We claim that momentum i :vpdsb xg3mh5 0w tff05w:*pfs conserved, yet most moving objects eventually slow down and stop.:p5sfg00 vftf wph3w d5b:x *m Explain.

When a person jumps from a tree to 1 7zou3bspn;)+ulknnthe ground, what happens to the momentum of the person upo npnl;u1bkns3z7 +o)un striking the ground?

When you release an inflated but untied balloon, why d a19pe0vox*eqzuk 5) coes it fly across the roomke5 ev* )zo0uaxp q1c9?

It is said that in ancient times a rit,,iw m n/ 7-vwhgv5smch 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 sh,ni7 , wstmv/5-g vwmhore. 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 zq79 9i1bw 0l ejt2rgyis essentially i7t0i 99geb1 y2 rjlzwqn a vacuum?

According to Eq. 7–5, the longer the impact time of an impulse, the smky8r0dnc l1 l1r+6ie7hyy c3 yaller the force can be for the same momentum change, and hence the smaller the deformation of the object on which the forcyr1 1c6d8kyeh iln 73yyl 0r+ce 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. Todafo,j8z( np knuo *ue9rlf1)rd9.7ox m y, though, cars are designed to have “crumple zoneso )lrn 9m(,onkz18 xre up97 *ofdfu.j” 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:uv3 sw1zpj6 low4-s e9s8dxmmts13/ uu onu 0 the air by the ba8u11wss-u :tpzu93 sd ux6m oo40vn3mwle/j stter?

Is it possible for an object to receive a larger impulse from a small tem9 l4ub+ m 3 hbn;xdlf++hz6force than from a large force? Expl9++lnzd fm6x;mtblu4e+ b h3 hain.

A light object and a heavy object have the same kinetic energy. Which has( kd4b8v8 -lrj b:ghye:xl,tdg-a 7lh the greater momentum? Explg(- bdl vrehblj 7 k -tx:8y4lhad,8g:ain.

Describe a collision in wh 9/dvcv)v:a, v.vgbkzich all kinetic energy is lost.

At a hydroelectric power plant, water is directed at high speed against tuy /n :1rkf4riyrbine blades on an axle that turns an electric generator. For maximum power generation, should the turbine blades be designed so that the water is bro1/r:niy kr4yfught to a dead stop, or so that the water rebounds?

A squash ball hits a wall at a b c,4w.r ubmx/w7n yy145 $^{\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 hardrk;:rb / 8pjw6xhjwb-+1lu x y steel plate (fixed to the Earth), from which it rebounds at very nearly its original speed. (a) Is the momentum of the ball conserved during any part of this process? (b) If we consider the ball and Earth as our system, during what parts of the process is momentum conserved? (c) Answer part (b 1:y 86prx rbkwh;lwbj+u-/jx) for a piece of putty that falls and sticks to the steel plate.

Why do you tend to lean backwg5ap c uo4 ;azge9q1,sard when carrying a heavy load in your arms?

Why is the CM of a 1-m l3/hwpigjxr :; 2j5uosfy5 n wm0m.k3t ength of pipe at its mid-point, whereas this is not true for y gj3rwyhsk0.t: jup o55/; fmmiw2n3xour arm or leg?

Show on a diagram how your CM shifts when you change from a lying position to a 1r -9zuibd6js sitti9sjzur6-b d1ing position.

If only an external force can change the momentum of the center of mash16ez6lp noa+ s of an objec+ao 6 16phnzelt, how can the internal force of an engine accelerate a car?

A rocket following a parabolic path through the air suddenly explodes into matz,o,,nkiuti5eaz euf */ /9 cny pieces. What can you say about the motion of this syst ozu*kci/f/z t 9,i ,e5entu,aem of pieces?

