We claim that momentum is conserved, yet most moving objects eventual(c: sm)) 7kvy(ktwdmwf tx6,sly slow down and stop. E ky , s6t(kfwmwd:))cm(v 7txsxplain.

When a person jumps from a tree to the ground, what happyz9s,l0 bswf 6xfr8 i8cf) 5zcens to the momentum of the person upon r8 cxs9f6z cfybif 805zs,) lwstriking the ground?

When you release an inflated but untied balloon, ru1, a:c3bc serbdy (;8l)zg 73 mall2i2vj yrwhy does it fly across the roomy3vb1 m y;8d:rab zcsll,rrge7 ) 2j23lcai(u?

It is said that in ancient t8.mpdiij39+ rpuwroc /wqt b/li np+ 6e2z8z8imes a rich man 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 shore. What could he have done to save himself had hrnuc. 2rqd 9wi t+w8o jz +8pzpeiip 8ml/63b/e not been so miserly?

How can a rocket change direction when it is far out paj81 lomzcdf)oh( *7 in space and is essentially in ahao pmf*8jz1 7(d)ocl vacuum?

According to Eq. 7–5, the longer the impr -o5me3bs/ffw 24hhzact 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 automobile collision and reduce the possfom2w4fes/h-5 3zr h bibility of fracture or death.

Cars used to be built as rigid as possible to withstand collisiomjxxjw*ugkr0s2 g (*6 ns. Today, though, cars are designed to have “cruj0 6*r*x(gkx2wjsgu m mple zones” that collapse upon impact. What is the advantage of this new design?

Why can a batter hit a pitched baseball further than a bae9 liv2*txwpnubb* (,ll tossed in the air by th9 w( xlvutp**ni, bbe2e batter?

Is it possible for an obgz/x(/wc 0g o.9o+8 ietw qohgject to receive a larger impulse from a small force than from a lh/ +t0oo8xqczg/w.g gw i9o(earge force? Explain.

A light object and a heavy object have the same kinetic energy. Whicp3 :/-zrkms y0gkkwc0za/ .kjh has the greater momentj0/mkksrcz/p.- g z3 ykwk0a:um? Explain.

Describe a collision in which all kinetic energy is loskgx8o6mjey( icc,yyz x -s(:,t.

At a hydroelectric power plant, waterhknd 7/1-kx ccos8m, r is directed at high speed against turbine blades on an axle that turns an electric generator. For maximum power generation, should the turbine blades be designed so that the water is brought to a dead stop, or so thatc 8 71,-x mscorkndk/h the water rebounds?

A squash ball hits a wameqch969y 9 si58e izyll 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 ojd2sad6o8jk(vf 9q7tnto a hard steel plate (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 par q v89a tj6sjd(2fdok7ts 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 qk z0k:mwhp0k.d,hu+your arms?

Why is the CM of a 1-m length of pipe at its mid-poi:e 0ba: 3.iqwxsotg6rfdu8(fnt, whereas this is not true for your arm o : gfra.x83tw b seqdfi0:uo6(r leg?

Show on a diagram how your CM shifts when you change from a lying poso8 v6d)*tgx y; f,zjrkition to a sitting position.,8) d;frt zyvjkgo*6x

If only an external force can change jo93vcaa02kct1,w)gbeq w g9 6 me 6hz0(bdqcthe momentum of the center of mass of an object, how can the internal forceq(t 6j2)w0c, kbc3ag1ah qvcwo9 gz 0ee6md9b of an engine accelerate a car?

A rocket following a parabolicku-izdku 76 m5 path through the air suddenly explodes into many pieces. What can you say about the motion of this systez5-i6dmuk uk7m of pieces?

  What is the magnitude of the momentum of a 28-g sparrow fl59h/r h l03vtct wx6jtying with a speed of $8.4 \; m/s$    $kg \; m/s$

  A constant friction force of 25 N j: e3mof* h gs z ur(wc30o/rt(-mzhg,acts on a 65-kg skier for 20 s. What is the skier’s change in velocity eh(s3ot*f j h30c um-wrgr,z(z/m :go?    m/s

  A 0.145-kg baseball pitched at 39 m/s is hit on a horizontal line drivc./ r*a fcno:gyqc 7i)e straight back toward the pitcher )y*cgc7cq. :nf/iroa 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 2xgc d8vk/wy ielv1+*6.40-kg package out horizontally with a speed of 10 m/s Fig. below Calculate the velocity of the boat immediately aftvv+ gx28cy/ ewklid1 *er, assuming it was initially at rest. The mass of the child is 26.0 kg, and that of the boat is 45.0 kg. Ignore water resistance. The magnitude of the velocity of the boat is    m/s

