We claim that momentumdjmhxk-a90u/ 7cj*gc. lb2a2 ni d;fk is conserved, yet most moving objects eventually slow down and ua22cj;/7 xlfmhdbc *9-.0 kkia jdgn stop. Explain.

When a person jumps from a tree to the ground, what happens to the mombj4/e4d wnpvc7+yn/ hentum of the person upon striking tybvwde+hp/c 4 /4n j7nhe ground?

When you release an inflated but untied balloon, why does it fl.nip d g(nty1jzsx7 -5y across the room?(7 j.xdpn5izg-nyt s1

It is said that in ancient times a rich maq1z-ek47l 4i:t vsz jxn with a bag of gold coins froze to death while stranded on a frozen lake. Because the ice was frictionless, he could not push himself to shore. What could he have done to save himself had he not btz1: slxv4e-7kzjqi4 een so miserly?

How can a rocket change direction whenmh,t q v8 tfa)fwq)de/1,j2gi it is far out in space and is essentially in a vacuum?qe)jgw)ft 2ah 1 f8d,v,i/mqt

According to Eq. 7–5, t4tgq9ae e(7, ldfx fs.bo;cr (he longer the impact time of an impulse, the smaller the force can be for the same momentum change, and hence the smaller the deformation of the object on which the force acts. On this basis, explain the value of air bags, which are intended to inflate during an automobile collision ol(79,cdfef tbexraq(.g4 ;sand reduce the possibility of fracture or death.

Cars used to be built as rigieqlp(b ,2pg .b8x*pwzd as possible to withstand collisions. Today, though, cars are desib q2z b,pw.(l8 xgpe*pgned to have “crumple zones” that collapse upon impact. What is the advantage of this new design?

Why can a batter hit a pitched baseball further than a ball tossed in the gb-r cyo)rz 0po e2tfgx7n 58+air by tf 5g 7-2yr+ czo0o)t8rbxpneghe batter?

Is it possible for an object to rens9je /*df b-oceive a larger impulse from a small force than from a bdn -jse/9 o*flarge force? Explain.

A light object and a heavy object have the 1k +cilff0/so same kinetic energy. Which has the greater momentum? Eo+1l k/fis 0fcxplain.

Describe a collision in which aa4yjksu fc ) -tj64l2fll kinetic energy is lost.

At a hydroelectric power plant, wateoa.t 3- 54 hgub(twaqyr is directed at high speed against turbine blades on an axle tbu qawy5-4t.ta g3 o(hhat 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 wall aqaew , kmxt 1.9(+;afqt ahzy/u4 et+lt 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 pe 97jc w1s*cnl0jr hbf;,3bpknx- 9 bylate (fixed to the Earth), from which it rebounds at very nearly its original speed. (a) Is the momentum of the ball conserved during any part of this process? (b) If we consider the ball and Earth as our system, during what parts of the pr*nrbjcb9wp1 x3s;7b hnj ye -c,l9k0focess 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 hf5nn vz:woa2d+6s, y d):y zxieavy load in your arms?

Why is the CM of a 1-m length of pipe at its mid-point, whereas this is not true:qrom/. ,on tu for your arm or /t.omn,u: qo rleg?

Show on a diagram how your CM yiqa(e)zkyi-w00 7vu shifts when you change from a lying position to a sz)wqaky e0-iiyu70 (v itting position.

If only an external force can change the momentum of tg7tyvpx599 wfhe center of mass of an object, how can the internal force 7tvwxp9y9 gf5 of an engine accelerate a car?

A rocket following a parabolic path through the air sudjrowa - rl4/cxh,8mt+r on0 7rz5nuo 7denly explodes into many pieces. What can you say about the tro+ nahn07u-or4r 57 ,j wrlxo mcz8/motion of this system of pieces?

