We claim that momentum is conserved, yet most moving 5a6)zl55 sdz9v pvrc mobjects eventually slow down and s)vl95dz6 c asz55vpmr top. Explain.

When a person jumps from a tree to the ground, what happenrd xr7c, .rdd6k0nxn om3-ko5s to the momentum of the person upon striking the ground?d 5r, kx0nod.o 7k3-dx m6ncrr

When you release an inflated but untied balloon, why doesbfs;o ws,5*tmvu,e q; it fly across the room? m 5sbvw;et; s*,oq,uf

It is said that in ancient times a rich madpe6 bwu)+xf)3 bq;kn ja(g/o n 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 coe)6 /dkpgjbxu;3awn+ q)f(ob uld 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 essential/ivs- (gir sb/ly s/(v irb/-gsiin a vacuum?

According to Eq. 7–5, the longer the impact time of an impujp* **2duyqj+*ku xede m+;vhlse, 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 ai p ey*e*qv*;u2+jh mdkx+ *jdur 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 witp; o /yi*3yp8 eu7uamij;49 yxwyf6uvhstand collisions. Today, though, cars a;4vy ufwuj p6y *e xy;io3yiam7/u8 9pre designed to have “crumple zones” that collapse upon impact. What is the advantage of this new design?

Why can a batter hit a ri+;2exbo; lt6x)dw o pitched baseball further than a ball tossed in the air by ool;;x)r+2 ebd xt w6ithe batter?

Is it possible for an object to receive a larger impulse from aj6*8)u6vvz9 b t wusma small force than tv8*)vmbu6u9 jws za6from a large force? Explain.

A light object and a heavy objeccxs9 e 2xn yi n5*h7oet:i4nozix8).lt have the same kinetic energy. Which has the greater momentum? Explaino i 9i)*syt. nx 2zl7nnhi4xeco5: e8x.

Describe a collision in which all kinetic energy is;n 499nxlt vf0ibp :0dxgfkk5 lost.

At a hydroelectric power plant, watertzshe- :rjx// is directed at high speed against turbine blades ont s:jx- r/ehz/ 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 that the water rebounds?

A squash ball hits a wall at a-d.k skk3my3 m 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-zg5wiwg. 9mu h onto 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 parts of the proce 5-zgw ui.9gmwss 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 wh5:q m h8:;qysx)ykz6j x2rr smen carrying a heavy load in your arms?

Why is the CM of a 1-m length of pipe at i- bg nosh08pvb zg*h4:ts mid-point, whereas this is not true sh:8 vgbgnopz*h04-b for your arm or leg?

Show on a diagram how your CM shifts when you chf8io*o,taqe*lt p :sd qm14u3 ange from a lying position to a sitting positio pldi,* ftos aqq1t3muo4 e*:8n.

If only an external force can change the momentum off+rw73 eu6yr8 8vs 1q0zu.aja4aa g uw the center of mass of an object, how can thza4 f8 w8 3 671+g.euavauasjyurrwq0e internal force of an engine accelerate a car?

A rocket following a parabolic path through the air suddenly explodes3yiwz wpr+*os h.4x1w into many pieces. What can you say about the motion of this system of piece .pxww* iw1ozh+r4y 3ss?

  What is the magnitude of the momentum of a +oia ds 0syc5j8f4n2 e28-g sparrow flying with a speed of $8.4 \; m/s$    $kg \; m/s$

  A constant friction force ofnoem1y w 2v;e) 25 N acts on a 65-kg skier for 20 s. What is the skier’s )eym;v21n owechange in velocity?    m/s

  A 0.145-kg baseball pitched at 39 m/s is hit on a horiz /*x4ij.6a rmu/qxyej ontal line drive straight back toward the pitcher at 52m/s If tjyi*u/e4 j.amqxx/ 6 rhe contact time between bat and ball is $3\times10^{-3}$s calculate the average force between the ball and bat during contact.    N

