We claim that momentum is conserved, yetbuj602k 11anj *v oggh most moving objects eventually slow down and a vgoj n*1b6uj0k 2gh1stop. Explain.

When a person jumps from a tree to the ground, what happens to the momentum of t3j5/xcy tk7 f/mj; grc4ivx9; c7 whmrhe person upon striking the ground f/jtmxvxhwcrj4m ckc5/73r;;9 yg7 i?

When you release an infla /wc1pgxx wc52ted but untied balloon, why does it fly across the room?5p2xwwc gx /c1

It is said that in ancient times a rich man with a bag of gz sxps0 g,gr66old coins froze to death while stranded on ag, s srgx606zp frozen lake. Because the ice was frictionless, he could not push himself to shore. What could he have done to save himself had he not been so miserly?

How can a rocket change direction whe* lkrh(: hk sd32nhr0tn it is far out in space and is essentially h2r tnk*shrl 0d(:k3hin a vacuum?

According to Eq. 7–5, thpuvj(p9) b r2ce longer the impact time of an impulse, the smaller the force can be for the same momentum change, and hence the smaller the deformation of the object on which the force acts. On this basis, explain the value of a jr(ub29) cvppir bags, which are intended to inflate during an automobile collision and reduce the possibility of fracture or death.

Cars used to be built asx )p1:bn clg(j rigid as possible to withstand collisions. Today, though, cars are designed to have “crumple zones” that collapse upon impaclcp:nj)b ( gx1t. What is the advantage of this new design?

Why can a batter hit a pi(nos w8x dp)pvt5 ay 7bo-n5g:tched baseball further than a ball tossed in the air by the baygto dx85- o)75vw(n:a snpbp tter?

Is it possible for an object to receive a0)uc 9hkvx4o7biq0rmc8 go d*t d6t:e larger impulse from a small force than from a large force? Ex8:e0*60icqvg kmthtx4bc9rd od)u o 7 plain.

A light object and a heavy object have the same kinetic energy. Wh9bv;p1 ijtqg0cab ,p9ich has the greater momentum? Explain.ip;9b0qa j,tp cv g19b

Describe a collision in which alra65yduk t3 c,ndyo,1d *jw7s l kinetic energy is lost.

At a hydroelectric power plant, water is direk4 .kjlg cq g,1n(;jpskb/mt5cted at high speed against turbine blades on an axle that turns an electric generator. For maximum power generation, should the turbine blades be designed so that the water is brought to a dead stoknm;sc kjk(qbp1ltg4g.5j /,p, or so that the water rebounds?

A squash ball hits a wall g6wk9hp,4ocj 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 hacr3od ,g53 dg on0o(nard 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 t ,3r(5ng3g odnda0 ocohe process is momentum conserved? (c) Answer part (b) for a piece of putty that falls and sticks to the steel plate.

Why do you tend to lean backward when carrying a heavy load in you ux)nk )b-aaz kq9x4y(r arms?

Why is the CM of a 1-m length of pipe at its mid-point, whereas this ismvq. kd:ofzw4 o( q y04f9ihe2 not true29k (vff.qze4mh oq 0:woi4 dy for your arm or leg?

Show on a diagram how your CM shifts when you change fr /jrfd5o:vhhz) od+)q z72 yuxom a lying position to a s7y/zd5 q dfj+)hru xoh2)o z:vitting position.

If only an external force can cha q2z-f,nlfeck. kbbr p a34m20nge the momentum of the center of mass of an object,cfbl-2k,z4km 0 pn2b.qafer3 how can the internal force of an engine accelerate a car?

A rocket following a parabolic path twitlz 3wsf, k 0s89rhtmk o*43hrough the air suddenly explodes into many pieces. What can you say about the motion o9f3rs tt 80*3oi ,mkwsk4zlwhf this system of pieces?

