We claim that momentum is conserved, yet most moving objects eventually slow d, ew:)z5mskxnown and stop. Exeswkz5) nm,:xplain.

When a person jumps yd(tpik,u/ii+0v(m8b p,kvdcj , 2bdfrom a tree to the ground, what happens to the momentum of the person upon strikingikip vbd(t8u/ kvc( dp2 djy mb0i+,,, the ground?

When you release an inflated bu( ehqvs( m-pm wjn dq(ro4o.ymc1;/4yt untied balloon, why does it fly across the room? ;o(1wdrn4s -m/(hq 4.y q vpycjmem(o

It is said that in ancient times u kct:o p2h.km/rw1h 7d /a8ada rich man with a bag of gold coins froze to death while stranded on a frozen lake. Because the ice was frictionless, he could not push himself to shore. What co 1domd/:kw8hu haa.r/7p ck2 tuld he have done to save himself had he not been so miserly?

How can a rocket change direction when it is far out in space and is esxj w;;)tr;hrm6v2 zopsentially in a vacuujhrw62m) ;; otvxp z;rm?

According to Eq. 7–5, the longer the),(tr98es sl9kmjy ay impact time of an impulse, the smaller the forca tyjls) k s9,e9(r8yme 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 reduce the possibility of fracture or death.

Cars used to be built as rigid as possible to withstand cojovk424sc9/ y/glohzup w; 5 ullisions. Today, though, cars zv; phu5jgk/9/ 4 uyw4 2colsoare designed 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 nik ag;v:hjz9sso e-9.av c7b3c+c5kair by the bi7 kj9bokscha -+n5v3c;vg :a s cez.9atter?

Is it possible for an object to receive a larger impulse from qz:68uhnlm6o q s x8lp;wfu7 : mp+cl7 hpsm):a small force than from a large fowcu oq 7 67npsf6l8um)h l:q+:;mxmlp:8s pz hrce? Explain.

A light object and a heavy object have the same kinetic energy. Which xznvi++ ,xq/8y0 md nohas the greater my8xn0 ond/x i+zm +,vqomentum? Explain.

Describe a collision in which all kinetic energy i g)u91k va vgtt-72ptis lost.

At a hydroelectric power plant, w* o /a wi(2 +ji89t,b5igzcwayegj 0wwater is directed at high speed against turbine blades on an axle that turno*0c, az5j/i +8wiwtjw gayiw(b2g9 es 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 at a 4jrwe;7 qn3me7 5 $^{\circ} $ angle as shown in Fig. below. What is the direction (a) of the change in momentum of the ball, (b) of the force on the wall?

A Superball is dropped from a height h onto a hard steel plate (fixed to i)g. *3 qyqk xbd/2.pwpp0thethe Earth), from which it rebounds at very nh .p xdq) pegq0y*btw3k2 ip/.early 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 backward when carrying a heavy load in your fmyqrz8,n 3l q./d -dfarms?

Why is the CM of a 1-m length of pipe/r6pmdgi 7tzny7z -1 k at its mid-point, whereas this is not true for your arm or miyz pg7z d-n/1t76rkleg?

Show on a diagram how your CM shifts when you chmz6xy p1u ;7 wcy*lb6xange from a lying position to a sitting position.mz;l1*yxb6x7ywcu p 6

If only an external force can change the momentum of5 avhh43ls)m9wzps: r s8rat(nfz88l the center of mass of an obje8p8hzt):sz8( ar h3flma45 l vn9s swrct, how can the internal force of an engine accelerate a car?

A rocket following a parabolic path through the air suddenly explodes into manh5 wy bp/ 4zq1nimrn9pww. yuehi1(bp*d):+ by pieces. What can you say about the w:nuz nhprbye* 15h4q+ )wbppyd 9(ibw.m/1i motion of this system of pieces?

  What is the magnitude of the momentum of a 28-g sparrow flying with aeis): ,a7fmpu speed of $8.4 \; m/s$    $kg \; m/s$

  A constant friction force of 25 N acts on a 65-kg skier for /)y t dtmvy5y220 s. What is the skier’s change in veloc vyd)ytm/t2y5ity?    m/s

  A 0.145-kg baseball pitched at 39 m/s is hit on a horizontal line d:d*u ((le, 7vfsdlhdyrive straight back toward the pitcher at 52m/s If the contact time between b(f,y7(d vdlld ehu*:s at 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 package out horizontally with a speed otzs+trq+ yi:,ne7 lk8f 10 m/s Fig. below Calculate the velocity of the boat immediately after, assuming it was initially at rest. The mass of the child is 26.0 kg, and that of the boat is 45.0 kg. Ignore ztty7sq:8ki+ en+ ,r lwater resistance. The magnitude of the velocity of the boat is    m/s

