We claim that momentum is conserved, yet n2k6qvig pwy+9mn 6 xv)v-m)xmost moving objects eventually slow down and stop. E-6 x96n 2n+ myvpqw)mgv) kivxxplain.

When a person jumps from a tree to the ground, what haznabnk rl / ,r 53b+qdy;8tlf8ppens to the momentum of the person upon striking the grouk83bd8 a5lt,qzr y+ rlfn; bn/nd?

When you release an inflated but untied balloon, why does it f1/mf t anlrt.t1 usus3g4 h;*gly across the room*tg .gr1/tntl3u s u;1fams4h?

It is said that in ancient times a rich qgeh i(68.6o.h;tsviy mq8qxman with a bag of gold coins froze to death h86vqy( ig6e sm 8q; .o.ixqhtwhile 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 he not been so miserly?

How can a rocket change direction when it is far out in space and is essenti e2bwv :.xv p+vsm.wf/ally in a ms/ e vb :.xwf2vwp+.vvacuum?

According to Eq. 7–5, the longer the impact time of j:dqzlhk6( q4oey t3/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 intend/ 3jd4y6h(:t qlkeozq ed to inflate during an automobile collision and reduce the possibility of fracture or death.

Cars used to be built as rigid as possible to withstqy- z w,6zaj v,5kxiq+ :dy6baand collisions. Today, though, cars are designed to have “crx zk5,y +zya6,6idbq j:wva-qumple zones” that collapse upon impact. What is the advantage of this new design?

Why can a batter hit a pitched baseball further than a ball on 1dbw*n fld6i,in /vr 0,*rptossed in the air by thef1i/,0 vd6 p*i *or,r wndnlnb batter?

Is it possible for an object to receive a larger impuls6z )d ml:9wvk0hjec )re from a small force than from a la 96r0 zemj)d:hklvcw )rge force? Explain.

A light object and a heavy object have the same kinetic en ;nq3wfup0/ch ergy. Which has the greater momentum? /;ncf w3hu0qp Explain.

Describe a collision in4l*j vf*+ 4bfq )hdrucfc- rvk8.b u9f which all kinetic energy is lost.

At a hydroelectric power plant, water is directed at higvcf 511ml2zjx h speed against turbine blades on an axle that turns an electri5vf12xc 1zjl mc generator. For maximum power generation, should the turbine blades be designed so that the water is brought to a dead stop, or so that the water rebounds?

A squash ball hits a wv l*nsn6h 3k 4n5oi2dkall 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 age8r50*cn-) ckm8otjm7 4bn:rjp x; gh4v mlj height h onto a hard steel plate (fixed to the Earth), from which it rebounbnc n;m04ke *mxhr:) mrvj cltggp4-j5o 87 j8ds 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 leanky-bq-y/ bsfgqo23lokj 7e)e ug ( n68 backward when carrying a heavy load in your arms?

Why is the CM of a 1-m length of pipe at its mid-p6+ru icu)n a6woint, whereas this is not true for your arm or leg6aw+ nr)uu c6i?

Show on a diagram how you:hr+6 j4yhwpzpu)jpz** *fdw r CM shifts when you change from a lying position to a sitting pfp 4wzz :p+rhh pdw*6 **juy)josition.

If only an external force can change the momentum of the cent ss l8 qavz43jkkke;q ),-t+g,+gkj oqer of mass of an object, how can the internal +jjk3 4q+gz ,,gkav sql kks-eqt)8 o;force of an engine accelerate a car?

A rocket following a parabolic path through the air suddenly expj2i9ivrxt p 1l)1 r a+8ehy(qyv 4rbp-lodes into many pieces. What c-a+r4e2b ivxpr p 1rvht9 i()8yjy1lqan you say about the motion of this system of pieces?

  What is the magnitude of the momentum of a 28-g sparrow flying with a speed of 3jqr yey7,v/4uac un 3$8.4 \; m/s$    $kg \; m/s$

  A constant friction force of 25 /xcphle(cqe0)qye5,6 +zot nN acts on a 65-kg skier for 20 s. What is the skier’zoyqe c( he/tc,l6+n x50)qep s change in velocity?    m/s

  A 0.145-kg baseball pitche w9xwufz8s92c d at 39 m/s is hit on a horizontal line drive straight back toward thcwz9fx w89u2s e pitcher at 52m/s If the contact time between bat and ball is $3\times10^{-3}$s calculate the average force between the ball and bat during contact.    N

  A child in a boat th(-be ,.7rne q gawlf3zrows a 6.40-kg package 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 rl,w 7r3.zq (ae-bgfneesistance. The magnitude of the velocity of the boat is    m/s