  What is the magnitude of the momentum of a 28-g sparrow fw8z3z3 9utjnflying with a speed of 8.4 m/s nz9jz83wft 3 u   $kg\;m/s$

  A constant friction force of 25 N acts on a qqq( pao4uy*k1*mdu. 65-kg skier for 20 s. What is the skier’s change i ma*pdq*(4ku.1oq q yun velocity?    m/s

  A 0.145-kg baseball pitchy 2ss:yf;h)m .8lq 41whoptvu0 edno(ed at 39 m/s is hit on a horizontal line drive straight back toward the pitcher at 52m/s If the conuonp4oslh:qw. 2m )f8t(;1yydh ve0stact 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 horizontally with a splgy qc3,(- 5 ji51odfx*jldjx eed of 10 m/s Fig. belj5j,c *dg(qlol j5dy1 xi- fx3ow 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 exertedrixjdao12m(;ktz 5,p q(gyf4 on a rocket, given that the propelling gases are expelle2mjr y zkgx(4 dqf,5; ot(p1iad at a rate of 1500kg/s with a speed 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 touchdown is t*u2 c.xvfx z jj)5x7b5d)ur,bhj *ozyackled from beh 5ch*b ub2uvxof.5,*)d)xyr7 jzxj zjind. When he was tackled by an 85-kg 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 k ta-bqb k j7aa(*f)m/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. Wa /bk7 (t-k* )qbjamfahat will be the car’s new speed?    m/s

  A 9300-kg boxcar traveling at 15m/s strikes a second boxcar at rest. )g0 m2aqtdv dmf4s;20wzkj, x3s) you The two stick together and move3d0j) vqk4 2 w 02)t fzxgsa,o;udmsmy off with a speed of 6m/s What is the mass of the second car?    m/s

  During a Chicago storm, winds can whip horizontal*ejrafco*/*i6 db 6enh1g 6gm ly at speeds of 100km/h If the air strikes a person at the rate of 40kg/s per square meter and is brought to r oa6ce6gh rbjg16fm*d */ine*est, 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 speed of 8.6m/s oz3g 4jdqpb 3ouxon 856n a level track. Snow begins to fall vertically and fills the car at3 qobn xuzj3dpg46o58 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 6zs;7j.tdyvc 420m/s emits an alpha particle in the direction of its velocity, and the remaining nucleus slows to 350m/s If the alpha particle has a mass of 4.0 u ytvcz6d. j7; sand the original nucleus has a mass of 222 u, what speed does the alpha particle have when it is emitted?    m/s

  A 23-g bullet traveling 230m/s penetrates a 2.0-kg block of wood andoh xy11j;m ti2 emerges cleanly at o1t1;j mxiy2h 170m/s If the block is stationary on a frictionless surface when hit, how fast does it move after the bullet emerges?    m/s

  A 975-kg two-stage roc)vhizd,8m1h yket 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 ,+6iuy l3x -gm2wscbymew d-6outer space with a velocity of 115m/s To alteyu,lbc6d3x2 iems+m6 y- w -wgr its course by 35.0 $^{\circ} $, its rockets can be fired briefly in a direction perpendicular to its original motion. If the rocket gases are expelled at a speed of 1750m/s how much mass must be expelled?    kg

  A golf ball of mass 0.045 kg is hit off the teew5)z xdfgn- p: at a speed of 45m/s The golf club was i-) f pnxdg5wz:n 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 strikknw9o;wh 86t ses a nail at a velocity of 8.5m/s and comes to rest in a time interval of 8.0 ms. (a) Whawhtsk;68on w9 t 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 strikes a wallep2ba-*7gikg 88n1 nc1zr 5 zlwez*ku at a 45 $^{\circ} $ angle and rebounds with the same speed at 45 $^{\circ} $ (Fig. 7–32). What is the impulse (magnitude and direction) given to the ball?   kg*m/s to the  ----待选择----leftright 

