We claim that momentum is conserved, yet most md8yyq2 upq,- qutf s+w( hp1-0qvw:kmoving objects eventually slow down and stop. Expu1w:+-,2k dwup- vy hp80sqyfmq qq (tlain.

When a person jumps from amslu0f an mprjo.7n0r5;, 9ec tree to the ground, what happens to the momentum of theumon f 9ps.r, a7rm;enl0 j5c0 person upon striking the ground?

When you release an inflated but untiedovw;x6 kw jw+3 balloon, why does it fly across the room?63 jwkv+ox;w w

It is said that in ancient times a rich man with a bag of gold c72v n2otwkn023m :g+laqx gh ioins froze to death while s2 k2 nx72tog gq:m+ivhnlaw30tranded 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 he not been so miserly?

How can a rocket change direction when it is far out in sp q0p :yzafp5lh2 z15g 0olrl7race and is essentially iz7l azlg05 :pp01r2rfh yq5l on a vacuum?

According to Eq. 7–5, the longer the impact time of an impvsf+y;j v2 5cpulse, 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 intended to inflate during an automobile collision and ;5yv+j 2cpfsv reduce the possibility of fracture or death.

Cars used to be built as rigid as0nb,p0i hwrd : ,xeh+g possible to withstand collisions. Today, though, cars are designed to have “crumple zones” that collapse upon impact. Whawhbe0 gihr:xp, d0n+,t is the advantage of this new design?

Why can a batter hit a pitched baseball furrna)hp ) nxlp/q k3;ye(-mpv1 ther than a ball tossed in the air by the em)1yp)alknprq ;x-h (/vnp 3 batter?

Is it possible for an object to receive a larger impulse from a smallm)sc8 xwmby ;4 force than from a large forc8mxybcwms4;) e? Explain.

A light object and amfp77zvbnfss,w2i 5ru , 88xbux.g)p heavy object have the same kinetic energy. Which has the greater momentup w8p7bfv8m,zb f ir7 xu)n.x,us2 gs5m? Explain.

Describe a collision -j627;b(dg vuinksxm in which all kinetic energy is lost.

At a hydroelectric power plant, water is directed at high speed agais8nlp x u94 p))n, ryf0( p.rqqibxne-nst turbine blades on an axle that turns an electric generator. For maximum power generation, should the turbine blades be desnf)q. u) pxxislnrnp4bqe,8 9- ryp (0igned so that the water is brought to a dead stop, or so that the water rebounds?

A squash ball hits a wall at 9cgi t5ivtvbp+d ()h: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 (fi 50katkx- bq:dxed to the Earth), from which it rebounds at very ne xtk50k bq-:daarly 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 lean backwar liw)h-exe)t o2:5* rwwuf;y kd when carrying a heavy load in your arms?

Why is the CM of a 1-m length of pipe at its mid-pop4cukji) /t -tint, whereas this is not true i)-c/puk 4ttjfor your arm or leg?

Show on a diagram how your CM shifts when you change fh sk(8;dao:nrrom a lying position to a soa rn8dhks: ;(itting position.

If only an external f+ b7/jmu.o mpjorce can change the momentum of the center of mass of an object, how can the internal force of an.uj/mo+7p bj m engine accelerate a car?

A rocket following a parabolic pat1morbw v4vj;*vx9. mbh through the air suddenly explodes into many pieces. What can you say about the motion *bmrvjv; w9 m4o1.vxb of this system of pieces?

  What is the magnitude of the momentum of a 28-g sparrow flying with a s6tbn7+ jd9oc - yijt.4z0 fgwspeed of $8.4 \; m/s$    $kg \; m/s$

  A constant friction force of 25 N acts on a 65-p44m7it dk e-g u0dcx7kg skier for 20 s. What is the skier’s changeit4 px7demgu 7d4k-0c in velocity?    m/s

  A 0.145-kg baseball pitched at 39 m/s is hit on2h92 f7pc egg4 q9g nbd(yk8la a horizontal line drive straight back toward the pitcher at 52m/s If the contact time 2gyl p 8ace7nqkgf 9b42d(h9g 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.h 8sr-qu--cmu xkx9 x+40-kg package 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 tr+khu x-cs8uxq- x -9mhat 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 tha-ft44iqjw .dft the propelling gases are expelled at a rate ijqt wf -44d.fof $1500 \; kg/s$ with a speed of $ 4\times10^{4 } \; m/s$ (at the moment of takeoff). F =    $\times 10^7 \; N$