  A child in a boat throws a 6.40-kg package out horizo spw/ 8;xz u s4-un.pnfmmvc*8ntally with a speed of 10 m/s Fig. below Calculatnv*w8p/ms 8 f ;smuc.n zx-4upe the velocity of the boat immediately after, assuming it was initially at rest. The mass of the child is 26.0 kg, and that of the boat is 45.0 kg. Ignore water resistance. The magnitude of the velocity of the boat is    m/s

  Calculate the force exejs dl 5eb1-5izmtw. 8jrted on a rocket, given that the propelling gases are expelle 5ts58ljm.1 dzj -iwebd at a 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 3*hv. p 15lvqwq/sb mpd.l a3uu7 o7smat $4.1 \; m/s$ 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 ba qusnxf a-n.xcj7(4lmm688 car travels alone on alevel frictionless track with a constant speed of 18m/s A 5350-kg load,initially at rest, is dropped onto the car. What will m usfn6x c jm n8aab(ql-487.xbe the car’s new speed?    m/s

  A 9300-kg boxcar traveling at c(0ar anjn ,3si0vva+$15 \; m/s$ 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 horiz: pm5eg7ddd78hx ;usx hkw:dibzd;*vg x72g1ontally at speeds of 100km/h If the air strikesk x hgx:;mpg*bv7idud5w81:27ged d;xzd7 h s a person at the rate of 40kg/s per square meter and is brought to rest, estimate the force of the wind on a person. Assume the person is 1.50 m high and 0.50 m wide. Compare to the typical maximum force of friction $\mu\approx1.0$ between the person and the ground, if the person has a mass of 70 kg.    N
$F_{on person}$  ----待选择----<> $F_{fr}$

  A 3800-kg open railroad car coasts along with a constant speebqv,t 6)0cez ud of 8.6m/s on a level track. Snow begins to fall vertically ac)t,u 0 qebz6vnd 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 an alpha particle in the 8(sux2 5oiwa5 w: mjv uwar4oh;-*hphdirection of its velocity, and the remaining nucleus slows to 350m/s If the alpha particle has a mass of 4.0 u ho4waw: vi8 5w; um-5s hau*poh(2j rxand 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 pt+/in x(2rfe* d ),, mcxvpgjkenetrates a 2.0-kg block of wood and emerges cleanly at 170m/s If the block is stationary on a )mvfx2ep k j*,+,grt(/ dcix nfrictionless surface when hit, how fast does it move after the bullet emerges?    m/s

  A 975-kg two-stage roc *kyy4bj;z(f;* 0rrw fvxu* iyket is traveling 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 wityp;dyfgy7ugbj u.8++ h a velocity of 115m/s To alter it gy.8+uby yp 7udjg;+fs 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 hit off the tee at a speed of 45m/s Theqz6v ,v:pvorq pv3m0z75*bms golf club was in copz zvqv:q pv s06o 3,5mr7m*bvntact 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/sx36tdp0jzr-dr d9 ax:h:dx5 u and comes to rest in a time interval of 8.0 ms. (a) What is the impulse given to the nail? p -3z96:5dxxr0ud jx t:dhadr   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 ffkkd56yuf7(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 crastuu/ 4q/yyu 4dd:u re)hworthiness of new automobile models. Carud:u dr/ 4u )/uqey4tys 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 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 ih 0v1d godx8om1nhmo;r8d2 l1n 0.75 s by a head-on tackle by a taco81ho 1gdm2;l1m8ondvrd 0 x hkler 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 0.06g r7*fx lz.wv60 kg) points in the +x directi.7r*fv wl6xzg on and is given by the graph of Fig. 7–33 as a function of time. Use graphical methods to estimate
(a) the total impulse given the ball    N*s
(b) the velocity of the ball after being struck, assuming the ball is being served so it is nearly at rest initially.    m/s

