We claim that momentum is conserved,zem:wo g)*sq,+f u qlqq8 4opg hdy10) yet most moving objects eventually slow down am4u g:doey)*0gqh)q zq18f+ oq ,lpswnd stop. Explain.

When a person jumps from a tree to the ground, what happens to the moment/ i c;vwghtxj5gqgq19 pv 8u0.um of the person upon striki8.05u q xpch9jgi q1wgvtvg;/ng the ground?

When you release an inflated but untied balloon, why does it fc;boy+ /n7y wm,qsruc/*g nc 0ly across the roomccn 7gnywqros *;y,/uc+/b 0m?

It is said that in ancient times a/+)z eoz oejlyu2r79j 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 he n r+zyjjoelu 9/ezo7 )2ot been so miserly?

How can a rocket change direkg/: y (uusv8cep4k4lkw4)ym ction when it is far out in space and is essentially in a vacuum?wg)ek4m uk4 vk/(u8y4l c p:sy

According to Eq. 7–5, the longer the impact timer(b7/i dt 3ye)3f astj 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 bag)f (jitystbe37dr3a /s, 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 posdki+m k t,6+ jty(irs2sible to withstand collisions. Today, though, cars are designed to have “crumple zones” that collapse upon impact+ jkit,r2ty+k6dm( is. What is the advantage of this new design?

Why can a batter hit a pitched baseball further than a ball t kq+/a6k lgy5;w0y qbfossed in the air by the batteaqk y b5gyq;0/wkf+l6r?

Is it possible for an object to receive a lah b(c r09t l30-pcl7p/ x6 nuki ocwvi,vfb:c0rger impulse from a small force than from a large fn9cct0 vxpo-w, l r 7 p0ikcb( ihc6blu/3:0vforce? Explain.

A light object and a heavy object have the same kinetic energy. Which h c5y sp i62+;6j.hswlpye b-izas the greater mo 2y;wpp- 6i 5e6c h.b+iljszysmentum? Explain.

Describe a collision in which all kinetib5x .w1zfub/ jk vi+:6rck1 jfc energy is lost.

At a hydroelectric power plant, wat:y z l/.setzwxf6ye9bj71(pcer 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 7sjzw/l 1.xtp(zfy:e 9ebc y6water is brought to a dead stop, or so that the water rebounds?

A squash ball hits a wall at a 45u1( a 0ljnvl0e lhn f82*l5ipcsga(q1 $^{\circ} $ angle as shown in Fig. 7–30. What is the direction (a) of the change in momentum of the ball, (b) of the force on the wall?

A Superball is dropped from a height h onto a hard steel plat l1et/gwvg2pisgw ,-j( rf2.m e (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 process is m 2 gwef-2lw 1 ,gmrt/j.sg(ivpomentum 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 carm0tp7 jte djuxy5nie4c +/1:;al* ljl rying a heavy load in your arms?

Why is the CM of a 1-m length of pipe at.hg (- lczb(wzl.+hxl its mid-point, whereas this is not true h .wxl-(zl(.gzb +hlcfor your arm or leg?

Show on a diagram howp*6iibjqt 0s48ru (le your CM shifts when you change from a lying position to a sitting pit u4jis(8ebl*r6q p0osition.

If only an external force can change the momenavv 0jh))kc) ctum of the center of mass of an object, how can the i) c)) avhjv0cknternal force of an engine accelerate a car?

A rocket following ah -lx 21 lhahxrseis5k7:;s-s parabolic path through the air suddenly explodes into many pieces. What can you say about x hi 5s:l-h1-ke;lahrsx2 7ss the motion of this system of pieces?