  A 95-kg halfback moving aty6;+yl6x/ rrgpgz 9f n $4.1 \; m/s$ 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 nq1dl)uiem + 2ipr9 2won alevel frictionless track with a constant speed of 18m/s A 5350-kg load,impdr q92+1wi ulie2n )nitially at rest, is dropped onto the car. What will be the car’s new speed?    m/s

  A 9300-kg boxcar travelim w+68iutp6bxng 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, winx+ ciwp23ekgj d0 i9,zds 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 broip+dg 3ki,wc0xz9ej2 ught 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 on a x*3gc w1:jbi ry4b 8ae3 -iihdlevel track. Snow bicjd 4i83eyb13-bg*i wa xrh: egins to fall vertically and fills the 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 moving r yrdq6n:w) a4at 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 6dn4)q :rywranucleus 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 penmi4cph 1. 1pypetrates a 2.0-kg block of wood and emerges cleanly at 170m/s If the block is statio 1c.1ppmiyh4 pnary 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 a speed o4 b-kbuof)8igf $5.80\times10^3\mathrm{~m/s}$ 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 op+ah a2jm 2xp09c/qsis traveling in outer space with a velocity of 115m/s To alter its course bysc9+hp 202aomqapjx/ 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 g* -ki16 +wdpq:nqsn noff the tee at a speed of 45m/s The golf club was in contng*n:6nsk+p qdi1wq-act with the ball for $3.5\times10^{-3}$s Find (a) the impulse imparted to the golf ball,    kg*m/s
(b) the average force exerted on the ball by the golf club.    N

  A 12-kg hammer strikes a nail at a velocity of 8.5m/sukj z3i vf+/k. and comes to rest in a time interval iju3z+vkf./k 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 and spszqb:x 7lvscs/8xx2m qg8w9z 3o9 o 4eeed 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 of nedvqx 4thrw/1blo(h8dn 8q(7 rw automobile models. Cars are tested by smashing them into fixed, massive48qrxdbt(onh17 vrl /8qd h(w 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 vigheykr9e- bwi3 : 9*4m/s to the east and is stopped in 0.75 s by a head-on tackle by a t9e- 9ihk bie *3y:wrvgackler running 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 (massz( wyf-tq40rex3 lh j2 0.060 kg) points in the +x direction and is given by the graph of Fig. 7–33 as a functh-w( q l2j0zyfxe4t3r ion 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 the lower leg gh rv(2h4uxt*ovn )o4bone of either*xvoht (h on) gur2v44 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 bone is $170\times10^6\mathrm{~N/m^2}$ and its smallest cross-sectional area is $2.5\times10^{-4}m^2$ [Hint: Do not try this experimentally.]    m

  A ball of mass 0.440 kg moving east (+x direction) with a speed of juy ;2f b5arh/w2kgx+ collides head-on with a 0.220-kg ball at rest. If the collision is perfectly elastic, what will be the speed and direction of each ball after the2fgk2h b5auxy /j +wr; 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 hea /fosex eqv ,xd00kid1x72 p:ad-on collision with a 0.900-kg puck initially at rest. Assuming a perfectly elastic collision, what will be the speed and direction of each object after the collision?Let A represent the 0.450-kg puck, and let B represent thev/sd2di: 1f0,qxx70ek o xape 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-oavx/1k ,k8b- xoypoi+n 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 reprey /okb1+p x8k,va-oi xsent 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 c3o lt -tf-p+hy k3/dq 85ncionollides 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 yn o8k/d 3 t+ht--ci 3oqlnp5fthe 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 speepc-xx: nb,y fb+o(/z vd of 8.5m/s collides head-on and elastically with another ball n,/cb zovbxx +:(- pyfinitially at rest. Afterward the incoming softball bounces backward with a speed of 3.7m/s Calculate
(a) the velocity of the target ball after the collision    m/s
(b) the mass of the target ball.    kg
(Let A represent the moving softball, and let B represent the ball initially at rest.)

  Two bumper cars in an amusement park ride collide elastically as:: vbcezv ,yfaa0v ,i6 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 approaches at 4.5m/s and car B is moving atv6f:yv ebva 0 :iaz,,c 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 e f*t pclk: 1hqk3h gihwit-0z-qh0- 6collision with a second ball initially at rest. The second ball-k1 zicpg k6*tihhq0hw:lt0 3fh -qe- moves off with half the original speed of the first ball.
(a) What is the mass of the second ball?    kg
(b) What fraction of the original kinetic energy $(\Delta\mathrm{kE/KE})$ gets transferred to the second ball?   