  What is the magnitude of the momentum of a 28-g sparrow flying with artfm5,d3m wz) speed of $8.4 \; m/s$    $kg \; m/s$

  A constant friction force e;7eh) 81+jlgflway:*r fn s o)ckjj:of 25 N acts on a 65-kg skier for 20 s. What is the skier’s change in v7 :s:gl)+f*y )jr fj a o1;cjelk8whneelocity?    m/s

  A 0.145-kg baseball pitched at 39 m/s is hit on a horizontal line drivedc3adxwz p.1+ :-epgx straight x- 3 :gzxc.wpeadd1+pback toward the pitcher 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 pack bttqj5(ued0f )nw +p.age out horizontally with a speed of 10 m/s Fig. below Calculate the velocity of the boat immediatelybd0 w) jf5( tpnq+t.eu after, assuming it was initially at rest. The mass of the child is 26.0 kg, and that of the boat is 45.0 kg. Ignore water resistance. The magnitude of the velocity of the boat is    m/s

  Calculate the force exerted on a rocketd654(e v2h em3 szseja, given that the propelling gases are expelled at ase 6 dhsz m2e5eaj34(v rate of $1500 \; kg/s$ with a speed of $ 4\times10^{4 } \; m/s$ (at the moment of takeoff). F =    $\times 10^7 \; N$

  A 95-kg halfback moving q+j.id6i.wu4f gai (q*w; p,a ur0xqh 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 alet(*q8 9bujd ry8+*;ojia h bawvel frictionless track with a constant speed of 18m/s A 5350-kg load,initially at rest, is dropped onto the car. What will be the car’s new speed?aab *b;j8 hjwqur 98o( *id+ty    m/s

  A 9300-kg boxcar traveling(fs mq3z7xjxre ab+x0u) *h+l at $15 \; m/s$ strikes a second boxcar at rest. The two stick together and move off with a speed of $6 \; m/s$ What is the mass of the second car?    $m/s$

  During a Chicago storm, winds can whip horizontally at sffhb+o nbm62j4k 2 r2apeeds of 100km/h If the air strikes a person at the rate of 40kg/s per sq knmf6ar4 22h+fb2 jobuare 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 4 v usd*jsc hm d.;feolk4g3o,s6 cd.wj6,lc5.6m/s on a level track6 u,*hj v om.clkcsd wd4.sc e654s3d,fl; ojg. Snow begins 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 at 420m/s emits an alpha particle in the dirfrc zuma+63+d ;):hpdec 2q vqection 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 +2vz ;qhem6fcrca + )p dudq3:a mass of 222 u, what speed does the alpha particle have when it is emitted?    m/s

  A 23-g bullet travel4vg4).g hck tming 230m/s penetrates a 2.0-kg block of wood and emerges cleanly at 170m/s If the block is stationary on a k. hvcm 4)4tggfrictionless surface when hit, how fast does it move after the bullet emerges?    m/s

  A 975-kg two-stage rocket is ov.i ;54ml 3nfn(tt zktraveling 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 spa r:0vih zg2uv6)iu k8oce with a velocity of 115 v r6u2vkg:8 iiho0zu)m/s 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 h a, nfjsn,n40)s,)z5vys iaa the tee at a speed of 45m/s The golf club was in contac,0)an5,,hsnni af z)a ssy4j vt 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/s and comes to rest in km 2p+syz j33qa time interval of 8.0 ms. (a) What is the impp2z3mykjs q3+ulse 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 strikesd2ufuwcv- :kcc 4cjo+il(7 - v 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 crashworth(7z. n2ht*tmws nvkd5iness 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 car by tn (nz.*h 27ttvdsmw 5khe 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 0.4d,xv7 u htf9-xzf 9sq75 s by a head-on vx4z, dq9x-9fh7utf stackle by a tackler 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 (mass 0.060 kg) points in t1fn39 5p ygdymhe +x direction and is given by the graph of Fig. 7–33 as a function of time. Use graphical methop f gyy5m39nd1ds 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-k (tx64u7+aal:re +4wgamh )e q;gowg og person jump without breaking the lower leg bone of either leg? Ignore air resistance and assume the CM of the person moves a distance of 0.60 m from the standing to the seated positio ):;ewt +l4xga mg674w eoquhaar+ o(gn (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 (+y9ze8( *gz2zl1s3b+uf 5gnoqgprjl. x direction) with a speed of collides head-on with a 0.220-kg ball at rest. If the collision is perfectly elastic, what will be the speed and direction of each ball after the cobzoe9nj s(zl*r3 8g1 .g5fgpuy+ z2lq llision?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 spe51uuwz3. 2m1ekkh bwk ed of 3m/s has a head-on collision with a 0.900-kg puck initially at rest. Assuming a perfectly el2eb ukz u1.kw13km5hw astic collision, what will be the speed and direction of each object after the collision?Let A represent the 0.450-kg puck, and let B represent the 0.900-kg puck. v'$_A$ =    m/s ----待选择----eastwest  v'$_B$ =    m/s ----待选择----eastwest 