  Calculate the force exertedurtnndu)1 ,xihz4 /a+ on a rocket, given that the propelling gases are expelled at a rat+udthin xz) /rna4,1u e 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 moving75 d7ulm. otvz at $4.1 \; m/s$ on an apparent breakaway for a touchdown is tackled from behind. When he was tackled by an 85-kg cornerback running at $5.5 \; m/s$ in the same direction, what was their mutual speed immediately after the tackle?    $m/s$

  A 12,600-kg railroad cg0him1 d*an o(ar travels alone on alevel frictionless track with a constant speed of 18m/s A 5350-kg load,initially at rest, a0 i1oh*( mndgis dropped onto the car. What will be the car’s new speed?    m/s

  A 9300-kg boxcar trave4-f,l1jlvfl.q g5 7d xl,z:g. fsv cumling 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 hori h*4dc4l5hb fuf .j2rizontally at speeds of 100km/h If the air strikes a person at the rate of 40kg/s per square meter and is broug fubf4rh c j4*h25dli.ht 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 coaseot 0tkzd* n/hfyq wk0e+r531ts along with a constant speed of 8.6m/s on a level track. Snow begins to fall vertically ahr+ 0dk3 0 o/ktn t*1yezqfw5end 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 420m/s emits 0;03c9pfqktsmoa n k8an alpha particle in the direction of its velocity, and the remaining nucleus slows to 350m/s 8903a ns omkqc0ptf;kIf 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/s penetrates a 2.0-kg block of w l6qulf6(lr.um;vn hx a+c2+pood and emerges cleanly at 170m/s If the block is stationary on a frictionless surface wh c6lvunrm u lhl.6x( f2+qpa+;en hit, how fast does it move after the bullet emerges?    m/s

  A 975-kg two-stage rocket is 8kh;y/vabxm ksl98+ dtraveling 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 kx,4 2 udq 9+tbyd 7/zgex2i,;xkgceglg is traveling in outer space with a velocity of 115m/s To alteyxeck g27bxz qit4u+2;, /dx9g gdel,r 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 kgm yuif -l89a0f is hit off the tee at a speed of 45m/s The golf club was fl0u -8yi a9mfin 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 and comes to r/p0a1-xmo 7q xinx, seest in a time interval of 8.0 ms. (a) What is the impulse given to the nai7xn,1is-q 0o/ x maxpel?    kg*m/s
(b) What is the average force acting on the nail?    N

  A tennis ball of mass m=0.ck xde2ealg9(*1 v 9pd06kg 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 of the crashworthiness of new automobil+4e*v onh g*e k/d .ppa-x5w/w2joiume models. Cars are tested by smashing wj p*m.-ou +pa5xg 4ne hw/ id2/vk*oethem into fixed, 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 e) ics87 ph)5vv,zrfn by a head-on tackle by a tackler runningc )8z , 7pn)frvhs5eiv 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 acting on a tennis ball (mass 0.0: y h3r*qfv.0ry.hs w.o5 ksts60 kg) points in the +x direction and is given by the g :v.wsy3k*tsrho . f5.0qhrs yraph 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 ju -h1b6rg:,celaf 9ch6ztp u/xmp 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 to the seated position (that is, in breaking the fall). Assume the breaking strength (force per unit area) of bone is fhcc-pul6abg9/x6: rte 1,h z$170\times10^6\mathrm{~N/m^2}$ 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 o1 bkk:v t*1nulf 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 b 1utlvnkk:*1each 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 collisionb bvap t;c9 )6n,afh8az um.5p with a 0.900-kg puck initially at rest. Assuming a perfectly elastic collision, what will be the speed and direction of each object after the collision?Let A represent the 0.450-kg puck, and let B represent the 0.900-kg ,9a.a mvp68cht p;fz5) buanbpuck. v'$_A$ =    m/s ----待选择----eastwest  v'$_B$ =    m/s ----待选择----eastwest 

  Two billiard balls of equa,sc ,grc 4a-tml 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 that direction the positive direction.Let B represent the ball movina c,-mrs4tgc, g at 3.00 m/s in the opposite direction. ) v'$_A$ =    m/s v'$_B$ =    m/s

  A 0.060-kg tennis ball, moving withktxia- 3:qe1piwm ;xxcr5u 28 a speed of 2.5m/s collides head-on with a 0.090-kg ball initiallyc ex;t-iax28m:w kr1i5uq3x p 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 onn .o)z(naa-a *;nas95arwulc5 h6 dtf 8.5m/s collides head-on and elastically with another ball initially at rest. Afterward the incoming softball bounces backward wit a(ar55-cdn aau ) lahtw*ons. n;zn69h a speed of 3.7m/s Calculate
(a) the velocity of the target ball after the collision    m/s
(b) the mass of the target ball.    kg
(Let A represent the moving softball, and let B represent the ball initially at rest.)

