We claim that momentum is conserved, yet most moving objectsq0r8/6ro coh a eventually slow down a/rr6o8h0co q and stop. Explain.

When a person jumps from a tree to the ground, what happ)zmq p hehji3mv-7up,*rm)v6 ens to the momentum of the m3u- 7pv v)*m6)pzjhq i,hmreperson upon striking the ground?

When you release an inflated but untied balloon, why does4vl*o 5avzzm(w8l 1 wrnp8 gk) ivcs30 it fly across the room)m 1zlw 8z*sacirn3pw04klv v8gov(5?

It is said that in ancient times a rich man with an- a*;tg8rzwb ,hx qb/ bag of gold coins froze to death while stranded on a bzb/a trqh8*x;nw, -gfrozen 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 chad6e rgx 3be +(9u;lo:s 4kfv-zrksk(dnge direction when it is far out in space and is essentially in a vacuum?egflbude9rk s(4z+s:x6r k3d - k;ov(

According to Eq. 7–5, the longer the impact tim(zyho+w g1m; oe of an impulse, the smaller the force can be for the same momentum change, and hence the smaller the deformation of the object on which the force acts. On this basis, explain the value of air bags, which are intende+hgw1(yooz; md 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, t-iee gs9;xrl9t(irf6)g p tc .hough, cars are designed to have “crumple zones” that col.9 )fr-gl i6 psegi9txect;r(lapse upon impact. What is the advantage of this new design?

Why can a batter hit a pitched baseball further thanqd*ornsa0 y7tny - :1g a ball tossed in the air by1:r0nqsg -d7o*aynty the batter?

Is it possible for an object to rece.z.o whzn e gwv(g,m0(ive a larger impulse from a small force than from a large fz(o,g.h zvg 0.nwwme(orce? Explain.

A light object and a heavy object have the same kinetic ene -2(7mhr bhzlj/(nwb prgy. Which has the greater momemh-z/(nrlpj7 b2wbh( ntum? Explain.

Describe a collision z1gm,t5ab oubw67 j8qin which all kinetic energy is lost.

At a hydroelectric power plant, water is directed at high speed ae q na5iuuj:.bwp152 sgainst 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 stop, or so tha5i wj quansbe:5 2p1.ut the water rebounds?

A squash ball hits a wall at xb1x wp8m0v:gpg2y3eg)gy4 t a 45 $^{\circ} $ angle as shown in Fig. below. What is the direction (a) of the change in momentum of the ball, (b) of the force on the wall?

A Superball is dropped from a height h l9ofij)tsa2; fch:f5 qys 45h 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 to);9csjiaf5 l s :qhfhf5t2y4 he 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 backward when carrying a heavy tq1b zo2- pcc6load in your arms?

Why is the CM of a 1-m length of pipe at its mid-point, wfb-dsyyicrbr t f/dhy9*9 6 90hereas this is not true for 9b/06t brc* fr hysiyy9d9d f-your arm or leg?

Show on a diagram how your CM shifts when you change from a l,2)0mixh zlxo ying position to a sitting positii ml,)hz 2xx0oon.

If only an external force w.s ddhg )p ouis8585v4xi:tqhf-:nc can change the momentum of the center of mass of an object, hot4 s:ixq8dvf 5. 5dhhn up)gw-ocs8:i w can the internal force of an engine accelerate a car?

A rocket following a parabolic path through the air suddenkhu7,djs6/k*tqw (spx2c /u nly explodes into many pieces. What can you say about th/uukhq/wxptk2n j6 7(,cs *s de motion of this system of pieces?

