We claim that momentum is conserv:bso9d5 so7vted, yet most moving objects eventually slow down and st579ovssd: b otop. Explain.

When a person jumps from a tree to the ground, what happens to th +o4o wji+ulf1e momentum of the person upon striking thj1l 4++oowfiue ground?

When you release an inflated but untgwfwujxj),wkn y/ ,y,yn2o wc :q(;: zied balloon, why does it fly across the room?yw; fy/w,2q (cw jkgjnzunw ,oy):x:,

It is said that in ancient :-dfj- ppdlm5 times a rich man with a bag of gold coins froze to death while stranded on a frozen lake. Because the ice was frictionless, he could not push himself to shore. What could he have done to save h-djmf5p:l-d pimself had he not been so miserly?

How can a rocket change direction when it is far oui(f qgc2m +2dkt in space and is essentially in a va(ic2gm qk fd2+cuum?

According to Eq. 7–5, the r8.hys; 3pevc migc9gl 48uxy8;es 9eqqd3w+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 air bags, wl4 v. g e38qx;c9e mh9s8yquse+;p3 r8iy gwdchich are intended to inflate during an automobile collision and reduce the possibility of fracture or death.

Cars used to be built as rigid as possible to w) y;9yrwkub6r d o0cxv+z1p(nithstand collisions. Today, though, cars are designed to have “crumple zones” that collapse up o y0y)9 rdw6vz;cr+ubn1p (kxon impact. What is the advantage of this new design?

Why can a batter hit a pitched baseball further than a ball toszqc;q6r.acu + gh3 q+ssed in the air by the bas6g3ch.qra qcz+qu;+tter?

Is it possible for an object to receive a larger impulse from a small i u h8;n.n*+qqek ufi:force than+q8 k u*n: ifqieu.;nh from a large force? Explain.

A light object and a heavy object have the same kinicst7,y4 zhv. etic energy. Which has the greater momentum? Explain.v7z. hc4yti ,s

Describe a collision in which all kin, m*+vye) vypbetic energy is lost.

At a hydroelectric power plant, water is jmgo9bzp0m( 4directed 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 tha zb9 mojgp0(m4t the water is brought to a dead stop, or so that the water rebounds?

A squash ball hits a wakd 5-m7ebd /blll at 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 fa ua f5spgis+.;p,cj-rom 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 and sticks .+uppijfcg5,a as- ;sto the steel plate.

Why do you tend to lean backward when carrq7xzml*89iz v :7baj jying a heavy load in your arms?

Why is the CM of a 1-m length of pipe at its mid-pg0 .uompzmu 5 anm)(l;q usq;0oint, whereas this is not true for your a mn;u zqs()5o;m pq0um.gu0alrm or leg?

Show on a diagram how your CM shifts when you change from a lying position to gcekc;u3,a- ba sitting posi ,uccegbk3a; -tion.

If only an external force can change the momentum of the cenhjwb, 4rxkld x--7re :ter of mass of an object, how can the internal force of an engine accel-h7l jrb:,- e wxrxk4derate a car?

A rocket following a parabolic path through the air suddenly explody; d 64toq:d(o9i abcqes into many pieces. What can you s:yo;btqa idc d6q(o94ay about the motion of this system of pieces?

  What is the magnitude of the momentum of a 28-g sparrow flying withl7l .m:mqi 0 cswe8o5;lued1k a speed of $8.4 \; m/s$    $kg \; m/s$

  A constant friction pcd: e nm9b/ t8miu/wm1nhk59force of 25 N acts on a 65-kg skier for 20 s. What is the skier’s change in velocity? 9u cbpw ike/nmdn1:9m8 h5/mt   m/s

  A 0.145-kg baseball pitched at 39 m/s is hit on a hori 3 izb wgvby 9r8vj:l/h 4e)-l.z1lecrzontal line drive straight back toward the pitcher at zjler4wyg.l virbz)9 hc1 l3e:/8 b-v 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 packagef m82ul5pjt.qs em89(sv j4kj out horizontally with a 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. Igno jkmljq( p9 t5jum.f2 v84ss8ere water resistance. The magnitude of the velocity of the boat is    m/s

