We claim that momentum is conserved, yet most movin 4ks (s ks/wxxymlm9 mt() o:)us0jzz4g objects eventually slow down and stop. Expl4sstxo xmmj( :s/) lzsyuk 0)w4 (m9kzain.

When a person jumps from a tree to the ground, what happens to the momentuhneue,4lc*a0 f )ok m4m of the person upon strikiln e4um o04akf*h,e)cng the ground?

When you release an inflated but untied balloon, why does it fly across the rovheu. tffzre6-aisnd9*2rp.e:.h2u om?erf 2h2 : u.tsi6 . *zdhnp-ureeav9f.

It is said that in ancient times a rich man with a bag of gold coins froz 34s5bs( 0ka(oeo. ieupj1vrte to death while stranded on a frozen lake. Because the ice was frictionless, he could not push himself to shokpe5ja(ut ebr o04 (1os.vs3ire. 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 inhf +lfl46 /xr 7gby;qxgbw0-j space and is essentially xg/bfg6 -wxhjfbr y;l7+l0q4 in a vacuum?

According to Eq. 7–5, the longer the impact time of an impulsew;q-c . qbz hvaw0rl87 jlqd7 s)f3,r23o bert, the smaller the force can be for the same momentum change, and o7v.;- qa3r) 3 qjw, tcz 2f0r8wl7hbsbdqlerhence the smaller the deformation of the object on which the force acts. On this basis, explain the value of air bags, which are intended to inflate during an automobile collision and reduce the possibility of fracture or death.

Cars used to be built as rigid as possible to withstand collisions. Today, ;xwrmwq8amo),if/8bc y q6i;though, cars are designed to have “crumple zones” that collapi, 8 qb6cr;q)am;yfi/owxw8 mse upon impact. What is the advantage of this new design?

Why can a batter hit a pitched baseball furti;.qz7f-jjn epcdj )1her than a ball tossed in the air by thefijj)nj1. ;zedc qp 7- batter?

Is it possible for an object to receive a larger ikz pwrim l 8fr0.zi 8mqn2371luk865yvydb e;mpulse from a small force than from a large2 kyzlnimuq8 .3 mf5z1r60p8 bwi7;ke8y rvl d force? Explain.

A light object and a heavy object have the same kinetic en8w*x xqgcx ;o wfgky+i//2l a9ergy. Which has the greater momentumw;gfa w 9/lk*2xic/xxq+ g8oy? Explain.

Describe a collision in which all kin *b)d e v+jd*mx;px4paetic energy is lost.

At a hydroelectric power plant, water is directed at high speed against tur6pc w.oz goeb0l 2d9/sbine b20 /sdwlocgbo 9 e.p6zlades on an axle that turns an electric generator. For maximum power generation, should the turbine blades be designed so that the water is brought to a dead stop, or so that the water rebounds?

A squash ball hits a way5uk yu6*xzs .ll at a 45 $^{\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 plate (fcl(s9n e uzy7)7mu xm4k2yr t8ixed to the Earth), from which it rebounds at very nearly its original 2u lzumne(8c x t4yym )7k9sr7speed. (a) Is the momentum of the ball conserved during any part of this process? (b) If we consider the ball and Earth as our system, during what parts of the process is momentum conserved? (c) Answer part (b) for a piece of putty that falls and sticks to the steel plate.

Why do you tend to lean backa tfq0v nl0 ,jhr:mavsuv267v d7 5sc2ward when carrying a heavy load in your arms?

Why is the CM of a 1-m length of pipe at its mid-point, w+jjsy 3t5)x,2vxi znv(;a*q8khevw. hg ey z )hereas this is not true hkva.3y(q;xyhzvjeex* + g5 zjt ) vi8)2sn,w for your arm or leg?

Show on a diagram how your):fnv:c irq,q CM shifts when you change from a lying position to a s)qfi,:rv : cnqitting position.

If only an external force can change the momentum of the center w5tsj)t a11qwrt *(bd of mass of an object, how can the internal force of an engine accelerat wttja5bwds)q*r1 1( te a car?

A rocket following a parabolic path 9jw9 b ,8cpkxdthrough the air suddenly explodes into many pieces. What can you say about the motion of th8cb9kwx9 pj, dis system of pieces?