  Calculate the force exerted on a rocket, given that the propelling ge4 ;rnhmj:uig,3y 2 pyases are expelled at a rate of : pi4,yn2 e3hug jrm;y$1500 \; kg/s$ with a speed of $ 4\times10^{4 } \; m/s$ (at the moment of takeoff). F =    $\times 10^7 \; N$

  A 95-kg halfback moving +b s: f05y*i(ispacmg at $4.1 \; m/s$ on an apparent breakaway for a touchdown is tackled from behind. When he was tackled by an 85-kg cornerback running at $5.5 \; m/s$ in the same direction, what was their mutual speed immediately after the tackle?    $m/s$

  A 12,600-kg railroad car travels alone on alevel :+4 vobe;ux+yalgrqb 4r* b 1ua9-nxp frictionless track with a constant speed of 18m/s A 5350-kg load,initially atob 1bg -v4rr4a uuy;plnax:eb9q+ *x+ rest, is dropped onto the car. What will be the car’s new speed?    m/s

  A 9300-kg boxcar traveling zz6x/hna a *1nat $15 \; m/s$ 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 y bnmgw0)16zpk 2szey.9 01l bwse5my of 100km/h If the air strikes a person at the rate of 40kg/s per slyzm50zs)es 0 2ebk p 9 g1wbnyw.1my6quare 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 railroad39d.(ji- utqtjsq q,p car coasts along with a constant speed of 8.6m/s on a level track. Snow begins to fall vertically and fills the car at a rate of 3.5kg/min Ignoring f ,j( psdt-i.utqj q93qriction with the tracks, what is the speed of the car after 90.0 min?$\approx$    m/s

  An atomic nucleus initially movinv34)dxjl px),jy )w0chaf7m eg at 420m/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 nwpm dxx)0lv4ay fj)jh73)e, c ucleus has a mass of 222 u, what speed does the alpha particle have when it is emitted?    m/s

  A 23-g bullet traveling 2i;u tb mm 7)qq; bj7m-)comx1n30m/s penetrates a 2.0-kg block of wood and emerges cleanly at 170m/s If the block is stationary on a frictionless surface when hit, how fast does it move after the bullet em qnmmj1 i)bxc77tqb; ;-uo) mmerges?    m/s

  A 975-kg two-stage rocket is traysa b;d qn 8iqbuivc61ys./ )(veling 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 space with o )wrn;+n mdv:a velocity of 115m/s To alter its cour)vo mwr n:n+;dse 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 uj pwok*tp09 2is hit off the tee at a speed of 45m/s The golf club was i w02u*p kp9otjn 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 nlx9x*m z3 yy3vy,ld 3mail at a velocity of 8.5m/s and comes to rest in a time interval of 8.0 ms. (a) What is the impulse given ,39zv3yxd lmxyl*m3 y to the nail?    kg*m/s
(b) What is the average force acting on the nail?    N

  A tennis ball of mass m=0.06kg and speed v=25m/s strikes a wall at a 48jq lqd+) wru h38of9k5 $^{\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 nfex /w p xjs*5/-g82 p/azhalsew automobile models. Cars are tested by smashing them into fixed, massive barriers at 50km/h (30 mph). A new model of mass 1500 kg takes 0.15 s from the time of impact until it is brought to rest. (a) Calculate txe/ *apxg szha l5fjs/8wp/ 2-he 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 )ax9 a7 mn;v:mnb5vchwmuc+1stopped in 0.75 s by a head-on tackle by a tack5h c7xan;m 1b9avu +vc:mmnw)ler 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 acting on a tennis ball (mass 0.060 kg) points in the +x direpu:5x0y0lu5 e,dlq1o.jt w d qction and is given by the graph of Fig. 7–33wy ld5j0t1d uqoxqp0e. :5,lu 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 lower6f m1wtclt- n.09kbnc leg bone of either ncbw. 0kt -lm1t9c6nfleg? 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 $170\times10^6\mathrm{~N/m^2}$ 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 (+xappmm js bp,,mhlsy,t41gb1 x5 k;5)z direction) with a speed of collides head-on with a 0.220-kg ball at rest. If the collision is perfectlygkm,pab; s,mm bxths15z4ypl )p51 ,j 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 spe l5o(qe/w.e ined of 3m/s has a head-on collision with a 0.900-kg puck initially at rest. Assuming a perfectly elastic collision, what will be the speed and direction of each object after thnleiq( 5ow. e/e collision?Let A represent the 0.450-kg puck, and let B represent the 0.900-kg puck. v'$_A$ =    m/s ----待选择----eastwest  v'$_B$ =    m/s ----待选择----eastwest 