  From what maximum height can a 75-kg person jump without breakio2 9 gtjq.xrp)ng the lower leg bone of either leg? Ignore air resistance and assume the CM of the person moves a distance of qr)jpo.t9x g20.60 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 w 6dr oqh+fe50al) * hcfjc e+-j(x*r*gj9ilx (+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 spefwre-ij jcrcqo+90 g*6*5jxlhx(lfd+)* a heed 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 e1awt i c*p 4lux6b998 envzk2kast with a speed 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 the colliwae 6lci*vpb xt9ku291kn8z 4 sion?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 undergozan y/ ut :f*42hb 6ynurl*wz; 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 moving at 3.00 m/s in the opposite direction. ) vbf/*u hn6 2nwa z;:*lyt4 yuzr'$_A$ =    m/s v'$_B$ =    m/s

  A 0.060-kg tennis ball, moving with a speed of 2.5m- 1xslza8zfp 5/s collides head-on with a 0.090-kg ball initially moving away from it at a speed of 1.15m/s Assuming a perfectly elastic collision, what are the speed and direction of each ball after the collision?(Let A represent the 0.060-kg tennis ball, and let B represent the 0.090-kg bxl az1-f5p 8zsall.)v'$_A$ =    m/s v'$_B$ =    m/s

  A softball of mass 0.220 kg that is moving with a speed offj 3(x l:zg j 1w gz,q,+tmbut5*kc3ub 8.5m/s collides head-on and elastically with another ball initially at rest. Afterward the incoming softball bounces backward with a speed of 3.7m/s +c3ugz b j(l 15,tmq wxg:u*b,zj3tfkCalculate
(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 on p1;.ll8ez6la+ o . (mylhicale approaches the other directly from the r . l;c 8z6 oleyala(h+l.lipm1ear (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 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 secon,x)eh4c x- rdzd ball initially at rest. The second ball moves off wit x4 x)rc,ezh-dh half the original speed of the first ball.
(a) What is the mass of the second ball?    kg
(b) What fraction of the original kinetic energy $(\Delta\mathrm{kE/KE})$ gets transferred to the second ball?   

  In a physics lab, a cube slides down a frictionless incline as shown in Fin9jmea ow-+0n g. 7–35, and elastically strikes another cube at the -o0a9j newmn +bottom that is only one-half its mass. If the incline is 30 cm high and the table is 90 cm off the floor, where does each cube land? [Hint: Both leave the incline moving horizontally.]$\Delta x_{m}$$\approx$    m $\Delta x_{M}$$\approx$    m

ake the general case of a zy:*gom3d: cbn 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 experimh):nfktjs;7 6b(pvz q ent, projectile 1 results in a maximum height h of the pendulum e)6z;(fk tphjs v:qn7bqual to 2.6 cm. A second projectile causes the the pendulum to swing twice as high, $h_2=5.2\mathrm{cm}$ The second projectile was how many times faster than the first? $v_1$ =    $v_2$ ([color=rgba(0, 0, 0, 0.85)]Round to three decimal places)

  A 28-g rifle bullet traesrj*pyt b -;6ui ;8.o0wzkldveling 230m/s buries itself in a 3.6-kg pendulum hanging on a 2.8-m-long string, which makes the pendulum swing upward in an arc. Determine the vertical and horizontal components of 8*lot;ij s-bzyd6e0 kwu.p;r the pendulum’s displacement.vertical$\approx$    m horizontal =    m

(a) Derive a formula for the fvjg3i 5m9 37)a nwdt7vkoc4gzraction of kinetic energy lost, $(\Delta\mathrm{KE/KE})$ for the ballistic pendulum collision of Example 7–10. (b) Evaluate for m=14g and M=380g

  An internal explosion breaks an object, initially at rest, intov, d.:drj z u) ltdo65sgb/n-e two pieces, one of which has 1.5 times the mass of the other. If 7500 J were released in the explosion, how much kinetic e ed. v/z)j-d ,rgt5s6nbu:lodnergy 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-xon:h3wn1 sy2/k01wort sov9wnf w6 )kg SUV stopped at a red light. The bumpewroht s302 o1f)wn6ov/ nx1yww9kns:rs 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 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 oet*r ,e;bee;eq e;om3muzms *6h (ws6f 1.20 m. Approximately how many bquho; ;e3,6 eemm(w ;*tzes s mr*6eerebounds will the ball make before losing 90% of its energy?   