  What is the magnitude of the momentum of a 28-g sparrow flying wit0e oq:erf*tf,n .p5p zh a speed of 8.4 f ne:eofp 5, pq.rzt0*m/s    $kg\;m/s$

  A constant friction force of 25 N acts on a 65-kg skier for 20 s. What is the ,u5dx y6 wvoa.v;kzt )skier’xkaz6 v owyduvt,)5 .;s change in velocity?    m/s

  A 0.145-kg baseball pitched at 39 m/s is hit on a horizontal line drive str xg d9nchazwc*n.w:9( aight back toward (nhc. c n9ww*x9da:gz the 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 throws a 6.400jkggh 06svp3jx.baelb6+q 0 -kg package out horizontally with a speed of 10 m/s Fig. b06gsp +h j v0gx06j.bke3albq elow 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 resistance. The velocity of the boat is    m/s

  Calculate the force exerted on a ve 252i;affm yrocket, given that the propelling gases are expelled at a rate of 1500kg/s with a speed a;iyf e5v22m fof $ 4\times10^{4 }$ (at the moment of takeoff).$a\times10^7$ N a =   

  A 95-kg halfback moving at 4.1m/s on an )w0jqych:o( aiz bp79e( h nv8apparent breakaway for a touchdown is tackled from behind. When he was tackled by an 85-kg cornerback running at 5.5m/s)bjvz 9eho7:qnpa(y0cwi8h ( in the same direction, what was their mutual speed immediately after the tackle?    m/s

  A 12,600-kg railroad car travels al2qn0dhejwq3ip 5*q;lone on alevel frictionless track with a constant speed of 18m/s A 5350-kg load,initially at rest, is qw3q5hd*ij2 ; qnle0p dropped onto the car. What will be the car’s new speed?    m/s

  A 9300-kg boxcar trave8 lw;u5vso6u7g c+ ulgling at 15m/s strikes a second boxcar at rest. The two stick together and move off with a speed of 6m/s What is the ma;lwv u 6o5gu g+8sc7ulss of the second car?    m/s

  During a Chicago storm, winds can whip horizontal4 v4;e( jt4ip nqybfes;w lk6-z5jb i9ly at speeds of 100km/h If the air strikes a person at the rate of 40kg/s per square meter and is brought to rest, estimate the force of the wind on a person. Assume the person ie5;j4qs pl 4kwt f6i b;v9e(-jnbyi4z s 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 ar en .9hwy5h 0tc ,jtt*vjdm*9o/ pv7v constant speed of 8.6m/s on a level track. Snow begins to fall vertically anrwn ,**cem.h v vp9t jjv/90t5otdh7yd 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 fhg6os,0rony4 p,f e5 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, pgfso0654 ,h yrefno 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 czag8f(2i; d d4.dnliblock of wood and emerges cleanly at 170m/s If the block is stationary on a frad;.lic( g4 8i2 dfzndictionless surface when hit, how fast does it move after the bullet emerges?    m/s

  A 975-kg two-stage rocket is traveling at hs(kx( o1io h;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 3180jb; xw ,y0e*axf2kyp- kg is traveling in outer space with a velocity of 115m/s To alter its course 0xwx a*bjk;,fp2- ey yby 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 hi(pyfs41)1j4mvul3) uvnvmcg t off the tee at a speed of 45m/s The golf clubgv)p(mfvm ylu413j nv4 u) s1c was in contact with the ball for $3.5\times10^{-3}$s Find (a) the impulse imparted to the golf ball,    kg*m/s
(b) the average force exerted on the ball by the golf club.    N

  A 12-kg hammer strikes a l9cif rov1)e6 w v;j/xnail at a velocity of 8.5m/s and comes to rest in a time interval of 8.0 ms. (a) What is iw6vvr1/;xcl e )of9jthe impulse given to the nail?    kg*m/s
(b) What is the average force acting on the nail?    N