  Two billiard balls of equal mass undergo a perfectly etn+ ,kd+md3 8pz n ndb /cg,kv2jk48wdlastic 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 represent the ball moving at 3.04b,d8nmwdcn p ,3+k2gt zk8dj/kvd n+ 0 m/s in the opposite direction. ) v'$_A$ =    m/s v'$_B$ =    m/s

  A 0.060-kg tennis ball, moving with au)rcv9zr,6 5 w)bszdndng* t2 speed of 2.5m/s collides head-on with a 0.090-kg ball iztw d5ugn2nzb,v6 )r)9 * dsrcnitially 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 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 x n/ l(,ik .we-jgfc3tdnp1 2hspeed of 8.5m/s collides head-on and el/. k,x enf3-lgch p2it(1 jdnwastically 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 elastically as one approaim.0x xdxf (x9ches the xxfixd m9 0.x(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 3.7m/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 sec7 gdretc ay682ond ball initially at rest. The second ball moves off with half the original speed of6y7dctg8ra2e 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 frictionle lafbpqt ooa2827x,a1/,c wrv ss 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 i ax,aro71 ,qvlopfcb2t8a w/2s 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 ang *;b;n lckni1bfx6( e object 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 quo9-x:ta rm)gj pz33experiment, projectile 1 results in a maximum height h of the pendulum equal to 2.6 cm. A second pr33xu rmqao z-)pjt g:9ojectile causes the the pendulum to swing twice as high, $h_2=5.2\mathrm{cm}$ The second projectile was how many times faster than the first? $v_1$ =    $v_2$ ([color=rgba(0, 0, 0, 0.85)]Round to three decimal places)

  A 28-g rifle bullet traveling 230m/s buries itself in /o5/4cp:2jx a6; hqfl9pqkeks ) hb vka 3.6-kg pendulum hanging on a 2.8-m-long 2f kp4 ;exkj95oqs/cvl/qh:6kpa bh ) string, which 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 )js5wgtm5jknp3e jbgqb xi9 q1: n:40energy 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 brea.2l7bc o: omcpy0kbqs:49 udbks an object, initially at rest, into two pieces, one of which has 1.5 times the mass of the other. If 7lcsd quyp k4o2bcm7.b 0o9: :b500 J were released in the explosion, how much kinetic energy did each piece acquire? (Let A represent the heavier particle, and B represent the lighter particle. ) KE'$_A$ =    J KE$_B$ =    J

  A 920-kg sports car collides into the rear edrm. +-cm05ui 6xgf/t sx1tae nd 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 ud msxa/+5. t mrtecg6 10-xfifriction 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 i7)7m g age vzn+jf9(l1.50 m and rebounds to a height of 1.20 m. Approximately how many rebounds will the ball make before losing)e (7+vg9lf miza7jng 90% of its energy?   

A measure of inelasticity in a head-on collision of two objects is the coeffici4k3aaazi vx( -uy(8af enta 3(ivak(u8az-a 4xfy 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 twwi1l 5 p.gyb)w dl28nyo pieces, one with three times the mass of the other. A depression is made in both faces of the cut, so that a firecracker can be placed in it with the block reassembled. The reassembled block is set on p5i ).wwn1lgyd28 byla rough-surfaced table, and the fuse is lit. When the firecracker explodes, the two blocks separate and slide apart. What is the ratio of distances each block travels? ----待选择----1/91/101/81/6 

  A 15.0-kg object moving in the +x direction at 5.5m/s collides head-on wi fj/9z( (6o :vqx.auzlvlc /gith a 10.0-kg object moving in the -x direction at 4m/s Find the final velocity of each mass if: oz6( vajux:l/fcgz q( v.il9/
(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 deccdt:)d9tyfm - 1f-shtwi-3qqbwuony l8 , 2b ,ays into a second nucleus, an electron, and a neutri c dty19s md w,-tflit: yn8 )hb--qqwbu3,2ofno. The electron and neutrino 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 mass m 72dprn+e ckorj3b *)$m_\mathrm{A}=0.400$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 colli2a n(/ xhyu0qr(m3hh p9 ubrzw+ ;7gybsion between two objects of equal mass, each having initial speed the two move ofyu+bz7;2hbh (r0 wyma/gu9 h(nxpr3 qf together 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 the origiehdr)hjc3 *x3n 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 their two spjc3e hrxh*)3 deeds? 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 c cfq7fy229.oa pt9g euollision with another atom at rest. After the impact, the neon atom treuqc9t2ff2ogp 7 9a.yavels 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 aikm8-nuhbaz5t +a+z( 5y-uo fnother atom at rest. After the impact, the neon atom tru +mz5nbi-+- 8 a 5aozyk(ftuhavels 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. 7–38. Specify re)kb; o54nuno pgmhq 4*lative to the lef;nb4o hp nmuq*ko54)g t-hand 1.00-kg mass.    m