  Two bumper cars in an amusement park ride collide elastically as one approache()/ry, pj(01lcnaj 2gzhsr) hk1b bb;j j -yics 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 ;jijr bl)kz1nha-ypcrsj/b2( h y,c) 1 bj0 g(at 4.5m/s and car B is moving at 3.7m/s calculate
(a) their velocities after the collision v'$_A$ =    m/s v'$_B$ =    m/s
(b) the change in momentum of each.$\Delta p_{\mathrm{A}}$$\approx$    kg*m/s $\Delta p_{\mathrm{B}}$$\approx$    kg*m/s

  A 0.280-kg croquet ball makes an elastic he dxp 06:5 wpn6 kiixyvxq-(mt;ad-on collision with a second ball initially mq-n6d( pki p:tw50xy6vx;i xat rest. The 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 frictionless7enxcl*bou/ 5 incline as shown in Fig. 7–35, and elastically strikes another cube at the bottom that is only one-half its ma/boc*xune l 57ss. 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 nsni 35 zsby ,b8mdzho6.0 x,+(msb3timci:c 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, projectile 1 results in a maximum height xocfr0lp)71o*kiwb)ubw o;)3 u3fbayz e)v : h of the pendulum equal to 2.6 cm. A second projectile causes the the pendulum to swing x)b07*o )caufow3:) kezb rw)v1p;bf o i3uyl 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 hangi; ) vh5tpzs:h2a5zxqnng on a 2.8-m-long string, which makes the pendulum swing upward in an arc. Determine the vertical ans tpx5a5vqhh)nz :2z;d horizontal components of the pendulum’s displacement.vertical$\approx$    m horizontal =    m

(a) Derive a formula for the fraction of kipo3ng (f1/5l c jv4hsenetic 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 br)q i(n v4a 7c4.pu0;zmcwkcb yeaks an object, initially at rest, into two pieces, one of which has 1.5 times the mass of the o u(nc 0iyakvcc.mp;qw )b7z44ther. 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 in3m(4tz naj6dol y (ht)to the rear 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 impact. What was thatmzl aht)dj4( yt6 o(3n 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 2fpp 5g8xgi+de37dx r*m3i eaxb,qd 6of 1.20 m. Approximately how many rebounds will the ball make before losing 90% of i7+m6 5rgxxqbd8gafe3p *xd i,i de3p2ts energy?   

A measure of inelasticity in a head-on collision of two obj3sje 4+sgvh-bt+evt 6m*x7 wrects is the coefficient of restitution, e, defined as3*mr-+ hx v+tj6ves7betw g4s$e=\frac{\nu_\mathrm{A}^{\prime}-\nu_\mathrm{B}^{\prime}}{\nu_\mathrm{B}-\nu_\mathrm{A}},$
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 piecz:nb ds 06 f jo3l.9luuknyo dk(;. dm62u5ksnes, one with three times the mass of the other. A depressi56zu;f2ksu0 dy 9l ud.6ndoks:3o (jn.k bmnlon 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 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 collides4f)io7) ,qfuuhe2ifo head-on with a 10.0-kg object moving in the -x direction at 4m/s Find the fo)7ffi24oe ih,qfu ) uinal 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 res :z*/lf2ocpmkqa t9-zt decays into a second nucleus, an electron, and a neutrino. The electron and neutrino are emitted at right angles and have momenta of a- q*m29z:tk zopfl/c$9.30\times10^{-23}kg\cdot m/s$ 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 mass dv)9e2 d9ctbqleh ; 2e$m_\mathrm{A}=0.400$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 o5)fbk zi73whgs /c r6rbjects of equal mass, each having initial speed the two move off together with speed v/3 What was the angle between their initial cfs 3/5irbz r67k ghw)directions?    $^{\circ} $

  Two billiard balls of equal ma7ds a)0 rpnco.u jno5m 5glx0-ss 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 5gjx0nn0s. dl5 p-r)ou7aocm 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 another atom at n7m 8dh-7*qlp7rw g )inxp4so rest. After the impact, the neo7 8xp-4 qngmsw hp)on r7l7*din atom travels away at a 55.6 $^{\circ} $ angle from its original direction and the unknown atom travels away at a -50 $^{\circ} $ angle. What is the mass (in u) of the unknown atom? [Hint: You can use the law of sines.](Let A represent the incoming neon atom, and B represent the target atom) $m_B$   u