  A tennis ball of mass m=0.06kg and speed v=25m/s strikes a wall at a 44h ohl21hgnpyot8-9 j5 $^{\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 cras ,hhe(k nd)2tvhworthiness of new 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 the average force exerted on the (2v h)ke,td nhcar 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 0.75hh3 w(zxsa. :ps /km:h s by a head-on tackle by a tackler running due west. Cask 3:w:s/h h.zax(hmplculate
(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 dikl)w t6gimiubpxxt3:7s gax0 /.u2 t*rection and is gkux/i30*ltai )tbmt27xu.: 6gpwsx 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 22s).xlifd4-: uaks3mbb hi wperson jump 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 3: ssw4df lb-haui 2)mbi.xk2breaking 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 do*i,2zur tet1m,k ) seast (+x direction) with a speed of collides head-on with a 0.22 st *mu,ted,2i )orz1k0-kg ball at rest. If the collision is perfectly elastic, what will be the speed and direction of each ball after the collision?Let A represent the 0.440-kg ball, and B represent 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 spqw5 u5q8r*6n) jeapdo i-j:h heed of 3m/s has a head-on collision with a 0.900-kg puck initially at re8*jh:j-6u5 w don rhi 5pq)aeqst. 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 puck. v'$_A$ =    m/s ----待选择----eastwest  v'$_B$ =    m/s ----待选择----eastwest 

  Two billiard balls of equal mq sbd, 7 o)m(prfz,boxc+- .(vm7tfla ass 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 moving at 3.00 m/scxm+ d,m s (lbpb., 7t)oo-va(fqrfz7 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-rh-4aj .koz 9kon with a 0.090-kg ball initially moving away from it at a speed of 1.15m/s Assuming a perfectly elastic collisio 4 o-z9rkj.akhn, 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 m05okf 2zuo 27yvn 5 3lvk) xbis. e;tjaydn:i)oving with a speed of 8.5m/s collides head-on and elastically withny f5si:v0bn2zk k 2lv3ej dyo.tiao5ux));7 another ball initially at rest. 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 ride collide elastically as one approaches/e-6fqqq6 n jx the other directly from the rear (Fig. 7–34). Car A has a mass of 450 kg and car B 550 kg, owing to differences in passenger mass. If car A approaches at 4.5m/s and -qqnj/fe6x6 q 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 balzlmkr ;5)+e( (4fm *evt scobul makes an elastic head-on collision with a second ball initially at rest. The second ball moves off with half the originl u (mv*zf4etkb;seo m cr5(+)al 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 494 cdj +;jqsgzuk2zuc-6mhwincline as shown in Fig. 7–35, and elastica md2kqz6cu4 ;c4hjjz+w-g9 su lly strikes another cube at the bottom that is only one-half its mass. If the incline is 30 cm high and the table is 90 cm off 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 objkm:36 e8t n+gdulnr: uxqe- w/ect 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 experiments,, gh bf eguyja+-.w+, projectile 1 results in a maximum height h of the pendulum equal to 2.6 cm. A second projectile causes the the pendulum to swing twice as sy,jfh,begw-g+. a +uhigh, $h_2=5.2\mathrm{cm}$ 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-k ,jy,i5m ldpxhp(v-fvgik.16 g pendulum hanging on a 2.8-m-long string, which makes the pendulum idkp5, 1-vij. hxyp v6g, (mlfswing upward in an arc. Determine the vertical and horizontal components of the pendulum’s displacement.vertical$\approx$    m horizontal =    m

(a) Derive a formula for the fraction of kin,wa*,ja0ph 8+cwn4ovwscij 3etic energy lost, $(\Delta\mathrm{KE/KE})$ for the ballistic pendulum collision of Example 7–10. (b) Evaluate for m=14g and M=380g

  An internal explosion breaks an object, initially at rest, into two piemqee.- n)+m gjces, one of which has 1.5 times the mass of the other. If 7500 J were released in the explosion, how much kinetic energy did each piece acquire? (Let A represent the heavier particle, and B represent the lighter particle eqjmm +)-.gen. ) KE'$_A$ =    J KE$_B$ =    J

  A 920-kg sports car collides/f5e;ds4q ipg 1l(k* zxm8 ech into the rear end of a 2300-kg SUV stopped at a red light. The bumpers lock, th/;hd8el 4ksxc i5z( *fqgep m1e 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 of 1.20 m. A ,jmr-n vutq5*pproximately how many rebounds will the bj,vum* 5nt -qrall make before losing 90% of its energy?   