  The distance between a carbon atom (camj5b(9.r +pkyvdm ($m_{\mathrm{C}}=12\mathrm{u}$) 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 2.5 -sggvbxpcu z2r;)8,b0 m behind the front of the car. How far from the front of the car wilb,zs)g;- rp cb8gxuv 2l the CM be when two people sit in the front seat 2.80 m from the front of the car, and three people sit in the back seat 3.90 m from the front? Assume that each person has a mass of 70.0 kg.    m

  A square uniform raft, m xhm1 ky4lzlb 0.:uj1q*jte( 18 m by 18 m, of mass 6800 kg, is used as a ferryboat. If three cars, each of mass 1200 kg, occupy its.0jqjmy t 14h(lu emb :x*l1kz NE, SE, and SW corners, determine the CM of the loaded ferryboat.$X_{CM}$ =    m $Y_{CM}$ =    m

  Three cubes, of sides m/(r ,zj5r4rc)tnv (l1tsumo $l_0$,$2l_0$, 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) pall+uhj3kncw0k0g,e h g5et has a load of identical cases of tomato paste (see Fig. 7–40), 0kkwc0g+g3 huj,he 5neach 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 , a2,q)k7x9krmnh uujcircular hole of radius R cut out of it. The center of the smallerxrn) j7k,ku9ahu, 2m q 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 hdt pg4q 8e9bro8h2k-are the same as those in Table 7–1, and calculate the mass of one of yokb d8p -rto h8ge942hqur legs.    kg

  Determine the CM of an outstretchedn jubz vd oivpq 5*+p/825by-n 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 4iydsvc 2xmz(03zu12hj wa o+bent at a right angle. Assume that the person j zhuvci2+2xya (z1 40m3 dowsis 155 cm tall. $X_{CM}$ =    cm $Y_{CM}$ =    cm

When a high jumper is in a position such that his arms and legs are hanginf6lv6 n-:nxcb g vertically, and his trunk and head are horizontal, calculate how far below the torso’s median line thec 6lx:-fnv6nb CM will be. Will this CM be outside the body? Use Table 7–1.

The masses of the Earth and Moonp4 0btptu nqw+x+tm22mg:bl 5og r, w.fs*2hj 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 y-wctpw8k13jmi c; t)man stand 10.0 m apart on frictionless ice.
(a) How far from the woman is their CM?    m from the woman
(b) If each holds one end of a rope, and the man pulls on the rope so that he moves 2.5 m, how far from the woman will he be now?    m
(c) How far will the man have moved when he collides with the woman? He has moved    m from his original position

  A mallet consists of a unn zm(vza(t 7c)2 yw+)j2afgqmb f 99jhiform cylindrical 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 shown in Fig. 7–42. If this mallet is tossed, spinning, into the air, how far above the bottom vm ftq+(w9 2) 9y cz2z7gaj(jn)hbmfa of the handle is the point that will follow a parabolic trajectory?    cm

  A mallet consists of a uniform cylindrical head of m)d.k5obqa wn ow1- o+dass 2.00 kg and a diameter 0.08od-)do bn5aow 1kq w+.00 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 Ex4t:bz tolr4w.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 s /cgm;8yzm)kq0yo)4o -glyfptationary with respect to the ground. A passenger, of mass m, then climbs out and slides down a rope with speed measured wmkz0;l4oqyop m /cg8yf)gy )-ith respect to the balloon. With what speed and direction (relative to Earth) does the balloon then move? What happens if the passenger stops?

