball tossed in the air by m:w,23abug.t lo h mo iut3a2:the batter?

Is it possible for an object to receive a lar+dhg 4bc( q,* 6exw8m iqxt8dyger impulse from a small force than from a la(,68 *cdxqxt8hbg yeimwdq+4 rge force? Explain.

A light object and a heavy obii3sn/ *mdmv 6d jg0i/ject have the same kinetic energy. Which has the greate6mdn3/i/0 mdsjiiv* gr momentum? Explain.

Describe a collision in whtn w+c a xo/i*/:c1jxhich all kinetic energy is lost.

At a hydroelectric power pl,cyh/owmob(;2q::1lsw: ewi i m6j qcant, 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 iscjm6iyh21qb ,emi wloq:w s o(:w:;/ c brought to a dead stop, or so that the water rebounds?

A squash ball hits a4m9nl .0heqxry c/n-b wall 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:6ticp xq; e*n xbs3:z height h onto a hard steel plate (fixed to the Earth), fzb;6 p*xnq::sxie 3t crom 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 steel plate.

Why do you tend to lean backward when carrying a heavy load in your a7wv/ f5ub 1fvf u.e:tb ogb7y9rms?

Why is the CM of a 1-m length of pipea1y+a ie/fcf9 z22f9-mooc oa at its mid-point, whereas this is not true for ya2y i +ao o 91fcf2c9-aeom/zfour arm or leg?

Show on a diagram holx7.jt5yyvz-a og3ar: /t;mx w your CM shifts when you change from a lying position to a sittot r5y vya- gxa;tz7/3x:mj .ling position.

If only an external forcew.-8vx p5tm zv can change the momentum of the center of mass of an object, how can the in5xv-mt .zv8p wternal force of an engine accelerate a car?

A rocket following a parabolic path through the air suddenly explou3g 6y,ulfr mx7ey ;:tdes into many pieces. What can you say a eyxl,gm:6;3u t7ruyf bout the motion of this system of pieces?

  What is the magnitude of the momentum of a 28-g sparrow flying with a speed ofm.,rgd;;vsco/ ac m2 k $8.4 \; m/s$    $kg \; m/s$

  A constant friction force of 25 N acts on a 65-kg skier for 2 6etfro ,/mw;s0 s. What is the skier’s change in velocwe,; st/6f rmoity?    m/s

  A 0.145-kg baseball pitched at 39 m/s -hl59aoti8q h is hit on a horizontal line drive straight back toward the pitcher at 52m/s If the contact time beti haq8ot h95-lween 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 packagettj(y +d *4usz out horizontally with a speed of 10 m/s Fig. below Calculate the velocity of the boat immediately after, assuming it was initially at rest. The mass of the child is 26.0 kg, and that of the boat is 45.0 kg. Ignore water ry4(s+* ztd jtuesistance. The magnitude of the velocity of the boat is    m/s

  Calculate the force exerted on a rocket, given that the peta2oa:g ly(ul3 b g6rnq2)*xropelling gases are expelled at a o y2xqa*) ugra6(b3tll :ng2e 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 at g 4 r5 ox66:by:y bigcb:hgjy+ud/l)t$4.1 \; m/s$ 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 alevel friction ;b+g95m dhxgsh wc-p/23iza vless track with a constant speed of 18m/s A 5350-kg load,initially at rest, is dropped onto the car. What wilv-xsa3g;dwghc z9m h2p+ 5 b/il be the car’s new speed?    m/s

  A 9300-kg boxcar trav;gwvl zkb;*apcat/8c1 t k9 g5eling at $15 \; m/s$ strikes a second boxcar at rest. The two stick together and move off with a speed of $6 \; m/s$ What is the mass of the second car?    $m/s$

  During a Chicago storm, winds can whip horizontally at speeds of 100kxdj*o;n-lq o pib 13w0la4 s((k ei9idm/h If the air strikes a person at the rate of 40kg/s per square meter and is brought to red4d*ilajp;oln( bi -1(i9 3sqe 0wxokst, 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 with a constam /7 *yr*xgd w(67nxb;fpemkdnt speed of 8.6m/s on a level track. Snow begins to fall verticallxxm7r (;ywe6*m*p ddg/fb 7n ky 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 moving at 420msit id/eo;/ pb2 k6g.b/s emits an alpha particle in the direction of its velocity, and the remaining nucleus slows to 350m/s If the alpha particle has a mass of 4.0 u and the original nucleus has a mass of 222 u, what speed does the alpha particle .6 ;ekb/obi s gpt2id/have when it is emitted?    m/s

