We claim that momentum is conserved, yet pj/isbwna/, 3most moving objects eventually slow down and stpsa/,3ijn/ wb op. Explain.

When a person jumps from a tree to the ground, what happens to the momentum ofqn4w88 )m ohqv the person )woq8v8 mq n4hupon striking the ground?

When you release an inflated but untied balloon, why does it flye9p-4bcvq.)) rhhe ug across the room?p49hg -bechq))u er. v

It is said that in ancient times a ry 38v*w;kt0s+cn( gfpjgfu-i7ln-sy( nadg/ ich man with a bag of gold coins froze to death while stranded on a frozen lake. Because l 0 nf;8vw s* g-(-f nga+nj7y(s tgu/3ypkcdithe 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 chang(+gwuq qrf7 q)peuc80e direction when it is far out in space and is essentially in q0uw qpe ()fuq+87crga vacuum?

According to Eq. 7–5, the longer the impact timeip:f3c 05 orwy of an impulse, the smaller the force can be for the same momentum change, and hence thp05if co :ryw3e 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 posww3*z/ey f ues uahn+vcy/ a 5duw1(08sible to withstand collisions. Today, though, cars are designed to have “crumple zones” that collapse upon impact. What is the n*ysh(uay/v0af/c3 de 5 ue 8z+uwww 1advantage of this new design?

Why can a batter hit a pitched baseball(lt nsoedh )98yo0va obeo 4*8 further than a ball tossed in the air by the bat eoyl)0de o(ao48hvo9s *t8b nter?

Is it possible for a71su..e:onew;qif oue qd+,o n object to receive a larger impulse from a small force than from a large force? Explain.qunoeos:+q eue 7i,d;o 1w .f.

A light object and a hmidzg9 a 720gkmxhp 8; os81o 9mwyxg.eavy object have the same kinetic energy. Which has the greater momentum? Ex18ogyhs27.k8o m9z9dmp a gm gi0xx;wplain.

Describe a collision in which 8 j*a,hu 1oc4dfhsjy8 hb56kyall kinetic energy is lost.

At a hydroelectric power plant, water is directed ae/v-id(4 am- ox*ueow a34owl t high speed against turbine blades on an axle that turns an electric generator. For maximum poa3we/oeo u(a- lxw d*v o44im-wer 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 walo3 .67k t 7e-bnfexqzgl 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 fror 0pmwury( h,4m a height h onto a hard steel plate (fixed to the Earth), from which it rebounds at very nearly its original speed. (a) Is the momentum of the ball conserved during any part of this process? (b) If we consider the ball and Earth as our system, during what parts of the process is momentum conserved? (c) Answer part (b) for a piece of putty that falls aurmy,0 rhw (p4nd sticks to the steel plate.

Why do you tend to leapaz tv 9ih/egdv//a0wv 6 j77on backward when carrying a heavy load in your arms?

Why is the CM of a 1-m length of pipe at its mid-point, whereas this is no u4ow p9i( 53xb. vie0qa3fyelg:iv;et true f (aeq;ivp 03 w549lfbuv 3eeg iiy.xo:or your arm or leg?

Show on a diagram how your CM shifts when you change from a lying position to a msy5c 7eze*y7sitting posi57eyze mc *y7stion.

If only an external force can change the momentum of the center of man,ub(a2 ). ycwmqyy xo,1x u(bss of an objenuwc( (,m1, bbyy oyxq2).u xact, how can the internal force of an engine accelerate a car?

A rocket following a parabolikyr60mzq t+pnfh,; x. m6-haq4j j0nz c path through the air suddenly explodes into many pieces. What can you say abo6fmm6j+ . rh0,0n z;h4yatj -zxqpk qnut the motion of this system of pieces?

