We claim that momentum is conserved, yet most moving objects k 7 (w ;c1 qqwl-ctd6p0oo9ljpg:a j3yeventually slow down and stop. pcp ;-co 1gw0ay9q7l wq:t(kjjo 36dlExplain.

When a person jumps from a tree to the ground, what he0*n 3is ywbyz (tkga3/-xe)ngqse /*appens to the momentum of the person upon striking bwe/0ztki-)gnx/e a3 (ns ye3*qy*gsthe ground?

When you release an .c k w:u.l)lwnmvbf;:o d 5l/uinflated but untied balloon, why does it fly across the room?.fkw dv/bc lw5u:u)n;:lom . l

It is said that in ancient times a rich man with a bag of gm,6oi)u b(zh1l1g m wa7sd jd7old 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 himself wh io7 bld jz(),um1a7dm6 s1ghad he not been so miserly?

How can a rocket change direction when it is far out in60oqujrolp8lx-y. . yu uh(8m space and is essentially in a vacuum?.mo uyp-0 ljh8ouxuy.r 8q6l (

According to Eq. 7–5, the longer the impact tivz4 x sbb6(vz4me of an impulse, the smaller the force can be for the same momentum change, and hence the smaller the deformation of the object on which the force acts. On this basis, explain the value of air bags, which are intended to infz4szvv6bb4x (late during an automobile collision and reduce the possibility of fracture or death.

Cars used to be built as rigid as possible to with.bz bq7 va ehg((c3crxxq 5(5mq+yd-sstand collisions. Today, though, cars are designed to have “crumple zones” that collap-gq5x d q.e(vaym (rcbb(sz+x q7h5c3se upon impact. What is the advantage of this new design?

Why can a batter hit a pitched baseball fu 73a) sbslbt-arther than a ball tossed in the air by the batteal t bs3)a-7sbr?

Is it possible for an object to receive a larger impulse from a small force f5eyvu +pr(6 4+)ktf n3wyshathan from a large foy+nha 6(+u)tep5fws v kyr4 3frce? Explain.

A light object and a heav1mirbf3)cl(1yz,-v 3 mwwd gky object have the same kinetic energy. Which has the greater momentum? (b zmdl w3 11rf3yimkv,gcw-)Explain.

Describe a collision in whichzr:r+(/ va8 saehbm x fk)z24p all kinetic energy is lost.

At a hydroelectric power plant, water is directed at high speed against ;g dqb rkq)n9w cf2;ik77 k/rvturbine blades;9dkbr /q )if;q7c vr7kgwkn2 on an axle that turns an electric generator. For maximum power generation, should the turbine blades be designed so that the water is brought to a dead stop, or so that the water rebounds?

A squash ball hits a wacjs+e.ah ffnv8m m n47131qe s+ls4sap:q2vhll 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 fori) +3uwz4k,ok)0 euy momv9rom 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 dm+eoo 4)3) 0 kiyu ,um9wzkvoruring 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 backward when carrying a heavy loab)f) +pusgf e:d in your arms?

Why is the CM of a 1-m length of pipe at its mid-point,- lh(mo. ex*20t8y qlr trby0b whereas this is not true for l02rb8ye.t*h lb-0r oy q tm(xyour arm or leg?

Show on a diagram how your CM shifts when you change from a,fqf y;.qdzpkocyng. 7y 2 0o5 lying position to a sitting;g0f 2opyf.koc .y q 5znqyd,7 position.

If only an external force can change the momentum of the center of mass6g9;th xl rm2a of an object, how can the internal force of an ex9 mal;2g 6rthngine accelerate a car?

A rocket following a parabolic path through the air suddenly explodes into mae2a .j p4xcli-2fwa6wny pieces. Whapf ae-6xj2w 4 wai.2clt can you say about the motion of this system of pieces?

  What is the magnitude of the momentum of a 28-g sparrow flying with a speg (yk:md- hie;ed of $8.4 \; m/s$    $kg \; m/s$

  A constant friction force of 25 N actszghe.8g8 ;tf n on a 65-kg skier for 20 s. What is the skier’s change in ve fhge88;zng.t locity?    m/s

  A 0.145-kg baseball pitched ,aa5 ea9y*z 7o nd9yooat 39 m/s is hit on a horizontal line drive straight back toward the pitcher at 52m/s If the contact time between bat and ball is ynd ,7o9yae*o 9zoa5a $3\times10^{-3}$s calculate the average force between the ball and bat during contact.    N