  You are the design engineer in charge of the crashworthiness of nxff7i-6mg)5. 57 a y3g kvhadmdr-aoq ew automobile models. Cars ar o v)x7yg 3fq-hrd-m5.ka5aifa 6gdm7 e 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 hi onsc8x2e)mggw 80 5to the east and is stopped in 0.75 s by a head-on tackle by a tackler running due west. Calcg5n cxm )208wh igoe8sulate
(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) poi dcjo/;pro:r9nts in the +x direction and is given by the graph of Fig. 7–33 as a function of time. Use graphical methods trrdpoj9 ; oc/:o 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 withs7 wtyz:* hdbhm6zq o7j .7kc2out breaking the lower leg bone of either leg? Ignore air resistance and assume the CM of the perso6z*j7wht:q 7yshk.ob2 7zdmc n moves a distance of 0.60 m from the standing to the seated position (that is, in breaking the fall). Assume the breaking strength (force per unit area) of bone is $170\times10^6\mathrm{~N/m^2}$ and its smallest cross-sectional area is $2.5\times10^{-4}m^2$ [Hint: Do not try this experimentally.]    m

  A ball of mass 0.440 kg moving east (+x direction) wi4w1n(kfr8 hb2 6tz,o 1dw yygnth a speed of collides head-on with a 0.220-kg ball at rest. If the collision is perfectly elastic, what will be the speed and direction of each ball after the collision?Let A represent the 0.440-kg ball, and B r281n4 hy wbo1 (6nfwd, zrygtkepresent 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 2rjs:: myozuj) g*nio bme231speed of 3m/s has a head-on collision with a 0.900-kg puck initialmgi 3j*s)n:z2b ooy:j2me ru1ly at rest. Assuming a perfectly elastic collision, what will be the speed and direction of each object after the collision?Let A represent the 0.450-kg puck, and let B represent the 0.900-kg puck. v'$_A$ =    m/s ----待选择----eastwest  v'$_B$ =    m/s ----待选择----eastwest 

  Two billiard balls of equal mass undergo arp *z 1*6a bzqk,)2m fc/dlshv perfectly elastic head-on collision. If one bad1amq bzp*z r, skhf)v/c2l6*ll’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. ) v'$_A$ =    m/s v'$_B$ =    m/s

  A 0.060-kg tennis ball, moving wi jg6 of)7l80u4g dyw y/vry8tith a speed of 2.5m/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 arr/)6tyj4gdg0lvo7 88 uw yyife 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 k qfk0x.z,to 2hg that is moving with a speed of 8.5m/s collides head-on and elastically with another ball initially at rest. Afterward the incoming softball bxfo0kq tz2h,. ounces 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 appr6sck+a( w6nnc +rs zu2glnr77oaches the othe7 76r(ssn2cw+nnkarz +g cul6r 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 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 collisi.wuwbn3z 55 9kx/ziwi:9sanson with a second ball initiallyzs w s:9nux/5wwi b.n9az3i5k at rest. The second ball moves off with half the original speed of the first ball.
(a) What is the mass of the second ball?    kg
(b) What fraction of the original kinetic energy $(\Delta\mathrm{kE/KE})$ gets transferred to the second ball?   

  In a physics lab, a cube slides d 0kf/5rmml4n6co 2bte msb3,pown a frictionless incline as shown in Fig. 7–35, and elastically strikes another cube at the bottom that is only one-half its mass. If the incline is 30 cm high and the table is 90 cm off the floor, where lops30/,4b 5mc remnb62tkfm 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 object of :myu;b39khpby..u hxrv4 b+ j mass m$_A$ and velocity v$_A$ elastically striking a stationary object of mass head-on. (a) Show that the final velocities v'$_A$ and v'$_B$ are given by$v_{\mathrm{A}}^{\prime}=\left(\frac{m_{\mathrm{A}}-m_{\mathrm{B}}}{m_{\mathrm{A}}+m_{\mathrm{B}}}\right)\nu_{\mathrm{A}},v_{\mathrm{B}}^{\prime}=\left(\frac{2m_{\mathrm{A}}}{m_{\mathrm{A}}+m_{\mathrm{B}}}\right)\nu_{\mathrm{A}}.$(b) What happens in the extreme case when m$_A$ is much smaller than m$_B$ Cite a common example of this. (c) What happens in the extreme case when m$_A$ is much larger than m$_B$ Cite a common example of this. (d) What happens in the case when m$_A$=m$_B$ Cite a common example.

