We claim that momentum is conserved, yet most movi4x:dewt pg rc. whyp*h5e-g as12+pq :ng objects eventually slow down hgw24p.*yerg1p: d tqcp-ae5 : hxsw+and stop. Explain.

When a person jumps from a tree to the ground, what happens cwp.q dmf/yys 8l ,b8qly ;-.wkec2;e to the momentum of the person upon striking the ground ;l;sq wkec.yw2pyfe y cb/8,8l mqd.-?

When you release an inflated but untied balloon, why does it fly across the rouiso; uw -4cila.6, yxom,l6oc syx . ui-ua;4wi?

It is said that in ancient times a ri s l4f-uno/ng1m npk/,ch man with a bag of gold coins froze to death while stranded on a frozen lake. Because the ice was frictionless, he could nopolsunn/,/-1fkn4 g m t push himself to shore. What could he have done to save himself had he not been so miserly?

How can a rocket change direction when it is far out in space and is emmfg17en 9d hegum/ -: n9+noyssentially in e g9n-fnng+memy7 :1o ud9 h/ma vacuum?

According to Eq. 7–5, the longer the impact time of an u dcm ezh0u.z-,:4ojsavi5c 9impulse, the smaller the force can be for the same momentu. vz0c u:9,h4smeuao ji c-dz5m 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 collisions.ja4,vo- gf z1fiw/ 4ab Today, though, cars are designed to have “z g,bj41aviw /o-a4ffcrumple zones” that collapse upon impact. What is the advantage of this new design?

Why can a batter hit a pitched baseball further 6gw7rhc:9azu than a ball tossed in the air by the ba :rwa6gh7u cz9tter?

Is it possible for an qouv:hn2 70 q sook4f1pxrxxq2v 6 :1vobject to receive a larger impulse from a small force than fr6vsfxx27u1o2r1xnq 4v: h o0 q:qvokpom a large force? Explain.

A light object and a heavy object have the sx4ghhpm(s q5c01w(ov nufgmk 3u g*;(ame kinetic energy. Which has the greater m u*gng1 c 35xpu0wvq (so(gh4;hfm (mkomentum? Explain.

Describe a collision in whichcy+ 8mn.yeiaup2t(-/ hs o2tf all kinetic energy is lost.

At a hydroelectric power plant, water is directed at high spea: p7wiuv/k6a ed against turbine blades on an axle that turns an electric generator. For maximum power generation, should the turbine blades be design67: apkvuw/a ied so that the water is brought to a dead stop, or so that the water rebounds?

A squash ball hits a wall at a orglvd:3l)8dxnf o*/ 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 + lyydxek2 2k/( qjxw: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 consiy+xlkyxj: 2(dq 2/ wkeder 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 ahkw/tg6rl q4, 8a m-obrms?

Why is the CM of a 1-mhfuhysi ( ) vtx8+nwyh.nr424 length of pipe at its mid-point, whereas this is not truenf nh()842 w.uxth+ v4yyhisr for your arm or leg?

Show on a diagram how your j;x5 a.qsz9k 9l/ ;xk w(31nl6fj j1adsmmzeqCM shifts when you change from a lying position to a a 6 qj kzx m/;519 al zj(;1fsj3exq.ndks9mwlsitting position.

If only an external force can chlrmc,-, f: k4vfjb,eeange the momentum of the center of mass of an objectle,f,vfk c-e: mbr4 j,, how can the internal force of an engine accelerate a car?

A rocket following a parabolic path t d8q5r+dfcm 6pco21h xhrough the air suddenly explodes into many pieces. What can you say about the motion ofo5pm fh6dcr xc2d8+ 1q this system of pieces?