  A 23-g bullet traveling 230m/s penetrates a 2.0-kg block of wood and emerge8ko0y8 2k:qhakzay(r s cleanly at 170m/s If the bloc:yr k0z8aaohq8y 2 (kkk 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 tr.t(:m oxld+d *j b(vjotbq0w6aveling at a speed of $5.80\times10^3\mathrm{~m/s}$ with respect to Earth when a pre-designed explosion separates the rocket into two sections of equal mass that then move at a speed of $2.20\times10^3\mathrm{~m/s}$ relative to each other along the original line of motion. Let “A” represent the upper stage (that moves away faster) and “B” represent the lower stage.
(a) What are the speed and direction of each section (relative to Earth) after the explosion? $v'_A$   m/s  ----待选择----away from the Earthtowards the Earth  $v'_B$   m/s  ----待选择----away from the Earthtowards the Earth 
(b) How much energy was supplied by the explosion? [Hint: What is the change in KE as a result of the explosion? $a\times10^8$ a =    J

  A rocket of total mass 3180 kg is traveling in outer sujjh3(b s,cg-pace with a velocity of 115ms h -b3uj,c(gj/s To alter its course by 35.0 $^{\circ} $, its rockets can be fired briefly in a direction perpendicular to its original motion. If the rocket gases are expelled at a speed of 1750m/s how much mass must be expelled?    kg

  A golf ball of mass 0.045 kg is h 28f. :mzevm,biu)m xiit off the tee at a speed of 45m/s The golf club was in contaez.28) mv f mi,bmi:uxct 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 (6w2 )bb/nbvgom h 7fba velocity of 8.5m/s and comes to rest in a time interval of 8.0 ms. (a) What is the impulse given to the nailbg/ob72hwmnbb v(6 )f?    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 walq 8o60g aipw6/rkr2v+xk+i izfe9c uh3hk5x ) l 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 automobile t;gn yd)j97 n w7qu/shmodels. Cars are tested by smashing them into fixe/sqd;yw t79hg7jn nu )d, massive barriers 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 htx1(jx ; nascp8 fdruf1c 270head-on tackle by a tackpujfct0r2h1x (s ;1xcn 7af8dler running due 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 actinoldr1d3wnl 2, g on a tennis ball (mass 0.060 kg) points in the +x direction and is given by the graph of Fig. 7–33 as a function of time. Use graphical methods to estimal, 3rdndwo2 l1te
(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 t*g;ix i vs1f+she lower leg bone of either leg? Ignore air resistance and assume the CM of the person moves a distance of 0.60 m from the standing to the seated position (that is, in breaking the fall). Assume the breaking strength (force per unit area) ofs fxs+vi;1i*g 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 egrvt2kaq5 z3wg9psd/ ffg8fk b*:m /-ast (+x direction) with a speed of collides head-on with a 0.220-kg ball at rest. If the collision is perfectly elastic, what will be the speed and direction of each ball after the collision?Let A represent the 0.440-kg ball, and B represent the82rgfpz/39 k:5v *dkgqswt /ffm -gba 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 collision wc e ,bxxy(o (d;xq2w.zith 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 pdox;x,q y(x2bzwce(.uck. v'$_A$ =    m/s ----待选择----eastwest  v'$_B$ =    m/s ----待选择----eastwest 

  Two billiard balls of equ4u5wypi kd9dmqhkn7 /v7w0p 7al mass undergo a perfectly elastic head-on collision. If one ball’s initial speed was 2m/s and the other’s was 3m/s in the opposite direction, what will be their speeds after the collision?(Let A represent the ball moving at 2.00 m/s, and call t d p9mn 4iwv/h70kdy7wq75uk phat 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, movind(9x +zw(kyw fdgv7 x3g with a speed of 2.5m/s collides head-on with a 0.090-kg ball initially moving away from it at a speed oyk+7( vd9 (3dgzwwfxx f 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 thatomsn2)tp5sux0 g u7e*m.ys7 i is moving with a speed of 8.5m/s collides head-on and elastically with another ball initially at rest. Afte tig 7se u5mp72usn.0y)x*omsrward the incoming softball bounces backward with a speed of 3.7m/s Calculate
(a) the velocity of the target ball after the collision    m/s
(b) the mass of the target ball.    kg
(Let A represent the moving softball, and let B represent the ball initially at rest.)