A measure of inelasticity in a head-on collisn4 gppw3 en+45bm1hk3m h;aqu3 tuiz4ion of two objects is the coefficient of restitution,pe3gmk+uih5 4bam qtznw1p 3 ;n4uh43 e, defined as$e=\frac{\nu_\mathrm{A}^{\prime}-\nu_\mathrm{B}^{\prime}}{\nu_\mathrm{B}-\nu_\mathrm{A}},$
where $\nu_\mathrm{A}^{\prime}-\nu_\mathrm{B}^{\prime}$ is the relative velocity of the two objects after the collision and $\nu_\mathrm{B}-\nu_\mathrm{A}$ is their relative velocity before it.
(a) Show that e=1 for a perfectly elastic collision, and e=0 for a completely inelastic collision.
(b) A simple method for measuring the coefficient of restitution for an object colliding with a very hard surface like steel is to drop the object onto a heavy steel plate, as shown in Fig. 7–36. Determine a formula for e in terms of the original height h and the maximum height h’ reached after one collision.

  A wooden block is cut into two pieces, one with three times the mass of thexz0ei ,y5q 1ed 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,q5z ,xeiy d10e 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;.m09 awoulgs gu.4b.ape7r+x direction at 5.5m/s collides head-on with a 10.0-kg object moving in the -x direction at 4m/s Find the finalus4a rgb a0glwoxp ..9ue. m;7 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 ;8 )mebk d91 lo3wve)jltvxws7e8eb (electron, and a neutrino. The electron;l8s(lwwd3)oj9b178ve )ek bet exmv and neutrino are emitted at right angles and have momenta of $9.30\times10^{-23}kg\cdot m/s$ and $5.40\times10^{-23}\mathrm{~kg}\cdot\mathrm{m/s}$ respectively. What are the magnitude and direction of the momentum of the second (recoiling) nucleus?    $ \times10^{-22}$    $^{\circ} $ from the momentum of the electron

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

  Billiard ball A of mass ey4pce(n0p * f ejcv)eb6z: uqy1.)mx$m_\mathrm{A}=0.400$kg moving with speed $\nu_\mathrm{A}=1.80$m/s strikes ball B, initially at rest, of mass $m_\mathrm{B}=0.500$kg As a result of the collision, ball A is deflected off at an angle of 30.0 $^{\circ} $ with a speed $\nu_\mathrm{A}^{\prime}=1.10$m/s (a) Taking the x axis to be the original direction of motion of ball A, write down the equations expressing the conservation of momentum for the components in the x and y directions separately. (b) Solve these equations for the speed v'$_B$ and angle $\theta_{\mathrm{B}}$ of ball B. Do not assume the collision is elastic. $\theta_{\mathrm{B}}$ =    $^{\circ} $ v'$_B$ =    m/s

  After a completely inelastic collision between two objects of equal mass, ,)me bbj956, e id w*inaot5 ob;*pcfzeach having initial speed the two move off together with speed v/3 Ww ;,aftb z*o bicj m oe*6i5e5dp9b,)nhat was the angle between their initial directions?    $^{\circ} $

  Two billiard balls of equal mass move at right angles anyj 6 o:d0.as ,c*vljxxd 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 badxlv 0.,j *o 6jsx:ycall 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) makeooyl(-* 4:jabg2yqjbs a perfectly elastic collision with another atom at rest. After the impact, the neon atom travels a2 j 4yb*bqo -ljgy:o(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 aq5 98(bl 9ujq .v4vaeckpvu 3rqi(o+dtom at rest. After the impact, the neon atom travels away at a 55.vup9ckq lb(8q35vo.eairv q 9(+4jud6 $^{\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 shown inl)nydw so0cmufe (*,. Fig. 7–38. Specify rela, s(l0odn)ye.uf wm*ctive to the left-hand 1.00-kg mass.    m

  The distance between a /dvvu(w3 ym .3q05dc0oflu+cxgjio 7carbon 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 2.50bm cdaoe b::l 9k(1-j 8i1lqnf pm5f;d m behind the front of the car. How far from the front of the car will the CM be when two people sit in the front seatc( -m i1 :n 5m pbddbq:8alkf;9folje1 2.80 m from the front of the car, and three people sit in the back seat 3.90 m from the front? Assume that each person has a mass of 70.0 kg.    m