  In a physics lab, a cube slides down a frictionless incline as showfqcipmj+ nt z:v,9cr a )f;j9ws73 ks(n in Fig. 7–35, and elastically strikes another cuk t nj vj9(r,mw+q;:9)3s cfafci7 szpbe 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 leave the incline moving horizontally.]$\Delta x_{m}$$\approx$    m $\Delta x_{M}$$\approx$    m

ake the general case of an object o4zb)ks k3bo6 q6tm o+jf 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 i7ymswfl*kd jl z. ewh*p:3 tn2:1jki:n a maximum height h of the pendulum equal to 2.6 cm. A second projectile causes the the pendulum to sjdw7* hlp.:me :1w it3*ks zj klyfn:2wing 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 its.y*npjmiyb9bc/;c .,* u o)qxqm h3g qelf in a 3.6-kg pendulum hanging on a 2.8-m-long string, which makes the pendulum swinm i j9xou;,h)pynqb y.qm*c3 * .gcbq/g 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 gjs s; m5u7w)l7ry7xuthe 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 bz ld049 ozov9sreaks an object, initially at rest, into two pieces, one of wh oz94sdvlz90 oich 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 inw3o1 j y,f gxy3wd9ym4:*epgbto the rear end of a 2300-kg SUV stopped at a red light. The bumpers lock, the brakes are locked, and the two cars skid forward 2.8 m before stopping. The police officer, knowing that the coefficient of kinetic friction between tires and road is 0.80, calculates the speew f*:ywm 34 3yoyeg9bxpg 1d,jd 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 ,0c t *-ek 9b,-fr:gd komopwg6ms9xnof 1.20 m. Approximately how many rebounds will the ball make before losing 90% of ik pgro,btn-c9-g*s w96dex: f , omk0mts energy?   

A measure of inelasticity in a head-on collision of t ww/a26w8gfp swo objects is the coefficient of2a8ps6 /wgww f 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 mass of the othe3(j 9 uju.2r0pxklp6i2k zn5 obl j,uxr. A depression is made in both faces of the cut, so that a firec6bk 3uuuj52k l z ox0,2jp9rpxn( jil.racker 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 a4abyod )h ln0.t 5.5m/s collides head-on with a 10.0-kg object moving in the -x direction aty4n b). dh0oal 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, as73ei(wo/hp0 s zh 7ccn electron, and a neutrino. The electron and neutri/s 7c0iehs7o(h3c w pzno are emitted at right angles and have momenta of $9.30\times10^{-23}kg\cdot m/s$ and $5.40\times10^{-23}\mathrm{~kg}\cdot\mathrm{m/s}$ respectively. What are the magnitude and direction of the momentum of the second (recoiling) nucleus?    $ \times10^{-22}$    $^{\circ} $ from the momentum of the electron

  An eagle ($m_{\mathrm{A}}=4.3\mathrm{kg}$) moving with speed $\nu_\mathrm{A}=7.8\mathrm{~m/s}$ is on a collision course with a second eagle ($m_{\mathrm{B}}=5.6\mathrm{kg}$) moving at $\nu_{\mathrm{B}}=10.2\mathrm{m/s}$ in a direction perpendicular to the first. After they collide, they hold onto one another. In what direction, and with what speed, are they moving after the collision? v =    m/s $\theta$ =    $^{\circ} $ rel. to eagle  ----待选择----AB 

  Billiard ball A of maez gw*a;: xuk)ss $m_\mathrm{A}=0.400$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 bet1uyflu m0m gh6+ -lqs6t:s1mqydj5k.ween two objects of equal mass, each having initial speed the two move off together with speed v/3 What was the angle between their initial directions? + tm.-kgsh1dm6yu:5j fyq0q61 lms lu    $^{\circ} $

  Two billiard balls of equal mass move at right angles and meet aqyqabrj8ovjdy) -9(uxo 7 w49t 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 anoj9xy 8q9wbr(4qdv )auj7-yo d 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 wi;wo5w 9g -yazyth another atom at rest. Aao wz9w-y5; ygfter the impact, the neon atom travels away at a 55.6 $^{\circ} $ angle from its original direction and the unknown atom travels away at a -50 $^{\circ} $ angle. What is the mass (in u) of the unknown atom? [Hint: You can use the law of sines.](Let A represent the incoming neon atom, and B represent the target atom) $m_B$   u