  What is the magnitude of the momentum 6 mz1q/1e g tc4,lyklifevw.vz (po/; of a 28-g sparrow flying with a speed of $8.4 \; m/s$    $kg \; m/s$

  A constant friction force of 25 N acts on a 65-kg skier for 20 s. What is t-rkwjf fv o3w3(3;( (rylucqxhe skier’s change in v(;3 oyjqwwf3 (rrx(lu -kc3fvelocity?    m/s

  A 0.145-kg baseball p9hyth32 y*pb0;a m-xnyev(ui itched at 39 m/s is hit on a horizontal line drive straight back toward the ait-y(ph*; bymu0nh 3yv2x9e 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 horizontally with a speed of 10 vz0f70csq;te q * och0i+ds;ir +uk1x 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 txc7v ;d0s tu ;f1 00ci+o*ezkhrq+sqihat of the boat is 45.0 kg. Ignore water resistance. The magnitude of the velocity of the boat is    m/s

  Calculate the force exerted on a rocket, given that the propelling gases are expdzys 7zd.gud8s,/ ri5elled ag,/ 8dyid5z.zsr su7dt a 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 w.dvmd er9opxc e0 mr.a2/x(1at $4.1 \; m/s$ 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 aleve/z+cb xaic+1 el frictionless track with a constant speed of 18m/s A 5350-kg load,initially at rest, is d1 / +cxa+zecbiropped onto the car. What will be the car’s new speed?    m/s

  A 9300-kg boxcar traveling at 2itdj ,4)zk ue3g9m c ,kf)dmj$15 \; m/s$ 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,p)l pj:3o )jdv winds can whip horizontally at speeds of 100km/h If the air strikes a person at the rate of 40kg/s per square meter and is brought to rest, estimate the force of the wind on a person. )j )vplj p3o:dAssume 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 8.6p lp6kk39;mu1g :yax nm/s on a level track. Snow begins to fall vertically and fills the cargkyaku m1pn;:6p9x3 l 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 initiaxyhnbii6b3b6m t: k3 - 69yqrglly moving at 420m/s emits an alpha particle in the direction of its velocity, and the remaining nucleus slows to 350m/s yrb b6 6hi :-b93gimxqt6ynk3If the alpha particle 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 a 2.0-kg block of wood and eme9bcq-834wf ne tk+ odarges cleanly at 170m/s If the block is stationary on a frictionless surface when hit, how fast does it move after the no eq4a 3wk-f +dt9c8bbullet emerges?    m/s

  A 975-kg two-stage rocket is traveling gqfg- b.lu w9:at a speed of $5.80\times10^3\mathrm{~m/s}$ with respect to Earth when a pre-designed explosion separates the rocket into two sections of equal mass that then move at a speed of $2.20\times10^3\mathrm{~m/s}$ relative to each other along the original line of motion. Let “A” represent the upper stage (that moves away faster) and “B” represent the lower stage.
(a) What are the speed and direction of each section (relative to Earth) after the explosion? $v'_A$   m/s  ----待选择----away from the Earthtowards the Earth  $v'_B$   m/s  ----待选择----away from the Earthtowards the Earth 
(b) How much energy was supplied by the explosion? [Hint: What is the change in KE as a result of the explosion? $a\times10^8$ a =    J

  A rocket of total mass 3180 kg is traveling in outer space with a velocity of+(uud8y .,pgg 7t6b5vjm1kqse5s ajzjrv,n* 115m/s To al,muy, zggjvk d65ap qtnv8 1 s+. *j5besur7(jter 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 thszg.3n39sk-t5b5a:9uhxh a qbr ; f ofe tee at a speed of 45m/s The golf club w59za5;n.k or3bu s -fxgqahh9: 3sftbas in contact 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 bd2 c)lq9:uyda time interval of 8.0 ms. (a) What is the impulse given to the nail?:)yl2cd9dq bu    kg*m/s
(b) What is the average force acting on the nail?    N