  In a ballistic pendulum experiment, projectile 1 results in a maximuyn8(4syu 8tl0w aa:w5dsl*kiyh e;; zm height h of the pendulum equal to 2.6 cm. A second projectile causes the the pendu8; hs4z(*iw8nywk u a5 e0aly:;lsdty lum 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 230y8f3 *dpboj+rm/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 tf d+o *rj3py8bhe pendulum’s displacement.vertical$\approx$    m horizontal =    m

(a) Derive a formula f heb(qm6tts h32+8zcbor the fraction of kinetic energy lost, $(\Delta\mathrm{KE/KE})$ for the ballistic pendulum collision of Example 7–10. (b) Evaluate for m=14g and M=380g

  An internal explosion breaks an kh /u/o q9zpb9m9c2xe object, initially at rest, into two pieces, one of which has 1.5 times the mass of the other. If 7500 J were released in the explosion,k92p oxqz/m/cue9b 9h 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 o f:zyg ya g2-.qbb2d7*pbp xs:f a 2300-kg SUV stopped at a red light. The bumpers lock, the brakes are locked, and the two cars skid forward 2.8 m before stopping. The police officer, knowing that the coefficient of kinetic friction between tires and road is 0.80, calculzpdb:x .2gq y*bpba2g7-y:sf ates 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 heijz9-qgtz 7 s6a1u8ygight of 1.20 m. Approximately how many rebounds will the ball make before losing 90% of its energugg-a iz8y76j 9zt q1sy?   

A measure of inelasticity in a head-on collision of3u v* hq5au7sbscx+s / two objects is the coefficient of restitution, e, defined aus+3u q/ sx5 sbhac7*vs$e=\frac{\nu_\mathrm{A}^{\prime}-\nu_\mathrm{B}^{\prime}}{\nu_\mathrm{B}-\nu_\mathrm{A}},$
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 thezzd j49gy 8ux3 mass of the other. A depression is made in both faces of the cut, so that a firecracker can be placed in it with the block reassembled. The reassembled block is set on a rough-surfaced table, and the fuse 39 uyjz48g zxdis 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 collides d(th ch.8n.yb dln3u- head-on with a 10.0-kg object moving in the -x direction at 4m/s Find the final velocity of eacntn .d.yuhl8 h(3dc-bh 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 i .kl a1b2h/a dqq0.h/prstnx*nto a second nucleus, an electron, and a neutrino. The electron and neutrino an./adahkh .t/ r2 1 0lqxs*pqbre 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 ri e /5dh.sei r6v1t6x *6gxwb$m_\mathrm{A}=0.400$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 objectlh642 w1hm hp c)zli3bs of equal mass, each having initial speed the two move off together with speed v/3 Whapmh2lh 1i3wzc 6b4 l)ht was the angle between their initial directions?    $^{\circ} $

  Two billiard balls of equal mass move g,ttt2vjt*a b ;**ns8lr o.tjat right angles and meet at the origin of an xy coordinate system. Ball A is moving upward along the y axis at 2m/s and ball B is moving to the right along the x axis with speed 3.7m/s After the collision, assumed elastic, ball B is moving along the positive y axis (Fig. 7–37). What i*j;t2nl* b ts8 r.otjta tg,v*s the final direction of ball A and what are their two speeds? direction of ball A is  ----待选择----x directionx direction v'$_A$ =    m/s v'$_B$ =    m/s

  A neon atom (m=20u) makes a perfectly elastic cobrphs 23ir h/(llision with another atom at rest. Ahbh( p3s /2rirfter the impact, 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

  A neon atom (m=20u) makes a perfectly elastic collision with ano-0zo )unv-k yfther atom at rest. After the impact, the neon atom travelo kz-yn f)0vu-s 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 system shown in Fig..chccz h.+q,j 7–38. Specify relative to the left-hand 1.00-kgq .+ hhcjc.z,c mass.    m