  A neon atom (m=20u) makes i vwk ywto)-9-2g raj/a perfectly elastic collision with another atom at rest. After the impact, the neon atom yo -wr2jtia9 g)v-w/ ktravels away at a 55.6 $^{\circ} $ angle from its original direction and the unknown atom travels away at a -50 $^{\circ} $ angle. What is the mass (in u) of the unknown atom? [Hint: You can use the law of sines.](Let A represent the incoming neon atom, and B represent the target atom) $m_B$   u

  Find the center of mass of the three-mass system shown in Fig. 7p t z1)r;po)rc–38. Specify relaticot )r)p zp;r1ve to the left-hand 1.00-kg mass.    m

  The distance between a cb f)7+es.udd9c+z siparbon 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 the car. How y53nnc8pj ) bffar 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 thrnnp3ybj f c)85ee people sit in the back seat 3.90 m from the front? Assume that each person has a mass of 70.0 kg.    m

  A square uniform raft, 18 m by 18 m, of mass 6800 kg, is used asu: i(,m8 bm ,fn3uj-z6g)/ xtqx paaxj a ferryboat. If three cars, each of mass 1200 kg, occupy its NE, SE,t3uz/(68 nx p: b,qfmj, -jigxa) axmu and SW corners, determine the CM of the loaded ferryboat.$X_{CM}$ =    m $Y_{CM}$ =    m

  Three cubes, of side*..syyqz6b9w3 zx9rwxn sop2 s $l_0$,$2l_0$, 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 m ,l)j;i :qy;hxxggqq8-1uxgff+lh4 identical cases of tomato paste (see Fig. 7–40), each of which is a cube of length l. Findgh; jqgix ffq8-gl x4+yuh:1m,;x)lq 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 plarhgl c-. *jlx-lzvm / u6wp:e3te of radius 2R has a circular hole of radius R cut out of*urzvle:wl/h jm .c -px3-g6l it. The center of the smaller circle is a distance 0.80R from the center C of the larger circle, Fig. 7–41. What is the position of the center of mass of the plate? [Hint: Try subtraction.]   R

  Assume that your proportions are the same as those in Table 7–1, and calculate ny 915wkusrt6t7 jh0 fp ,5qbbthe mass of oneq95,n7 5yrtbtuskhf jw 06p b1 of your legs.    kg

  Determine the CM of an outstren.aj1iq crmskf -or0;njh, 29tched arm using Table 7–1.   % of the person's height along the line from the shoulder to the hand

  Use Table 7–1 to calcut p)wd29bemac,2 3e :lx)6k sgkz.e etlate the position of the CM of an arm bent at a right angle. Assume that the person is 155 e lx 2e.pz)g3ek6a ew),t tm:9c2db kscm tall. $X_{CM}$ =    cm $Y_{CM}$ =    cm

When a high jumper is in a position such that his akaitzd us) 433rms and legs are hanging vertically, and his trunk and head are horizontal, calculate how far below the torso’s median linutdi3sz k)a 34e the CM will be. Will this CM be outside the body? Use Table 7–1.

The masses of the Ea c.tc7 jt8q)jmrth 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 10.0 m apart /)bt i.z27ffyccl)mm 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 heahq y0q30g d2sed of mass 2.00 kg and a diameter 0.0800 m mounted on a uniform cygsqe 0yqd0 2h3lindrical 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 masm -4ru;uu lcu r5s*;vxs 2.00 kg and a diameter 0.08 cxlv -uu4s;5ru;ru* m00 m mounted on a uniform cylindrical handle of mass 0.500 kg and length 0.240 m, as shown in Fig. 7–42. If this mallet is tossed, spinning, into the air, how far above the bottom of the handle is the point that will follow a parabolic trajectory?    d    d

  (a) Suppose that in Example 7–u0gy xyp+n/ 3s14 (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,1a cl5xs sorw2qn30+ 9 ep9puz 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 ballooa3es5qn plxs9ur+pcw10 o2 9zn then move? What happens if the passenger stops?

