We claim that momentum is conserved, yet most mov/-h8 9vtta3spo(plw;z ati / ving objects eventually slow down atlv8p9 psoia /wha3t-(v;/ tznd stop. Explain.

When a person jumps from a tree to the ground, what happens wt olj47hjwdl2d4g 3:j d z/r1to the momentum of the person upon3w2dz7w: 4jo4rj g1 dtll/hdj striking the ground?

When you release an inflated but untied balloon, why does itc6k2uia9j-y )q7) 2e c 1gbn.sowunnm kql o5, fly across the room2 y2c)qa los7ou5)b ui9enwn6 km-g c,j1n.kq?

It is said that in ancient times a rich man with a bgw/8omuwvy bu ) 7pq+c1ra( )gag of gold coins froze to death while stranded on a frozen lake. Because the ice was frictionless, he could not pushm7g)bu owuq/1yvgc w(a p8r)+ himself to shore. What could he have done to save himself had he not been so miserly?

How can a rocket change direction when it is far out in space andx .f72vk s3wla8s6h or is essentially in awa8v6 2 .o3hrfs7l kxs vacuum?

According to Eq. 7–5, the longer the impact time of an impulwp:b0xm/r q 23s5nqom lzy;r8se, the smaller the force can be for the same momentum change, and hence the smaller the deformation of the object on which the force actzw b mrx m503lyp2r :8n;/qsoqs. 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 riqtb.f/6ph gme f01cwffzr+; y,-2nd)w ) lpobgid as possible to withstand collisions. Today, though, cars are designed to have “c/tbw2 pf.ffdozelgw6bfr-c 0q 1),ym hn) p ;+rumple zones” that collapse upon impact. What is the advantage of this new design?

Why can a batter hit a pitched baseball fk28vzp6 -hkt f mgrmj*:uoy 32urther than a ball tossed in the air by o*r tz2 v2hpfj6 um8ygm-k:k3the batter?

Is it possible for an object to receive a la2(ee0q 1m*7znbujt .ls7 dnz;)vophr rger impulse from a small force than from a large force? Expla n b7)e2sej*mq;v(lzudz7 p nrt0h. o1in.

A light object and a heavy object have the sa5 mts369n3hc fs2h mhlf*92;ggaepqm me kinetic energy. Which has the greater momentumhf* 26mmh ntg 9hlpc9;23ssafe3g q5m? Explain.

Describe a collision in which all kinetic energyn65lw a9mmgkh-kl(f+ /v) gwd is lost.

At a hydroelectric power plant, water is directed at high speedxzn(x jh.: 6wf against turbine blades on an axle that turns an electric generator. For maximum power generation, should the turbine blades be designedjz:6( nw .xxfh so that the water is brought to a dead stop, or so that the water rebounds?

A squash ball hits a wap+ba /vnvy e3hul); a7ll 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 from a height h onto a hard steel plate (fixed v-;eoq-qy t y*to the Earth), from which it rebounds at very nearlyvt q- e;y-q*oy 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 m :zekd.)z 5 kjge+t,oload in your arms?

Why is the CM of a 1-m length of pipe at its mid-point, whereasc 3u6p/ jxywa7-:ejsz this is not true for y:x 73cpws-zy /u6jjea our arm or leg?

Show on a diagram how your CM shifts when you change from a lar j a7//8gkem 5;k5iya :i:re4ah1coyslk8bying position to a siteak m :7srg4;a1o/ c5i5k 8hkejiab ry:l8/ ayting position.

If only an external force can change h e(1 h9apdb uxabfpgsv2(0il. e+c 2.the momentum of the center of mass of an object, hgfpd+.ahc ( e2ab 1.9(isbelpxu2v 0how can the internal force of an engine accelerate a car?

A rocket following a parabolic path throu9trvp ewf -4tct*t6 9ogh the air suddenly explodes into many pieces. What can you say about the motion of this system of piec*p6 - t9f9wov4retttces?