  Two billiard balls of equal mass undergo a euo. 0q+qc/1w+vue yxperfectly 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 mu vqwe+. q /1yo+xe0ucoving at 2.00 m/s, and call that direction the positive direction.Let B represent the ball moving at 3.00 m/s in the opposite direction. ) v'$_A$ =    m/s v'$_B$ =    m/s

  A 0.060-kg tennis ball, moving with a speed of 2.5m/s collides head-on with a k fgey:25)k;.g ujlb;6neiw7 *u skex0.090-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?(Let A represent the 0.060-kg tennis ball, and let B r )x6lnk;.7:ey isue5kj g; ug 2e*fwkbepresent the 0.090-kg ball.)v'$_A$ =    m/s v'$_B$ =    m/s

  A softball of mass 0.220 kg that is moving with a speed of 8 fr-og3s6. p,nz6l nvx.5m/s collides head-on and elastically with another ball initially at f6pz6.nx o3 ,lnsv-g rrest. Afterward 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 9 bway7pp0:ghzf/+a o ride collide elastically as one approaches the other directly from the rear (Fig. 7–34). Car A has/y: g7 +apz wa9p0fbho a mass of 450 kg and car B 550 kg, owing to differences in passenger mass. If car A approaches at 4.5m/s and car B is moving at 3.7m/s calculate
(a) their velocities after the collision v'$_A$ =    m/s v'$_B$ =    m/s
(b) the change in momentum of each.$\Delta p_{\mathrm{A}}$$\approx$    kg*m/s $\Delta p_{\mathrm{B}}$$\approx$    kg*m/s

  A 0.280-kg croquet ball makes an elastic head-on collision with a second ball v7g+bgf yo//3dkxe1yinitially at rest. The second ball moves off with half the ood/7+k1gf y/ y vbgxe3riginal 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 fy1 -e es e6wwg aib6u*stf*t*8rictionless 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 is 30 cm hbau g-s8 yee1*6*s 6iwtfte*w igh 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 o5wr*79je. 3e pbmem do9wf pa0f 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 exhbgzru gir,, pr/:cc6 8x+(faperiment, projectile 1 results in a maximum height h of the pendulum equal to 2.6 cm. A second projectile causes the the pendulum to swin+,f(6rgz8 b c pr /xci,ruh:gag 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 hxd,8 u -vhst7shvl34uanging on a 2.8-m-long string, which makes the pendulum swing upward in an arc. Determine ththv7slu-48xuv 3sh,d e vertical and horizontal components of the pendulum’s displacement.vertical$\approx$    m horizontal =    m

(a) Derive a formula for thq avhkgdpr0o529 /dig(c u+r .e fraction 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 al6 cvep i) -o-ej5 fzvwvop+4w2hdh25t rest, into two pieces, one of which has 1.5 times the mass of the other. If 7500 J were released in the explosion, howo-5 4-v oh+pzcdvel6w2e ih5f) j pvw2 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 omvbge- l g2tu63np,8 collides into 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 that speed?(Let A represent the sportslge ,ugt bnp6mvo 3-82 car, and B represent the SUV) $\approx$    m/s

  A ball is dropped from a height of 1.50 m and rebounds toyl uzhs.fc fy0 z98).j a height of 1.20 m. Approximately how many rebounds wi0sf9zu)c f ..lz8 yyjhll the ball make before losing 90% of its energy?   

A measure of inelasticity in a head-on collision of two objecd gnos 4z0)cd)ts is the coefficient of restitution, e, defi)dognzc)d 0s4 ned 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 times2lo*m o7 :oqo. s4(batdew9yx 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 separate and slide o s oob 7*:ea(txw4.2lqmdo y9apart. 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,z. qv ya; eexd*bgpo1* c2j/tm/s collides head-on with a 10.0-kg object moving in the -x direction at 4m/s Find the f.a**;,doevje z y2xb1/p cqtginal 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, an electro94+bqdsv/x ,nu )k dnlrul;5p n, and a neutrino. The electron and nell r)+dnp b /;q,u5kvd49ns xuutrino 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 mass rpvj7c/2;zw- hs phh;pn 7mtz75r ) ff$m_\mathrm{A}=0.400$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 bu d(sm3kw3 j)detween two objects of equal mass, each having initial speed the two move off together with speed v/3 What was the angle between their initial directions3ku dm)sj 3d(w?    $^{\circ} $

  Two billiard balls of equal mas)o /nct9mrz 2fmw ,4wts 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 th,/rw9 otm ftn4c mwz2)e collision, assumed elastic, ball B is moving along the positive y axis (Fig. 7–37). What is the final direction of ball A and what are their two speeds? direction of ball A is  ----待选择----x directionx direction v'$_A$ =    m/s v'$_B$ =    m/s