  Two bumper cars in an amusement park ride collide elastically asb ah 03t:(iusc 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 is movst: uhi(ac3b 0ing 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 u ld8mwhm /pmi (xl ,9oitj+a2.eb3 r(an elastic head-on collision with a second ball initially at rest. The second ball moves off with half the original speed of the f xeo8(d +b 3./pi9j ,h2wua mrlitlm(mirst 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 slideh6 *bkmfbx 4sea t06 v,e7-nqls down a frictionless incline as shown in Fig. 7–35, and elastically strikes another cube at the bottom that is only one-half its mass. If the incline ise7ekmv-l* b n4 ,6fxt0ahb sq6 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 o5 w/:6, bzblezbn ;pyei(nxd,f 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, prvhbl0u9 cm 0r/ v:4zyaz *,6fift,cus ojectile 1 results in a maximum height h of the pendulum equal to 2.6 cm.vz*0fiv c,m,6 ulsz4 a tuyc9rh0/fb : 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 buries itself in a 3.6-kg pendulum ,ciuxi0 bq 9bk37epd 2h bd7d6hanging on a 2.8-m-long string, which makes the pendulum swing upward in an arc. Determine the vertical bbhk03692d bu cd7p eqxdi,i7 and horizontal components of the pendulum’s displacement.vertical$\approx$    m horizontal =    m

(a) Derive a formula for the fraction of kie4qr c- 5mx+0n4pe xygi7h.d)sf3a aynetic 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 pieces, onty/jahekk4 7c:i )9fre of which has 1.5 times the mass of the other. If 7500 J were released in the explosion, how 4ch:tk jeka)7f9y /ir 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 stoppedt1krhp7/j,k9zu u:kr 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 coeft:kh/kr91z,p uj7urk ficient 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 from a height of 1.50 m and rebounds to a hc6i9vze :( fo hrzi,e+eight of 1.20 m. Approximately how many reboundsh:f c9vzz ir6e oi+(,e will the ball make before losing 90% of its energy?   

A measure of inelasticity in a head-on collision of two objects is the coe ms) 8w/)zwanox;.g gwfficient of restitution, e, g )o s/n wgm;wzw.ax8)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 int/-7u;+vqr2 o )h kxgyp4qwmhjo j; q6d9k8y nto 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 the fuse is lit. o+4n67hvo2dr;) tjx q/ kqmqh 8kp 9ywguy-;jWhen 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 head-on wcr5 5p2m dee:hyg4iu 1( /fvowith a 10.0-kg object moving yu1 4wf e(eihmov5cg5r /2 dp: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 restsmg3.j xjv7pvc-y+-e:uq5m n decays into a second nucleus, an electron, and a neutrino. The epm3y:eg+j5qn 7uv mx-c-vs. jlectron and neutrino 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 mas d+;u* ,g,fewhreirb9s $m_\mathrm{A}=0.400$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 twoe rslp6-u-g .q2/o xrv objects of equal mass, each having initial speed the two move off together with vrgrq. o xp2s -l/ue-6speed v/3 What was the angle between their initial directions?    $^{\circ} $

  Two billiard balls of equal mass move at right angles and 1sah,nrx3v1k uwe (7dmeet 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? direcn,11(shda kv 7xuer 3wtion of ball A is  ----待选择----x directionx direction v'$_A$ =    m/s v'$_B$ =    m/s

  A neon atom (m=20u) makes a perfectly elastic collision with another atom at remaq,ai 2/ pmqaon14 4bst. Aftermbopn,iq 4a12ma4 /a q 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

  A neon atom (m=20u) makes a perfectly elqstpk 4+alur:ac3dz*y-8e 7 e astic collision with another atom at rest. After the impact, thedl4a c-7 era pu*q3s:y zk+8te neon atom travels away at a 55.6 $^{\circ} $ angle from its original direction and the unknown atom travels away at a -50 $^{\circ} $ angle. What is the mass (in u) of the unknown atom? [Hint: You can use the law of sines.](Let A represent the incoming neon atom, and B represent the target atom) $m_B$   u