  Calculate the force exerted on a rocket, given that the prope/+q(-qjlxhhi:* e n uhlling gases are expelled at a h: lenjih/-h(+ *uxqqrate 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 moving4okqpk qc6 7(f at $4.1 \; m/s$ 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 alone on alevel frictionless tutx8j :x)wt4r*7c)srv oh 5 v15zita orack with a constant spevotwt5)usjtv7c8i x5a )r 4h1xr oz:* ed 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 traveling at1hnj*mg/b.+ * q abrtq $15 \; m/s$ 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, windsf 7loeo z90x0o can whip horizontally at speeds of 100km/h If the air strikes a person at the rate of 40kg/s per square meter and is brought to 9x0eoo0f 7lozrest, 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 .:nm4q o84ep2zopht pconstant speed of 8.6m/s on a level track. Snow begins to fall vertically and fills .qpz2h ppo :e8om44t nthe car at a rate of 3.5kg/min Ignoring friction with the tracks, what is the speed of the car after 90.0 min?$\approx$    m/s

  An atomic nucleus initially movingoilf:-jakg 2:4u( j: kjp h:w6ts*mrp at 420m/s emits an alpha particle in the directiowm(j4is:h2-*6jka: jgpf tor kplu: :n of its velocity, and the remaining nucleus slows to 350m/s If the alpha particle has a mass of 4.0 u and the original nucleus has a mass of 222 u, what speed does the alpha particle have when it is emitted?    m/s

  A 23-g bullet traveling 230m/s penetrates a 2.0-kg 8w(1hp5 glsd v/ty n-;( swycsblock of wood and emerges cleanly at 170m/s If thecsys(5dwpw;(lgt1 s/hvy -8 n 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 is3y *naq4ct r5z+b45rcdvs2mg 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 masss 3ec5p7b7gguf sgxpf 3f7/ 0x 3180 kg is traveling in outer space with a velocity of 115m/s To alter its course by /3fxp sgc73 7ef5s0guxfgpb 7 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 xzxd3bx8y0 * fis hit off the tee at a speed of 45m/s The golf club was in b8x xx 0f*zyd3contact 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 rh 69z1/)fwc 9py gxe4 sjlgs*velocity of 8.5m/s and comes to rest in a time ing 4z6p9fxsehw jyrg s1*)9l /cterval of 8.0 ms. (a) What is the impulse given to the nail?    kg*m/s
(b) What is the average force acting on the nail?    N

  A tennis ball of mass m=0.06kg anklnsl ,l+ f9*nd speed v=25m/s strikes 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 crashworthiness ohh s0i,z9yzp mp; qn(b5oj91of 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 tis bqhz,1p0nj(i9p5 ym zo ;oh9me of impact until it is brought to rest. (a) Calculate the average force exerted on the car by the barrier. $\approx$$a\times10^5$N a =   
(b) Calculate the average deceleration of the car.    m/$s^2$

  A 95-kg fullback is running at 4m/s to the east an0 bfwxqcp*81ykyu/7(hm g 0gl d is stopped in 0.75 s by a head-on tackle by a tackler r uy 00 gw/1qhck*fgpbl7x8 y(munning due west. Calculate
(a) the original momentum of the fullback    kg*m/s
(b) the impulse exerted on the fullback    kg*m/s
(c) the impulse exerted on the tackler,    kg*m/s
(d) the average force exerted on the tackler.    N