  A neon atom (m=20u) makes a perfectly elastic collision with an4oii7 zz+b 0sh sy89znother atom at rest. After the impact, the nzh 9yo7s+nizis4 8 z0beon 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- dcd +j- ba;)zf *sg7h2b97bmoq uyk.hmass system shown in Fig. 7–38. Specify relative to the left-hand 1.00-kd9.ha d2yh*f+;czug7k sjbq )-ombb7g mass.    m

  The distance between a c*+* hgt9fp o2jvb/nagarbon 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 w ox25yzlam:qg o+/yx-8sr 9vbehind the front of the car. How far from the front of the car will the CM be when two mo:woy y z+axx89qg v5/l2r s-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,5xdce8 v808upe hda jy0b 6hi- is used as a ferryboat. If three cars, each of mass 1200 kg, occupy its NE, SE, and SW corners, determine the CM ov08exhbuy 6ed p88 idja0 h-c5f the loaded ferryboat.$X_{CM}$ =    m $Y_{CM}$ =    m

  Three cubes, of sides nkd72mk(xvhq b gw*pd 8h4,e2$l_0$,$2l_0$, 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 l atbx/)f.kn5ku k(6 ntoad of identical cases of tomato paste (see Fig. 7–40), each of which is a cube of length l. Find the center of gravity inxakk(ntnfu6 bk ).5/t the horizontal plane, so that the crane operator can pick up the load without tipping it.$X_{CM}$ =    l $Y_{CM}$ =    l

  A uniform circular plate of radius 2jvz +n8pda* lw613zl0qfk9ly R 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, k8l 3lj+ 0vqfln69 a*pzy1zd wFig. 7–41. What is the position of the center of mass of the plate? [Hint: Try subtraction.]   R

  Assume that your proportions are the same as those in Table 7–1, and v qz ox ce;yk;2el9q4/calculate the mass of one ofee/y zqlq9v;oc;k 24x your legs.    kg

  Determine the CM of ytv oic0 u2,es3jrmgg4-g wvsc66 c55 an outstretched arm using Table 7–1.   % of the person's height along the line from the shoulder to the hand

  Use Table 7–1 to calcula iht/rp7tj+1q te the position of the CM of an arm bent at a right angle. Assume that the person iqhjitrp/t71+ s 155 cm tall. $X_{CM}$ =    cm $Y_{CM}$ =    cm

When a high jumper is in a position such that his arms and legs aret:*o+sa ,t8mgfqznz 3rw3ticf: +oe c90/jnq hanging vertically, and his trunk and head are horizontal, calculate how far below the torso’s median line the CM will be. Will this CM be outside the body? Use T/t atznqo3s9: c: z q*icg3+r0,mf w8o+nfjetable 7–1.

The masses of the Eark xolr,b;08m zth and 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 fr;uxl sf)pq;*mkn) /qcw83 igzictionless 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 pq94ik/ bx(r+6 xipru 0.0800 m mounted on a uniform cylindrical handle of mass 0.500 kg and length 0.240 m, as showk/(xuq9rpp ixb+i64 rn 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 ddaem;hfwod6 c nmpw+-72tu d ei4x/ ()iameter 0.0800 m mounted on a uniform cylindrical handle of mass 0.500 kg and length 0.240 m, as shown in Fig. 7–42. If this mallet is tossed, spinning, into the air, how far an6(7/amd m -ch)fitwe ou d +we24px;dbove the bottom of the handle is the point that will follow a parabolic trajectory?    d    d

  (a) Suppose that in Examplh/u)x g7ury8v e 7–14 (Fig. 7–29), $m_{II}$=3$m_{I}$ Where then would $m_{II}$ land?    d(Round to two decimal places)
(b) What if $m_{I}$=3$m_{II}$    d

A helium balloon and its gondola, of,(yph /bs:is n mass M, 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) does the balloon then move? What happens if the passenger ,:(ishnyp s/b stops?

  An 0.145-kg baseball pitched horizontally at strikes a bat and is ponhjdaubz2 u ( *p80-gepped straight up to a height of 55.6 m. If the contact time is 1.4 ms, calculauu*(eznh-2a0bd g8 jpte the average force on the ball during the contact.    $^{\circ} $

  A rocket of mass m traveling wicq+;0 bg h0q+shw:fn5p c1m yeth 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)u ct31yisig- 6m)ehx with the corner pocket shot shown in Fig. 7–43. Relative dimensions are also shown. ) 6x -ic1i3)gheymu stShould the player be worried about this being a “scratch shot,” in which the cue ball will also fall into a pocket? Give details.