  What is the magnitude of the momentum of a 28-g sparrow flying with a speevw4z8j/gfb+ t d of 8.4 z8+ j wb4/fgtvm/s    $kg\;m/s$

  A constant friction force of 25 N acts on a 65-kbi21ccqw az /2vtdn,3g skier for 20 s. What is the skier’s change in velocity?2nt, c wci/2az1d3vqb    m/s

  A 0.145-kg baseball pitched at 39 m/s is hit on a horizontal linuqg9g lxvcod: 9n3- ,se drive straight back toward the pitcher at 52m/s If the contact tinlxo,3s:qcgv -d gu99me 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 horizontally with a spe dx(;/eg:thq+w8u q lzed 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 thehd/+(quxqe zl8gw ;: t boat is 45.0 kg. Ignore water resistance. The velocity of the boat is    m/s

  Calculate the force exerted on a rocket, given that the propellingk igsw5 o1h-q4 gases are expelled at a rate of 1500kg/s with a speedso-qk gi 4h51w of $ 4\times10^{4 }$ (at the moment of takeoff).$a\times10^7$ N a =   

  A 95-kg halfback moving at 4.1m/s on an apparent breakaway for a touchdownemqd6 *(kbb8c is tackled from behind. When he was tackled by an 85-kgkbe c8 m6(d*bq cornerback running at 5.5m/s in the same direction, what was their mutual speed immediately after the tackle?    m/s

  A 12,600-kg railroad car t s rg11rf+0krgravels alone on alevel frictionless track with a constant speed of 18m/s A 5350-kg load,initr1f10 g ksgr+rially at rest, is dropped onto the car. What will be the car’s new speed?    m/s

  A 9300-kg boxcar traveling at 15m/s strikes a second boxcar at rest. The twxo5o5ij+oc/joon 9 9ip; kst8o stick together and move off with a speej+k5 tj9s8x o;i/c5nop9oio od of 6m/s What is the mass of the second car?    m/s

  During a Chicago storm, windsp rnkyx.8 *ecrc1rsl7pm,ks0: y:wp9 can whip horizontally at speeds of 100km/h If the air strikes a person at the rate of 40kg/s per square meter and is broxep p c0: ws,yc1rmlr pnysk9r:8.7k*ught 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 525if4 2rye) hsygr zva 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 friction with the tracks, what is the speed r4y2rf ziv s5)hg2e5yof the car after 90.0 min?$\approx$    m/s

  An atomic nucleus initially moving at 420m/1oj p f;e/ d*b-ola8xks emits an alpha particle in the direction of its velocity, and the remaining nucleus slows to 350m/s If the alpha particle has a mass of 4.0 u and the original nucleus has a mass of 222 u, what*- f e/18o;ab kpjdlox speed does the alpha particle have when it is emitted?    m/s

  A 23-g bullet traveling 230mk0-e,zxz v9 z22fo0fs1 mgcan/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 emerges?vgfzk2e2 91 -fs zzm0c,xno0 a    m/s

  A 975-kg two-stage rocket is )y+hj ne,8o tdfbsm- *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 st llnx374w*t -:qnnd traveling in outer space with a velocity of 115m/s To alter its 7t lqns3t l w4d*:xnn-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 qg*pibw3 ui(5 The golf club wab*wugpi ( iq35s 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 nail at a velocity of 8.5m/s anj ljj ak ,t28cmwpz2+4w5 3*jo;ejb mgd comes to rest in a time interval of 8.08jb 3w mje2ajljt4w jm p2+,g5*;zkoc ms. (a) What is the 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 str83otao /9 zb5yqc r(fhikes a wall at a 45 $^{\circ} $ angle and rebounds with the same speed at 45 $^{\circ} $ (Fig. 7–32). What is the impulse (magnitude and direction) given to the ball?   kg*m/s to the  ----待选择----leftright 