  The distance between a carbonyjwij**koe (6 ( 8zlzf 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 fro.q6d t (1bao0csxyfju ic(l)0 jnoe0j9e; ,r wnt of the car. How far from the front of the car will the CM be when twoc .,j(q6ljbt)c0xe1i0jo ur s y9aoe0;(fw n d 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 myqpin6+ q.zb 09oj7gbc u01 t6800 kg, is used as a ferryboat. If three cars, each of mass 1200 kg, occupy its NE, SE, and SW corners, determine the CM of the loaded ferrybo1gtm oj+ i0pn0q 9uqbbc.6z 7yat.$X_{CM}$ =    m $Y_{CM}$ =    m

  Three cubes, of sidesoe,*y-zo abk2 $l_0$,$2l_0$, 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 pyczg28npyj88 gvq49 2 cejv- haste (see Fig. 7–40), each of which nyq2y8- z98vjcv pheg4c jg2 8is a cube of length l. Find the center of gravity in the horizontal plane, so that the crane operator can pick up the load without tipping it.$X_{CM}$ =    l $Y_{CM}$ =    l

  A uniform circular plate ofqhdfciwa v2a6 *k9t 47 radius 2R has a circular hole of radius R cut out of it. The center of the smaller circle is a distance 0.80R from the center C of the larger cirh9d7 at 2wv*ck4a fi6qcle, 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 q 970lmm,ta vn3nu ab6l5f +ovjq6i g8in Table 7–1, and calculate the mass o76bqn 8mg3o9avmql0 ujl fi56+vnat,f one of your legs.    kg

  Determine the CM of an ouhza:1nwz257cx; md 33r,nbndyhrsy 2 tstretched arm using Table 7–1.   % of the person's height along the line from the shoulder to the hand

  Use Table 7–1 to calculate the position of the CM of an;7a c+cde 5ukbt+f s0g arm bent at a right angle. Assume that the person is 155 cm tall. d5+70+tecc u;sf ab gk$X_{CM}$ =    cm $Y_{CM}$ =    cm

When a high jumper is in a position such that his arms and h3us d64efsp g*etl3u- c( 21alzu3lu legs are hanging vertically, and his trunk and head are horizontal, calculat4lszl lee3 3p 3d(us2hu1*6u fauc g-te 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 y tng65orwu /uiyhmu .(a2z9c59d 2tp(i. x fvand Moon are $5.98\times10^{24}$kg and $7.35\times10^{22}$kg respectively, and their centers are separated by $3.84\times10^{8}$m (a) Where is the CM of this system located? (b) What can you say about the motion of the Earth–Moon system about the Sun, and of the Earth and Moon separately about the Sun?

  A 55-kg woman and an 80-kg man stan;)p s iyxw2*knd 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 m -y 3knkjw0kdx98*rr 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 rk-*3jxrny 8mwk0d 9 kof the handle is the point that will follow a parabolic trajectory?    cm

  A mallet consists of a uniform cylindrical head of mass 2.00 kg and a diameter lt k+hc-jywplnw0pf5; sy //nj0aw0 cn 93e f;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 trajectory?lfp0fhyk9t5w selnanp+0ny;jc /w0;c 3 /j w-    d    d

  (a) Suppose that in Exampletr2jdy y9/uli)emk0c2i/ it ; 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 in the ayqc cjvjm+ppp c.ag5/8;jb9j) ;m4th3wc ow0ir and stationary with respect to the ground. A passenger, of mass m, then climbs out and slides down a rope with speed measured with respect to the balloon. With what speed and direction (relative to Earth) does the balloon then move? What happens w + qp94ccv.c3twj;/ h m;pap cj0ymbj)5o j8gif the passenger stops?