  What is the magnitude of the momentum of a 28-g sparrow flying with a xz1co/+y f3jf speed of $8.4 \; m/s$    $kg \; m/s$

  A constant friction force of 25 Nj+ 6kxzy4zgq)/ikkpu .1+m;e mgoi: g acts on a 65-kg skier for 20 s. What is the skier’s pkk)gm ioq /1.zuy4zi kg:g6;j e+mx+ change in velocity?    m/s

  A 0.145-kg baseball pitched at 39 m/s iozy-. 8jb*cx gxzz+ h5s hit on a horizontal line drive straight back toward the pitcher at 52m/s Ih-z8o5+bgc zx.x jy*z f 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 speed of xrr- 8 v2f(u 1e0dpepb 10 m/s Fig. below Calculate the velociedrbr 2e8fp -px v1(u0ty of the boat immediately after, assuming it was initially at rest. The mass of the child is 26.0 kg, and that of the boat is 45.0 kg. Ignore water resistance. The magnitude of the velocity of the boat is    m/s

  Calculate the force exerted on a rocoj 92 2clznqg(2zlx2qket, given that the propelling gases are expelled az( zo22 2n2 lcjqglx9qt a rate of $1500 \; kg/s$ with a speed of $ 4\times10^{4 } \; m/s$ (at the moment of takeoff). F =    $\times 10^7 \; N$

  A 95-kg halfback moving atfg3t 6ix) fkubpeqeoe 4v)9- + $4.1 \; m/s$ on an apparent breakaway for a touchdown is tackled from behind. When he was tackled by an 85-kg cornerback running at $5.5 \; m/s$ in the same direction, what was their mutual speed immediately after the tackle?    $m/s$

  A 12,600-kg railroad car travels alo-wgp )jpi2v- yl:twy:: hx8 wvne on alevel frictionless track with a constanthtvpywp x)wyw::v: -i 8l -2gj speed of 18m/s A 5350-kg load,initially at rest, is dropped onto the car. What will be the car’s new speed?    m/s

  A 9300-kg boxcar travelizfa2ut cg.:cam 619 zwng at $15 \; m/s$ strikes a second boxcar at rest. The two stick together and move off with a speed of $6 \; m/s$ What is the mass of the second car?    $m/s$

  During a Chicago storm, winds can whip horizonta (q )0eqz7q.f(rv rnec elh;v.lly at speeds of 100km/h If the air strikes a person at the rate of 40kg/s per square meter and is b..qelferqr cq ezv(n; 0h 7v()rought 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 a9c6 2 :nb)nlaplknofj/. un1y constant speed of 8.6m/s on a level track. Snow begins to fall vertically and fills the car at a rate of 3.5y9ln j:n1c2/nn. k6u)bp flaokg/min Ignoring friction with the tracks, what is the speed of the car after 90.0 min?$\approx$    m/s

  An atomic nucleus initially moving at 420m/s emits an alpha particle in the (w xfifb9 s9oi6(stf)/i w.f ydirection of its velocity, and the remaining nucleus slows to 350m/s If the alpha particle . iyfx(ftb9 9wws)/fsoi(6f i 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 penetrates a 2.0-kg block of wo h1k0a 8y2kht dgcxx(q6h9i 8dp3c-bxod and emerges cle dx62 iy93xcgatx08k(d -hh1p 8kchbqanly at 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 rocket is traveling at aecu)6cf 7sik, speed of $5.80\times10^3\mathrm{~m/s}$ with respect to Earth when a pre-designed explosion separates the rocket into two sections of equal mass that then move at a speed of $2.20\times10^3\mathrm{~m/s}$ relative to each other along the original line of motion. Let “A” represent the upper stage (that moves away faster) and “B” represent the lower stage.
(a) What are the speed and direction of each section (relative to Earth) after the explosion? $v'_A$   m/s  ----待选择----away from the Earthtowards the Earth  $v'_B$   m/s  ----待选择----away from the Earthtowards the Earth 
(b) How much energy was supplied by the explosion? [Hint: What is the change in KE as a result of the explosion? $a\times10^8$ a =    J

  A rocket of total mass 3180 kg is traveling in outer space with a velots6q s6msih0(w v(/bjcity of 115m/s To alter its course by b mh/ijt(vss66 ws0(q35.0 $^{\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 z b0zied3u2 u8 gm n.1 1+1ql5yprv,ci,lpjueis hit off the tee at a speed of 45m/s The golf club was in contact with thi1v prz , y3c+0. u11lu jp85mgdzq,libneu2 ee 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 a1)rwr -u1; *fblzztjp nd comes to rest in a time interval of 8.0 ms. (a) What is )fuw1-ztp1* jrl; zrbthe impulse given to the nail?    kg*m/s
(b) What is the average force acting on the nail?    N

