We claim that momentum is conserved, yet mostsab u,p 4pl42w moving objects eventually slow down and sb,l4p 2aw4pu stop. Explain.

When a person jumps from :jbgn4d( f /qodcf4; kh*tl8ta tree to the ground, what happens to the momentum of the person upon striking the gqclg8t(/ *k;:nfdh4df ob4 tjround?

When you release an inflated but untied balloon, why does it fly acro sbno,k5 gp 5p3hf64kbss the room?ohk4,3bfp k6 g5b5nsp

It is said that in ancient times a rich man with a bag of gold coins fr0w97ck y;hpk moze 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 himself had;mphk0k y 9w7c he not been so miserly?

How can a rocket change direction when it is far out in space and is esst/7j-yxv +gp7 wg mg)f/ovf2centially in a vacugo2v//7wg7jt vgx- yp fm+cf )um?

According to Eq. 7–5, the longer the impact time of an impulseyu;npq1 j6xjk1ujs)e/ fd /ih4l lg,-, the smaller the force can be for the same momentum change, and hence the smaller the deformation of t;jli6 /xjeskj np-1)4fuy,hu /ql1 dghe 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 po 9py wyw o3r(..k/fjpjssible to withstand collisions. Today, though, cars are designed to have “crumple zones” that collapse upon imp pf/ jk w.(y.9ojywrp3act. What is the advantage of this new design?

Why can a batter hit a pitched baseball further than a ball tossed in the k5 yd1m;5fllpgzua 7)air by the bam7l51lpyak ud z);5gftter?

Is it possible for an object to receive a larger impulse frou-i s;:g rnj1rm a small force than from a larus:r irjn1-g ;ge force? Explain.

A light object and a heavy object have the same kinetic energy. Which has thkiw:d * 9lymt:s4g tvo7l;* ple greater momentum? Ext voty9*l 7:m4 *lw:gksp ;ldiplain.

Describe a collision in which all kinetic energy is kygnf arewh2abwvvsz-: 3 i+ , 2l0*:4ugluj5 lost.

At a hydroelectric power plant, water is directed at high speed ag sr+hfaag0c5j -rr 6)oainst turbine blades on an axle that turns an elecg6rj5arr)o + hc0s a-ftric generator. For maximum power generation, should the turbine blades be designed so that the water is brought to a dead stop, or so that the water rebounds?

A squash ball hits a wall r bqar l /s/d2)fwi2 b0.g4tt h(mm vtk.0y*cqat 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 onto a hard steel plate (fixed to pviyky k68 80dthe Earth), from wh0kvdyyki8 p86ich 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 to the steel plate.

Why do you tend to le8v(t:ppct iu; an backward when carrying a heavy load in your arms?

Why is the CM of a 1-m length of pipe at its mid-point, whereasr;ovv1 na 98fu this is not true for yo8rf9;v1no vauur arm or leg?

Show on a diagram how your zcp4)s 1l9cyume jk kvy(e/wo4q24b .CM shifts when you change from a lying position to a sitting py(o/e4s plc9q bkvuwmck2 1yj4e4)z .osition.

If only an external f2s3 ua uf4asp(orce can change the momentum of the center of mass of an object, how can the inu2af4a3 sp su(ternal force of an engine accelerate a car?

A rocket following a parabolic path throu(u;n rvi dklap+mh7f0:a 1d o/gh the air suddenly explodes into many ra+ hda/1 ip7;l0kdvo:(m ufnpieces. What can you say about the motion of this system of pieces?

  What is the magnitude of the momentum6t dyb5+,q.jkx(i m a5 oalhn9 of a 28-g sparrow flying with a speed of $8.4 \; m/s$    $kg \; m/s$

  A constant friction force of 25 N acts on a 65-kg skier r9aii3p9y lt5- w3vmafor 20 s. What is the skier’s change in velocity? 9p-i5 mta9 3iarvyw l3   m/s