  A tennis ball of mass m=0.06kg and speed v=25m/s strikes a wall at a 4+iq/,/5 vvh )gavoyoq5 $^{\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 engi47csjh1z9h m t9lvn7nvht) k,neer in charge of the 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 untilv,l h)7sthj471nknzmv 99hc t it is brought to rest. (a) Calculate the average force exerted on the car by the barrier. $\approx$$a\times10^5$N a =   
(b) Calculate the average deceleration of the car.    m/$s^2$

  A 95-kg fullback is running at 4m/s to the e7ud gnp4pe36iast and is stopped in 0.75 s by a head-on taci4p7g pe3 u6dnkle 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:da(,cya vc5:yek+ q f tennis ball (mass 0.060 kg) points in the +x direction and is given by the graph of Fig. 7–33 as a function of time. Use gr:yf k5qc,dy+ecava( :aphical methods to estimate
(a) the total impulse given the ball    N*s
(b) the velocity of the ball after being struck, assuming the ball is being served so it is nearly at rest initially.    m/s

  From what maximum height can a 75-kg person jump without breaking the lower 5k5( bcknlgadh(lmtubau,u )*t . ;y 3leg bone of either leg? Ignore air resistance and a) l a unk,h55uc.ytkd bgtl ;3muab((*ssume the CM of the person moves a distance of 0.60 m from the standing to the seated position (that is, in breaking the fall). Assume the breaking strength (force per unit area) of bone is $170\times10^6\mathrm{~N/m^2}$ and its smallest cross-sectional area is $2.5\times10^{-4}m^2$ [Hint: Do not try this experimentally.]    m

  A ball of mass 0.440 kg moving eastp:t 4 5czrl+6yqpxd/k (+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 directrpt c/ z kxd6l:45qyp+ion 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, niq y8.:*bjdmj-z 6i2vlr f.wmoving east with a speed of 3m/s has a head-on collision with a 0.900-kg puck initially at rest. Assuming a perfectly elastic collision, what will be the speed and direction of each object after the col-.6y*bnwr zqm.vl2idi f:8jj lision?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 o2ga-kcy5 ab+b n,0kta perfectly elastic head-on collision. If one ball’s initial speed was 2m/s and the other’s was 3m/s in the opposite direction, what will be their speeds after the collision?(Let A represent the ball moving at 2.00 m/s, and call that dir-b b2ygoaknka0+ct, 5ection 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 with a 0.n,or 85hbq .xc090-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.,n8hcox5q rb 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 m q;5to. ywow*qr;6goc0:b xd9l 2nqmboving with a speed of 8.5m/s collides head-on and elastically with another ball initially at rest. Afterward the incoming softbarxlbo0 dw*q.w 2q;c:m;ngq9toy 5bo 6ll 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 ridoyjyc2;a7gwwk h98- ie 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 jk9g7hi; w a2c-y8woymass. 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 collisx8 hgfi*j mkq)*qx ik:ol4 6q6ion with a second ball initially at rest. The second ball moves off with half the original sp8q:qh)o k6gjlfi*qxm 6ix k*4eed 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 d* ch6cog6s(e :wn,xd+ jw ewuycf u pt;c249*oown a frictionless incline as shown in Fig. 7–35, and elastically strikes another cube at the boonc( xjh;y6*: spe29fedc og wucw cw,t*4+ u6ttom 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 objec4yth-1leml oi47+hgtt of mass m$_A$ and velocity v$_A$ elastically striking a stationary object of mass head-on. (a) Show that the final velocities v'$_A$ and v'$_B$ are given by$v_{\mathrm{A}}^{\prime}=\left(\frac{m_{\mathrm{A}}-m_{\mathrm{B}}}{m_{\mathrm{A}}+m_{\mathrm{B}}}\right)\nu_{\mathrm{A}},v_{\mathrm{B}}^{\prime}=\left(\frac{2m_{\mathrm{A}}}{m_{\mathrm{A}}+m_{\mathrm{B}}}\right)\nu_{\mathrm{A}}.$(b) What happens in the extreme case when m$_A$ is much smaller than m$_B$ Cite a common example of this. (c) What happens in the extreme case when m$_A$ is much larger than m$_B$ Cite a common example of this. (d) What happens in the case when m$_A$=m$_B$ Cite a common example.