  What is the magnitude of the momentum of 4dbx j* 3d(qilq,bv- :aj8yfma 28-g sparrow flying with a speed of $8.4 \; m/s$    $kg \; m/s$

  A constant friction force of 25 N ac)bn) ( ouwt9s)ntw /mvts on a 65-kg skier for 20 s. What is the sk)) s v tn)tum9bo(/wnwier’s change in velocity?    m/s

  A 0.145-kg baseball pitched at 39 m/s is hit on a horizontal line dridxu l6jlma57j tj+98 qve straight batlj a8l5x 6duqjm+7j9ck 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 package out horizhexd7 pqn /9,ni32nusontally with a speed of 10 m/s Fig. below Calculate the velocity of the boat immediately after, assuming it was initially at rest. The mass of the chq/d n, supn73e9hnix 2ild 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, xv)pj;b4o cak+tl+s on a rocket, given that the propelling gases are expelled at a rate ofl t po;+ab4v sxc)k,+j $1500 \; kg/s$ with a speed of $ 4\times10^{4 } \; m/s$ (at the moment of takeoff). F =    $\times 10^7 \; N$

  A 95-kg halfback movibr50bnt6o(v2t; ve sang 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 xg- +7yd: vmucalevel frictionless track with a constant speed of 18m/s A 535mxy -v+cd7g u:0-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 atq nn7hz*fy qkdmc8n;/yq*p0 - $15 \; m/s$ 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 yf+jtroc8g ,wp0s:2xq y/ h exo8a-s,at speeds of 100km/h If the air strikes a person at the 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 maxip /8oh:o g,s fe+x jxa- r0y2qcsyw,8tmum force of friction $\mu\approx1.0$ between the person and the ground, if the person has a mass of 70 kg.    N
$F_{on person}$  ----待选择----<> $F_{fr}$

  A 3800-kg open railroad car coasts along with a constant speed of 8.6m/s on a la 78b0oil:9y7*htpt,egeyd c2mj q i8evel track. Snow begins to fall vertict7p hi8 ct8q jmeo :b29l7da*yg iey0,ally 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 em k5 pw2 to e(ke2wskgw7i 7yr*;3ee3qbits an alpha particle in the direction of its velocity, and the remaining nucleus slows to 350m/s If the alpha particlwise (5or k;yk p *ebeqw737g322wekte has a mass of 4.0 u and the original 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+ bt*+v gjv6mrhbfk2e j2,8rn a 2.0-kg block of wood and emerges cleanly at 170m/s If the blockt j6r,j 2h+b kbv8rmf+en2g* v is stationary on a frictionless surface when hit, how fast does it move after the bullet emerges?    m/s

  A 975-kg two-stage rocket is traveb9x0i 5oc5fuo ling 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 318i0p,(s v :d+ jh8efz aq1w6zun0 kg is traveling in outer space with a velocity of 115m/s To alter its course byja+p, qiev dzn0wh18( f6 uz:s 35.0 $^{\circ} $, its rockets can be fired briefly in a direction perpendicular to its original motion. If the rocket gases are expelled at a speed of 1750m/s how much mass must be expelled?    kg

  A golf ball of mass 0.045 kg is hit off the tee at a speed of 45m:nvoqt) 9qltiy.0qo. 3 7gpe m/s The golf club was in clg3qi7. :.mytopvt0) qe on9qontact 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 velocm:va(m1kl96i jen-u8z,xzm k ity of 8.5m/s and comes to rest in a time interval of 8.jmm6imn,ka1lz 8zvux9-:k ( e0 ms. (a) What is the impulse given to the nail?    kg*m/s
(b) What is the average force acting on the nail?    N

  A tennis ball of mass m=0.06kg and speed v=25m/s strikes a wall az*6f4(/uwkcirhdl ik -2eb i0 t 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 th3ggxgnv smahe*azr8, v0 n 2*7e crashworthiness of new automobile models. Cars are tested by smashing them into fixed, massive barriers at 50km/h (30 mph). A new model of mass 1500 kg takes 0.15 s from the time of impact until it is brought to rest. (a) Calculate the average force exerted on the car by the barrier. ,g3 8*nv7 0 sra 2emzgng*xvah$\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/sxey el8,7 f0 w,/duwof to the east and is stopped in 0.75 s by a head-on tackle by a tackler80 oxlw/w,def7u ,yfe 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 tennishg:2/0ccszl7 b6bee l ball (mass 0.060 kg) points in the +x direction and is given by the graph of Fig. 7–33 as a function of 2l6ge0b7zslcc:e h/btime. 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 9tcal0c qi-,vlx8sheea . 5*xa 75-kg 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 .90caaei c-8*he,tq x xs5llvm 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 unz;3u5,u ptms t 0rp6of collides head-on wittps53,0u6mrn;upzu th 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 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 witx vql73w j.ul9h a speed of 3m/s has a head-on collision with a 0.900-kg puck initially at rest. Assuming a perfec ljxw v37ul.q9tly 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 perfec18+2bzheg s y 02 wu65zyb+z or:xpkfin+fup.tly elastic head-on collision. If one ball’s initial speed was 2m/s and the other’s was 3m/s in the opposite direction, what will be their speeds after the collision?(Let A represent the ball moving at 2.00 i :uyh 0+xf pn+o5 eb2gszzfyk821.6uwbrpz+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 head-on witkgs,dk.s(- 1 -hqywith a 0.090-kg ball initially moving kh- qy1.sg-(,swtik d 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 wit1eo*pzb1)mzs hiv/ ez2xt /g3h a speed of 8.5m/s collides head-on and elastically with another ball initially at rest. Afterwa/ b*1zt evsz) g2o/mp1hz3 xeird 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 co nak7lzh j*o92llide 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 dzolka7hj* 9n2 ifferences 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 coll;ojapj*8yy(ebv /h/ cision with a second ball initially at rest. The second ball moves off with half the original speed of the firsbyhj aej;pcvy/*8 ( /ot 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 friction y r s/aiiq7ac:.8z)saxo)o2cless incline as shown in Fig. 7–35, and elastically strikes another cube at the box)cz/ q7iaa.ai:ry8 )sso2octtom that is only one-half its mass. If the incline is 30 cm high and the table is 90 cm off the floor, where does each cube land? [Hint: Both leave the incline moving horizontally.]$\Delta x_{m}$$\approx$    m $\Delta x_{M}$$\approx$    m