  What is the magnitude of the momentum of a 28-g sparrow flying with a spee+v +vcr6rgq 6a 38derbd of 8.4 m/s a vr3c6rr+qedb g8 v6+    $kg\;m/s$

  A constant friction force of 25 N acts on a 6gn,m-.u)gn 0 tndiuv,5-kg skier for 20 s. What is the skier’s change in velog ,d.u-u) gitnmn0vn ,city?    m/s

  A 0.145-kg baseball pitched at 39 2afgi*ig.n*bo d f20sm/s is hit on a horizontal line drive straight back toward the pitcher ats2 n.fg2gbo*ai *0f id 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 6.40-kg package out horizontally with a q g ua+emg6l6)speed of 10 m/s Fig. below Calculate the velocity of the boat immediately after, assuming it was initially at rest. The mass of the child is 26.0 kg, and that of the boat is 45.0 kg )m6egq gau+l6. Ignore water resistance. The velocity of the boat is    m/s

  Calculate the force exerted on a rocket, given that the propelling gasesoxd885ojhd+ 9to dduw9gf eleh1 u/;/ are expelled at a rate of 15to5ld gjd8/ ehhdf8ox o;dw + 1euu9/900kg/s with a speed of $ 4\times10^{4 }$ (at the moment of takeoff).$a\times10^7$ N a =   

  A 95-kg halfback moving at 4.1+na ue;:.tsi ezoi9v 0m/s on an apparent breakaway for a touchdown is tackled from behind. When he was tackled by an 85-kg corne0 si:9t+on ;zeua.vierback 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 travels alone on alevel frictionle*t/dtx4mehuwa- 74h ess track with a constant speed of 18m/s A 5350-kg load,initially at rest, is dropped onto the car. What will w4hthex-*7 m uet /4dabe the car’s new speed?    m/s

  A 9300-kg boxcar traveling at 15m/s strikes a second boxca f nup-sdkr9dsno4 v.)/435nw y* tgnsr at rest. The two stick together and move ofn.nd/nt ds9)psr kf4 nvu5gyo w3 s4*-f with a speed of 6m/s What is the mass of the second car?    m/s

  During a Chicago storm, winds can whip horizontally a*brfd,x 8 t7jvt speeds of 100km/h If the air strikes a person at the rate of 40kg/,7 8fjb xtd*vrs per square meter and is brought to rest, estimate the force of the wind on a person. Assume the person is 1.50 m high and 0.50 m wide. Compare to the typical maximum force of friction $\mu\approx1.0$ between the person and the ground, if the person has a mass of 70 kg.    N
$F_{on person}$  ----待选择----<> $F_{fr}$

  A 3800-kg open railroad car coasts along with a constant speedt8 mhr6 bhrow6wl5u12 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 fric6uhwwo16 rmbt2rl 8 5htion with the tracks, what is the speed of the car after 90.0 min?$\approx$    m/s

  An atomic nucleus initially movinl0g;lmnxldi( gv2b 3z7idd;/a +enz 2 g at 420m/s emits an alpha particle in the direction of im0da;d+l zd2 n;ilelnx( 3/7bi2gv gzts 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 speed does the alpha particle have when it is emitted?    m/s

  A 23-g bullet traveling 230m/s pev(+f94s fzh4 pasok2anetrates a 2.0-kg block of wood and emerges cleanly at 170m/s If the block is stationary on a frictionless surface whenss4pa 4v9+zh(ak o2ff hit, how fast does it move after the bullet emerges?    m/s

  A 975-kg two-stage rocket iso d +zr it;u3s3bf;)x,bju4nya6yb b6el/3yo 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 travelinr /ht)pc-)fl9p9k:43rg ml le7xeb ndg in outer space with a velocity of 115m/s To alter3 k)e9p-9xn clf le/4dlt7rr ):gpmbh 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 tee at a speed of 45xrhru 83k:p :ym/s The golf club was in con:yku:rh3xr8 p tact 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 and comes to r6d2m-ewhh7 xch6kv- west in a time interval of 8.0 ms. (a) What is the impulse given to thv6h--x wd w2hk7c me6he 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 stric6)gi d: zmp6m q:rlj 7dq.ab)kes 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:*s5 zu;ef uvuacs 1g3 crashworthiness 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 car by the barrieru:v13*zc5su a e s;guf. $\approx$$a\times10^5$N a =   
(b) Calculate the average deceleration of the car.    m/$s^2$