  An 0.145-kg baseball pitched horizont3 w7++ vgokzzqally 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 fowzv7+ zg k+q3orce on the ball during the contact.    $^{\circ} $

  A rocket of mass m traveling with speecvi)1u,huzy 289oo tkjlc o,.d $v_0$ along the x axis suddenly shoots out fuel, equal to one-third of its mass, parallel to the y axis (perpendicular to the rocket as seen from the ground) with speed 2$v_0$ Give the components of the final velocity of the rocket.$P_x$: v'$_x$=    $v_0$
$P_y$: v'$_y$=    $v_0$

A novice pool player is faced with the corner pocket shot shown in F4wu)g b n3p*q*s) xrtiig. 7–43. Relative dimensions are also shown. Should the player be worried about this being a “scratch shot,b *us*rw3 x)qnti4pg )” in which the cue ball will also fall into a pocket? Give details.

  A 140-kg astronaut (including space suit) acquires a speed of 2.5m/s by push 1l uk /vxrwi+9-ztd;ring off with his lu+drx 1ti/-; k9vz wrlegs from 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 othe*2vafji0dm - ;c ppa)cr 80 kg, are initially at rest in outer space. They then push each othemj0c2a icd)av f ;-pp*r apart. How far apart are they when the lighter astronaut has moved 12 m?    m

  A ball of mass m makes a head-on elastyz2mt*l gr9dlx5c56 cic collision with a second ball (at rest) and rebounds in the opposite 5dz9ltl26 cgrxmyc *5direction 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 cojwxupy.jk- s/9 v rc1+urt 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 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 fricjvrk/- 9 ywj1.c pxu+stion 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 st6ye/p z3/zex oeps 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 foo/ey /zepz3x6urth bounce when the ball reaches the bottom of the stairs?

  A bullet is fired ve;j/ 5f bz7ffqgrtically into a 1.40-kg block of wood at rest directly above it. If the bullet has a mass of 29.7b;/5ff gj fqz0 g and a speed of 510m/s how high will the block rise after the bullet becomes embedded in it?    m

  A 25-g bullet strikes and becomes embedded in a 1.35-kg b t/ux)xmbfi1k yw,*w)lock of wood placed on a horizontal surface just in front of the gun. If the coeff 1)x mwiuw) b,xt*fky/icient 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 a fy knxncx0otj0ta a+ 52.r9p.nd 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 rn 0a+.0p tyx2xcto5j9aknf .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 5*l7p+mkdy jn 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 ( cwske3. zeo.suddenly broken apart into two fragments by an explosion. One fragment acquires twice the kinetic energy of ekwe(.co3 .sz the other. What is the ratio of their masses?   

  The force on a bulleie1-;nwv3 xbg1 ,etblm3 yj7ut is given by 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.:(a0l2wuf.qh x +d;lcg qv8syvo h2z $m_A$ = 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 19rb 1 j.gs wqu++wjvwnr;n;yradioactively into an alpha particle and a smaller nucleus. What will be the speed of thisgs+91n;qw bjru.w1yw;+ r vnj recoiling nucleus if the speed of the alpha particle is $ 3.8\times10^{5 }$m/s Assume the recoiling nucleus has a mass 57 times greater than that of the alpha particle.    m/s

  A 0.25-kg skeet (clay target) is fired at an anglewj:25x8gh8:d.rolot bcwp *l 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=2.2kgx21.yeyy0hr8 )h g jea 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), what it47 uoi9vk:+g.oh) kgdmoo z0gy3 y1ns 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 ag3)ty dogh+v4o1zkuo9:o iyn k 7m.g0gain?    kg (Let A represent mass m, and B represent mass M.)

  The gravitational slingshot effect. Figure 7–47 shos vw q,m42.8 gill6 jhfhlz2o6 91j cfwl.fi4dws the planet Saturn moving in the nev9 2lwc4ifh8j1w 2gqdzo6f li . 6.s4fjm,hllgative x direction at its orbital speed (with respect to the Sun) of 9.6km/s The mass of Saturn is $5.69 \times10^{ 26}$kg A spacecraft with mass 825 kg approaches Saturn. When far from Saturn, it moves in the direction at 10.4km/s The gravitational attraction of Saturn (a conservative force) acting on the spacecraft causes it to swing around the planet (orbit shown as dashed line) and head off in the opposite direction. Estimate the final speed of the spacecraft after it is far enough away to be considered free of Saturn’s gravitational pull.    km/s