  A child in a boat throws a 6.40-kg packagedemsg l2*p 6 3l7 umsenv r2b;ne.ti-- out horizontally with a speed of 10 m/s Fig. below Calculate the velocity of the boat immediately after, assuming it was initi*-m; u lses2nvnri3 m-p.db26etlg 7e ally 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 the propelling gasxi n32pyxbp1 1es are expelled at a ry12 ibpxnp3x1 ate of $1500 \; kg/s$ with a speed of $ 4\times10^{4 } \; m/s$ (at the moment of takeoff). F =    $\times 10^7 \; N$

  A 95-kg halfback moving at y+ouhwvgem 2j87mri c.*d m/8$4.1 \; m/s$ 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 2hmw qk oa35h3travels alone on alevel frictionless track with a constant speed of 1mohqaw353 hk 28m/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 w iz+*qcb w91kat $15 \; m/s$ 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 stob x1e4;c4 n oav9ffg(jrm, winds can whip horizontally at speeds of 100km/h If the air strikes a person at the4e4 fo j;ag(b1f9vcnx rate of 40kg/s per square meter and is brought to rest, estimate the force of the wind on a person. Assume the person is 1.50 m high and 0.50 m wide. Compare to the typical maximum force of friction $\mu\approx1.0$ between the person and the ground, if the person has a mass of 70 kg.    N
$F_{on person}$  ----待选择----<> $F_{fr}$

  A 3800-kg open railroad car coasts along with aqq(p 160 vuwfe 0nez3u constant speed of 8.6m/s on a level track. Snow begins to fall vertically and fills the car at a rate of 3.5kg/min Ignoring fricti60q0v qwez e(3f1nup uon with the tracks, what is the speed of the car after 90.0 min?$\approx$    m/s

  An atomic nucleus initially moving at 420m/s emits an alpha particle in jp 6y +ck3jt97jjqgy;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 ma7q6 ;jct9 kjy3y+p gjjss of 222 u, what speed does the alpha particle have when it is emitted?    m/s

  A 23-g bullet traveling 230m/s penetrates a 2.0-kg block xvq;lxm.e)/lgygx9 (of wood and emerges cleanly at 170m/s If the block is stationary on a frictionless surface when hit, how fast does it move after(gxm9ye l/x);v g xl.q the bullet emerges?    m/s

  A 975-kg two-stage rocket is travelk6bc u g*uy,ih) lglu k7ep-6-oos+c4ing at a speed of $5.80\times10^3\mathrm{~m/s}$ with respect to Earth when a pre-designed explosion separates the rocket into two sections of equal mass that then move at a speed of $2.20\times10^3\mathrm{~m/s}$ relative to each other along the original line of motion. Let “A” represent the upper stage (that moves away faster) and “B” represent the lower stage.
(a) What are the speed and direction of each section (relative to Earth) after the explosion? $v'_A$   m/s  ----待选择----away from the Earthtowards the Earth  $v'_B$   m/s  ----待选择----away from the Earthtowards the Earth 
(b) How much energy was supplied by the explosion? [Hint: What is the change in KE as a result of the explosion? $a\times10^8$ a =    J

  A rocket of total mass 3180 kg is traveling in outer space with a velocity oxr+s+e( o rmv+f 115m/s +e (vrmxos++r 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 t*x:dd0p g /kjg ;may/qhe tee at a speed of 45m/s The golf club was in contact with the ball for /gq /j*gmp:yxk dda;0 $3.5\times10^{-3}$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 strikmbfan 9yauua7n6u2( /es a nail at a velocity of 8.5m/s and comes to rest in a time interval of 8.0 ms. (a) What is the impulsf9u67 (yu2/ab aannum e given to the nail?    kg*m/s
(b) What is the average force acting on the nail?    N

  A tennis ball of mass m=0.06kg and speed v=25m/s strikes a wall at ae9 ;itg ; fq+hsxcl82r 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 er m9/ --kco jsfto1v1vfi h*p5ngineer in charge of the crashworthiness of new automobile models. Cars are tested by smashing them into fixed, massive barriers at 50km/h (30 m-/c jh*fr5ks v-v1of9m1pto iph). A new model of mass 1500 kg takes 0.15 s from the time of impact until it is brought to rest. (a) Calculate the average force exerted on the car by the barrier. $\approx$$a\times10^5$N a =   
(b) Calculate the average deceleration of the car.    m/$s^2$

  A 95-kg fullback is running at 4m/s to the east and is stopped in 0.75 s b/y4ho 3endrby1c zl)/ y a head-on tackle by a tackler running due west. Calculatcr 1o4y y/b)z3lned/ he
(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 (mb8qe7 dce37 r9f7 o5nwelw 0adass 0.060 kg) points in the +x directio7leed7c3o9en0rdwb a q 5fw87 n and is given by the graph of Fig. 7–33 as a function of time. Use graphical methods to estimate
(a) the total impulse given the ball    N*s
(b) the velocity of the ball after being struck, assuming the ball is being served so it is nearly at rest initially.    m/s