ake the general case of an object of s /-fgn9n8x fkmass 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 experimen2iu5 (uoze1kkt, projectile 1 results in a maximum height h of the pendulum equal to 2.6 cm. A second projectile causes the the pendulum to swing twice as h(k u51uzkie2 oigh, $h_2=5.2\mathrm{cm}$ 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 3.6xsy2 o*:ds;1dqlroax u1w,i )-kg pendulum hanging on a 2.8-m-long string, which makes the pendulum swing upward in an arc. Determine the vertical and horizontal comaoo21sq;y l, d i*s)w1 xxrd:uponents of the pendulum’s displacement.vertical$\approx$    m horizontal =    m

(a) Derive a formula for the fraction of kinetic energy lo :ufxtz 9f;xi(zw17wsst, $(\Delta\mathrm{KE/KE})$ for the ballistic pendulum collision of Example 7–10. (b) Evaluate for m=14g and M=380g

  An internal explosion breum,w+,d5ap: fra mt/iu, y5njaks an object, initially at rest, into two pieces, one of which has 1.5 times the mass of the other. If 7500 J were released in the explosion, how much kinetic energy did each piece acquire? (Let A represent the heavier particle, and B represent the lighter partita:rf dy/nja 5mi ,u5wm+p ,u,cle. ) KE'$_A$ =    J KE$_B$ =    J

  A 920-kg sports car collides into the rear end of a 2300-k caw 6b8sldcr,-+ 9-bekw:idng SUV stopped at a red light,a9brnsicwcw +-8- kdd b :6le. 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 sports car, and B represent the SUV) $\approx$    m/s

  A ball is dropped from a height of 1.50 m and rebounds to a height of 1.2;6peqzv +m/yt ku9g +kk9 kgb50 m. Approximately how many rebounds will the ball make before losing 90% of its enerk 5tkk/ k mup g9zgy;6+e+9qvbgy?   

A measure of inelasticity in a head-on collision of two onsfszm )ami1y-sgs di(2)g86bjects is the coefficient of restitution, e, defined a6 (ag)-nz21ssyimg)mf 8 dssis$e=\frac{\nu_\mathrm{A}^{\prime}-\nu_\mathrm{B}^{\prime}}{\nu_\mathrm{B}-\nu_\mathrm{A}},$
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 *b,s , hb wby)+,liamyinto two 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 y+b,l,sih*b)ma w,by reassembled. The reassembled block is set on a rough-surfaced table, and the fuse is lit. When the firecracker explodes, the two blocks separate and slide apart. What is the ratio of distances each block travels? ----待选择----1/91/101/81/6 

  A 15.0-kg object moving in the +x direction at 5.5m/s collides head-on wit92(tmtdb8 q/o) ud yvlh+dir -h a 10.0-k+d tb8r 9h qlmdoi y-d()t/2vug object moving in the -x direction at 4m/s Find the final velocity of each mass if:
(a) the objects stick together;   m/s
(b) the collision is elastic; v'$_A$ =    m/s v'$_B$ =    m/s
(c) the 15.0-kg object is at rest after the collision;   m/s ----待选择----not reasonable reasonable 
(d) the 10.0-kg object is at rest after the collision;   m/s ----待选择----not reasonable reasonable 
(e) the 15.0-kg object has a velocity of 4m/s in the -x direction after the collision. .   m/s ----待选择----not reasonable reasonable 
Are the results in (c), (d), and (e) “reasonable”? Explain
( Let A represent the 15.0-kg object, and let B represent the 10.0-kg object.)