  Calculate the force exerted on a roczt m6p2a)/kan( /ugabket, given that the propelling gases are expelled at a ratp )z amat2//baug kn6(e 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 movingsovv)t 8ts 3(i at $4.1 \; m/s$ on an apparent breakaway for a touchdown is tackled from behind. When he was tackled by an 85-kg cornerback running at $5.5 \; m/s$ in the same direction, what was their mutual speed immediately after the tackle?    $m/s$

  A 12,600-kg railroad car travels alone on alevel frictionless trac q9 (5+uxn6,zr7o *edl4kgio .q5lmbv et ov6mk with a constant speed o5to.d or*e6 5+zvl(b ,7 ox6emlq u4qk9mgnvif 18m/s A 5350-kg load,initially at rest, is dropped onto the car. What will be the car’s new speed?    m/s

  A 9300-kg boxcar travelin4:sk x0w5mgcb g 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 speeds of 100km/h If thep9 98ybcjpp7t air strikes a person at the rate of 40kg/s per squarb9yp pcpj t987e 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 y8y7 szk gy-sb,xjs;q1e (ah5msh.b,along with a constant speed of 8.6m/s on a level track. Snow begins to fall vertically b.;xq ke hsa5syzs s ,hg myj1by8,-(7and 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 th,5y j8m;hoz(d i gjhj58y(lo oe 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 8gzoho(yjjjd8oli5; mh(5 y,nucleus has a mass of 222 u, what speed does the alpha particle have when it is emitted?    m/s

  A 23-g bullet traveling 230m/s penetrates a 2.0-kg block.(c ci.n m)zs) sxbopv+2is r( of wood and emerges cleanly at 170m/s If the block is stationary on a frictionless surfc() c.s isixn) ps .+vor2(zmbace when hit, how fast does it move after the bullet emerges?    m/s

  A 975-kg two-stage rocket igyy6n528m bxt *z c1lv6cuu) ms traveling at a speed of $5.80\times10^3\mathrm{~m/s}$ with respect to Earth when a pre-designed explosion separates the rocket into two sections of equal mass that then move at a speed of $2.20\times10^3\mathrm{~m/s}$ relative to each other along the original line of motion. Let “A” represent the upper stage (that moves away faster) and “B” represent the lower stage.
(a) What are the speed and direction of each section (relative to Earth) after the explosion? $v'_A$   m/s  ----待选择----away from the Earthtowards the Earth  $v'_B$   m/s  ----待选择----away from the Earthtowards the Earth 
(b) How much energy was supplied by the explosion? [Hint: What is the change in KE as a result of the explosion? $a\times10^8$ a =    J

  A rocket of total mass m3kgv 69ufuq 6zs:e:q p8; tb xcec85t3180 kg is traveling in outer space with a velocity of 115m/s To altm6v :uc;3 qe6tg bu:89fq psz85t kecxer 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 hi2ktkpotae x2n7(5 + xft off the tee at a speed of 45m/s The golf club was in contact with the ball for52xxft+t a(oe7nk p k2 $3.5\times10^{-3}$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 a s-2;a:znis. osa9kc zt a velocity of 8.5m/s and comes to rest in a time interval of 8.0 ms. (a) What is thz.:kos9za2;cas ins - e 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 speed v=25m/s strikes a w2*poy k s6mn*rg,phrf4r2t9 b all 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 oqgd..q, hfj))l h(e bn s5ac9fw5gnb(f 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 thefh)dbnab(.g9cnjq)s5.f , q 5geh (wl 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 ijf//j hw3qhg .n 0.75 s by a head-on tackle by a tackler running due west. Calch/ jjhqw3.gf/ ulate
(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 yqzj41 ;u94cv )wac ln.gaes2ball (mass 0.060 kg) points in the +x direction and is gaz2ys.na g;euqjl cwc4v9)1 4iven 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.u tk nk2yjvl*jd;h50 can a 75-kg person jump without breaking the lower leg bone of either leg? Ignore air resistance and assume the CM of the person moves u j2 vjh.kkl5nt*d;y0 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 k gs - vxftd3chzbx(3ge6v+a,9g moving east (+x direction) with a speed of collides head-on with a 0.220-kg ball at rest. If the collis9h63, +tvx vacbgf3 (xd esgz-ion is perfectly elastic, what will be the speed and direction of each ball after the collision?Let A represent the 0.440-kg ball, and B represent the 0.220-kg ball. $v'_A$    m/s  ----待选择----eastwest  $v'_B$    m/s  ----待选择----eastwest 