  A 0.145-kg baseball po eusfo(5ab: wet* x p;mb,,.pitched at 39 m/s is hit on a horizontal line drive straight back toward the pitchmou:*ews;e5ob,pbfa,t .x p(er at 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 pahw8yr* q;xs. v283 )jjyn zfyackage out horizontally with a speed of 10 m/s Fig. below Calculate the velocity of the boat immediately after, asy a;.2z* jvsn w8ryx8f)qjy 3hsuming 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 rocket, given that th w l0kmnel,7hue1g ;f.e propelling gases are expelled at alfn7 ewg; l10u emk,h. 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 movinggw 2wde- po(z, uoze3 ,5unn9g 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 a 5)d8b5 7 ycgepwrb/calevel frictionless track with a constant speed of 57a /c8dpb g cy5bre)w18m/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 atdyii+ gu:(l/ f $15 \; m/s$ 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 th5 ql/uc 6,2 1hqmfushorizontally at speeds of 100km/h If the air strikes a person at the rate of 40kg/s per squarlqs,5uht cuhf/qm 162 e 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 speed of 8.6m/s o65c-9yq cnxc xduyles-) 6pe3n a level track. Snow begins to fall vertically and fills the car at a rate of 3.5kg/min Ignoring friction with the tracks, what is thcxu5ex3q c6c 6plsy-e-d)y n9e speed of the car after 90.0 min?$\approx$    m/s

  An atomic nucleus in0p*,xx wosvjvs7y+ r7itially moving at 420m/s emits an alpha particle in the direction of its velocity, and the remaining nucleus slows to 350m/s If the alpha particle has a mass of 4.0 u and the original nucleus has a mass of 222 u, what speed does the alpha pary*0 vs7,j +7vros xpxwticle have when it is emitted?    m/s

  A 23-g bullet traveling 230m/s penetq1h j16c d 5e0a6v 46huzkpfdrrates a 2.0-kg block of wood and emerges cleanly at 170m/s If the block is stationary on kjf4 5dp vzhcaqhr1 6d01 u66ea frictionless surface when hit, how fast does it move after the bullet emerges?    m/s

  A 975-kg two-stage rocket is travelx)e 4f+m f1hhk2:wcbk(mq, ffing 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 gwia81p./(ys -z*lnxo4w alf kg is traveling in outer space with a velocity of 115m/gai4- w /(zxply.ow*sn8f al1s To alter 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 45m/s Thek5*q59-j y(v-gx9r (s q e z+kdffwlcg golf club was in contact with the ball fo9g- (q r(fv5lz yk*ew-qsjd9+5 kxcfgr $3.5\times10^{-3}$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)d1,hgd8nsc q/gx x s6 of 8.5m/s and comes to rest in a time interval of 8.0 ms. (a) What is the impulse given to the nai6g1)qds8s /nxcx d ,hgl?    kg*m/s
(b) What is the average force acting on the nail?    N

  A tennis ball of mass m=0.06kg and speed vuddol-;(et6xw8wwg bt h ++ f+=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 :9eiac9 (2rpr uo mz d6l;wh9bml , pr5b6u-mmin charge of the 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 c 9amm- 9,z rlih9pue;(mlrb5:um 2rcdpb6 ow6ar by the barrier. $\approx$$a\times10^5$N a =   
(b) Calculate the average deceleration of the car.    m/$s^2$

  A 95-kg fullback is running at 4m/s to the east and is stopped in 0.73n bwwt 4e1,l:gh:, :f g.r1mxkdmicd5 s by a head-on tackle by a tackler runnil g:gebtddkf w1mcimr:n .31x,w, 4:h ng 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 inms+kfuzy f+mm1a/0 u2 the +x direction and is given by the graph of Fig. 7–33mz0 mu /+afum+fyk12s 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 bre /jo gz8y0fc8paking 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 unit area) of bpy8/f8cjgo0 z one 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 movr;zj 6 v/: eqhro;9ni-d.tbwxing east (+x direction) with a speed of collides head-on with a 0.220-kg ball at rest. If the collision is perfectly ela9/nrrv.;i jz-bt6 :hxd;w oqestic, 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, qsjzs5 ls7e( ru)hv//bcx d 9*moving 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 be the speed and direc 9xd s(hue bc/5rs szq7v)/jl*tion 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 ma, -ugvl 1i1cggss undergo 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 ball moving at 2.00 m/s, and call that direction the positive direction.Let B represengcuvl 11g-ig,t 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, mbstc ur,- w4(,jw.z -il cgi8xoving with a speed of 2.5m/s collides head-on with a 0.090-kg ball initially moving away from it at a speed of 1.15m/s Assuming a perfectly elastic collision, what are the speed and direction of each ball after the collision?(Let A represent the 0.060-kg tennis bal zsl-.txg (i8,,-icwucwb4 jrl, and let B represent the 0.090-kg ball.)v'$_A$ =    m/s v'$_B$ =    m/s