  A 95-kg fullback is running p ck9amk rh.;*at 4m/s to the east and is stopped in 0.75 s by a head-on tackle by a tackler running due west. Calculate ak9*kmc p;h.r
(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 psog ; *-8he lw-3 8c8x3gn+sxcqwg ym(mass 0.060 kg) points in the +x direction and is given by the graph of Fig. 7–33 as a function of time. Use grgs ;-h m8x*o8wnxc3ecqyls+ 8 3p wg-gaphical 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 c7mav tbchw -.9;9xq wlan 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 bre cvwh9tl-w7 xa qb.;m9aking 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 dire /m( hlus kiv1e-xz7e6bz3 q4pction) with a speed of collides head-on with a 0.220-kg ball at rest. If the collision is perfectly elastic, what will be the speed and direction of each ball after the collision?Let A represent the 0.440-kg ball, and B representkzi 7x/bluvs63pmz1 e4-e (hq 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 oo62ur:ugn/ o -gp caq4f 3m/s has a head-on collision wit:4 2upnrg6uo /goaq -ch 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 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 unr/haka/ef;m0)2d 5g s ar2kiq 3fzqz1dergo 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 bal5) e0 2ra/;mqgskfrh/2zd fi1k3 aazql 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 with ajqbydi39/y+kgw d c49 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 Assumibwkyq 9/y+i3c 9 d4djgng 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 of 8.5m/s coleco-i m3g7 w4dzslp6brt i-4vg(4q b 5lides head-on and elastically with ams547qbb vz 4 3g4do(we6p-ctrilgi- nother 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 av efzuwwimdo9 3.( q(ww e;3b/pproaches 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 approachw/voef3zww;(u qb9d e iw.3(m es at 4.5m/s and car B is moving at 3.7m/s calculate
(a) their velocities after the collision v'$_A$ =    m/s v'$_B$ =    m/s
(b) the change in momentum of each.$\Delta p_{\mathrm{A}}$$\approx$    kg*m/s $\Delta p_{\mathrm{B}}$$\approx$    kg*m/s

  A 0.280-kg croquet ball makes an elastic head-on collision with a seconks1pg8d- b/a3f4clc9 exhq-i d ball initially at rest. The sesc-a/c-ex f 14d ih pqbg938klcond 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 down a frictionleskx a )glw*56gfcfnw 23s incline as shown in Fig. 7–35, and elastically strikes another cube at the bottom that is only one-half its mass. If thefxw6n kaggc 2 *f5l)3w 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 object of mac9 akmd u5iega(gi io8y:(1crzf: p8 +ss 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 ex9x)h4 gkqpls)+ z 89h:slmj hpperiment, projectile 1 results in a maximum height h of the pendulum equal to 2.6 cm. A second projectile causes the the pendulum to s9lpklsm :j) g4 )hxsz+ 89hqphwing twice as high, $h_2=5.2\mathrm{cm}$ The second projectile was how many times faster than the first? $v_1$ =    $v_2$ ([color=rgba(0, 0, 0, 0.85)]Round to three decimal places)

  A 28-g rifle bullet traveling 230m/s buries itself in a 3.6-kg pendulum hv k; ;naf.x yqvg u/+dn;y()zpanging on a 2.8-m-louy qkg/;zxv f.+;) ndnvp ya(;ng string, which makes the pendulum swing 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 ,m68qm nevc5hof kinetic energy lost, $(\Delta\mathrm{KE/KE})$ for the ballistic pendulum collision of Example 7–10. (b) Evaluate for m=14g and M=380g

  An internal explosion breaks an object, iqm 7vr:z5*xs unitially at rest, into two pieces, one of which has 1.5 times the mass of the oth7v5*ur zx smq:er. 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 2300:4qf;pdms d+1: :ocad,so azq-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 betweedoca1;d spo zmq,d as4f ::q+:n 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 heightwm t2i4zn vu0/4;h tph)c of+x of 1.50 m and rebounds to a height of 1.20 m. Approximately how many rebounds will the ball make before losing 90% of its04 /t2+ wczh) ftm ;4unihvxpo energy?   