  A neon atom (m=20u) makes a perfectly elast wd:paeiyhs1lt3 d;i ad.95u( ic collision with another atom at rest. After the impact, the neon atom tras 9ytl:ahddp;.da e1w(3uii 5vels 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 another(x/mtlwc/; uh atom at rest. After the impact, the neon atom travels away at a 55.6 mwxu t//(;clh$^{\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 sho/i(sv ;y )zhu ;igg 29;ydnnrgwn in Fig. 7–38. Specify relative to the left-ha2 iz/sv;rud( n;yngghi9 g )y;nd 1.00-kg mass.    m

  The distance between a i;7kmq(vek7 z 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 behiqg/r(dpd wq / p5ias:,nd the front of the car. How far from the front of the car will the CM be when two people sit in the front seat 2.80 m from the front of the car, and threr:(i/5da, gpsp/d qw qe 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.k,;vmp/g03 5p jjtbd+j(xgq f If three cars, each of mass 1200 kg, occupy its NE, SE, and SW corners, determine the CM of the lo(3txg/kj+ qbjjg; f0 ppd ,mv5aded ferryboat.$X_{CM}$ =    m $Y_{CM}$ =    m

  Three cubes, of sides 6;8a*o v0hpyknr68m4stypjc $l_0$,$2l_0$, 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 t m718v6nfqj8e f skn c6vwv74romato paste (see Fig. 7–40), eavf4q6v88nmke c7vr7s61jnf wch of which is a cube of length l. Find the center of gravity in the horizontal plane, so that the crane operator can pick up the load without tipping it.$X_{CM}$ =    l $Y_{CM}$ =    l

  A uniform circular plat ay jpu 7:+;zto-4bo (tvpx*lbmv):dse of radius 2R has a circular hole of radius R cut out of it. The center of the smaller circle is a distance 0.80R from the center C of the larger circle, Fig. 7–41. What is the position of the center of mass of the plate? [Hint: Try subtractp*zo b) tydax+:lvto; b ps-7v4(jm:uion.]   R

  Assume that your proportions arpy z,e/i 4v-e6k bi;hke the same as those in Table 7–1, and calculate the mass of one of yoi ez ;pk /,4e6vih-kybur legs.    kg

  Determine the CM of aluc-* 2941ukwxfv xd.m qeao7 n 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 calculate the po4 lyg3fo7ml x0fr t0bw3 l9a2lsition of the CM of an arm bent at a right angle. Assume that the person3lb2xla 094f 7rlt fg ym0lw3o is 155 cm tall. $X_{CM}$ =    cm $Y_{CM}$ =    cm

When a high jumper is in a position such that yen 3o )/;,3j ( a;osm;exrcdf+jamgo his arms and legs are hanging vertically, and his trunk and head are horizontal, calculate how far below the torso’s median line the CM will be. Will this CM be ( ejxrgf oc3 e3soan+m ,o;d;ay;)/mjoutside the body? Use Table 7–1.

The masses of the Earth a - 95y*xapx zqewh4m2mnd 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 mkz3af) -qtp1( wb ;jf yya 0ys(yshj.-an 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 87jh (m hn ghss,b34;phno)uucylindrical head of mass 2.00 kg and a diameter 0.0800 m mounted on a uniform cylindrical handle of mass 0.500 kg and length 0.240 m, as shown in Fig. 7–42. If this mallet is tossed, spinning, into the air, how far above the bottom of the handle is th h(hbms);h7 u3suonh4g8 nj ,pe point that will follow a parabolic trajectory?    cm

  A mallet consists of a uniform cylindrical head of mass 2.00 kg a. /msi ftwxf+4f v7*c1 (lixjend 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, how far above the boe.m*wt 7/lc( i1vffxj4x fsi+ttom of the handle is the point that will follow a parabolic trajectory?    d    d

  (a) Suppose that in Example 7–14 (Fig5mgwhj4ye/q ,ky,dl dvz n234c o1i b.. 7–29), $m_{II}$=3$m_{I}$ Where then would $m_{II}$ land?    d(Round to two decimal places)
(b) What if $m_{I}$=3$m_{II}$    d

A helium balloon and its gondola, of mass M, are in the air and stationary *l.zkfolkfd1 xk 4/-y jx3l)gwith respect to the ground. A passenger, of mass m,fzflkk3jxx l.dl1g4 *)-yo/k 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 stops?