  In a ballistic pendulum experiment, projectile 1 results in a maximum height h zaqz+f jggs +v; (v1.kof the pendulum equal to 2.6 cm. A second projectile causes the the v1v fj+k .q(szgg az+;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 a 3.6-kg pendulum hami 4l:;7vm7u/lwg+gq3umdx rnging on a 2.8-m-long string, which makes the pendulum swing upward in an arc. Dete:/7+m immg 3xu wg;7rd4ulvqlrmine the vertical and horizontal components of the pendulum’s displacement.vertical$\approx$    m horizontal =    m

(a) Derive a formula for the fraction of kinetic enermc90z x 95046s+buyjvcxg aqi gy 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 breaks an object, initially at rest, into two piecesha6wy 84mplc9 , 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 m6l4h9py8 wacrepresent the lighter particle. ) KE'$_A$ =    J KE$_B$ =    J

  A 920-kg sports car collides into the rear end of a 2300-kg SUV s. qoaz:m+(m2yj+v ov)jajg r1 topped at a red light. The bumpers lock, the brakes arej. 2(++gmmrqy)zjav j1ao:ov 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 1.50l 1v5+9 ju fuohru: 40-bifhek m and rebounds to a height of 1.20 m. Approximat-4jf:ku o9 1uel0hvb+ 5uhr fiely how many rebounds will the ball make before losing 90% of its energy?   

A measure of inelasticity in a head-on collision of two objects is t0 s;hjbh* m1hhhe coefficient mh ; jb1h*s0hhof restitution, e, defined as$e=\frac{\nu_\mathrm{A}^{\prime}-\nu_\mathrm{B}^{\prime}}{\nu_\mathrm{B}-\nu_\mathrm{A}},$
where $\nu_\mathrm{A}^{\prime}-\nu_\mathrm{B}^{\prime}$ is the relative velocity of the two objects after the collision and $\nu_\mathrm{B}-\nu_\mathrm{A}$ is their relative velocity before it.
(a) Show that e=1 for a perfectly elastic collision, and e=0 for a completely inelastic collision.
(b) A simple method for measuring the coefficient of restitution for an object colliding with a very hard surface like steel is to drop the object onto a heavy steel plate, as shown in Fig. 7–36. Determine a formula for e in terms of the original height h and the maximum height h’ reached after one collision.

  A wooden block is cut into two pieces, one with three times the mass of thpqb:;q go,:v*l30xnu 0b3bn;tzx zwh e other. A depression is made in both faces of the cut, so that a firecracker can b ;b bzl3hoq3*nzgnx0:qxv:wtu ,p;0 be placed in it with the block reassembled. The reassembled block is set on a rough-surfaced table, and the fuse is lit. When the firecracker explodes, the two blocks separate and slide apart. What is the ratio of distances each block travels? ----待选择----1/91/101/81/6 

  A 15.0-kg object moving in the +x direction at u+e 3ig e+ 5-zsx1lffu9v9sym 5.5m/s collides head-on with a 10.0-kg object moving in the -x direction at 4m/s Find the finav9 f ufui gee 3x-1m5+l9+syszl 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 ele oi9sgpfoubi:) /5vc- ctron, and a neutrino. The electron and neutrino are emitted at right angles and have momenta -iuso:g c o 95bvfi/)pof $9.30\times10^{-23}kg\cdot m/s$ 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 mas b t29ij0au z 5moah0nma.r*b-s $m_\mathrm{A}=0.400$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 inelasti0jrq7 , yw6pgfc collision between two objects of equal mass, each having initial speed j0 ,7fw6rqg yp 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 od2;59iu9u2 -k :un; xdoinhm n -ci;pgzk8dzz rigin 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 pgm:2dn u zihz;x-d; kn8u2k i i99 n5co-u;zdthe 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 elastiz ;2 p+gi2; xnfj;xuaic collision with another atom at rest. After the impact, the neon atom travels away;2npag; zfx2u+j i ;xi 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 perfecmzk j2/l1*1l 4t lz .zm(glrobtly elastic collision with another atom at rest. After the l4llz t/m*oj 2z.k1bglrm(1 zimpact, 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 oy2egvuc.otyc,ie + wku e (z1;g-5-q af the three-mass system shown in Fig. 7–38. Specify relative to the left-hand 1.00-uc+ k - ,gv(zc eo e.y25yu-iwt1qa;egkg mass.    m