  A tennis ball of mass m=0.06kg and speed v=25m/s strikes a wall at aqr8b 4eg;x k(t 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 n xm2 ;/ymw)abpew automobile models. Cars are tested by smashing them into fixed2aybmx /m;w)p , 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/jo hxx, zsv. p*/lex2 gtic,6z,,jdl4s to the east and is stopped in 0.75 s by a head-on tackle by a tackler running due west. Ce,tl2,/cxj pxxzh.sz4vji* , 6ld , goalculate
(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) pointsvvozs -: 9s8nv in the +x direction and is given by the z 8v-v9:vson sgraph of Fig. 7–33 as a function of time. Use graphical methods to estimate
(a) the total impulse given the ball    N*s
(b) the velocity of the ball after being struck, assuming the ball is being served so it is nearly at rest initially.    m/s

  From what maximum height can a 75-kg person jump without breaking 4jd0x3rc 7nvj 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 positi0rj j7xd v34cnon (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 dire:kinkl 21uhs6ction) with a speed of collides head-on withu2i hnl:skk 16 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 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, movingfi/uz(+.;tzvclp htrkr 6 g79 east with a speed of 3m/s has a head-on collision with a 0.900-kg puck initially at rest. Assuming a perfectly elastic collision, what will u.( 7zl6rt /zg9+tipr v;hkc fbe 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 a perfectly elastic head-on collileeix0fe,.r8 cquk4zm 0ru dg4m 5:)psion. 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 th m i:zk5e.gfr u eu80mce,xr4p) 04ldqat 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/s collin o-1-3dkf v+67gjf;uwjwm y wdes 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 ar jw3+ f 6u j;vmo-17fdwg-knywe 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 collidepew9h t0 f;djn0ns7*ts head-on and elastically with another ball initially at rest. Afterward the incoming snpn 97f*wdts0 et0; jhoftball 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 ela45azx a5m+a+hiwf. w6zb,8pifwg /pxrar e*+ stically as one approaches the other directly from the rear (Fig. 7–34). Car A has a mass of 450 kg and car B 55ze5fp+whaxazf8 ,gp5ama/xw6w+r.*i r i +4 b 0 kg, owing to differences in passenger mass. If car A approaches at 4.5m/s and car B is moving at 3.7m/s calculate
(a) their velocities after the collision v'$_A$ =    m/s v'$_B$ =    m/s
(b) the change in momentum of each.$\Delta p_{\mathrm{A}}$$\approx$    kg*m/s $\Delta p_{\mathrm{B}}$$\approx$    kg*m/s

  A 0.280-kg croquet ball makes an elastic head-on collision with h;d:4u s khw2ta second ball initially at rest. The second ball moves off with half the original sp kus2 h;td:4wheed 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 fri(/q krs/apt p6ctionless 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 does each cube land? [Hint: Both leavpkp/( aq6rs /te the incline moving horizontally.]$\Delta x_{m}$$\approx$    m $\Delta x_{M}$$\approx$    m

ake the general case of an object of gr9v63l3 s4v zyry y7,rmjgd4mass 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, projectihg3timzq *, x3+/fta ale 1 results in a maximum height h of the pendulum equal to 2.6 cm. A second projectile causes the the pendulum to swing twice asq+ /z xa,ht3tmg*fi3a 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 travelin8mdi ir1;vyqtgy75 r / 6zbetwqqq4+-g 230m/s buries itself in a 3.6-kg pendulum hanging on a 2.8-m-long string, which makes the pendulum swing upward in an arc. Determine the vertical and horizontal compoqyi ;q t75y/g1+zq8 t-bvr iqd4mw6ernents of the pendulum’s displacement.vertical$\approx$    m horizontal =    m