  Suppose the force acting on a tennis ball (mass 0.060 kg) points in the +ppwhtu4x /0n 1x direction and is given by the graph of Fig. 7–33 as a14/twp p 0uxnh 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 r /c09okjdm6l person jump without breaking the lower leg bone of either leg? Ignore air resistance and assume the CM of the person moves a distance of 0.60 m from the standing to the seated position (that is, in breaking the fall). Assume the breaking strength (force per r/lkj9m06oc d 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 mko oatd)my f 4ivq+x i,b,(b76oving east (+x direction) 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 spef i tb,qdx,bkai +v4)76m(yooed and direction of each ball after the collision?Let A represent the 0.440-kg ball, and B represent the 0.220-kg ball. $v'_A$    m/s  ----待选择----eastwest  $v'_B$    m/s  ----待选择----eastwest 

  A 0.450-kg ice puck, moving east with a speed of 3m/s has a head-on collision w 8 hmap5 4baqd(2hy;spith a 0.900-kg puck ini;h5yd ap(4m2ph8bqa stially 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 undx.4opt,y lcn*p6m5wx+ urzk 5ergo a perfectly elastic head-on collision. If o5 n l. rxmpz56w*pt x4kuyo,+cne ball’s initial speed was 2m/s and the other’s was 3m/s in the opposite direction, what will be their speeds after the collision?(Let A represent the ball moving at 2.00 m/s, and call that direction the positive direction.Let B represent the ball moving at 3.00 m/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 collides head-on withe u; an2qmw61f a 0.090-kg ball initially moving away from it at a speed of 1.15m/s Assuming a perfectly elastic collision, what are the speed and direction of each ball after the collision?(Let A represent the 0.fa 61mqe uw;n2060-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.j3p7pyke154mmp /p xj5m/s collides head-on and elastically with another ball initially at rest. Afterward the incoming softball bounces backward with a speed/357jjy4m1pm pkp px e 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:akc bhgc*x 5t6rl9)e as one approaches 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 approacha b*)x klccge6t9 hr5: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 h8v tk.bjmzsgw6jq0 u+ig,x6;ead-on collision with a second ball initially at rest. The second ball moves off with half the original kg0juv ;sbmq+6w t.xi6z8gj ,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 fb)gv2ub 2. o gx7fso: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 : b.2fgs2o7vb) fguoxoff 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 objectq gupv+f9i(3tjfg. 9jss4e:s of mass m$_A$ and velocity v$_A$ elastically striking a stationary object of mass head-on. (a) Show that the final velocities v'$_A$ and v'$_B$ are given by$v_{\mathrm{A}}^{\prime}=\left(\frac{m_{\mathrm{A}}-m_{\mathrm{B}}}{m_{\mathrm{A}}+m_{\mathrm{B}}}\right)\nu_{\mathrm{A}},v_{\mathrm{B}}^{\prime}=\left(\frac{2m_{\mathrm{A}}}{m_{\mathrm{A}}+m_{\mathrm{B}}}\right)\nu_{\mathrm{A}}.$(b) What happens in the extreme case when m$_A$ is much smaller than m$_B$ Cite a common example of this. (c) What happens in the extreme case when m$_A$ is much larger than m$_B$ Cite a common example of this. (d) What happens in the case when m$_A$=m$_B$ Cite a common example.

  In a ballistic pendulum experiment, projectile 1 results in a maximum height hc. pv1l 84b(vrgnez u8 of the pendulumvg4 v(bne r8lpz1.u8c equal to 2.6 cm. A second projectile causes the the pendulum to swing twice as high, $h_2=5.2\mathrm{cm}$ The second projectile was how many times faster than the first? $v_1$ =    $v_2$ ([color=rgba(0, 0, 0, 0.85)]Round to three decimal places)

  A 28-g rifle bullet traveling 230m/s buries itself ir 2milynl 5kda88aq.6 n 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 the pendulum’s displacemedaqmy 8rln5.82lak6i nt.vertical$\approx$    m horizontal =    m

(a) Derive a formula for tmd2lu 25bh:m ruk/itc5jjsah gh:ni 94+;2 qh he 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 brearw(a;;4 du owtz88t7 kc g3,nlb*hz syks an object, initially at rest, into two pieces, one oa8b gzths(w*nr, o ck78 tz4 l;yu;3dwf 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. ) KE'$_A$ =    J KE$_B$ =    J

  A 920-kg sports car collides into the rear end of a 23009p bo o.5lexb0y0tf3q wl(,zc. mx+pl-kg SUV stopped at a red light. The bulol5 3 p. .q9ebzt ym,wfc0lpbx0x +o(mpers 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, 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 reboundswj-xp1mdjv0 q-g7d n/ to a height of 1.20 m. Approximately how many rebounds will the ball make before losing 90% of/nwp- j g-dd1 7vmqx0j its energy?   