  What is the magnitude of the moagzf m,4*de7uixa9+afy1h t 4mentum 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 ywth,ewb ,; v1)gg 8r oeleiplx227 4d20 s. What is the skier’s change in veloc2g e8 7yeowgdprxb;4e,it l2whl, 1)vity?    m/s

  A 0.145-kg baseball pitched at 39 m/s is hit on a1k7eufkf, r)h horizontal line drive straight back toward t7eukf 1r,hf)khe 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 hp+.nzu 2lc ,rjorizontally 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 child is 26.0 kg, and that of the boat is 45.0 kg. Ip2 zr+c.un l,jgnore water resistance. The magnitude of the velocity of the boat is    m/s

  Calculate the force exerted on a rocket, given thlm6ce120let s3b:h(i :o ukxsat the propelling gases are expelled 3: : 0eo cilsxu2kb(ltm 61hesat 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 3)rcedkbq(f-v1 i8 cqat $4.1 \; m/s$ 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 o7nmwswxc: 5rboy-yc+6o .tz, n alevel frictionless track with a constant speed of 18m/s A 5350-kg load,initially at rest, is dropped onto the 7csx.o:bn ,twm5w -ryy c 6z+ocar. What will be the car’s new speed?    m/s

  A 9300-kg boxcar travel wm l,6t6bka.king 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 h5viv8 qn 85ylthe air strikes a person at the rate of 40kg/s 58 5nv qvlyhi8per square meter and is brought to rest, estimate the force of the wind on a person. Assume the person is 1.50 m high and 0.50 m wide. Compare to the typical maximum force of friction $\mu\approx1.0$ between the person and the ground, if the person has a mass of 70 kg.    N
$F_{on person}$  ----待选择----<> $F_{fr}$

  A 3800-kg open railroad car coasts along with a constant speed of 8.6m/s on a k immh0.(ci: blevel track. Snow begins to fall vertically andiic .b(mm hk0: 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 pdamr 33 mpk3)rarticle in the direction of its velocity, and the remaining nucleus slows to 350m/s If the alpha particle has a mass of 4.0 u and the original nucleus )d akmmp33r3 rhas a mass of 222 u, what speed does the alpha particle have when it is emitted?    m/s

  A 23-g bullet traveling 28p g5vu xf6x11xqf5xmb g1,ss30m/s penetrates a 2.0-kg block of wood and emerges cleanly at 170m/s If the block is stationary on a frictionless surface when hit, how fast does it movvs5xg x p8q,f6ums 1g15xxb1fe after the bullet emerges?    m/s

  A 975-kg two-stage rocket is:bl1ca;ljg ;x 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 3180 kg is traveling in oqu 4nlnx- z 1e+6; zpg+z8bm8xzd9 afouter space with a velocity of 115m/s 8l-xg mx;a+18oznz4 db pzfnq9uz6 +eTo alter its course by 35.0 $^{\circ} $, its rockets can be fired briefly in a direction perpendicular to its original motion. If the rocket gases are expelled at a speed of 1750m/s how much mass must be expelled?    kg

  A golf ball of mass 0.045 kg is hit off the tee at a speed of 45m/s1 pzx1jdqv ezgqsfz;c .h)/ ;6 The golf club w6/q. cqjes1fg;pz;hv ) zz d1xas 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 gb(9il5v-5qsgjo 2sh of 8.5m/s and comes to rest in a time interval of 8.0 ms. (a) What iss-vsb lg5 9h25 j(oqig 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 a +wofm d /sbm,pb2gj)/+hhsv(nd speed v=25m/s strikes a wall at a 45 $^{\circ} $ angle and rebounds with the same speed at 45 $^{\circ} $ (Fig. 7–32). What is the impulse (magnitude and direction) given to the ball?   kg*m/s to the  ----待选择----leftright 

  You are the design engineer in 6e,wv)jxf77htvh,x q 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 f,vhfq67), hx7ve tx jwrom the time of impact until it is brought to rest. (a) Calculate the average force exerted on the car by the barrier. $\approx$$a\times10^5$N a =   
(b) Calculate the average deceleration of the car.    m/$s^2$

  A 95-kg fullback is running at 4m/s to the east and is stopped in ei ; *ponv .5r1rbj2a48ymqhl0.75 s by a head-on tackle by a tackler runninnb 1o emra2*8 i4 vpqh.r;l5yjg due west. Calculate
(a) the original momentum of the fullback    kg*m/s
(b) the impulse exerted on the fullback    kg*m/s
(c) the impulse exerted on the tackler,    kg*m/s
(d) the average force exerted on the tackler.    N