  You are the design engineer in charge of the crashworthine mywkxr.) (b-qss of new automobile models. Cars are tested-.m k(yw xbr)q 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 in 0.i:f1 ,hjzdrz475 s by a head-on tack:i rh14df z,jzle by a tackler 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 direcv45orj:t4-6w-usvw fnrl r/s tion and is given by the graph of Fig. 7–33 as a function ofv rww6u l-s/5onrv rs: t4fj4- 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 canrtm jndmy,96 5 a 75-kg person 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 breaking the fall). As mr5,j6tdy9 mnsume 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 (+x direction) with a s(4c*0jo vj .lg mho1wjpeed of collides head-on with a 0.220-kg ball at rest. If the collision is perfectly elastic, what will be the speed and direc .(1 jw0m lcjoo4h*gjvtion 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 speed of 3m/s h v a:f+3 4sr+r5sxinpwas 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 collision?Let A represent thxspv+3 wiarr :fns +45e 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 perfe - k1ge a:5ohe;6iptc*as8vnmctly 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 tha 1 paa5nv;h*6m:8 t-eocgisket 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/ 5udmqso/h- +4gma x;us collides head-on with a 0.090-kg ball initially moving away from it at a speo 5/;ua m- u+qxg4smhded of 1.15m/s Assuming a perfectly elastic collision, what are the speed and direction of each ball after the collision?(Let A represent the 0.060-kg tennis ball, and let B represent the 0.090-kg ball.)v'$_A$ =    m/s v'$_B$ =    m/s

  A softball of mass 0.220 kg that is moving with a speed xx+- i un fb/1ztr1ei+of 8.5m/s collides head-on and elastically with another ball initially at rest. Afterward the incoming softball bounces backward 1uex+ nirib1t+ -zx /fwith 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 approachesi(b,kwujo7v mty;u** the other directly from the rear (Fig. 7–34). Car A has a mass of 450 kg and car B 550 kg, owing to differences in passenger mass. If car A approaches at 4.5m/s and car B is movit mvjyuio,;b(7w *ku*ng 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 m y/,,buqmsf8 initially at rest. The second ball moves off with hq8,f s,yu/m mbalf 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 Fig. 7 ts d.s+vt7qiyr698z m–35, and elastically 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 movingy7+vq.r8st i69s dztm horizontally.]$\Delta x_{m}$$\approx$    m $\Delta x_{M}$$\approx$    m

ake the general case of a.,p kk/ovto +t+/ zslen object of mass m$_A$ and velocity v$_A$ elastically striking a stationary object of mass head-on. (a) Show that the final velocities v'$_A$ and v'$_B$ are given by$v_{\mathrm{A}}^{\prime}=\left(\frac{m_{\mathrm{A}}-m_{\mathrm{B}}}{m_{\mathrm{A}}+m_{\mathrm{B}}}\right)\nu_{\mathrm{A}},v_{\mathrm{B}}^{\prime}=\left(\frac{2m_{\mathrm{A}}}{m_{\mathrm{A}}+m_{\mathrm{B}}}\right)\nu_{\mathrm{A}}.$(b) What happens in the extreme case when m$_A$ is much smaller than m$_B$ Cite a common example of this. (c) What happens in the extreme case when m$_A$ is much larger than m$_B$ Cite a common example of this. (d) What happens in the case when m$_A$=m$_B$ Cite a common example.

  In a ballistic pendulum experiment, projectile 1 results in 37v eqjx 9(zcnrqjet7)o b .h8a maximum height h of the pendulumvjen8b9o7rj7 (3qzhx)t c .eq equal 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 traveling 230m/s buries itself in a dm:f) md7v dt23.6-kg pendulum hanging on a 2.8-m-long string, which makes the pendulum swing upward in an arc. Determine the ve7d:2fvmt dd)m rtical and horizontal components of the pendulum’s displacement.vertical$\approx$    m horizontal =    m

(a) Derive a formula for the fraction of kinetic energy lost, wi.ti,y g rj oq;yx8j0;lb0/v$(\Delta\mathrm{KE/KE})$ for the ballistic pendulum collision of Example 7–10. (b) Evaluate for m=14g and M=380g

  An internal explosion breaks an objecwm).p1 hlxws +0ir 5:: t)j9ocfnaie)ni op*d t, initially at rest, into two pieces, one of which has 1)rn d0*ap)l.) o51::tpei9x wcnifiowhs+ jm.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. ) KE'$_A$ =    J KE$_B$ =    J

  A 920-kg sports car collides into the rear end of a 2300-kg SUV stoppbq. buje8c c1/ed at a red light. The bumpers lock, the brakes are locked, and the two cars skid forward 2.cu8/. b jb1cqe8 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 oz / h,p(ggmlf;f 1.50 m and rebounds to a height of 1.20 m. Approximately how many rebounds will the ball make before losing 90% gmhzl g(f;p, /of its energy?   