  An 0.145-kg baseball pitched horizontally at stri gv pll7d77 wt,(a-bv0oftvi-kes 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 the ball durinatbpl7vvgv 7(it- d7lwo 0 -f,g the contact.    $^{\circ} $

  A rocket of mass m travel,,bpvapy5 b -a w*cki:ing with speed $v_0$ along the x axis suddenly shoots out fuel, equal to one-third of its mass, parallel to the y axis (perpendicular to the rocket as seen from the ground) with speed 2$v_0$ Give the components of the final velocity of the rocket.$P_x$: v'$_x$=    $v_0$
$P_y$: v'$_y$=    $v_0$

A novice pool player is faced with the corner pocket shot shown inviado16 no9d * Fig. 7–43. Relative dimensions are also shown. Should the player be worried about this being a “scratch shot,” in which the cue ball will also fall into a pocked* a9 iovdo61nt? Give details.

  A 140-kg astronaut (including space suit) acquires a speed of 2.5m/s b 4 yp.jbvp/3e9w nvmp1y pushing off with his legs from an 1800-kg s4.jbnwve/3 pm v19 ppypace 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 0jql9 0km4aakkg 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 ligh ml0j09qk k4aater astronaut has moved 12 m?    m

  A ball of mass m makes a head-on elastic collisionbo7dk y pl t4bo1)r2w8 with a second ball (at rest) and rebounds in the opposite direction with a speed equal to one-fourth its original speed. What is 2toyk7bopwdr14lb8 ) the mass of the second ball? $m_B$ =    $m_A$(Round to two decimal places)

  You have been hired as an expert witness in a court case inal 4gyx/yy): qpyi*,p sxlx.9volving 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 measured to be 0.60. Show that the driver of car A was exceeding the 55-mph .pxxly 9/4agx py,s:l)q iy*y(90km/h) speed limit before applying the brakes.    mi/h

A golf ball rolls off the top of a flightrcv xils8 rfpz -b/(59 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 collisb/f5z(ils98prx cvr -ions are perfectly elastic, what is the bounce height on the fourth bounce when the ball reaches the bottom of the stairs?

  A bullet is fired vertically into a 1.40-kg ecabs69*2 rqd3qsk q*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 high will the block r6qcs 2skrq9d3be *a q*ise after the bullet becomes embedded in it?    m

  A 25-g bullet strikes and becomes embedded in a 1.35-kg jn wn jyh)ony:/4g;,fblock 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 beforewjoy/ y fhjg);4n, n:n it comes to rest, what was the muzzle speed of the bullet?    m/s

  Two people, one of mass 75 kg and the ojn7 /m-3*brcfxknp +pr fa+ o(ther 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 will mobf-7pmrn jcpn3x /kfoar* ++(ve    towards the initial position of the 75 kg person(Round to two decimal places)

  A meteor whose mass wa m te3sob8gnlyqm79: fh t195as 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 isc 82e in2h4jg2bci8 6+vxtf3ekc0mcc suddenly broken apart into two fragments by an explosion. One fragment acquires twice the kinetic energy o +ei2 2 680f ce4cctmjk8ic3hngcvx2bf the other. What is the ratio of their masses?   

  The force on a bullet is given by the for061 -ztbb* a8(uzqdtsh 0ul lmmula F = 580-( $1.8 \times10^{ 5}$t) over the time interval t=0 to t = $3.0 \times10^{-3 }$s In this formula, t is in seconds and F is in newtons.
(a) Plot a graph of F vs. t for t=0 to t=3.0ms
(b) Estimate, using graphical methods, the impulse given the bullet.    N*s
(c) If the bullet achieves a speed of 220m/s as a result of this impulse, given to it in the barrel of a gun, what must its mass be?    kg

  Two balls, of masses .ii8r8yvg-lp $m_A$ = 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 dec0ho.;qr 0tf8l lwhhot6zoa5* k li;v3 ays radioactively into an alpha particle and a smaller nucleus. What will be the speed of this recoiling nucleus if the speed of the alpva;8 6flo wlkhzi oo0ltqhr5*3h;t .0ha 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 30lm8pt/lwp.rgxl/ ( *g t0f;s x $^{\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 s7 j iqc5s1(jyaonnfaj* 43i -5k jto.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 i5pf yg:+ )fxsayrsp2*s to rebound from M, slide up the incline, stop, slide down the incline, and collide wis)pfs ayx25ygr:f *p+ th M again?    kg (Let A represent mass m, and B represent mass M.)

  The gravitational slingshot effect. Figure 7–47 shows the planet Sap-h( ;0p9w ehgfr.6 w nqznb4uv qm,0mturn moving in the negative x direction at its ozvpp, 0nwm ng e9;(.wu0hmf brh -6qq4rbital 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