  A square uniform raft, 18 m by 18 m, of mass 6800 kg, is used as a ferryboat.k . wdtr*5az o1ll6(js If three cars, each of mass 1200 kg, occupy its NE, SE, and SW corners, determinl j*s56ar .wkzo t1l(de the CM of the loaded ferryboat.$X_{CM}$ =    m $Y_{CM}$ =    m

  Three cubes, of sidesxau dher21rac , dt:45qr0(jc $l_0$,$2l_0$, and $3l_0$ are placed next to one another (in contact) with their centers along a straight line and the $l=2l_{0}$ cube in the center (Fig. 7–39). What is the position, along this line, of the CM of this system? Assume the cubes are made of the same uniform material. $X_{CM}$ =    $l_0$ from the  ----待选择----leftright  edge of the smallest cube

  A (lightweight) pallet has a load of identical cases of tomato paste (see F0p/wp),v qois ig. 7–40), each of which is a cube of length l. Find the center of gravity iis,0)wq /pvp on 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 2R has a circula9mdrd 8el/v0;ymy n4 zr 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 platevn/809dd y m l4ymr;ez? [Hint: Try subtraction.]   R

  Assume that your proportions are the s,xh8g yjbkw)9;nhhp3 ame as those in Table 7–1, and calculate t3ygh,hnk8p ; 9j hw)bxhe mass of one of your legs.    kg

  Determine the CM of an outstretched anzt+u rkt8eu5h*x 90 8r6carjqw 2kc :rm 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 position of the CM of an arm bent at a righlz7 lh0td7 fgm6ki) b4t angle. Assume that the person is 155 cm talfm7g 40hk6tzdlbil 7 )l. $X_{CM}$ =    cm $Y_{CM}$ =    cm

When a high jumper is in a positi*uqoclj)g* t8 v.nz(non such that 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 willn8)gn.*jul(vz* otcq be. Will this CM be outside the body? Use Table 7–1.

The masses of the Earth and Mou/ewp8/ jrm9 bon 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 anhmt1 le7l*t- 2nlh6kzgz1 )bx 80-kg man stand 10.0 m apart on frictionless ice.
(a) How far from the woman is their CM?    m from the woman
(b) If each holds one end of a rope, and the man pulls on the rope so that he moves 2.5 m, how far from the woman will he be now?    m
(c) How far will the man have moved when he collides with the woman? He has moved    m from his original position

  A mallet consists of a uniform cylindrical head of mass 2.00 kgi/ *f2d/3px9g - yxloy+ dmpvb 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 folloxg *ivb9d+xp/ -lo23pyyd/mfw a parabolic trajectory?    cm

  A mallet consists of a uniform cylpafv15-b ai 7oek*: mrindrical 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 1oiar :k*5ef-7bvm ap the handle is the point that will follow a parabolic trajectory?    d    d

  (a) Suppose that in Exampl36l zfg r2aung(bm phb-10x 7se 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 mass M, are iipj0u u-cp 7 rmr :)23o9liluon the air and stationary with respect to the ground. A passengeu9lp3i-mru27 0joouirc: p l)r, 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 u1s8mqwei:8b3ow ) bzpitched horizontally at strikes a bat and is popped straight up to a height of 55.6 m. If the contact time is 1.4 ms, calculate the average force on the ball during t1 bqu:owmsz ) i3eb8w8he contact.    $^{\circ} $

  A rocket of mass m travelinw2-g7a6 ndzmfe4: njlg 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 coafcn9 fpw; 5x.rner pocket shot shown in Fig. 7–43. Relative dimensions are also shown. Sap;5fx cf9nw.hould 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 space sur,yw+ haoug /.p c.4hjit) acquires a speed of 2.5m/s by pushing off with his legs from anwh+4o/. jaygh ur.,p c 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 oipbv sd-g0 ocs 1e:d09ther 80 kg, are initially at rest in outer space. They then push each other apar eid1 -v0p9s:d0bgcs ot. How far apart are they when the lighter astronaut has moved 12 m?    m