  A 0.450-kg ice puck, moving east with a speed of 3m rfnb4dadtob,4-r0:m.nz ch,/s has a head-on collision with a 0.900-kg puck initially at rest. Assuming a r fb0 , d.d-:,abzr4 c4nnthmoperfectly elastic collision, what will be the speed and direction of each object after the collision?Let A represent the 0.450-kg puck, and let B represent the 0.900-kg puck. v'$_A$ =    m/s ----待选择----eastwest  v'$_B$ =    m/s ----待选择----eastwest 

  Two billiard balls of equal mass undergo a perfect9ng)3 5jks:j fgw-sdlxi, o; bly elastic head-on collision. If one ball’s initial speed was 2m/s and the other’s was 3m/s in the opposite direction, what will be their speeds after the collision?(Let A represent the badl9nk)sbj3xs;-gj,oi w gf5 :ll moving at 2.00 m/s, and call that direction the positive direction.Let B represent the ball moving at 3.00 m/s in the opposite direction. ) v'$_A$ =    m/s v'$_B$ =    m/s

  A 0.060-kg tennis ball, moving with a speed of 2.5m/s collides dbwgxfrtc0:u7 :8p5:+3y8qu.db2 trr khv tkhead-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 th b0ttbfp+u g q yr823c.vukkr:th7x r8:5:ddw e 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 0.2/wf 60fy5cy w7q qpgdhzh) i:*20 kg that is moving with a speed of 8.5m/s collides head-on and elastically with another ball initially at rest. Afterward the incoming softbalfp yfgdi q6qhwhz c50:/)y w7*l 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 a zy/fse1wj41jn amusement 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 mo4jw1ey1fs/z j ving 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 collisw6utlo 1-d/o uot aw;*ion with a second ball initially at rest. The secoo woua-6d t; wu*olt1/nd ball 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 frictio z7j k2zek97sfnless incline as shown in Fig. 7–35, and elastically strikes another cube at the bottom that is only one-half its mass. If the incline is 30 cm high and the table is 90 cm o97ks2zf ek z7jff 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 of mz* vq(wc,1h/dh(r hog ass 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, projgd)0;e -bad :t* ogumdectile 1 results in a maximum height h of the pendulum equal to 2.6 cm. A second projectile causes the the gtad:me) 0*-od bg; dupendulum 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 a 3.6-kg pendulock zs/ h2xb48um hanging on a 2.8-m-long string, which makes the pendulum swing upward in an arc. Determine the vertical and horizo8hc2 k4z s/xbontal components of the pendulum’s displacement.vertical$\approx$    m horizontal =    m

(a) Derive a formula for the fractionuxv4 p6 n ,(pevgye1q 5a6s2df 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 breakqafu : tm385(niejq7ojvmc5, s an object, initially at rest, into two pieces, one of which has 1.5 times the mass of the other. If 750q 78uf5 mc 3(oenjivm,5qjta:0 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 ;jfw30r+/ bhfq :podb;jjrq( o t3/pb6jt- nxcollides into 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 speed of the sports car at impact. What was that speed?(Let A represent the qp xjo-3+htf;o(pjj 6 :r ;fbnbqwj/ rb/3d0tsports car, and B represent the SUV) $\approx$    m/s

  A ball is dropped from a height of 1.50 m and r3 fisar.z)lc *ebounds to a height of 1.20 m. Approxi3c*.z)fil sramately how many rebounds will the ball make before losing 90% of its energy?   

A measure of inelasticity in a head-on collision of twon8lx 9om7yg:a objects is the coefficient of resti79 :xmyn8loag tution, 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 threena1aon5n4n tp/ u5q* q times the mass of the other. A depression is made in both faces of the cut, so that a firecracker can be placed in it with the block reassembled. The reassembled block is set on a rough-surfaced table, and the fuse is lit. When the firecracker explodes, the two blocks separate and slide apart. What is the ratio of distances each block travelso at*np5 5nnu/1q4 aqn? ----待选择----1/91/101/81/6 