A measure of inelasticity in a head-on collision of two objects is theo6 dq;pkw 7 b4cm/ff*r coefficient of restitution, e, defined /7qm corw*6p 4ff;kbdas$e=\frac{\nu_\mathrm{A}^{\prime}-\nu_\mathrm{B}^{\prime}}{\nu_\mathrm{B}-\nu_\mathrm{A}},$
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 p.m t+sju)26 alq:jpm el- 5krof 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 as+q 6r)jtk p:-m52jme. l uplthe 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 ingdua;1 j0afpi8 h z.;z the +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 fina01 uzjaha;8fz; g.d ipl 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 k-:g tha(eulgs .ggl -9)do.xat rest decays into a second nucleus, an electron, and a neutrino. The electron and neutrino are emitted at right angles and havgg-(hkld.:s 9ol).te-x u gage 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 maotfy yu1w y 24q1zi 5tn;8om1iss $m_\mathrm{A}=0.400$kg moving with speed $\nu_\mathrm{A}=1.80$m/s strikes ball B, initially at rest, of mass $m_\mathrm{B}=0.500$kg As a result of the collision, ball A is deflected off at an angle of 30.0 $^{\circ} $ with a speed $\nu_\mathrm{A}^{\prime}=1.10$m/s (a) Taking the x axis to be the original direction of motion of ball A, write down the equations expressing the conservation of momentum for the components in the x and y directions separately. (b) Solve these equations for the speed v'$_B$ and angle $\theta_{\mathrm{B}}$ of ball B. Do not assume the collision is elastic. $\theta_{\mathrm{B}}$ =    $^{\circ} $ v'$_B$ =    m/s

  After a completely inelastic collision bu/v9qy 0bq 3 f52x)avbxblc:ketween two objects of equal mass, each having initial spyf0ba qk x/vb)q9 :b2clxu3v 5eed the two move off together with speed v/3 What was the angle between their initial directions?    $^{\circ} $

  Two billiard balls of equal mass mozf .)jzl ,b6df;mz6va ve at right angles and meet at the origin of an xy coordinate system. Ball A is moving upward along the y axis at 2m/sj m6af .f, l6dvzbz);z and ball B is moving to the right along the x axis with speed 3.7m/s After the collision, assumed elastic, ball B is moving along the positive y axis (Fig. 7–37). What is the final direction of ball A and what are their two speeds? direction of ball A is  ----待选择----x directionx direction v'$_A$ =    m/s v'$_B$ =    m/s

  A neon atom (m=20u) makes a perfectly elastic collna2pf vc(nh).wxqd m,, 6)atxision with another atom at rest. After the impact, the neon a,,.)taa 2dwvq cn6x()hxf n mptom 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 collisiowwtox uao 6:,04yx-kawbp rx7k mn,qjh(* /1bn with another atom at rest. After the impact, the neon atom travels away atw*to( 1oywb/,nh 60x-abkxm: k r,xpaw7u4q j 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 .z mxto6td2be7q (c+kshown in Fig. 7–38. Specify relative to the left-hand 1.00-kg m.2 c+m z dqt(obe6xk7tass.    m

  The distance between a carbon atomvcjiekrz5 zpn 7 ,/)4e ($m_{\mathrm{C}}=12\mathrm{u}$) 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 t1 ul 0bnifygrn/1: -oahe front of the car. How far from the front of the car will the CM be when two people sit in the front seat 2.80 m from the front of the car, and three people sit in the back sea:bo/iy 0g1n 1ual frn-t 3.90 m from the front? Assume that each person has a mass of 70.0 kg.    m