  A softball of mass 0.220 k*qw9k1/shr 0bns s:a zkcp a:;g that is moving with a speed of 8.5m/s collides head-on zacpn: /k krsb0*1s:w 9saq;h and elastically with another 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 elastical-f vrzn6 m -b1xae.my+r ic3b8ly 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 teba 1- .f mrzbcxri-36+n vmy8o 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 collisionl1lo2l (zd e0pa66kvs with a second ball initially at rest. The second ball moves off wi(la1ol6zk0l2 psd6evth 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 fricf zl(o2r0p/4vxffeu. tionless 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: B ou0v .e(fxrfp 4l2zf/oth leave the incline moving horizontally.]$\Delta x_{m}$$\approx$    m $\Delta x_{M}$$\approx$    m

ake the general case of an ou4:uxflg,9veda 3h gg92;stfbject 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 h e1yfpixp) q 7 w86p3hk2pt8pkeight h of the pendulum equal to 2.6 cm. A secoypx) p8kt6qp fh8 piep2w731knd 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 itsel ro6y2e7fsmmep: z.s87+nqh i f in a 3.6-kg pendulum hanging on a 2.8-m-long string, which makes the pendulum swin27q i: es6ez7+pmso.n8 h mrfyg 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 l jwr /(nnzsu9prj)z9m( u3k: 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, into two pieces, v:aeca:e: -nmone 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 an-:cema :ev: represent the lighter particle. ) KE'$_A$ =    J KE$_B$ =    J

  A 920-kg sports car collides into the rear end of a 2300-kg SUV stopped af+0dr. nkhdzjkdji72b 4y;2)w ry3yl t a red light. The bumpers dk2nb+k.dy;rlyj0 3r y4jhizf2d) 7wlock, 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 reboun b6qc4i)vuifyzjql /1r:nn96ds to a height of 1.20 m. Approximately how many rebounds will the ball make before losing 90% o ) cznyiq6nq f4u:vr9lbj1i/6f its energy?   

A measure of inelasticity in a head-on colv hlq40/2 bomclision of two objects is the coefficient ofcvb4 20moh lq/ 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 mase x: :cy4rxiu(s 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 reassembledc(yi u e4x:r:x. 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 s+ iyw3qyoe+t/ .l*az+x direction at 5.5m/s collides head-on with a 10.0-kg object mstyey wi*3zqlo+ . a/+oving in the -x direction at 4m/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 rest decays into a second nucleus, an electrowl) cvw c 7;zso*)brn6n, and a neutrino. The electron and neutrino are emitted at rig;c7l svwwoc6rnb* ) z)ht 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 masgfglhp3z) gfwol w5 ;25b1ae/)o 9b tls $m_\mathrm{A}=0.400$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 objec q7s w43xbarp0ts of equal mass, each having initial speed the two move off pqa4 3xb0r ws7together with speed v/3 What was the angle between their initial directions?    $^{\circ} $

  Two billiard balls of equal mass move at :5, g *e pdrxapij sh+4hjpl6)right angles and meet at the origin of an xy coordinate system. Ball A is moving upward along the y axis at 2m/s and ball B is moving to the right along the x axis with speed 3.7m/s After the collision, assumed elastic, ball B is moving along the positive y axis (Fig. 7–37). What is the final direction of ball A and what are,jx):gppsid l64h+ ha5pr *ej 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 another atom at rsq5 ;nb-o er6hyug c h6:,0wmwest. After the imem ,su rwwo bg;hcn0q56-hy: 6pact, 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 an.wyzat p f ,+n)g5(cjnother atom at rest. After the impact, the neon ato) nyc. fzn,+(tapwg5jm 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 stw8b ab c86 27fa yn;x,dwc8veof4yz8ystem shown in Fig. 7–38. Specify relative to y8w ncbt7 6ey8;c4zab,a8f dx8 vfow2 the left-hand 1.00-kg mass.    m