  A 15.0-kg object moving in t5m:7(uu f2,d,iqbg oa;egk hxhe +x direction at 5.5m/s collides head-on with a 10.0-kg object moving in the -x direction ,hugxkg oa,5u m2e 7(:d;qf biat 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 sectbc1ty6 vl73tn(f-m ywo89 cbond nucleus, an electron, and a neutrino. The electron and neutrio cy v(8ctlt6f9-b 73yb1t nmwno 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 mar (7qp6fx tr32w*c,is-) cww6bhqn rc 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 between two objects ofo / 1b4yti9(md;pl pxah2:d jd equal mass, each having initial speed the two move off together with speed v/3 What wad lotddjm: /b 2p(ayixp91 h;4s the angle between their initial directions?    $^{\circ} $

  Two billiard balls of equal mass move at right angles and medsp3 w m+4x4rjet at the origin of an xy coordinate system. Ball A is moving upward along the y axis at 2m/s and ball B is moving to the right along the x axis with speed 3.7m/s After the collision, assumed elastic, ball B is moving along them4wp3 4+xsrdj 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 mjv:w 62miwx68e 8hjvf0 w2a welastic collision with another atom at rest. After the impact, the neon atom travels aw28m:v62wwmi j 8wxhf6av0w ejay 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 pe2dz8ne:qkf6;mtycu, 0e -elb; e vt6orfectly elastic collision with another atom at rest. After the impact, the neon atom trav;-e u6:kct nftd,2q0be e6lyeov8m;z els 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)(p rs5soq( *umgx; vo system shown in Fig. 7–38. Specify relativr( x 5u*mpoqg)os s(;ve to the left-hand 1.00-kg mass.    m

  The distance between a carb(8m8x0krqqbg ko 8x /xon 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 8d0 nfapc*/gxnky 1t+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 1+8g0n kcdax*/pyntf the front of the car, and three people sit in the back seat 3.90 m from the front? Assume that each person has a mass of 70.0 kg.    m

  A square uniform raft, 18 m by 18 m, of mass 6800 kg, is used as a ferrh9 ;btre/x-m6m lplj; yboat. If three cars, each of mass 1200 kg, occupy its NE, 6- me9hm/;b;lrljtxp SE, and SW corners, determine the CM of the loaded ferryboat.$X_{CM}$ =    m $Y_{CM}$ =    m

  Three cubes, of sidem)/ch5. hq3sstvu; hn 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 identical cases of tof4ajf qbc*rf p8-.e x6mato paste (see Fig. 7–40), each of which is a cube of length l. Find the center of gravity in the horizon-4b jr.8 f*fe6xafqcptal plane, so that the crane operator can pick up the load without tipping it.$X_{CM}$ =    l $Y_{CM}$ =    l

  A uniform circular plate of radius 2R has a circular hole of radiue v6r/cl ep4q3s R cut out of it. The center of the sl c6/r4qevp e3maller 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 proportion;p ) k3 yfqk69ie/47lvm2e, gnowl pnas are the same as those in Table 7–1, and calculate the mass of one of yel/ov wkk4q,gen n92;6fmipyla7)p 3 our legs.    kg

  Determine the CM of an outstretched arm using Table 7–1. b(3 narjt/z ;pp-as:e   % 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 *h8zolw q*/qlinevu9(h:,m j arm bent at a right angle. Assume that the person is 155 cm tall.lmhn q,8wlov*9e: hzju/i(*q $X_{CM}$ =    cm $Y_{CM}$ =    cm

When a high jumper is in a position such that hi ofgj(v*rm(:t s arms and legs are hanging vertically, r*(jfgm( :vto 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? Use Table 7–1.

The masses of the Earth and Moonl /1 ,b4wbak0k)eqoldvaz) 5g 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 (zffc4 h, zxc7on 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 head o: etpiyln 0tvkzlr.- 31,iwf:f mass 2.00 kg and a diameter 0.0800-i ki1 ,n3w p.f0rzytl l:e:vt 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?    cm

  A mallet consists of a uniform cylindricaw v-vplf nhk41/n: 4mgl head of mass 2.00 kg and a diameter 0.0800 m mounted on -lpk hv:gv n4w 4m1f/na 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 k6qzoapr l(91 mmgo- 8Example 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 stationaryk w)ebxao v loj83wl rm09t(42 with respect to thj tx)om l wlowa2039rk v8e(4be 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 passenger stops?

  An 0.145-kg baseball pitched horizontally at u)bsf-q)9cv1 h uvo.c strikes a bat and is popped straight 1ch c.o9-b vs q))vfuuup to a height of 55.6 m. If the contact time is 1.4 ms, calculate the average force on the ball during the contact.    $^{\circ} $

  A rocket of mass m traveling with 20mz6 c8roexn 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 shown i *e.g t9 v7r.insm6dmtn Fig. 7–43. Relative dimensions are also shown. Should the player be worried about this b* . trs7m m.gv69dienteing a “scratch shot,” in which the cue ball will also fall into a pocket? Give details.