  A radioactive nucleus at rest decays into a second nucleus, an e(e l m..w,okwmlectron, and a neutrino. The electron and neutrino are emitted at right angles and hm,k (ml.ew.w oave 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 6pyh2n- 0f wpc$m_\mathrm{A}=0.400$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 inelastics fc-lzodi6u (t9z9z: collision between two objects of equal mass, each having initial spe9id tu zz9s f-6(:lcozed the two move off 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 origij5fyn6w wza; /n 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 fzwy na5;6/jw 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) maj8t ofxc,vni4mv3o5 /kes a perfectly elastic collision with another atom at rest. After the impact, the neon atom travel 8 /45xi3njcv,vtoom fs 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 nr 5:9+-clqrtetb3/nqpitb*(eqpd7 another atom at rest. After tbpl r t/9tn c d5e+q*ite: 3(r-pq7nbqhe impact, the neon atom travels away at a 55.6 $^{\circ} $ angle from its original direction and the unknown atom travels away at a -50 $^{\circ} $ angle. What is the mass (in u) of the unknown atom? [Hint: You can use the law of sines.](Let A represent the incoming neon atom, and B represent the target atom) $m_B$   u

  Find the center of mass of the three-mass z12koryz )jxkw m8h) -))wwkv system shown in Fig. 7–38. Specify relativkw2rkwwz)om z1-hk8v )x)y)j e to the left-hand 1.00-kg mass.    m

  The distance between a6o. o c;k;k(tvys9gne3 tc;hd carbon 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 be86ue:vuwpa n5 hind the front 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 the car, and three people sit in the back seat 3.90 m from the front? Assume that each person has a m au w8nv5eu6:pass of 70.0 kg.    m

  A square uniform raft, 18 m by 18 m, of mass 6800 kg, is us5.ttgc4p -j 6lx 7u/zbmp6cxned as a ferryboat. If three cars, each of mass 1200 kg, occupy its NE, SE, and SW corners, determine the CM of the lo.j5x l7cmg/664 xptcz -putnb aded ferryboat.$X_{CM}$ =    m $Y_{CM}$ =    m

  Three cubes, of sides x5ji hh,1(l cv*oxekvr f a5)+$l_0$,$2l_0$, 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 hm+fa,ag5: b phas a load of identical cases of tomato paste (see Fig. 7–40), each of which is a cube of length l. Find the center of gravity in the horizontal plane, so that the crane operator can pick upbm: + pa,hfg5a the load without tipping it.$X_{CM}$ =    l $Y_{CM}$ =    l

  A uniform circular plate of radius 2R has a circu;/p4)ru u feqq) t(mjelar 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 cen (4r)qpf umq)/ ut;jeeter of mass of the plate? [Hint: Try subtraction.]   R

  Assume that your proportions are the sa .lz7unia3-1i1z5as h:uy sspme as those in Table 7–1, and calculate the masa 75u:n1lzzau iis13 .sh -ypss of one of your legs.    kg

  Determine the CM of an outstretcih jj av;142jghed 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 th qmmt1fbqhyv3i )5+1ce CM of an arm bent at a right angle. Assume t1qqcmbi)5y3+th m1v fhat the person is 155 cm tall. $X_{CM}$ =    cm $Y_{CM}$ =    cm

When a high jumper is in a position such6zdum ba)0be u a)neu/4++ esu that his arms and legs are hanging vertically, and his trunk and head are horizontal, calculate howu nz)uad)eb/e s6e 0+ uua4bm+ 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 Mav0cpp tq) ,-voon 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 frictionless ice680/zm d: 3z7,lefyhb slo6fylbkw/o.
(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.y z lo/j )o5 vdc86;)hgoz.bdk00 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 of the handle is the po/ vol8 z)6.)od5zjgh bc ko;dyint that will follow a parabolic trajectory?    cm

  A mallet consists of a uniform cylindrical head of mass 2.00 kg and a diameter b 65q ,ug39x7bgnom rf0.0800 m mounted on a uniform cylindrical handle of mass 0.500 kg and length 0.240 m, as shown in Fig. 7–42. I, b6or5mbg x9uf7 n3qgf 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 Examplyr snwrlj.fu ;4w-wf3 a 4*qsfu:3d: ze 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 its8h q 0cm+t: +g4x j/ijwh)vssg 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 tqvis)+jc:mg gh 4s j+xt/0w8hhe balloon then move? What happens if the passenger stops?