(a) Derive a formula for the 5t o/rh9xmcw6* ,tdjwfraction of kinetic energy lost, $(\Delta\mathrm{KE/KE})$ for the ballistic pendulum collision of Example 7–10. (b) Evaluate for m=14g and M=380g

  An internal explosion breaks an object, initially at rest, nt1i-ji9 uh b;f8ibz8into two pieces, one of which has 1.5 times the mass of the other. If 7500 J were released in the explosion, how much kinetic energy did each piece acquire? (Let A represent the heavier particle, and B represent the lighter particle. ) K z89;hu-tjn f1ibb8iiE'$_A$ =    J KE$_B$ =    J

  A 920-kg sports car collides intox1dg9p;t gbgbs i4b3:g 8 alh, the rear end of a 2300-kg SUV stopped at a red light. The bumpers lock, the brakes are locked, andxh:bgtlpgb8a9d, i; 4g 1bgs3 the two cars skid forward 2.8 m before stopping. The police officer, knowing that the coefficient of kinetic friction between tires and road is 0.80, calculates the speed of the sports car at impact. What was that speed?(Let A represent the sports car, and B represent the SUV) $\approx$    m/s

  A ball is dropped from a height of 1.50 m and rebounds to a height ot7zf7j yfn: *fi:(svzk8mgu0 f 1.20 m. Approximately how many rebounds will the ball make before losing 90% of its energy0ivmsjku z7gtf8z(::ynf f*7?   

A measure of inelasticity in a head-on collision of two objects lu+3dc hp /o9g5di2gv is the coefficient o u+2v9h l/dodic3g5 gpf restitution, e, defined as$e=\frac{\nu_\mathrm{A}^{\prime}-\nu_\mathrm{B}^{\prime}}{\nu_\mathrm{B}-\nu_\mathrm{A}},$
where $\nu_\mathrm{A}^{\prime}-\nu_\mathrm{B}^{\prime}$ is the relative velocity of the two objects after the collision and $\nu_\mathrm{B}-\nu_\mathrm{A}$ is their relative velocity before it.
(a) Show that e=1 for a perfectly elastic collision, and e=0 for a completely inelastic collision.
(b) A simple method for measuring the coefficient of restitution for an object colliding with a very hard surface like steel is to drop the object onto a heavy steel plate, as shown in Fig. 7–36. Determine a formula for e in terms of the original height h and the maximum height h’ reached after one collision.

  A wooden block is cut into two pieces, one with three times the kcgye p,4l8u 2mass of the other. A depression is made in both faces yg,42ckl up8e 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 collides headn,te nannoepgr1e:xu42t /-4xa9 )v kuvo1c5-on with a 10.0-kg object moving in the -x direction at 4m/s Find the final velocity of each mass if: ,r2ovp91aue eo 4ua4:1nt/nevxxn-n t)ck g5
(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 d3;.)x stn kruvecays into a second nucleus, an electron, and a neutrino. The electron and neutrino are emitted at right angles and h ;uk t.3v)xrsnave 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 mfz. d3doik r:a aupt8;(a(8ynass $m_\mathrm{A}=0.400$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 d /jmlux,swd+/nr; 6 le1.l ltobjects of equal mass, each having initial speed the two move off together with speed v/3 What waxd ;/lln l l.w/jrs 6um1te+d,s the angle between their initial directions?    $^{\circ} $

  Two billiard balls of equal mass move at right angles and meet -4x3tfbr, zsh 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 rigs,xhfr3tz4 b-ht 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 collision with anoa:v8vbo- j5of t.u-hqrp f93jther atom at rest. After thf9h v.tf 8o5ar-bo pj3uv-: jqe 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) make37o1p5idex k/pipigm t78 w 3vs a perfectly elastic collision with another atom at rest. Aiiw8dim3tp x753/ e p g7pk1ovfter 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

  Find the center of mass of the threvw2p a1tb1 it)n.g*gce-mass system shown in Fig. 7–38. Specify relt vi.wg1*pct)1a2n gbative to the left-hand 1.00-kg mass.    m