A measure of inelasticity in a head-on collision of twoy3s*,h hld j ,8ari68hs3lhax objects is the coefficient of restitution, d, 3l8s,hhaij lh3h8s a6x*yre, defined as$e=\frac{\nu_\mathrm{A}^{\prime}-\nu_\mathrm{B}^{\prime}}{\nu_\mathrm{B}-\nu_\mathrm{A}},$
where $\nu_\mathrm{A}^{\prime}-\nu_\mathrm{B}^{\prime}$ is the relative velocity of the two objects after the collision and $\nu_\mathrm{B}-\nu_\mathrm{A}$ is their relative velocity before it.
(a) Show that e=1 for a perfectly elastic collision, and e=0 for a completely inelastic collision.
(b) A simple method for measuring the coefficient of restitution for an object colliding with a very hard surface like steel is to drop the object onto a heavy steel plate, as shown in Fig. 7–36. Determine a formula for e in terms of the original height h and the maximum height h’ reached after one collision.

  A wooden block is cut into two pieces, one with three times t epegwb5 ;g8+, oby*vuhe 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 reassemg p;ebgu8,5*wv yeo+bbled. 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 ozc-g7. xor ep9y i:/;lw3vcfat 5.5m/s collides head-on with a 10.0-kg object moving in the -x direction at 4m/s Find the final velo g9xwcz; e:-/r i.lfocpy3v7ocity 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 electron, a(1xipr dffitg ;y(b/;* 527 psbpko kwnd a neutrino. The electron and neutrino are emitted at right angles and have momenta o2k oy1p i;rdpb( x;(fw* sg/ib57pkftf $9.30\times10^{-23}kg\cdot m/s$ 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 ycvd, u om0ce(v 50y1x$m_\mathrm{A}=0.400$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 inelasnqn;35 z.r3t 0z 0bqxx itgzt;tic collision between two objects of equal mass, each having initqqtzxgtxrz;z0i5n. b3 0tn3 ;ial speed the two move off together with speed v/3 What was the angle between their initial directions?    $^{\circ} $

  Two billiard balls of equal mass move at right angles and meet at the origzf 3g:np hjbkgyp: efq:a-3 )-in of an xy coordinate system. Ballq-3gjg)eyn f:a3bf:hkp -:z p A is moving upward along the y axis at 2m/s and ball B is moving to the right along the x axis with speed 3.7m/s After the collision, assumed elastic, ball B is moving along the positive y axis (Fig. 7–37). What is the final direction of ball A and what are their two speeds? direction of ball A is  ----待选择----x directionx direction v'$_A$ =    m/s v'$_B$ =    m/s

  A neon atom (m=20u) makes a perf e*zo (p3g;soeectly elastic collision with another atom at rest. After the impact, th(sop;eeg 3* zoe 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 perk9mh h*oc2 9fsfectly elastic collision with another atom at rest. After the impact, the neon atom travels awafck9m hhs29*o y 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 syss k )1ocw2rkze/;ilr; tem shown in Fig. 7–38. Specify relative to the l1es/r2)i;r ;cwo l zkkeft-hand 1.00-kg mass.    m

  The distance between a caru eg5gsl/o7 *bbon 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 of .l*7tnapx w:w the car. How far from the front twaw. 7lpn*x :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 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 kwfl867c2y p tdour*l rru0p97g, is used as a ferryboat. If three cars, each of mass79w72u6u0tlp r*y8droc fpl r 1200 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 b.dnzizp71x 0s $l_0$,$2l_0$, 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 tomar ,f;.52jmse 5a*tmgxbzv) xoto paste (see Fig. 7–40), each of which is a cube of length l. Find the center of gravity in the horizontal plane, so that e5z).fomxvbrm2,*;gjsx at5 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 radibd*/tu5t nj .nus R cut out of it. The center.5 du tt*njb/n of the smaller circle is a distance 0.80R from the center C of the larger circle, Fig. 7–41. What is the position of the center of mass of the plate? [Hint: Try subtraction.]   R