  From what maximum height can a f3ko p ,7o x 1bxd4v;qcjh8xd375-kg person jump without breaking the lower leg bone of either leg? Ignore air resistance and assume the Cjd1p 4xcqo,78 xkfh x3bvo3; dM 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 sj4/5q r1j) uvuw:x bsm7:ix d collides head-on with a 0.220-kg ball at rest. If the collision is perfectly elastic, what will be the speed and direction of each ball after the collision?Let A reprebqd ):1ruv4xxiuj/ 7m5jw ss:sent 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 collig. jas0y ,3mxtsion 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?Le.y ms,03j agxtt 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 equajdl3gb0/f kv :l mass 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 collvbl3gdfk:/ 0j ision?(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 um73j2v9u b qpof 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.v bmujp2q3 u97060-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 m ipe9d1zgb,3 8.5m/s collides head-on and elastically with another ball initially at rest. Afterward the 31b 9,imgpd ezincoming 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 ee3vjv *wc2r1ep o +/wamusement park ride collide elastically 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 approaches at 4.5m/s and car B is moving at 3 rpc/v*eweow2ev+j1 3.7m/s calculate
(a) their velocities after the collision v'$_A$ =    m/s v'$_B$ =    m/s
(b) the change in momentum of each.$\Delta p_{\mathrm{A}}$$\approx$    kg*m/s $\Delta p_{\mathrm{B}}$$\approx$    kg*m/s

  A 0.280-kg croquet ball makes an elastic head-on collision with a seco; . nuzgmyr.e0nd ball initially at rest. The second ball moves off with half the original speed of the first yu0r.ez.m g ;nball.
(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 shown in Fig. 76de er , subvzxm5f759–35, 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 d 957murvzf 5xe6, esbdoes 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 objnl0fgi1zillxwze5m7) ,fa c -e *y .3eect 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, projectil hkb05j kr4je5e 1 results in a maximum height h of the pendulum equal to 2.6 cm. A second projectile causehbk0jer4k5 5js 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 230l jkt4d))0vcgq+liopa j dhgs(56e: /m/s buries itself in a 3.6-kg pendulum hanging on a 2.8-m-long string, whic+6q)h jj5akdd4ls:i 0v/t oge(pcg)lh makes the pendulum swing upward in an arc. Determine the vertical and horizontal components of the pendulum’s displacement.vertical$\approx$    m horizontal =    m

(a) Derive a formula for the fraction of kinetic energy los vbt ,u :x wtpm6she98bk:gp23t, $(\Delta\mathrm{KE/KE})$ for the ballistic pendulum collision of Example 7–10. (b) Evaluate for m=14g and M=380g

  An internal explosion breaks an objecpnksg9sxiu;1-c9 l0 ft, initially at rest, into two pieces, one of which has 1.5 times the mass of the othe-gpfxsl is9;1nc0 ku9r. 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:62q 9:i tv(ngm ipfrm 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 speed of the sports car at impact. What was that speed?(Let A repregn:6p2f i9(i:m qrmvtsent 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 hei we:e:4zqvg 1rght of 1.20 m. Approximately how many rebounds will the ball ma:41ze vgeq:rw ke before losing 90% of its energy?   

A measure of inelasticity in a head-on collision of two objectk)x ;yc0nhmu*k)n 7jvs is the coefficien7hjx )c ); mk*y0vunnkt of 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, ons1 uozh lb1*z,gs0 4tn)5 nlene 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 reassembb0*5 hz1sonn l,ngest)u41l zled. 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 direc( 87goeh gk)oo.tc.)9sc ht38ehl t,pquci 9ction at 5.5m/s collides head-on with a 10.0-kg object moving inic9c9 hthc7 gp(s8)cgo8k,eu tho ).t.3l oqe 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 decayvoh y:lxtxsp(pya993c :p3 3 ys into a second nucleus, an electron, and a neutrino. The electron and neutrino are emitted at right angles and have momenta ofvl( :3c :3p yy o9sapth9xyxp3 $9.30\times10^{-23}kg\cdot m/s$ 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 ma*vfnr*o7z/i 9d ( kce.vlm, kdss $m_\mathrm{A}=0.400$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 betwee/hfuqgv9a 4cr sp r(4oq1r6f 1n two objects of equal mass, each having initial speed the two move off t 14sg(9 qpvhrq61fr/f4urcoa ogether with speed v/3 What was the angle between their initial directions?    $^{\circ} $