  Find the center of mass of the three-mass system sho3p2(n;e.wq.z6ze+ z f/ jksly wgsi4kwn in Fig. 7–38. Specify relative to the 6z/q wks gw( 2j 3plen;ys.4i. ezfz+kleft-hand 1.00-kg mass.    m

  The distance between a carb/iys wg-k4 dm4on atom ($m_{\mathrm{C}}=12\mathrm{u}$) and an oxygen atom ($m_{\mathrm{O}}=16\mathrm{u}$) in the CO molecule is $1.13\times10^{-10}$m How far from the carbon atom is the center of mass of the molecule?    $\times10^{-11}$m

  The CM of an empty 1050-kg car is 2.50 m behind the front tmrr9ib3az g(d b.8 0hof the car. How far from the front of the car will therb3b a8t (dhr.9i0mzg CM be when two people sit in the front seat 2.80 m from the front of the car, and three people sit in the back seat 3.90 m from the front? Assume that each person has a mass of 70.0 kg.    m

  A square uniform raft, 18 m by 18 m, of mass 6800 kg, is used as a ferryboat.y+v9c7tmcl7;f q /i by0.utyr If three cars, each of mass 1200 tuf9cy qctrbiym v/0 ;l+7y.7 kg, occupy its NE, SE, and SW corners, determine the CM of the loaded ferryboat.$X_{CM}$ =    m $Y_{CM}$ =    m

  Three cubes, of side jq/dlid2vsf 7t3o0,xs $l_0$,$2l_0$, 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 t9pa 64 srqrtdr2,2 xc qrjzi3/omato paste (see Fig. 7–40), each of which is a cube of length l. Find the center of gravity in the horizontal plane, sxrzqt ar, qrd6cj324si/92pro that the crane operator can pick up the load without tipping it.$X_{CM}$ =    l $Y_{CM}$ =    l

  A uniform circular plate of radius 2R has a circular hole of radiu gij yc:6lf8+2 f1v1mtrnuwu4s R cut out of it. The center of ther4cf11v m wjfut2:8ginl+ u6y 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.]   R

  Assume that your propob,+;flcyqp7(,hlcy), khgpr rtions are the same as those in Table 7–1, and calculate the mass of onc hp;,pyl+)f kbylhc7,g(r,qe of your legs.    kg

  Determine the CM of an outstretched arm using Table5 xnh8j* 2u3pj (vgcui.kr1 mg 7–1.   % of the person's height along the line from the shoulder to the hand

  Use Table 7–1 to calculate the position of the CM of an arm bent at a ri552zhv xx:p8s5 ex,i omvyb2 gght angle. Assume that the person is 155 cm ta5:xxx55ohe 8 z gb,2mpvysiv2ll. $X_{CM}$ =    cm $Y_{CM}$ =    cm

When a high jumper is in a position such i-wt,lqw7 * 5 ,vrjturthat his arms and legs are hanging vertically, and his trunk and head are horizontal, calculate how far below the tol5-t7, qvurjt r, w*wirso’s median line the CM will be. Will this CM be outside the body? Use Table 7–1.

The masses of the Earth and Moon arej4*t7 ngf*c;xmszd0 l $5.98\times10^{24}$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 friction4v+a+gfk+e gd ,oy ss8less 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 and a diameter t c3ger- vm-*n0.0800 m mounted on a uniform cylindrical handle of mass 0.500 kg and length 0.240 m, as shown in Fig. 7–42. If this mallet is tossed, spinning, into the air, how far ab tg n-e3crvm*-ove the bottom of the handle is the point that will follow a parabolic trajectory?    cm

  A mallet consists of a uniform cylindrical h (,;g*hu - v9ppg cf;w:1 nzwhwyb:eq 9:beoowead of mass 2.00 kg and a diameter 0.0800 m mounted on a uniform cylindrical handle of mass 0.500 kg and length 0.240 m, as shown in Fig. 7–42. If this mallet is tossed, spinning, into the air, ;p pbf; on,wwe*q(19hzwuh9y gwg-evbc:: :o 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 (Fig. 7zn3:q/(uqhr xg gt5(b–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 stat*vfiy3;ke.*m 2 yu jarionary 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 bal*j.rym*32yv i;af eukloon. 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 hfk/ ;/1dqgxj;d2e1 hdtqwy m7orizontally at strikes a bat and is popped straight up to a height of 55.6 m. If the contact time is 1.4 ms, calculate the average force on thex1hgtdqd7 f12; jewqdm k y//; ball during the contact.    $^{\circ} $

  A rocket of mass m traveling y r7mpy1 1ckd8with 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 -ca. 7)72p xeo wimi6zp dd /0en.u ;zm8adywfis faced with the corner pocket shot shown in Fig. 7–43. Relative dimensions are also shown. Should the player be worried about this ecazmdmi7ww2 )8nxdo;6uep z.a7.d i0p- f/y being a “scratch shot,” in which the cue ball will also fall into a pocket? Give details.