  An 0.145-kg baseball pitched horizontczp;g 0v cy4u/ally at strikes a bat and is popped straight up to a height of 55.6 m. If the contact time is 1.4 ms, calculate thz/;ccp gv04y ue average force on the ball during the contact.    $^{\circ} $

  A rocket of mass m traveit5arqap,r98b0;fh) vu(fxq+ k w ik7ling with speed $v_0$ along the x axis suddenly shoots out fuel, equal to one-third of its mass, parallel to the y axis (perpendicular to the rocket as seen from the ground) with speed 2$v_0$ Give the components of the final velocity of the rocket.$P_x$: v'$_x$=    $v_0$
$P_y$: v'$_y$=    $v_0$

A novice pool player is faced with the cornexq:4 )-naq cwxhpq93gr pocket shot shown in Fig. 7–43. Relative dimensions are also shown. Shou qng 4-qwx9)ax:3phcqld the player be worried about this being a “scratch shot,” in which the cue ball will also fall into a pocket? Give details.

  A 140-kg astronaut (includ*v+fwj8akx 4 *jrl qw/ing space suit) acquires a speed of 2.5m/s by pushing off with his legs from xwvr*akfj48 /jw q*+lan 1800-kg space capsule.
(a) What is the change in speed of the space capsule?    m/s
(b) If the push lasts 0.40 s, what is the average force exerted on the astronaut by the space capsule? As the reference frame, use the position of the space capsule before the push.    N

  Two astronauts, one of mass 60 kg and the other 80 kg, are initiallyearp9 aiq(;r5 at rest in outer space. They then push each other apart. How far apart are they when the lighter astronaut has moved pr5ia 9;(raqe 12 m?    m

  A ball of mass m makes a head-on elastic c7kzwt oip5q 9b57 77znht/e nsollision with a second ball (at rest) and rebounds in the opposite direction with a spn ks 7ip7z5e/botn5wq z977hteed 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 inc3g:fh6 c( hfovolving an automobile accident. The accident involved car A of mass 1900 kg which crashed into stationary car B of mass 1100 kg. The driver of car A applied his brakes 15 m before he crashed into car B. After the collision, car A slid 18 m while car B slid 30 m. The coefficient of kinetic friction betf6hgc: cohf3 (ween 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 o-;q5sauyq;dztsom:/ 7n; nv yf concrete 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 perfectly elastic, what is the bounce height on the fourth bounce when the ball reacheu;5my /s -z:at;sy;qqn d vo7ns the bottom of the stairs?

  A bullet is fired vertically into a 1.4az*d w0v td5e30-kg block of wood at rest directly above it. If the bullet ha t 0*a3d5dvewzs 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 embedded in a 1.35-kg block of wood placed on ux/p*- 0d 5zsz:rfvhb 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 bevb-urfzd 0*z/ph5:x sfore it comes to rest, what was the muzzle speed of the bullet?    m/s

  Two people, one of mass 754wz5tu4+xaji4eiu h1 kg and the other of mass 60 kg, sit in a rowboat of ma4 uh+iw4 t5ja4ezu i1xss 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 boat will move    towards the initial position of the 75 kg person(Round to two decimal places)

  A meteor whose mass 55+q6rtud gjb4 )f-c apiuq5 swas 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 an exployc ,te/cq +/l gsu5ypuyoz *k5*a6.kmsion. One fragment acquires twice the kineti gpk,u/ +c lys/o k**ta 5zy.q5cu6myec energy of the other. What is the ratio of their masses?   

  The force on a bullet is given by the formu69wo5hk9 i4/bmut e5ap9w x zgla 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 massesdducl( ef.d r55;6 tqh $m_A$ = 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 particle and a smal2 ryy dh h1bloo5at;/cfs8v-fn:;x5k ler nucleus. What will be the speed of this recoiling nucleux:5h-8hcby5fk; t; 1v rsodl/ foy2n as 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 firjwq 9+amkw5)dd n*1k ded 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 30ynwrygbr .mn.6s j)-bn1v s y35- :mls.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 limit on mass m if it is tozh 0p-cil6(ag63ai vo rebound from M, slide up the incline, 6ig0iaop- h3v( zlca6stop, slide down the incline, and collide with M again?    kg (Let A represent mass m, and B represent mass M.)

  The gravitational sli:sfgoy mg/,6 4)lyqpr ngshot effect. Figure 7–47 shows the planet Saturn moving in the negative x direction at its orbital speed (with respect 4)yoy/sg 6f:gqpmr l,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