A measure of inelasticity in a head-on collision of two objects is t/7 go1d 6hjq0m(mkjs ohe coefficient of restituqm 0/ 7jogs ohk(61mjdtion, 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, o vkz-7.tdc)c-trkq vsb) n25fne with three times the 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 is lit. When the firecracker explodes, the two blocks separate and slide apart. What is the ratio of distances eact7--2rndtck b )scv5 .f)vqkzh block travels? ----待选择----1/91/101/81/6 

  A 15.0-kg object moving in the +x direction at 56 wy;k.lso4vf.5m/s collides head-on with a 10.0-kg object moving in the -x direction at 4mk4;6 o wl.fvys/s Find the final velocity of each mass if:
(a) the objects stick together;   m/s
(b) the collision is elastic; v'$_A$ =    m/s v'$_B$ =    m/s
(c) the 15.0-kg object is at rest after the collision;   m/s ----待选择----not reasonable reasonable 
(d) the 10.0-kg object is at rest after the collision;   m/s ----待选择----not reasonable reasonable 
(e) the 15.0-kg object has a velocity of 4m/s in the -x direction after the collision. .   m/s ----待选择----not reasonable reasonable 
Are the results in (c), (d), and (e) “reasonable”? Explain
( Let A represent the 15.0-kg object, and let B represent the 10.0-kg object.)

  A radioactive nucleus at re o2lcky,p9 /vih4 tr-1vtqzung*) zd6st decays into a second nucleus, an electron, and a neutrino. The electron and neutrino are emitteu/r6 lhv) ko 4ctgz2zy,q9piv-d1tn *d 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 v p j 48cm60eql/awjjb4b :c8m$m_\mathrm{A}=0.400$kg moving with speed $\nu_\mathrm{A}=1.80$m/s strikes ball B, initially at rest, of mass $m_\mathrm{B}=0.500$kg As a result of the collision, ball A is deflected off at an angle of 30.0 $^{\circ} $ with a speed $\nu_\mathrm{A}^{\prime}=1.10$m/s (a) Taking the x axis to be the original direction of motion of ball A, write down the equations expressing the conservation of momentum for the components in the x and y directions separately. (b) Solve these equations for the speed v'$_B$ and angle $\theta_{\mathrm{B}}$ of ball B. Do not assume the collision is elastic. $\theta_{\mathrm{B}}$ =    $^{\circ} $ v'$_B$ =    m/s

  After a completely inelastic collision between two objects of eqy8f0 ;zcnv-4uff ieto5 mzb1* ual mass, each having initial speed the two move off together with speed v/3 What was the angle between their initial directionsc0-yvb un fioemzf z *45f;t18?    $^{\circ} $

  Two billiard balls of equal mass move at right)6t,pxk6 af2iaaggxopu/n; m/5is 6x angles and meet at the origin of an xy coordinate system. Ball A is moving upward along the y axis at am/ax;66)oisgu5 /kpxf 6ptx,gi 2 an2m/s and ball B is moving to the right along the x axis with speed 3.7m/s After the collision, assumed elastic, ball B is moving along the positive y axis (Fig. 7–37). What is the final direction of 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 a1ase ra+ym.7e perfectly elastic collision with another atom at rest. After the imp+s 1yaraee m.7act, 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 another atom atr4x9of ;fi/x s2t3rbu rest. After43otfi;us/r2b9fx xr 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 three-mass system shc5nc gqve 2mm n;dyl68urb 5)-own in Fig. 7–38. Specify rela grly;um 6b2ed8ccnq v 5mn)5-tive to the left-hand 1.00-kg mass.    m