A measure of inelasticity in a head-on collision of two objects is the coefficiebwebmf aw-4g;+8 hue*nt of restitution, e, defie-hbmbfag4u8wwe *+;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 psq(67wi+aa z8njz vo zo21 r*jieces, one with three times the mass of the other. A depression is made i+2ioa( qozs w1jzz6a8 7v jrn*n both faces of the cut, so that a firecracker can be placed in it with the block reassembled. The reassembled block is set on a rough-surfaced table, and the fuse is lit. When the firecracker explodes, the two blocks separate and slide apart. What is the ratio of distances each block travels? ----待选择----1/91/101/81/6 

  A 15.0-kg object moving in the +x direction at 5.5m/s/hyc7(ceuscwt.9j-uq0w)xc9/c; ugvq- mo i collides head-on with a 10.0-kg object moving in the -x direction at 4m/s Find the final velocity of each mass t/(c -ghqm 0xq9ucu-i.s;ywo9 ccue/)v j7cw 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, 2k6p4vs) hky8xvqo 2r and a neutrino. The electron and neutrino are emitted at right angles and have momenta8xrpv6qk 2) khv2yso4 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 fvny k dts3()1o-3ecs $m_\mathrm{A}=0.400$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 5 :2 burdwih0dmass, each having initial speed the two move off together with speed v/3 What was the angle betwh5udrdb20i :w een their initial directions?    $^{\circ} $

  Two billiard balls of equal mass move at right angles and meet at the uu cp-6q6qrf 6origin 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 directio66fpquuc-r6q n 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 pp-ohb0p.g6l v/i /pjb erfectly elastic collision with another atom at rest. After the impact, the neon atom tra/i ppo bv/jp .gb-0l6hvels 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) make79 bu8) pm(kxiy7p gfvgs-zf 6s a perfectly elastic collision with another atom at rest. After the impac9psgu 7v-(mb gzkypxif786)ft, the neon atom travels away at a 55.6 $^{\circ} $ angle from its original direction and the unknown atom travels away at a -50 $^{\circ} $ angle. What is the mass (in u) of the unknown atom? [Hint: You can use the law of sines.](Let A represent the incoming neon atom, and B represent the target atom) $m_B$   u

  Find the center of mass of the three-mass syste-5czb * k;crt)wvncf:m shown in Fig. 7–38. Specify relative -zcw tcb *nf c)r5:;vkto the left-hand 1.00-kg mass.    m

  The distance between a carbon ;w fb:8vez ib.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 tp;(qf+1fitd en f 1se)he car. How far from the front of the car will the CM be wn q+1(fip;e 1dse)fft hen 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 1841 n 2vmlb2xyk m, of mass 6800 kg, is used as a ferryboat. If three cars, eakl b m1n2xyv42ch of mass 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 sidesay(bg4uq: cql50 iv s. $l_0$,$2l_0$, 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 toa+y27 zd0k+ 5vdpcr iumato paste (see Fig. 7–40), each of which is a cube of length l. Finy+0 ivdp udkc+2a7rz 5d 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 plate of uf j47q(k/7 jna.wzz,te r-wyradius 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 w7 4 rnujej.- fky(zw,azq/t 7of mass of the plate? [Hint: Try subtraction.]   R

  Assume that your proportions are the same as those in Ta 3nv/s*2 e hcfb7pk.s+si3klqble 7–1, and calculate the mass of o/ 7ec vsssnhq3*libk+32f.kp ne of your legs.    kg

  Determine the CM of an outstretched arm using Table 7–1. cx 8puam.cs;rb0 ;+r bl2q o,z  % of the person's height along the line from the shoulder to the hand

  Use Table 7–1 to calcir7 )/* ylihsyulate the position of the CM of an arm bent at a right angle. Assume that the yls)iirh/ y*7 person is 155 cm tall. $X_{CM}$ =    cm $Y_{CM}$ =    cm

When a high jumper is in a position such thjrc ixs/)/19rbpd jm3 kak*x7at his arms and legs are hanging vertically, and his trunk and head are horizontal, ca/xd jms) /j9*xp3ia c7kk1rrblculate 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 acdam k/z0ea v3..szo 9nd 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 8iy :74r16r .ulj2ziebj *vh yc0-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 kg api/5,i k1nv)mki y +amnd a diameter 0.0800 m mounted on k)m 5pavim/i+,y1kn ia 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?    cm

  A mallet consists of a uniform cylindricalxkia-4(r qcj .+tru 2d 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 paraboldqu-t r cr2k+(jxia 4.ic trajectory?    d    d