  The distance between a ca+cxywbem /d9. rbon 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 fpp:ty w v4 r8m1*orch8ront 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 seat 3.90 m from the front? Assume that each person hay c:vo48r8 ptpw* mh1rs a mass of 70.0 kg.    m

  A square uniform raft, 18 m by 18 m, of mass 6800 kg, is used as a ferryhtc dsmi4bt x949./z 9og wr+yboat. If three ca9cgio.r9x 94d4 tbwm/hys t+ zrs, each 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 sides s+gifmbgt ,.w z)xqk/uo8 d84$l_0$,$2l_0$, 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 loiaus32fn 59;tuquq -qad of identical cases of tomato paste (see Fig. 7–40), each of which is a cube of length l. Find th q9quu52-; nf a3uqstie 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 pla:xb1wvs7i p 8hte of radius 2R has a circular hole of radius R cut out of it. The center of the smaller circle is a distsi71bpvh 8: wxance 0.80R from the center C of the larger circle, Fig. 7–41. What is the position of the center of mass of the plate? [Hint: Try subtraction.]   R

  Assume that your proportions are the same as those in Table f 96zewe6p bs.7–1, and calculate the ma pwf. 6b9see6zss of one of your legs.    kg

  Determine the CM of an outstrdrg:0-veg6 yaetched 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 a/)hg qrmrb/ c/qyk6p6f. l6syn arm bent at a right angle. Assume that the person is 155 cm t6sqqfy.y)rr/mbl/6kh g / 6cpall. $X_{CM}$ =    cm $Y_{CM}$ =    cm

When a high jumper is in a posqoe0nk7y34qu w cxv0 1ition such that his arms and legs are hanging vertically, and his trunk and head are horizontal, calculate how far bo ekxu3q401yc7w0nq v elow the torso’s median line the CM will be. Will this CM be outside the body? Use Table 7–1.

The masses of the Eaf xqr 0 x05p2.ytlvh6rrth and 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 stand 10.0mtmg;aruq 245j+f r k2 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 af1gm7n) pgz1and a diameter 0.0800 m mounted on a uniform cylindrical handle of mass 0.500 kg and length 0.240 m, am1f gnz7ag )1ps 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 cylindrical head of mae ;bv yt6s*,6y)cuy .vo twxz1ss 2.00 kg and a diameter 0.0800 m mounted on a uniform cylindrical handle of mass 0.500 k*zt6v1et;,c u xwv)yyb o6 sy.g and length 0.240 m, as shown in Fig. 7–42. If this mallet is tossed, spinning, into the air, how far above the bottom of the handle is the point that will follow a parabolic trajectory?    d    d

  (a) Suppose that in Example 7–14y09rqj6c m.lc e t -l1rpph2-c (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 go97epyqn2 q6rgk0r i(w -rgt3i ndola, of mass M, are in the air 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 if the passe0e ir 6r7-gpkwqt(g 2yq3 rin9nger stops?

  An 0.145-kg baseball pitched horizontally at strikes a bat .vu7p7wp/m y bd k;x(band is popped straight up to a height of 55.6 m. If the contact time is 1.4 ms, calculat mup / w(.yp;7xdb7vkbe the average force on the ball during the contact.    $^{\circ} $

  A rocket of mass m traveling with spn4ji 9r (ha*muo5i( j q-gg(yheed $v_0$ 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 ssv 2i 5c,xrd-*t:sfhwith the corner pocket shot shown in Fig. 7–43. Relative dimensions are also shown. Should the player be worried about this being a “scratch shot,” in which the cue ball will also fall into a pocket? Give dethxf: vrc5s* d-2, isstails.