  Two billiard balls of equal mass move at right angles and meet at thequ9 9jopu5jftn dcws4):. ,kf 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 rigt.fcn9 w,qj5p)fskd uo:u9 4jht along the x axis with speed 3.7m/s After the collision, assumed elastic, ball B is moving along the positive y axis (Fig. 7–37). What is the final direction of ball A and what are their two speeds? direction of ball A is  ----待选择----x directionx direction v'$_A$ =    m/s v'$_B$ =    m/s

  A neon atom (m=20u) makes a perfectly elastic collision with anotheth sa2u:kl;x3r n rn b-i/mwp:t3e/0fr atom at rest. After the impact, the neon atom travels away at a wpt- 3bm f/;3xils0 htrk/au2:enr:n55.6 $^{\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 anotherpcensgqwtd m3nyq9/5/51 j r) atom at rest. After the impact, the neon atom travels away at a 55.spyrnj5/e1 / q5q w 9ndm3ct)g6 $^{\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. 7–38.,r;5. usgabmx Specify relativb.ru,; gx5ms ae to the left-hand 1.00-kg mass.    m

  The distance between a carbon atom (yhb*e 863uyv d$m_{\mathrm{C}}=12\mathrm{u}$) 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 fro n6*ss ly8k b/0jj 6p3lgeb-fcnt of the car. How far from the front of the car will the CM be when two people sit in the front seat 2.80 m from the front of thj/c6 jlspgby63-bfks8l0ne* e 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 m by 18 m, of mass 6800 kg, is used as a ferrybs7/or kw*h:4unmopy c( 8je6 hoat. If three cars, each of mass 1200 kg,*6eyj(/h: khc4w 8oos7rnm pu occupy its NE, SE, and SW corners, determine the CM of the loaded ferryboat.$X_{CM}$ =    m $Y_{CM}$ =    m

  Three cubes, of sidesc z/9ofvn2.hl $l_0$,$2l_0$, 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 of7/yibhf, e*q2t k2e cc tomato paste (see Fig. 7–40), each of which is a cube of length l. Find the center of gravity in the horizontale 2/cqchb e2k7iyt, f* plane, so that the crane operator can pick up the load without tipping it.$X_{CM}$ =    l $Y_{CM}$ =    l

  A uniform circular plw piji +1uj0)uczs.,q ate of radius 2R has a circular hole of radius R cut out of it. The center of the smaller circle is a distance 0.80R from the center C of the larger circle, Fig. 7–41. What is the position of the center of mass of the plate? [Hint: Try subt qu, )0ju1cjp wi+.izsraction.]   R

  Assume that your proportions are the same asd24dxdal ,b+ 0jwudpe p;p-j; those in Table 7–1, and calculate the mass of on dd-20ua,bwj+4d l p;pjpdx; ee of your legs.    kg

  Determine the CM of an outstretched arm usi/-zwwhp6i 4x8ordn53n ds : thng 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 o/1+ ,hd+7wg*iy n d-xcd noxibent at a right angle. Assume thad/i xx n i1c+h-n+wod7y,g*odt the person is 155 cm tall. $X_{CM}$ =    cm $Y_{CM}$ =    cm

When a high jumper is in a position such that his armso. dqz dv 4hm6,o774dokdr6iv and legs are hanging vertically, and his trunk and head are horizontal, calculate how far below the torso’s median line the CM will be. Will this CM be outside the body? Us6d4h 6do7k.rv v,oqmi dz 7od4e Table 7–1.

The masses of the Earthor2j(1csu c1j 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 on frict9:-3 xdxggkl42o puma ionless ice.
(a) How far from the woman is their CM?    m from the woman
(b) If each holds one end of a rope, and the man pulls on the rope so that he moves 2.5 m, how far from the woman will he be now?    m
(c) How far will the man have moved when he collides with the woman? He has moved    m from his original position

  A mallet consists of a uniform cylindrical head of mass 2.00 kg andf qll-4.f ip l)ehtagwa5f1)3 a diameter 0.0800 m mounted on a uniform cylindrical handle of mass 0.500p fga34f)l1-ah tq.5 f) liwel 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 cylindricalih4i25r0jx- co2txkx head of mass 2.00 kg and a diameter 0.0800 m mounted on a uniform cylindrical handle of mass 0.500 kg and length 0.240 m, as sior-x xk5j i2c240txhhown 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 Examp )wk *.9jft,p dp8hagvle 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 vot29)k0kbdjx ,d,kd gondola, of mass M, are in the air and stationary with respect to the ground. A passenger, of mass m, then climbs out and slides down a rope with speed measured with respect to the balloon. With what speed and direction (relative to Earth) does the balloon then move? What happens if the passe0 db 2xd9, k)dojk,vktnger stops?