  (a) Suppose that in Ep-e;;pmqvij fc ev1 2+xample 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 masmp6.,s, puf zus M, are in the air and stationary with respect to the ground. A passenger, of mass m, then climbs out a6pf, u.ps z,mund 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 popped simzs41 xcw/w .traight up to a height of 55.6 m. If the contact time is 1.4 ms, calculate the average force on th4w/mzwi.1c s xe ball during the contact.    $^{\circ} $

  A rocket of mass m traveling with speed bz 4n*:rg; 2ad/mugnn$v_0$ 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 pock29r )dio+3l/joisi baet shot shown in Fig. 7–43. Relative dimensions are also shown. Should the player be worried about this being a “scratc9ooai /b) dsr32ilj+i h shot,” in which the cue ball will also fall into a pocket? Give details.

  A 140-kg astronaut (including space sui,z8 v;ulp2 b5j*;rfkbvk.eij t) acquires a speed of 2.5m/s by pushing off with his legs zklie,v;j r 5fv8* ub2 .pbk;jfrom an 1800-kg space capsule.
(a) What is the change in speed of the space capsule?    m/s
(b) If the push lasts 0.40 s, what is the average force exerted on the astronaut by the space capsule? As the reference frame, use the position of the space capsule before the push.    N

  Two astronauts, one of mass 60 kg and the ot74 eci7alk 0vlher 80 kg, are initially at rest in outer space. Thea ie07lvlk4c 7y then push each other apart. How far apart are they when the lighter astronaut has moved 12 m?    m

  A ball of mass m makes a head-on elastic collisiowmmappzwnkaud( g6 *fvfw 3:+ 5b*4+rd:n /ccn with a second ball (at rest) kwnc/dvr++:zmapfw * 3n(c 4u5wdg paf 6m:b*and rebounds in the opposite direction 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 witness in a courtv:kk53xrv hwlxf)5j i i+5 9qk case involving an automobile accident. The accident involved car A of mass 1900 kg which crashed into stationary car B of mass 1100 kg. The driverjh+ xlv5 35f)ikw:9riqx v5kk 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 z7dd- kvl6ud+steps of total vertical height 4.00 m. The ball hits four times on the way down, each time striking the horizontal part of a different step 1.0 m lower. If all collisions are perfectly elastic, what is the bounce height on the fourth bounce when the bal lu7d+d-dzk6v l reaches the bottom of the stairs?

  A bullet is fired vertically into a 1.40-kg block of woodr,t: lsf w0yd2sx( x7h 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 rise after the bullet becomes em(y x2w lt0sf rh,7s:dxbedded in it?    m

  A 25-g bullet strikes and becer h,o .b)pxw0z-dg-n omes embedded in a 1.35-kg block of wood placed on a horizontal surface just in front of the gun. If the coefficient of kinetic friction between the block and the surface is 0.25, and the impact drives the block a distance of 9.5 m before it comes to rest, what was ehrp-o )-dgw,n.0zbx the muzzle speed of the bullet?    m/s

  Two people, one of mass 75 kg z rk+g ec::0sk/y5zpoand 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 and in what direction will the boat move? Thzekc: 5oy: /gk+zr0s pe boat will move    towards the initial position of the 75 kg person(Round to two decimal places)

  A meteor whose mass was aboutamy;; k(y+bs d $ 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 fr8 hn (hb*y8zry d(s1cragments by an explosion. One fragment acqny(zhy (cr8db* 8hs1ruires twice the kinetic energy of the other. What is the ratio of their masses?   

  The force on a bullet is given by the formul(),p+,pmcjw8q xnbijj 8fmv*a 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,wo2(ol(e c onc.6kug $m_A$ = 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 lmc3w7piej ))-wtc-wqc uw0r)o,c i;;4jz zealpha particle and a smaller nucleus. What will be the speed of t lrctc e04imu3 jo;z7 )z))w cpq;cjwwi,--wehis 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 tf7::0wsdr oh(j do dt5arget) 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=2.2l k,tdiw,lbd37o *tl- kg slides 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)w(1 2vdnbgz-2m zhwt 6 /zmwp7, what is the upper limit on mass m if it is to rebound from M, slide up the incline, stop, slide down the incline, and collide with M am mz v1g6(bdz7nw2/-2whpwzt gain?    kg (Let A represent mass m, and B represent mass M.)

  The gravitational slingshot effect. Figure 7–47 shows th45;ekzb bxvn *e planet Saturn moving in the negative x direction at its orbital speed (with revb5kbzxn * ;4espect 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