  A 140-kg astronaut (including space suit) acquires a speed of 2.5m/s by pushin7h i 3 q8o5hun2w)yik-y 7jqd zd(uwb)g off with his legs fromn ouqw hh)i-ddk2uy j)qz 3yi (87w5b7 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 fngk32s/n,gp hw ;: ts80 kg, are initially at rest in outer space. They then push each other apart. How far apart are they when the lighter astronaut has moved 12 m?t , :ngspgwh3nf2s/; k    m

  A ball of mass m makes a head-on elastic collision with a second ball (at oo(0- g3jyyq2sguq8m rest) and rebounds in the opposiqog ym82jo 0-u(yg q3ste 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 iqnjn -q0dj/1court 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 c0i jdq1-jqn/n ar 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 concretea *lzjo0geuuq *8 6p(w 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 zq *eg6o0*jl 8(apwuu 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 at rest directly abov yr6iw(la;z:zv+odes5uta2k*3zqg hk 4)4ni e it. If the bullet ha4+63on*(wds lagyr4;q vte 5z:k aiz iu)h2kzs a 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 strikes and becomes e rnt,cz-44qynmbedded in a 1.35-kg block of wood placed on a horizontal surface just in front of the gun. If the coefficient of kinetic fricti4n t -qc,zynr4on between the block and the surface is 0.25, and the impact drives the block a distance of 9.5 m before it comes to rest, what was the muzzle speed of the bullet?    m/s

  Two people, one of mass 75 kg and the other of ixsyo-(1- 45i lkbnzb 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 ofi-sly1k-b 4bxi ( ozn5 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 a;s cigt g9i:k68pih -a kj1v+about $ 1\times10^{ 8}$kg struck the Earth ($m_E$=$6 \times10^{ 24}$kg) with a speed of about 15km/s and came to rest in the Earth.
(a) What was the Earth’s recoil speed?    $ \times10^{-13 }$m/s
(b) What fraction of the meteor’s kinetic energy was transformed to kinetic energy of the Earth?    $ \times10^{ -17}$
(c) By how much did the Earth’s kinetic energy change as a result of this collision?    J

  An object at rest is suddenly broken apart into two fragm9xs17 .drr)pwkgs+ coents by an explosion. One fragment acquires twice the kinetic energy of the other. What is the ratio of thei .r7xrd s9)o1cw +gkspr masses?   

  The force on a bullet is given by the fornj9e,8v7 n)18sedk uehx8l 8nzs hei (mula 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 ph1ppl 3hqp74 agbxi4 hjn-(gqp7(h, $m_A$ = 40g and $m_B$ = 60g are suspended as shown in Fig. 7–44. The lighter ball is pulled away to a 60$^{\circ} $ angle with the vertical and released.
(a) What is the velocity of the lighter ball before impact?$\approx$    m/s
(b) What is the velocity of each ball after the elastic collision?v'$_A$ $\approx$    m/s v'$_B$ $\approx$    m/s(Round to two decimal places)
(c) What will be the maximum height of each ball after the elastic collision?    m

  An atomic nucleus at rest decays radioactively into an alpha particlec,zpn p*; 1(ngmuij+i and a smaller nucleus. What will be the speed of this recoiling nucleus if the speed of the alpha particle ,g;1jpzum+np ni* ( icis $ 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 an8(. dpw0e /vi j1fgteugle 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 30.0)au6 oi,tie* e4k8ebhey4r ax 9:(cvh $^{\circ} $ incline which is 3.60 m high. At the bottom, it strikes a block of mass M=7kg which is at rest on a horizontal surface, Fig. 7–46. (Assume a smooth transition at the bottom of the incline.) If the collision is elastic, and friction can be ignored, determine
(a) the speeds of the two blocks after the collision,v'$_A$ =    m/s v'$_B$ =    m/s
(b) how far back up the incline the smaller mass will go. $\approx$   (Round to the nearest integer) (Let A represent mass m, and B represent mass M.)

  In Problem 79 (Fig. 7–46), what is the upper limit on mass m if it is t: gr/otm6l7+wq fn- pto rebound from M, slide up the incline, stop, slide dwontq rp7:+-/tf glm 6own the incline, and collide with M again?    kg (Let A represent mass m, and B represent mass M.)

  The gravitational slingshot eff1tvvxk ik7m ggy c(-(obl:vvw(;p-6mect. Figure 7–47 shows the planet Saturn moving in the negative x direction at its orbital speed (witgtkm- v v6m((xgvbw-cl;vkp ( 1i7y: oh 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