  The distance between 3itrrslgg z;( n7y;i8np)o/znp* n5h a 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 ca n/ut4t;0+dhv+pqsqir is 2.50 m behind 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 eacstun0iqp +vdq+ ;4ht/ h 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 ferryboat. I*ohgvv,8 k; m6+b i+tegd+ aaif three cars, each of mass 1200 kg, occupy its NE, SE, and SW corners, determ+*v,g+i t8ve6 ;g dam+hakb oiine the CM of the loaded ferryboat.$X_{CM}$ =    m $Y_{CM}$ =    m

  Three cubes, of sidesdjh4u+ifc 5: p $l_0$,$2l_0$, 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 casest r7hf/d;y b+ta-jl/a of tomato paste (see Fig. 7–40), each of which is a cube of tl7;/j ytda+ra/-h fblength 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 circular hole of radius R cut dn;yk(qv (fd6out 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 thv( ;(fk6nqy dde position of the center of mass of the plate? [Hint: Try subtraction.]   R

  Assume that your proportions are the same as those in Table 7–1, and c)2z2zl b4pw rtalculate the mass of one of y2l4zb2w)rpz t our legs.    kg

  Determine the CM of an outstretched arm using u4:hij;p(tob x4*ifr-ose m . 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 bent at d/4h/xolf 3ftf+nxi*a right angle. Assu /l xfoht/3f4f dn*+ixme that the person is 155 cm tall. $X_{CM}$ =    cm $Y_{CM}$ =    cm

When a high jumper is in a position such that his arms and legs are hangin)ju2j j6hu1/zjde 7f fg verticjj uj/)761zhjed ff2u ally, 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 Moo2 x-t qm.80 /1stgupv8aew4w )fk aypon 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 y*.-mla x fqc6 khnfp :;xq/lrv19kneyk) 6f;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 uniform cylindrical head of mass 2.00 kg and a /vqsxo2+y8 n+uqu/i(p2 zyri 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 tiuo+yv/rn 8i/uqpx2 z+( 2 yqshe handle is the point that will follow a parabolic trajectory?    cm

  A mallet consists of a uniform cylindrical head of m;gsfxj,bt m. r67k+nm4 4kds9t oi*mrass 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 tosse d7tm rkfm.;ng4*o ,9ts xr4+6mksbijd, 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 E5e;w da-y)pbp: x(bm qxample 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 th; l+ 6s wzl;vo82z-*ghbar wfte 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. Wilz ;ta;-gf b2row6zvs l*+h w8th 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 atbjcjra b) i3.2rkd)c2bc )2and is popped straight up to a height of 55.6 m. If the contact ta)3cd2 2jbbb)2ij. rccrk at) ime is 1.4 ms, calculate the average force on the ball during the contact.    $^{\circ} $

  A rocket of mass m traveling with speedp,v(l2c *kub :gm ;qja $v_0$ 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 in Fig. 7–4zcfby( j*e8j73. Relative dimensions are also shown. Should z f7bejc8* jy(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 sp jftoc+:+ l8xbeed of 2.5m/s by pushing off with his legs from an 18+ftbl:xc+j 8o00-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 oth ag5 bdfii8 +;rn3ua.ca)hw t(er 80 kg, are initially at rest in outer space. They then push each other apart. How far apart are they wh fiacd85tbu) 3anih(wg;.a+ ren the lighter astronaut has moved 12 m?    m