  The distance between a carbo ;(es64vnnhrb/g dy-m *y+bsbn atom ($m_{\mathrm{C}}=12\mathrm{u}$) and an oxygen atom ($m_{\mathrm{O}}=16\mathrm{u}$) in the CO molecule is $1.13\times10^{-10}$m How far from the carbon atom is the center of mass of the molecule?    $\times10^{-11}$m

  The CM of an empty 1050-kg car is 2.50 m behind the front of th5u1pzzc 9asqdh45d e /n7kp j)e 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 thcz sjzdh n1 aku95)e p/45dq7pat each person has a mass of 70.0 kg.    m

  A square uniform rafh tg9fm 8.ud0vroxu/ ,t, 18 m by 18 m, of mass 6800 kg, is used as a ferryboat. If three cars, each ovu ,r t.80ougxhm9 fd/f 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 yw/bd 7b:s9u,33tg jy)lwl wh $l_0$,$2l_0$, 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 v;/;my7eexapt/cmt f82*zq ol tj(f3identical cases of tomato paste (see Fig. 7–40), each of which is a cube of length l. Find the center of gravity in the horizontal plane, so that tmx2 tatyqffloep/(e73; zcj vm8* t/;he crane operator can pick up the load without tipping it.$X_{CM}$ =    l $Y_{CM}$ =    l

  A uniform circular plate of radius 2R has a cirhm+ (fb8e 3-fgscmn+jcular hole of radius R cut out of it. The center of the smaller circle is a 8h -3jmnf se(+mfgc+b 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 subtraction.]   R

  Assume that your propt.u +rp-jauszqnvo .: uvf8*3ortions are the same as those in Table 7–1, and calculate the mass ofj.38zuovav-f.q n:pu ru+st * one of your legs.    kg

  Determine the CM of an outstretched arts *tn0 iuy f:1p*g/prm 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 positiok qw, l , sqgoefe;m7n asdew+;r;1n1)n of the CM of an arm bent at a right angle. 7 d;qeek)enso l1r; qmww;g ,fas+n 1,Assume that the person is 155 cm tall. $X_{CM}$ =    cm $Y_{CM}$ =    cm

When a high jumper is in a position such that his arms and leoy m:wgyjd+ q6(-hc*yjx h2f v *r.b:xo3+qhzgs 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? Uhyh m+c jqd jyof*xghvb(6.-r+q o:z: yw3x*2se Table 7–1.

The masses of the Earth and Moon areawro/dq( / s9d $5.98\times10^{24}$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-v 8-:q+xihjx 7t u,c t,a3dy/wnt-irekg man stand 10.0 m apart on frictionless ice.
(a) How far from the woman is their CM?    m from the woman
(b) If each holds one end of a rope, and the man pulls on the rope so that he moves 2.5 m, how far from the woman will he be now?    m
(c) How far will the man have moved when he collides with the woman? He has moved    m from his original position

  A mallet consists of a uniform cylindrical hevh+/tx27fqkz w8l xk2ad 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+kxkwf 2zq7vl/t 28h x, 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 mass 2.00 kg and a diamete3 ves1gly 6y) sx.yt,nr 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 aiey.x6 l1s,nvy)syt g3r, how far above the bottom of the handle is the point that will follow a parabolic trajectory?    d    d

  (a) Suppose that in Example 7–14 (Filaz t2aq9a ,4ug. 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 gond j,ys;:lo/so lq*.utgola, of mass M, are in the air and stationary with respect to the ;/o*juqtso,gl. sy: lground. 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 passenger stops?