  An 0.145-kg baseball pitched horizontally at strikes a bat and is poppe(g/v w,a x+ogw-v p*xed straight 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 p/+w(,g*evav- g oxxw contact.    $^{\circ} $

  A rocket of mass m traveling with spz i 8xf:gjr(c,eed $v_0$ 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 pocketcr uz8hc /z* v;lhd w7crj6,o8mx:+x c shot shown in Fig. 7–43. Relative dimensions are also shown. Shou7u * cl 8:/r8zcj ,rmxvhx+cc;ozhw d6ld 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 suit) acquires a speed of 2.5m/s by pus i:bw)m)e 1vanhing off with his legs from an i)a)wbv:men 1 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 in x,nsstacj9ki1cb9;,k 2 ; mfbitially at rest in outer space. They then push each other apart. Ho j9i,c xb1 smt,n;;cb2kfak 9sw far apart are they when the lighter astronaut has moved 12 m?    m

  A ball of mass m makes a head-on elastic collisixp,kn8q i1) jhib /ii5hn9vhz 4w2;aton with a second ball (at rest) and rebounds in the opposite direction with a speed equal to one-fourth its original speed. What is the mass of the second bal954 ij qv ai) ;xth12n/ihz bi,hwknp8l? $m_B$ =    $m_A$(Round to two decimal places)

  You have been hired as an expert witness in a court case involving *zh95xexm vq9lc:/8xt7 x lynan automobile accident. The accident involxxlxmn*l8 e7 9th9v 5xc:/zy qved 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 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 flight1guu0 :y/8rp 1qwsqu6a w3q xvdud;3t 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. If all collisions are perfectly elastic, what is the bow spy 06q:1adqwtu3;1/ rgx3qd u8uu vunce height on the fourth bounce when the ball reaches the bottom of the stairs?

  A bullet is fired vertically into a 1.40-kg blpw(osj1 p3gd.kyk: 2w67bn r fock of wood at rest directly above (o: j.gw r32f7wdp bn6p1 kskyit. If the bullet 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 becomes embedc k ql7ld a-08nl8e3qaded in a 1.35-kg block of wood placed on a horizontal surfaca e83cqlldk qln -708ae 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 750 .j 5y h83mt88jru1uj i:shhgz2c bzu 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 th 0u:zy hjit 5hms uhcr3j8ub. 1zg82j8e 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 wrx +)q5jr:wv u1: m w2+kknsb )/dnkevd2amx2as 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 isimiem5 gxpj+;n 8s/e ; suddenly broken apart into two fragments by an explosion. One fragment acquires twicinsexe 8;ji g;m5p/+ me the kinetic energy of the other. What is the ratio of their masses?   

  The force on a bullet i38l5e5+cmd 4pj qcvhu r;ghm(s given by the formula F = 580-( $1.8 \times10^{ 5}$t) over the time interval t=0 to t = $3.0 \times10^{-3 }$s In this formula, t is in seconds and F is in newtons.
(a) Plot a graph of F vs. t for t=0 to t=3.0ms
(b) Estimate, using graphical methods, the impulse given the bullet.    N*s
(c) If the bullet achieves a speed of 220m/s as a result of this impulse, given to it in the barrel of a gun, what must its mass be?    kg

  Two balls, of massesp v-gxmmc5r( 5 $m_A$ = 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 radiquj72 us qt)3t*ng+udoactively into an alpha particle and a smaller nucleus. What will be the speed of this recoiling nucleus if thq tuuq+g32j*dus 7) nte 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 f/5l (l8 md ah ud2to6eexsrx, p-8-salired 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 t7-tix. q7e 7)yqmory v9bp,jslides 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 obs 7uxzw28 +sen(.rnw n mass m if it is to rebound from M, slide up the incline, stop, slide down the incline, and colli. esn 2wbun(+xwsr7z8 de with M again?    kg (Let A represent mass m, and B represent mass M.)

  The gravitational slingshot effect. Figure 7–47 shows the planet Saturn mqpwu+/2i7ip( tu:s n)sel *d koving in the negative x direction at *2n:i l/e wpkp(dt+qis7u)us its orbital speed (with respect to the Sun) of 9.6km/s The mass of Saturn is $5.69 \times10^{ 26}$kg A spacecraft with mass 825 kg approaches Saturn. When far from Saturn, it moves in the direction at 10.4km/s The gravitational attraction of Saturn (a conservative force) acting on the spacecraft causes it to swing around the planet (orbit shown as dashed line) and head off in the opposite direction. Estimate the final speed of the spacecraft after it is far enough away to be considered free of Saturn’s gravitational pull.    km/s