  A square uniform raft, 18 m bl p g0fc+x.sx/h zy9q*o5eai)l 5o,,bhtz r.hy 18 m, of mass 6800 kg, is used as a ferryboat. If three cars, each of mass 1200 kg9h 55tix .,s.eh ,h/clzf qoo +yxr*0 )zgbalp, occupy its NE, SE, and SW corners, determine the CM of the loaded ferryboat.$X_{CM}$ =    m $Y_{CM}$ =    m

  Three cubes, of sidesb(6s2f3pm 9o yv nbzt9 $l_0$,$2l_0$, 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 (seevols;69xpf)edalub1; :l i /er 5:qrs Fig. 7–40), each of which is a cube of length l. Find the center of gravity in the horizontal plane, so that the e:ob1frde/ s 9qls:rvau;5 l;)p6x licrane operator can pick up the load without tipping it.$X_{CM}$ =    l $Y_{CM}$ =    l

  A uniform circular plate of radiumkr*h 9semp61 s 2R has a circular hole of radius R cut out of it. The center of the smaller circle is a distance 0.80R from the center C of the larger circle, Fig. 7–41. What is the position of the center of mass of the plate? [Hint: Try sub*r91me6 phkm straction.]   R

  Assume that your proportions are the same as those in Table 7–1, and calculat 0 0o aggm*jzs8my4m7de the mass of one of your 7 jzsm84dmy0am*g o0glegs.    kg

  Determine the CM of an outstretched arm using Table 7–1.9 lr ovgu 51,fl4she,q   % 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 bensadsyy/mm ws8 1yzq6w2-; xm3t at a right angle. Assume that the per623as mdqm-wys;ywzy/s18mx son is 155 cm tall. $X_{CM}$ =    cm $Y_{CM}$ =    cm

When a high jumper is in a 9 zkgbv,j.)sk position 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 will be. Will this CM be outside the body? Use. sb)jgv kz9k, Table 7–1.

The masses of the Earth an c nxcv .)f10v.t8lrd eh-mc5sd 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 stany:h k;z ,wicim.t6+ he9;pustd 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 un0pwa3j5 +l4h a,n dcdniform cylindrical head of mass 2.00 kg and a diameter 0.0800 m mounted on a uniform cylindrical handle of mass 0.500 kg and length 0.240 m, as shown in Fig. 7–42. If this mallet is tossed, spinning, into the air, howh c40n5p3a+,l d andjw far above the bottom of the handle is the point that will follow a parabolic trajectory?    cm

  A mallet consists of a uniform cylindric xk 68pog0m;jq k-t0lh-/ni ihal 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 f/080p6okixh gn i --m hj;qtklar above the bottom of the handle is the point that will follow a parabolic trajectory?    d    d

  (a) Suppose that in Example 7–14 (Fig. 7–29), wf eci*+1dxd h8m)fw6$m_{II}$=3$m_{I}$ Where then would $m_{II}$ land?    d(Round to two decimal places)
(b) What if $m_{I}$=3$m_{II}$    d

A helium balloon and its gondola, of mass M, are in the air and stationf* -ag 8w/+ hddjcbcc/*scx3qary 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 ballood/-/ 8ac3hcjb+wx*cfdgs* c qn then move? What happens if the passenger stops?

  An 0.145-kg baseball pitched horizontally at strikes a u-fh7 b9 g*bmt +j/yxibat and is popped straight up to a 7t/x bh jgu*9 fb+yim-height of 55.6 m. If the contact time is 1.4 ms, calculate the average force on the ball during the contact.    $^{\circ} $

  A rocket of mass m traveling wiljpzm ti5(px,3vy))cth speed $v_0$ along the x axis suddenly shoots out fuel, equal to one-third of its mass, parallel to the y axis (perpendicular to the rocket as seen from the ground) with speed 2$v_0$ Give the components of the final velocity of the rocket.$P_x$: v'$_x$=    $v_0$
$P_y$: v'$_y$=    $v_0$

A novice pool player is faced with the corner pocket shot shown i6:xe unfg tl6j6 7,mben Fig. 7–43. Relative dimensions are also shown. Should the player be worried about thfebl ju6 :tg6,x7 m6enis being a “scratch shot,” in which the cue ball will also fall into a pocket? Give details.