  An 0.145-kg baseball pitched horizontally at -,hdyy( q 8q5e;cn1msja(i hmstrikes 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 forc1ah-(qn5(myqmh8 ci js,dye;e on the ball during the contact.    $^{\circ} $

  A rocket of mass m traveling with speedq199rkwc vut2rhmcj llp:hcr 2/5b ;. $v_0$ 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 sh p o1huy:/i3lhown in Fig. 7–43. Relative dimensions are also shown. Should the player be worried about this being a “scratch shot,” in whii/ h3lo:y1hupch the cue ball will also fall into a pocket? Give details.

  A 140-kg astronaut (including space suit) ab +,14yld z( zmw6i1 qurf9bdlyr2n1bcquires a speed of 2.5m/s by pushing off with his legs from an 1800-kg 9zrfbwru421b1, idn +( lyzbd1y l6qmspace 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 initial( afu0xcn1q1jz**ddj yp(0c xly at rest in outer space. They then cpj0*fad(udxnzq x1 c(0 1j* ypush each other apart. How far apart are they when the lighter astronaut has moved 12 m?    m

  A ball of mass m makes a head-on elastic collision with w oz7,)fhhk6oa second ball (at rest) and rebounds in the opposite direction with a speed equal t6h, 7ok hfzwo)o 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 cournw*:ppx2 .v no*lg/so t 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 an g: /ps2vx. oonl*w*ppplied his brakes 15 m before he crashed into car B. After the collision, car A slid 18 m while car B slid 30 m. The coefficient of kinetic friction between the locked wheels and the road was measured to be 0.60. Show that the driver of car A was exceeding the 55-mph (90km/h) speed limit before applying the brakes.    mi/h

A golf ball rolls off the top of a flightq3* e-5rwizb3 cl k*i,fyvy t+ of concrete steps of total vertical height 4.00 m. The k-,5*ilqyvit ec33+yr zfw b* ball hits four times on the way down, each time striking the horizontal part of a different step 1.0 m lower. If all collisions are perfectly elastic, what is the bounce height on the fourth bounce when the ball reaches the bottom of the stairs?

  A bullet is fired vertically into a 1.40-kg block of wood at rest directly abo52lv, 2wr2d-urm(i,t(zjksw5 ffoihzuw 8 r+ ve it. If the bullet has a mass of 29.0 g and a speed of 5 swr,(-o5j8u,z k 2lwvr w itd2mf (h2fz+r5iu10m/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- f(eri;x7oh v3kg block of wood placed on a horizontal surface just in front of the gun. If the coefficient of kinetic friction between the block and the surface is 0.25, and the impact drives the blockeh x7fr v;3(io 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 mk( a2v1viryp.ass 75 kg and the other of mass 60 kg, sit in a rowboat of mass 80 kg. With the boat initially at rest, the two people, who have been sitting at opposite ends of the boat 3.2 m apart from each other, now exchange seats. How far and in what direction will the boat move? The boa ir.p2ay1vv( kt will move    towards the initial position of the 75 kg person(Round to two decimal places)

  A meteor whose mass qgog 4:utjn 9,+yhs7k was 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 broken9j,es- 7luwmc apart into two fragments by an explosion. One fragment acquires twice the kinetic energy of t ljc-,9usew 7mhe other. What is the ratio of their masses?   

  The force on a bullet i t;xc.j yu1i,1u/vjb ls 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 7,;g (rqzeypyv g;7la $m_A$ = 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 pa2 kop2)qefua) i s4sj*rticle and a smaller nucleus. W)eu)of4ss 2kaqj*p2i hat 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 taj.u p0k, 7ug9 r/6sgr.j ugnzjrget) 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 30.0 czz 8:crk0/. vp drorp mw6,x1$^{\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), 7ddszk 6ffl 18what is the upper limit on mass m if it is to rebound from M, slide up the incline, stop, slide down the incline, and collide wit z8fl1d76kdsf h M again?    kg (Let A represent mass m, and B represent mass M.)

  The gravitational slingshot effect. Figure 7y ub1aikm 4:l,–47 shows the planet Saturn moving in the negative x direction at its orbital speed (with respect to the S:umki,bl 1a y4un) 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