  A 140-kg astronaut (includingano ivu8c xe 2gt7qn:zv u:w.z2a(7w; space suit) acquires a speed of 2.5m/s by pushing off with his legs from an 1800-kg space cap2u inq2a g:zw :vu(;txazw cen 7o8.7vsule.
(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 o5:pc3i cc6dtyjtkg0 : ther 80 kg, are initially at rest in outer space. They then push each oth:kc c3 pt:0y 6gt5dicjer apart. How far apart are they when the lighter astronaut has moved 12 m?    m

  A ball of mass m makes a head-on elai3d; 3aa0r )m5aj9g sjkynx+k stic collision with a second ball (at rest) and rebounds in the opposite direction with jarn k 0 s+)x y9i3dka53mgaj;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 witnecvpe05qp- b9xr j 9vv4ss in a court case involving an automobile accident. The accident invo9xj-vq 9pc r bv05evp4lved 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. 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 co ug5y7 tn hsgy0(5zj3nncrete 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 1.0 m lower. If all collisions are perfectly elastic, what isnn07thygy 3u zsg(55j the bounce height on the fourth bounce when the ball reaches the bottom of the stairs?

  A bullet is fired vertically 5 fe2 9rrm*wztinto a 1.40-kg block of wood at rest directly above it. If the bullet has a mass of 29.0 g and a speed of 510m/s how 5t mrw zf*9er2high will the block rise after the bullet becomes embedded in it?    m

  A 25-g bullet strikes a*c7.mhawqjo l9ln, k 9nd becomes embedded in a 1.35-kg block 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 muzzl*a.qm 7l khjwnl,o99ce speed of the bullet?    m/s

  Two people, one of mass 75 kg and the other of mass 60 kg, sit in ad7pq*mb omc f:job31/ itk +(u rowboat of mass 80 kg. With the boat initially at rest, the two peoplo/i mqu:ok 7b1t*jf3+cmbd p( e, who have been sitting at opposite ends of the boat 3.2 m apart from each other, now exchange seats. How far and in what direction will the boat move? The boat will move    towards the initial position of the 75 kg person(Round to two decimal places)

  A meteor whose mass was about ; algor78m:fx ymr7w1$ 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 +x2suwmf ynk0s.0mn) into two fragments by an explosion. One fragment acquires twice the kineti+kmsx.uy 0sn)0n2 fm wc energy of the other. What is the ratio of their masses?   

  The force on a bullet is given by the formula F = 580-0jlepn )y*,us u/b3ua8yq 6ec( $1.8 \times10^{ 5}$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 jw(hwj1dp (6w$m_A$ = 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 ali9jykb0 ( bgdeg4f 7q.pha particle and a smaller nucleus. What will be the speed of this recoiling nucleus if tei 47(dkgb 9jq0fy .bghe speed of the alpha particle is $ 3.8\times10^{5 }$m/s Assume the recoiling nucleus has a mass 57 times greater than that of the alpha particle.    m/s

  A 0.25-kg skeet (clay target) is fired at an angle of evkmj4cl z7m0tk 9a6s* c1cn9 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 slidqbat,g6k+ 7wx /i 3hzfes 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 limit on mass m ifuqsg-awi b /ds8ccxv3*d+ sj)sw5 t +. it is to rebound from M, slide up )aui.8b qv/cj sg++ 5w dctxs s3sd*w-the incline, stop, slide down the incline, and collide with M again?    kg (Let A represent mass m, and B represent mass M.)

  The gravitational slingshot effeini w 2h* vppm) 5to;zud848mn*(jakq ct. Figure 7–47 shows the planet Saturn moving in the negative x direction at its orbital speed (with respect to the Sun) of 9.6km/s The mass of Sai*)qa8z2ndpm4j(u vmh wki* ot8p 5;n turn 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