  A 140-kg astronaut (including space sud maprp/j8*w9it) acquires a speed of 2.5m/s by pushing off witpmda j8 rp9*w/h his legs 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 other 80 kg, are init0kj 6j*gs j3*osn.la*yg wg 3uially at rest in outer space. They then push each other apart. How far apart are they wk* nj3 jsjwgoy06ugga*.s*3 lhen the lighter astronaut has moved 12 m?    m

  A ball of mass m makes a head-on 8y;dmy lor89 eb2c v3felastic collision with a second ball (at rest) and rebounds in the opposit 2bf8ymc 9ode3 8;rlvye 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 court case involving s9(e7;vik1wk o yhn0j .kk,wr an automobile accident. The accident involved car A of mass 1900 kg which crashed into stationary car B of mass 1100 kg. The driver of car A applied his brakes 15 m before he crashed into car B. After the collision, car A slid 18 m while car B slid 30 m. The coefficient of kinetic friction between the locked wheels and the road was measu(w ky ik9nksv1or7. ;ej h,0kwred 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 tljh9i ns9 zbkf v.qc0 bb))23zotal vertical height 4.00 m. The ball hits four timesk.cfqzbh 0)jb) bzvi s9l n923 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 ball reaches the bottom of the stairs?

  A bullet is fired vertically into a 1.40-kg block of wood 8yfp r*2qhux 9at rest directly above it. If the bullet has hxrpu*y2 89fqa mass of 29.0 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 strikesgz4 , ;w(ftsgx and becomes embedded in a 1.35-kg block of wood placed on a horizontal surface just in front of the gun. If the 4,gfgxw;st z (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 the muzzle speed of the bullet?    m/s

  Two people, one of mass 75 kg and(b;t;jxr o m; 9fg)z21eze;dr bxb4sz the other of mass 60 kg, sit in a rowboat of mass 80 kg. With the boat initially at rest, the two pef (;bx1bex;rd 4s;;mzzog2er tbj)z 9ople, who have been sitting at opposite ends of the boat 3.2 m apart from each other, now exchange seats. How far and in what direction will the boat move? The boat will move    towards the initial position of the 75 kg person(Round to two decimal places)

  A meteor whose mass was aboulk2 wacic-(*d(r+ym9p s 7djkt $ 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 explosio nyye57 r9khix9,uq e*n. O79 h9unryqe5, xe yk*ine fragment acquires twice the kinetic energy of the other. What is the ratio of their masses?   

  The force on a bullet is given by the formula F luh2y,y10p blud lf+/= 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 h: pqw diin03-$m_A$ = 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 8g6yzn8qejt ) decays radioactively into an alpha particle and a smalle)68jyz8qtn egr nucleus. 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 ta)jd0u +9baxye: ze0hq 4eqe7 yrget) 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 slides down a -9bto+g zgzj3n p* -dz30.0 $^{\circ} $ incline which is 3.60 m high. At the bottom, it strikes a block of mass M=7kg which is at rest on a horizontal surface, Fig. 7–46. (Assume a smooth transition at the bottom of the incline.) If the collision is elastic, and friction can be ignored, determine
(a) the speeds of the two blocks after the collision,v'$_A$ =    m/s v'$_B$ =    m/s
(b) how far back up the incline the smaller mass will go. $\approx$   (Round to the nearest integer) (Let A represent mass m, and B represent mass M.)

  In Problem 79 (Fig. 7–46), what is hh r- :1a1rgnqthe upper limit on mass m if it is to rebound from M, slide up the incline, stop, slide down the incline, and collide wiq agr:h11rnh -th M again?    kg (Let A represent mass m, and B represent mass M.)

  The gravitational slingshot effect. Figure 7–47 shows the fm:y wz 1 ;g,x.6 svt(ab7 8rgman)qguplanet Saturn moving in the negative x direction at its orbital speed (with respect to the :7(rzyg a,un8q6.1 x)gvwgam ft m;bsSun) 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