  A ball of mass m makes a head-on elastic c 7-c*c5y c:qwtq r:hfgollision with a second ball (at rest) and rebounds in the opposite direction with a speed equal to one-fourth its hqgf cc5t-c*7yr:q:woriginal speed. What is the mass of the second ball? $m_B$ =    $m_A$(Round to two decimal places)

  You have been hired as an expert witness in a court case involvz ed3-v rf 9r359fiemming 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 brakzrfe9 3 vre 5i9m3-mfdes 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 flight of concrete steps of total vertical x9c *,orqzjdy ) nam54height 4.00 m. The ball hits*nd5acom) xryzjq49, four times on the way down, each time striking the horizontal part of a different step 1.0 m lower. If all collisions are perfectly elastic, what is the bounce height on the fourth bounce when the ball reaches the bottom of the stairs?

  A bullet is fired vertically into a 1.40-kg block of wood at rest direcg8+ 21: 7glw 9) kt3szspzrmi cimoo(stly above it. If the bull z: i1s8+okm()r2o3 gt9mig zsl7 cspwet 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 placed onabo 06gi w i8xlqtla*6jn9 (l+ a horizontal surface just in front of the gun. If the coefficient of ki6*bwlnq8gaijti09 lo(x+ a6l netic 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,:+ *smdrztnl z sy/3c/ sit in a rowboat of mass 80 kg. With the boat initially at r/nl/szcd t 3+ rz:m*ysest, 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 /(wb3o we;ie/dllelnh )5zv/about $ 1\times10^{ 8}$kg struck the Earth ($m_E$=$6 \times10^{ 24}$kg) with a speed of about 15km/s and came to rest in the Earth.
(a) What was the Earth’s recoil speed?    $ \times10^{-13 }$m/s
(b) What fraction of the meteor’s kinetic energy was transformed to kinetic energy of the Earth?    $ \times10^{ -17}$
(c) By how much did the Earth’s kinetic energy change as a result of this collision?    J

  An object at rest is suddenly broken apart into twg9qz;0yv p: x yrqp-x3o fragments by an explosion. One fragment acquires twice the kinetic energy of the other. What is the ratio of tq9py xz-p ;3 yqgv:0xrheir masses?   

  The force on a bullet is given by (ob/ y*z/jcv :t lm,s *0okspwthe 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 masses cu; *ss1gm:0 9/zwgilwb2 pgc$m_A$ = 40g and $m_B$ = 60g are suspended as shown in Fig. 7–44. The lighter ball is pulled away to a 60$^{\circ} $ angle with the vertical and released.
(a) What is the velocity of the lighter ball before impact?$\approx$    m/s
(b) What is the velocity of each ball after the elastic collision?v'$_A$ $\approx$    m/s v'$_B$ $\approx$    m/s(Round to two decimal places)
(c) What will be the maximum height of each ball after the elastic collision?    m

  An atomic nucleus at rest decays radioactively into an alpha partiu5h ,gigng 5ck5 -3kwrcle and a smaller nucleus. What will be the speed of this recoiling nucleus if the speed of the alpha particle is kw5i5-u ck5,rng hgg3 $ 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 fired ab74 m +sdf7g(lvmtbvh., : wzoyp)b/ xt 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 do/y8 a8t 6pwcouwn 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),ral wd2n1*9abkz t +u+ what is the upper limit on mass m if it is to rebound from M, slide up the incline, stop, slide down the incline, andzt 1l uk29b*ra+d wna+ collide with M again?    kg (Let A represent mass m, and B represent mass M.)

  The gravitational slingshot effect. Figur wl)kuxk: 1mb2bs:o*b e 7–47 shows the planet Saturn moving in the negative x direction at its orbital speed (wit 1mobkbux:2s*l wbk:)h 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