  The distance between a carbon atome58w zis:ta2q( kc nj/ ($m_{\mathrm{C}}=12\mathrm{u}$) 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 of6rmt3z wgk/sb l1. ;/ w/coolub(8v gkhn ab0* the car. How far from the front of the car will the CM be when two people sit in the f/kw mzvnw3b6/bggh c o8 l0*;tsbo/karlu.(1 ront seat 2.80 m from the front of the car, and three people sit in the back seat 3.90 m from the front? Assume that each person has a mass of 70.0 kg.    m

  A square uniform raft, 18 +skdt() t: rgam by 18 m, of mass 6800 kg, is used as a ferryboat. If three cars, each of mass 1200 kktt+:drs(g )ag, occupy its NE, SE, and SW corners, determine the CM of the loaded ferryboat.$X_{CM}$ =    m $Y_{CM}$ =    m

  Three cubes, of sides adxz5us ; yb5i 3c+s6q s0rze.$l_0$,$2l_0$, 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 of2hk g-pg3v7ja tomato paste (see Fig. 7–40), g3gp-javk2h 7each of which is a cube of length l. Find the center of gravity in the horizontal plane, so that the crane operator can pick up the load without tipping it.$X_{CM}$ =    l $Y_{CM}$ =    l

  A uniform circular plate of radius 2R has a circular hole of radiurh4f+qfqy9 : ms 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? hmffr9 4q:qy+ [Hint: Try subtraction.]   R

  Assume that your proportions are the same as those in Table 7–1, and d a 3ifdg;f)e81.glt(yk pa -:yni.ab calculate the mass of one of youg(gf.f8 ly keidip-3:)da .t; ana1ybr legs.    kg

  Determine the CM of anmo 6p12t* g6jodj( -x3umd6 a eeucj;k outstretched arm using Table 7–1.   % of the person's height along the line from the shoulder to the hand

  Use Table 7–1 to calculate the position of the CM of an arm bent at a right angl76* rhptrh6 nyay/: ffe. Assume that the perso/ 6af7ypy:tn *rhfhr6n is 155 cm tall. $X_{CM}$ =    cm $Y_{CM}$ =    cm

When a high jumper is in a position such that his arms and legs are hanging vertm y5,77fnuyk9n: ;q yd xyncy1ically, and his trunk and head are horizontal, calculate how far below the torso’s me c7xy u:fyymy;qnnd79n 1y 5k,dian line the CM will be. Will this CM be outside the body? Use Table 7–1.

The masses of the Earth and Moon are h 6eyfwa0/2 3xmp5ss/e x()ehw ilj*h$5.98\times10^{24}$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 10.0 m apart on frictio fi0djn e:8a5znless 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 unifor s nisf/gb m-n+u-il5.m cylindrical head of mass 2.00 kg and a diameter 0.0800 m mounted .m sl5 bi--isg+/unfn on a uniform cylindrical handle of mass 0.500 kg and length 0.240 m, as shown in Fig. 7–42. If this mallet is tossed, spinning, into the air, how far above the bottom of the handle is the point that will follow a parabolic trajectory?    cm

  A mallet consists of a uniform cylindrical head of mass 2.00 kg and a diameter dzs*+b drvy 98n r69nn 7mutpo93hb 4o0.0800 m mounted on a uniform cylindrical handle of mass 0.500 kg and length 0.240 m, as shown in Fig. 7–42. If this mallet is tossed, spinning, into the air, how far above the bottom of the handle is the point that witbd7+ uo n4ny9rn6bvs*m8o9p 3hd9 z rll follow a parabolic trajectory?    d    d

  (a) Suppose that in Exa)w,q6 oh0w esbqoi3)ample 7–14 (Fig. 7–29), $m_{II}$=3$m_{I}$ Where then would $m_{II}$ land?    d(Round to two decimal places)
(b) What if $m_{I}$=3$m_{II}$    d

A helium balloon and its gondola, of mass M, are in the air and sta5ub ld,h97r vn wj4ceu)h)y4rtionary 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? Wh)rw5e,c rd 9jblvu)uny7h h44at happens if the passenger stops?