  Assume that your proportions are the same as those in Table 7–1, and calv- nx3n 8lru cv 92ic-c5utu4hculate the mn5urch v9n vc4cit2 uu -x8-3lass of one of your legs.    kg

  Determine the CM of an outstretched arm) ss, , bb0z7qy )ecv9;wv3msylb -vuo7hywl0 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 positiovm ,(/pxd i.c54usmph.5q o cpn of the CM of an arm bent at a right angle. Ass4xio / c.qsc ,.pmmp5up vh5d(ume that the person is 155 cm tall. $X_{CM}$ =    cm $Y_{CM}$ =    cm

When a high jumper is in a position2wtiqn ych*3:5 czko) such that his arms and legs are hanging vertically, and his trunk and head are h 2)yi3c* w qnohc:kzt5orizontal, calculate how far below the torso’s median line the CM will be. Will this CM be outside the body? Use Table 7–1.

The masses of the Earth and Moon aouoxhahn9 baew.v : x9y 652-nre $5.98\times10^{24}$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 frictionles)weo1 )k bk(v f v4nnpq+ko jquqwf-l,1+vs87s 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 uz*veydw+6x1v ekc cke40/* tpes a2y(niform cylindrical 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 the point that will follow a parabolic trezt4 *(y10cea6/pyx wk +e esvvdk* c2ajectory?    cm

  A mallet consists of a uniform cylindricalobj rio0p )k dc,,x)z6 head of mass 2.00 kg and a diameter 0.0800 m mouxzcbp ,6j)) ior0 kd,onted on a uniform cylindrical handle of mass 0.500 kg and length 0.240 m, as shown in Fig. 7–42. If this mallet is tossed, spinning, into the air, how far above the bottom of the handle is the point that will follow a parabolic trajectory?    d    d

  (a) Suppose that in Example 7–14 (Figk);t xtawel.mo9 d m05. 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+aco5ggd(0i i3q + 8eald4 hvm, of mass M, are in the air and stationary with respect to the gro (g 3ieq 0gv+m+4aod8chldai5und. 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 stops?

  An 0.145-kg baseball pitched horizontally at strikes a bat and is popc+ nc7;v/wdf12vcv jie 4 ms-cn f4iy(ped straight up to a height of 55.6 m. If the contact time is 1.4 ms, calculate the average force on the ball durin( 24cweyimv1s;fn +fcivn 7 4dcj -c/vg the contact.    $^{\circ} $

  A rocket of mass m traveling wsim,e e,o/p; p d1a at+ c(kzbv0n;kh.ith speed $v_0$ along the x axis suddenly shoots out fuel, equal to one-third of its mass, parallel to the y axis (perpendicular to the rocket as seen from the ground) with speed 2$v_0$ Give the components of the final velocity of the rocket.$P_x$: v'$_x$=    $v_0$
$P_y$: v'$_y$=    $v_0$

A novice pool player is faced with the corner pocket shot 5x 3ky.k y8ojl7u;s *j g-tblwa8/bxmshown in Fig. 7–43. Relative dimensions are also shown. Should the player be worried about this being a “scratch shot,” in which the cue ball will also fall into a pocket? Givml k;3*g.xyx8 js 8otwbauj-5 /kl7bye details.