  An 0.145-kg baseball pitched horizontally at strikes a bain(;6 9 xow atdjh,pqu*-qu+ut and is popped straight up to a height of 55.6 m. Ip,j *q nuau;(9 +x-td huq6oiwf 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+66)oz htdchb speed $v_0$ along the x axis suddenly shoots out fuel, equal to one-third of its mass, parallel to the y axis (perpendicular to the rocket as seen from the ground) with speed 2$v_0$ Give the components of the final velocity of the rocket.$P_x$: v'$_x$=    $v_0$
$P_y$: v'$_y$=    $v_0$

A novice pool player is faced with the corner pocket shot 1gcm2 e1z) ymeshown in Fig. 7–43. Relative dimenszy mgm1)ec2 1eions are also shown. Should the player be worried about this being a “scratch shot,” in which the cue ball will also fall into a pocket? Give details.

  A 140-kg astronaut (including space susw5d*k f:j5 voit) acquires a speed of 2.5m/s by pushing off with his legs fj:wsvko5 5 f*drom an 1800-kg space capsule.
(a) What is the change in speed of the space capsule?    m/s
(b) If the push lasts 0.40 s, what is the average force exerted on the astronaut by the space capsule? As the reference frame, use the position of the space capsule before the push.    N

  Two astronauts, one of mass 60 kg and the other 80 kg, are initially at reoh4r9qq-0k rwlw/t *zst in outer space. They */qz4hlrw rq9wk-0to then push 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 casi n ;bh+q -:.pyt+ylollision with a second ball (at rest) and rebounds in the opposite direction with a speed equal to one-fourth its original speed. Wh; lba-t .syy :+i+nqhpat 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 authf88h5m; uker/q, nr yomobile accident. The accident involved car A of mass 1900 kg which crashed into stationary car B of mass 1100 kg. The driver of car A applied his brakes 15 m before he crashed into car B. After the collision, car A slid 18 m while car B slid 30 m. The coefficient of kinetic friction between the locked wheels and the road was measured to 8k5h8q;yrrn u/e ,hmfbe 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 c vmayz 6n,w) :f3o5dtx z(;ygflight of 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. Ifzmdo: c);z3 x5g vf,wt6nayy ( 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 02)clkn;nb zne.0 xxpblock of wood at rest directly above it. If the bullet has a macnk .n)20b p;exxl0n zss 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 bec +s33gbkxv:j 3h5ehsbgxm, .b omes embedded in a 1.35-kg block of wood placed on a horizontal sur,eb5gvbxm3g: 3shx3j.b+ks hface 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 comes to rest, what was the muzzle speed of the bullet?    m/s

  Two people, one of mass 75 kg and the other of mass 60 kg, ats68uv)jz; 8ac(c8g1 b ybyhsit 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. Howby 8hysauz c)v ;8(j 8a1cg6bt far and in what direction will the boat move? The boat will move    towards the initial position of the 75 kg person(Round to two decimal places)

  A meteor whose mass was aboz *-wgj v(q1ycvciu 27ut $ 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 suddet;xo km rrj9quxet-4 +05en.enly broken apart into two fragments by an explosion. One fragment acquires twice the kineou0r9 etnk 4xjtmqr+;ex-e5. tic energy of the other. What is the ratio of their masses?   

  The force on a bullet is given by the formulahcw5 cp:h5 s6;gv opq.gv6vf7 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 1; nlul+4 d ;0tphuifq/ 7gpzv$m_A$ = 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 pp03m.5 zul 8i:/5bzao hxrsn(wweg k 5article and a smaller nucleus. What will be the speed of this recoiling nucleus if tha:hrizg5wnm oxskz 8u53 bl(e/5w p.0e 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 tdy5fv + 4 wzbzqbg dtb4toe;y/:z 95:darget) 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=2.2u(txmr*wz w0(kg slides down 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 limit oc mg3+ ugrkhnih8-r4 4n mass m if it is to rebound from M, slide up the incline, stop, slide down the incline, and collide witr84imu4cgrk- h+ h 3ngh M again?    kg (Let A represent mass m, and B represent mass M.)

  The gravitational slingshot effect. Figure 7–47 s b5*w vmz11msehows the planet Saturn moving in the negative x direction at its orbital speed (with respect to the Sun) of 9.6km/s Th vm 5w1esz1bm*e 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