  A 140-kg astronaut (inclu/m bi*7ovsii2sl*0y mding space suit) acquires a speed of 2.5m/s by pushing off with hoi msiy2/0m*b7 svl *iis legs from an 1800-kg space capsule.
(a) What is the change in speed of the space capsule?    m/s
(b) If the push lasts 0.40 s, what is the average force exerted on the astronaut by the space capsule? As the reference frame, use the position of the space capsule before the push.    N

  Two astronauts, one of mass 60 kg aa7eyq3 cj ,8uajktf0d/v-- g9n2z tnqnd the other 80 kg, are initially at rest in outer space. They then push each other apart. How far apart are they when the lighter astronatg,nzqjfv / 37ak qe9-td0c28 yj -unaut has moved 12 m?    m

  A ball of mass m makes a head-on elastic collision with a second ball (at rest) g ju+t hdw99 dqh6 *lwb(*l9dmand rebounds in the opposite direction with glwud6j* h ( ldtdm9*9 wq+bh9a speed equal to one-fourth its original speed. What is the mass of the second ball? $m_B$ =    $m_A$(Round to two decimal places)

  You have been hired as an expert witnessbu2gxf tsb8)w73djse79dg ( c in a court case involving an automobile accident. The accident involved car A of mass 1900 kg which crashed into stationary car B of mass 1100 kg. The driver of car A applied his brakes 15 m before he crashed into car B. After th7 s2sbeu 7b9dfgd 83tj(wx )gce 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 flight of concrete steps of total vejb lvzpb(zg 6c dzwl,/y67r0xi 1)g6 mrtical 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 ai/ b1gcgzw6 )j7(bzvp lzrx60dy 6ml, re 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 *xl, kl-k uo4 um:h8rzlll.yrb:5l(ggvq* c0 a 1.40-kg block of wood at rest directly above it. If the bullet has a mass of 29.0 g and a speed of 510m/s how high will the block rise after the bq k:b40l:hlg lzuxolm(g** vluklc85r .,r-yullet becomes embedded in it?    m

  A 25-g bullet strikes and becm+rpas1b 6cre.ra7p xlsbw5+m9 / id-9z 7 ymnomes embedded in a 1.35-kg block of wood placed on a horizo bar9zw+icy9l- xeprdnmm/6sp 7 mbr.a1+7s5 ntal surface just in front of the gun. If the coefficient of kinetic friction between the block and the surface is 0.25, and the impact drives the block a distance of 9.5 m before it 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, sit in a rowboat ofsx 6uwp e .5kg2,::hczcv/gxe mass 80 kg. With the boat initially at rest, the two people, who have been sitting at opposite ends of the boat 3.2 m apart from each other, now exchange seats. How far and in what direction will the boat move? The boask5cp:ue x6vghz/x,c2g. ew:t will move    towards the initial position of the 75 kg person(Round to two decimal places)

  A meteor whose mass was abbmosz t7o*dq+jh 2ga (b97diu (c.l: vout $ 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 fragmenu m)1 u4/x qko*oir6xats by an explosion. One fragment acquires twice the kinetic energy of)uor 6*x x1mo4a kui/q the other. What is the ratio of their masses?   

  The force on a bullet is given by x5 lw+ (kz-jgfthe 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 massesm( wf;zo7 qz 2k6x9tot $m_A$ = 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 radioactivelwlf 6lfc h4gap74z3 z0y into an alpha particle and a smaller nucleus. What will be the speed of this recoiling nucleus if the speed of thf4lwlz 40cahz 7pf6g3 e 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 (clak s 6dnvz.9kr:y target) 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=2.2kh f-r442o+sk2 rg46oy2 rubdmvwf ue8g 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 on mass m ifpvgib4*-m*ync4 , a7k oj/ xxd it is to rebound from M, slide up the incline,c bd 4xom y/gj7,piv4a* nk*x- stop, slide down the incline, and collide with M again?    kg (Let A represent mass m, and B represent mass M.)

  The gravitational slingshot effect. Figure 7–47 shows the plan 8eoym2 d9w-gyet Saturn moving in the negative x direction at its orbital speed (with respect to the Sun) of 9.6km/s The ma82 -me ogyd9wyss 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