  A 140-kg astronaut (including space sufy j,r sf+nce;-)zuxk:q9 (ioit) acquires a speed of 2.5m/s by pushing off with his legs from an +s-9 nxuyez;q:ij,c o ffk)r(1800-kg space capsule.
(a) What is the change in speed of the space capsule?    m/s
(b) If the push lasts 0.40 s, what is the average force exerted on the astronaut by the space capsule? As the reference frame, use the position of the space capsule before the push.    N

  Two astronauts, one of mass 60 kg and the other 80 kg,f.5 ovhygj: j2x )rcf. are initially at rest in outer space. They then push eyvxgf 2j:. froch5).jach other apart. How far apart are they when the lighter astronaut has moved 12 m?    m

  A ball of mass m makes5ariihya8,.pt ; cb8 4byt4aq a head-on elastic collision with a second ball (at rest) and rebounds in the opposite direction with a sp;ibt8 4 cpaa5t8yqy.ib4, rhaeed equal to one-fourth its original speed. What is the mass of the second ball? $m_B$ =    $m_A$(Round to two decimal places)

  You have been hired as an expert witness in a court case involving an automobileqbh.-xuvth )wth1e , ; 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. q;t ),wb-he u1xhhvt 0.60. Show that the driver of car A was exceeding the 55-mph (90km/h) speed limit before applying the brakes.    mi/h

A golf ball rolls off the top of a flight of concrete steps of total vertlo ji2g7tcj9:c ,7 qhzical height 4.00 m. The ball hits four times on the way down, each time striking the horizontal part of77 ,joci:2jqczh t9lg a different step 1.0 m lower. If all collisions are perfectly elastic, what is the bounce height on the fourth bounce when the ball reaches the bottom of the stairs?

  A bullet is fired vertically into a 1.40-kg block of wood8+.rv;7rt 6kw qefbhky6aqx8 at rest directly above it. If the bullet has a mass of 29.0 g 8qhbtk+va86x6y .rkqf wre; 7and 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 h7y y llign+** q2dr)xbecomes embedded in a 1.35-kg block of wood placed on a horizontal surface just in front of the gun. If the coefficn) yixr ql l*dy72*gh+ient of kinetic friction between the block and the surface is 0.25, and the impact drives the block a distance of 9.5 m before it comes to rest, what was the muzzle speed of the bullet?    m/s

  Two people, one of mass 75 kg and the other of mass 60 kg7+c30ose kr nq, sit in a rowboat of mass 80 kg. With the boat initiaconk7+s 0er 3qlly 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 move    towards the initial position of the 75 kg person(Round to two decimal places)

  A meteor whose mass was as 8nnz(r2u0z tjqhky:5hh .ljuvh9)2bout $ 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 izz,99 cm 3 pxlzo,7w3oea *mwfnto two fragments by an explosion. One fragment acquires twice the kineti9w3o,oe7,pm azw9 x3lmz fc *zc energy of the other. What is the ratio of their masses?   

  The force on a bullet is given by716lnb6 dd t7rh ipt*a e9fg6t the formula 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 ; cuwky;*isq0 $m_A$ = 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 anl 579 jkgmsc. aam(t345atnkd t/;z fn alpha particle and a smaller nucleus. What will be the speed of this recoiling nucleus if t 4jz5 c7fsg5nnl; /k(a 39.d katttmamhe 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 angiyveo-+u s(l1 le of 30 $^{\circ} $ to the horizon with a speed of 25m/s (Fig. 7–45). When it reaches the maximum height, it is hit from below by a 15-g pellet traveling vertically upward at a speed of 200m/s The pellet is embedded in the skeet.
(a) How much higher did the skeet go up?    m
(b) How much extra distance, $\Delta{x}$ does the skeet travel because of the collision? $\approx$   

  A block of mass m=2.2kg slides d ( gbyq4cl,pnnai//v3gn l6 5vown 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 is to ,sy5qe doxtzox( 479cp7h c 5d:x r;ennvy/f2rebound from M, slide up the incline, stop, sl zvs r2 7,exy5x (qf /4oend5poht; x:7cc9ydnide down the incline, and collide with M again?    kg (Let A represent mass m, and B represent mass M.)

  The gravitational sling cv pv7t56 xm,ho:zwk)x*aik5 shot effect. Figure 7–47 shows the planet Saturn moving in the negative x direction at its orbital speeda 7cv56htxpiz)owk*m, 5:xvk (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