  An 0.145-kg baseball pitched horizontally at strikes a ba4 lm9du0ll,sa t and is popped strai ma9l lluds4,0ght up to a 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 with sevhr)i7m 4 vqoaqppqo 9s1 );1peed $v_0$ 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 wfd5rw5.3px i3 i3w(uya8-ocs ud k,n 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 whicid 8r 3fusw,w3 ky a35c( w.npoiuxd-5h the cue ball will also fall into a pocket? Give details.

  A 140-kg astronaut (including space suit) acquires a 58is*yuq 2 p 0a6oz7cdng, gezspeed of 2.5m/s by pushing off d57*opi,a e2 c6sznyuq z8 0ggwith 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 g kuj4oa t *4b(yr2.p; j0zhyj80 kg, are initially at rest in outer space. They then push each other apart. How far apart are they when the lighter astronau 2 y4rko4g0;zaujb(jt* hy pj.t has moved 12 m?    m

  A ball of mass m makes a head-on elastic col;*zi tzgwi 7iw 6a46.1+cvlptgzg ad3lision with a second ball (at rest) and rebounds in the opg4tazp wzw6;g vli iai3+ g 6z1d7.*ctposite 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 an automobil6qi.1wm9kek /c n0b dke 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 sedkbw q1c 0i9n.km/k6lid 18 m while car B slid 30 m. The coefficient of kinetic friction between the locked wheels and the road was measured to be 0.60. Show that the driver of car A was exceeding the 55-mph (90km/h) speed limit before applying the brakes.    mi/h

A golf ball rolls off the top of a flight of concrete st3 , *: sybnhe*np1fftveps of total vertical height 4.00 m. The ball hits four times on the way down, each time striking ten* s f fvpt31nybh,*:he 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 dir aop6b a ,x5x)aby/if 5r5;atbectly above it. If the bullet p)tbaab5y oxf6ab;a5, rx5i/has 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 becomhu9tby0du7k-o q (8znap 2+ftes embedded in a 1.35-kg block of wood placed on a horizontal surface just in front of the gun. If the coefficient of kinetic friction between the block and the surface is 0.25, and the impact drives the block a distance of 9.5 m before it comes9 hb(2p0no td u -kaf8yz7t+uq to rest, what was the muzzle speed of the bullet?    m/s

  Two people, one of mass zoj 1dcn3:fu)tx;-o:kn hza375 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 fa-ta;kc z zun 3xoo)nh31 f:jd:r 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 w ylnd/ui:k)*m as 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 fragments by anp0we;oc3u: r9 tjt(wd explosion. One fragment acquires twice the kinetic energy of the other. What is the raw03:tjewu9( rtc;d optio of their masses?   

  The force on a bullet is given by the :)g.xwr; lhvrformula 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 masses5phfa)hauf nv 6uj 6 mo4*v:l0 $m_A$ = 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 dn/rsoo0q wkw yx 0edz47;vo ):ecays radioactively into an alpha particle and a smaller nucleus. What wendw7ov)s 00 orwzq:y/okx4; ill 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 target) is fired at an angle cdv33cxn cr-h h iam.y 7wd9;5uu5ia3 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 dr ;t8j,e --wifua0dde0 ng v*yown a 30.0 $^{\circ} $ incline which is 3.60 m high. At the bottom, it strikes a block of mass M=7kg which is at rest on a horizontal surface, Fig. 7–46. (Assume a smooth transition at the bottom of the incline.) If the collision is elastic, and friction can be ignored, determine
(a) the speeds of the two blocks after the collision,v'$_A$ =    m/s v'$_B$ =    m/s
(b) how far back up the incline the smaller mass will go. $\approx$   (Round to the nearest integer) (Let A represent mass m, and B represent mass M.)

  In Problem 79 (Fig. 7–46), what is the upper li3 w/+arp ic.pqmit on mass m if it is to rebound from M, slide up the iacrp 3+ i/qp.wncline, stop, slide down the incline, and collide with M again?    kg (Let A represent mass m, and B represent mass M.)

  The gravitational slingshot effect. k76ef5 iu66w ehe lbh7Figure 7–47 shows the planet Saturn moving in the negative x direction at its orbital speed (with respect to the Sun) of 9.f667 u lhee7kei6whb56km/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