  A ball of mass m makes a head-on elastic collision with a second ball (agx 9ksjaksk)wbgj 0q :10b m96t rest) and rebounds in the opposite direct 1 6w:jjakb0 gskm9)sbq 9gkx0ion with a speed equal to one-fourth its original speed. What is the mass of the second ball? $m_B$ =    $m_A$(Round to two decimal places)

  You have been hired as an expert witnedw+ 9dl:ly o6rl3o1gl ss in a court case involving an automobile accident. The accident involved car A of mass 1900 kg: ll3l1drdgwl69oy+o which crashed into stationary car B of mass 1100 kg. The driver of car A applied his brakes 15 m before he crashed into car B. After the collision, car A slid 18 m while car B slid 30 m. The coefficient of kinetic friction between the locked wheels and the road was measured to be 0.60. Show that the driver of car A was exceeding the 55-mph (90km/h) speed limit before applying the brakes.    mi/h

A golf ball rolls off the top of a flight of concrete steps of *j n jvk q4*3a8qnxkv+total vertical height 4.00 m. The ball hits four times on the way down, each time s*n*xakkqv3jj84 q vn +triking 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 bottom of the stairs?

  A bullet is fired vertically into a6/yml 1g-z gfgdou4gtl(q p9; 1.40-kg block of wood at rest directly above it. If the bullet has a mass of 29.0 g and a spee6-q(dz9 pt /; mgufloggy4gl1 d of 510m/s how high will the block rise after the bullet becomes embedded in it?    m

  A 25-g bullet strikew6w t7qf03fd- z z.lj h/ha/as1b*aw ns and becomes embedded in a 1.35-kg block of wood placed on a horizontal surface just in front of the gun. If the coefficient of kinetic*az lf/f/zd3 b-qha0tn.hwaw6 7 j 1sw 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 s3 ,cy4su19 k7p:qwala*jrbv 75 kg and 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 andac 1s4qpl :7sa3vyk 9j*u,wbr 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 waxp xt9 m 0u2s.1qf- f8s,monscs 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 expl(pi; agu gn+.iosion. One fragment n(ug+ a ;g.ipiacquires twice the kinetic energy of the other. What is the ratio of their masses?   

  The force on a bullet is given by 7 rjtcs9 i+kk*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 b/4gm;db+(8 n zftob lqw27bn$m_A$ = 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 and a)w) oib/hl0 ts smaller ns /)i0bltwh) oucleus. What will be the speed of this recoiling nucleus if the speed of the alpha particle is $ 3.8\times10^{5 }$m/s Assume the recoiling nucleus has a mass 57 times greater than that of the alpha particle.    m/s

  A 0.25-kg skeet (clay target) 42yz8kn7i**lnxybc33dx xn i is fired at an angle of 30 $^{\circ} $ to the horizon with a speed of 25m/s (Fig. 7–45). When it reaches the maximum height, it is hit from below by a 15-g pellet traveling vertically upward at a speed of 200m/s The pellet is embedded in the skeet.
(a) How much higher did the skeet go up?    m
(b) How much extra distance, $\Delta{x}$ does the skeet travel because of the collision? $\approx$   

  A block of mass m=2.2kg slic4c jb3kt ip7/ obarz )5ht8u6des 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), whatap 67 h xhi22lh5mlt5j/zeh:y is the upper limit on mass m if it is to rebound from Ma52p ljhith7zy56/x: hleh2m, slide up the incline, stop, slide down the incline, and collide with M again?    kg (Let A represent mass m, and B represent mass M.)

  The gravitational slingshot ef(p:95ni4k-bm)rv3mfbl s ez qfect. Figure 7–47 shows the planet Saturn moving in the negative x direction at its orbital speed (with respect to the Sun) of 9.6km/s The zbifenk- v (:9m4 mls b)qp35rmass 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