  An 0.145-kg baseball pitch9k, 8if4pb ocled horizontally at strikes a bat and is popped straight up to a height of 55.6 m. If the contact time is 1.4 ms, ca8i l, p9c4kfbolculate the average force on the ball during the contact.    $^{\circ} $

  A rocket of mass m travelinf jrd y:bq0h 9 qv/;7zz/c4gdmg with speed $v_0$ along the x axis suddenly shoots out fuel, equal to one-third of its mass, parallel to the y axis (perpendicular to the rocket as seen from the ground) with speed 2$v_0$ Give the components of the final velocity of the rocket.$P_x$: v'$_x$=    $v_0$
$P_y$: v'$_y$=    $v_0$

A novice pool player is faced with the cornvx4h h(s) 0uuier pocket shot shown in Fig. 7–43. Relative dimensions are also shown. Should th uh4ux0(ihvs) e 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 mcw ;kng f;ha*9vu+bhzr ;a,9 pushing off with his +rfu, v ac bg;*9;hn9kz;hmawlegs from an 1800-kg space capsule.
(a) What is the change in speed of the space capsule?    m/s
(b) If the push lasts 0.40 s, what is the average force exerted on the astronaut by the space capsule? As the reference frame, use the position of the space capsule before the push.    N

  Two astronauts, one of mass 60 kg and thky.hiff 5hl:+ e other 80 kg, are initially at rest in outer space. They then push each other apar f5k lhhyi:.f+t. How far apart are they when the lighter astronaut has moved 12 m?    m

  A ball of mass m makes a heaib/p4q +0 ey*bi7rzmtnjc j (9d-on elastic collision 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 thezn(4jrtiim+* 9/07b cjy qb ep second ball? $m_B$ =    $m_A$(Round to two decimal places)

  You have been hired as an expert ken fxhqnb1 f l d8aew54bn+657s.8om tqt9*switness 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 m8em5sn n 4b+9q75 86txqef*hfoast dkn .b1lw 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 flight of coo 980*3r8krz n7 ljzmy inx;sencrete steps of total vertical height 4.00 m. The ball hits four times on the way down, each time striking the horizon ; rijzm 3znsn*09 ek7ox8r8lytal part of a different step 1.0 m lower. If all collisions are perfectly elastic, what is the bounce height on the fourth bounce when the ball reaches the bottom of the stairs?

  A bullet is fired vertically into a 1.4yh r;lca00 1p lf-jy+e0-kg block of wood at rest directly above it. If the bul0lcpf+yhe j y01-a;rllet 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 embedded in a 1.35-kg block of wood placedl(sr4 hwhfxbz494 6 /b4ogx hd on a horizontal surfax4 hrbb ow9hl4x6(4 /hg4zf sdce 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 qe/- yakyl/ x5kg and the other of mass 60 kg, sit in a rowboat of mass 80 kg. With the boat initially at keyl-qy//5 ax rest, the two people, who have been sitting at opposite ends of the boat 3.2 m apart from each other, now exchange seats. How far and in what direction will the boat move? The boat will move    towards the initial position of the 75 kg person(Round to two decimal places)

  A meteor whose mass was a ria:vibg875 r7y ,jnhbout $ 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 broo.1v jg)fyhrz( +bg1u8xxgk5z *i/raken apart into two fragments by an explosion. One fragment acquires twice the +o1g)xigv ax 1f./uzjg(b r *rk8zyh5kinetic energy of the other. What is the ratio of their masses?   

  The force on a bullet ifcnbz1b h,8:c 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 massesx8 y c+j ciy sz5l/r:bzv2 x;:xhlp5*p $m_A$ = 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 at8bkxsg jq w85m4d*qh 5 rest decays radioactively into an alpha particle and a smaller nucleus. What will be the speed ob8q s j*qh54mkx5gw d8f this recoiling nucleus if the speed of the alpha particle is $ 3.8\times10^{5 }$m/s Assume the recoiling nucleus has a mass 57 times greater than that of the alpha particle.    m/s

  A 0.25-kg skeet (clay tarrrjf5dzj 9ii s86p)s93bbo 6x,g34 b p4yuqi tget) 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=2.2kg slides down a 30.0 2*-ked yggnl7.c1 dyw $^{\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. 7–4m (wxl;s/* coa6), what is the upper limit on mass m if it is to rebound from M, slide up the incline, stols( caw m/x*o;p, slide down the incline, and collide with M again?    kg (Let A represent mass m, and B represent mass M.)

  The gravitational slingshot effect. Fi ;dhaky*8hy g*gure 7–47 shows the planet Saturn moving in the negative x direction at its orbital speed (with d; hg*8y* yhakrespect 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