  A 140-kg astronaut (including spvl )bzyuc-g4qfq 8m(4.1 qf;bn j9saaace suit) acquires a speed of 2.5m/s by pushing off with his legs frv(-gf. lfajuc9b1by4an 4qzsq ;8 )q mom 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 ,i0rrz+pg 5, ord0v jti6eto.the other 80 kg, are initially at rest in outer space. They then push each other apart. How far apart are they when the lighter astronaut i6 pv to+e r0j irdoz0rt.,,g5has moved 12 m?    m

  A ball of mass m makes a hee:huc**kfeahgf 6a* )ki ur+ .ad-on elastic collision with a second ball (at rest) and rebounds in the opposite direction with a speh+c :i)afk *.eeuku6ragh** fed 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 wiuq9x, w2tu r.ytness in a court case involving an automobile accident. T, x2tr .9uyuqwhe accident involved car A of mass 1900 kg which crashed into stationary car B of mass 1100 kg. The driver of car A applied his brakes 15 m before he crashed into car B. After the collision, car A slid 18 m while car B slid 30 m. The coefficient of kinetic friction between the locked wheels and the road was measured to be 0.60. 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 o+mr dt.kdv1h- 01-.zhqwcg adf a flight of concrete steps of total vertical height 4.00 m. The ball hits four times on the way down, each time striking the horizontal part of a different step 1.0 m lower. If all collisions are perfectly elastic, what is the bounce height on the fourth bounce when the ball reaches the -zh-..darkdg1vhwmd 1 qc t+0bottom of the stairs?

  A bullet is fired vertically into a 1.40-kg block of woodrkb7*u i8 uv(x at rest directly above it * kvuirxu7(b8. If 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 w4 mb+y, /i+iazu3ri jof wood placed on a horizontal surface just in front of the gun. If the coefficient of kinetic friction between the block rj3+w/mi +,yi4 a buziand 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 anol.chw; g428pftou)kymz06j, dbb /g d the other of mass 60 kg, sit in a rowboat of mass 80 kg. With the boat initially at rest, the two people, who have been sitting at opposite ends of the boat 3.2 m apart from each other, now exchange seats. How far and4yoo6df)g0pw ,h j2m8.;/gl bcbztuk 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 waa*ieitv2 160jwn tzf;g7n pf9s about $ 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 explosion. Ox(o6h :g.e1w) k xe k5)enptfcne fragment acquires twice the kinetic energy of the other. What is the ratio of their m pxhfk:()x. n5 6tkeewe) cog1asses?   

  The force on a bullet is given by the formula),xbtgzg 8ry( 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 masses7jnub y0huw d*db; v -p60c9hz.)ovhc $m_A$ = 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 aniqhu u5rz/ ,)fd a smaller nucleus. What will be ti 5uz r),ufh/qhe speed of this recoiling nucleus if the speed of the alpha particle is $ 3.8\times10^{5 }$m/s Assume the recoiling nucleus has a mass 57 times greater than that of the alpha particle.    m/s

  A 0.25-kg skeet (clay target) is fired at an angle of 78, bn8 f12sv5xk f0mncuef ls30 $^{\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 sliks+zf;.jd ym4p4stb0mw ht.h3n *2lfdes 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 if it isk0+nx6p*hp wg ;,of :tdq r6od to rebound from M, slide up the incline, stop, slide down the incline, and collide wit6 f oxokpgw+,t6n:qr; dp0h*dh M again?    kg (Let A represent mass m, and B represent mass M.)

  The gravitational slingshot effect. Figure 7–47 shoufcr:7oe0vp 3), rb bb-s 9zkgws the planet Saturn moving in the negativrr u-s gf0pzo93bbv7k:bc ),ee x direction at its orbital speed (with respect to the Sun) of 9.6km/s The mass of Saturn is $5.69 \times10^{ 26}$kg A spacecraft with mass 825 kg approaches Saturn. When far from Saturn, it moves in the direction at 10.4km/s The gravitational attraction of Saturn (a conservative force) acting on the spacecraft causes it to swing around the planet (orbit shown as dashed line) and head off in the opposite direction. Estimate the final speed of the spacecraft after it is far enough away to be considered free of Saturn’s gravitational pull.    km/s