  Suppose the force acting on a tennis ball (mass 0.060 kg) pointsth21w ync7*xt*dr xg0rvyxb -,k -+ dh in the +x direction and is given by the graph of Fig. 7–33 as a function of time. Usey rc d*+*n wdxk 7h 02thg1t--yx,rxbv graphical methods to estimate
(a) the total impulse given the ball    N*s
(b) the velocity of the ball after being struck, assuming the ball is being served so it is nearly at rest initially.    m/s

  From what maximum height can a 75-kg person jump without breo)cb 0yuv3/v0m;thql,ms f94 wh3gfiaking the lower leg bone of either leg? Ignore air resistance and assume the CM of the person moves a distance of 0.60 m from the standing to the seated position (that is, in breaking the fall). Assume the breakingmq/ thlvs0 0gfi);3v,fmoh w ucy 349b 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 mbhdy v35p(3x9r0e d zmoving east (+x direction) with a speed of collides head-on with a 0.220-kg ball at rest. If the collision is perfectly elastic, what will be the speed and direction of each ball after 3(vrxdm0 d39y5 hepbzthe 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/s has a head-on ch1b3bls xw yed)ax/d. l(uqua;6p+ 5kollision with a 0.900-kg puck initially at rest. Assu bq1k)xd5hl+ sb au6.e wd;ypux3al/( ming a perfectly 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 perfectly elw,gmjfh,2p8 :/4peqhuuy , iik w 6di6astic head-on collision. If one ball’s initial speed was 2m/u,jph2,68 iwiui/4wqehp ,df yg mk6 :s and the other’s was 3m/s in the opposite direction, what will be their speeds after the collision?(Let A represent the ball moving at 2.00 m/s, and call that direction the positive direction.Let B represent the ball moving at 3.00 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 ,cnc t rx65p(sd*exy6a 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 eacd x psr6,excc65 *y(tnh 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 0.22nd x9wn /cx/3jhagbb) gxc6wu26 0 mo10 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 softball bounces backward with anu/)dcn /xj6c ah3xg0x gob62 wm1b w9 speed of 3.7m/s Calculate
(a) the velocity of the target ball after the collision    m/s
(b) the mass of the target ball.    kg
(Let A represent the moving softball, and let B represent the ball initially at rest.)

  Two bumper cars in an amusement park ride collide elastically asn)um 9mx7alp 5u9 ge,j 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 dif9uux,7jl5n m)me gp9 aferences in passenger mass. If car A approaches at 4.5m/s and car B is moving at 3.7m/s calculate
(a) their velocities after the collision v'$_A$ =    m/s v'$_B$ =    m/s
(b) the change in momentum of each.$\Delta p_{\mathrm{A}}$$\approx$    kg*m/s $\Delta p_{\mathrm{B}}$$\approx$    kg*m/s

  A 0.280-kg croquet ball makes an elastic head-on collision with a second bal 1qb*msqn)z5 b: ch;sul initially at rest. The second ball movq;nc*busm5b1 hz)s :qes 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 fris7ptl 0jj(g3 vctionless 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 off the floor, where does each cube land? [Hint: 3j70gpltvs j( Both leave the incline moving horizontally.]$\Delta x_{m}$$\approx$    m $\Delta x_{M}$$\approx$    m

ake the general case of an object x iusqc;yz9:9 whg;x7of 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 maximupzrv+sqeyaoye 2jr0 z6r-3 e.hmu-bx 6+x(a, m height h of the pendulum equal to 2.6 cm. A second projectile causes the the pendulum to swing twice a-6 0 xr+3v2- m(uxr+e. yehsop jye,rzzaqb6as 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 burss :br,ixc-/hq78:fb xfrz8lgzfw+ s/ t * ds6ies itself in a 3.6-kg pendulum hanging on a 2.8-m-long string, which makes the pendulum swing upward in an a zb-ls8xgzq sxh,68*w sd: brf/ +ir7t/cs:f frc. Determine the vertical and horizontal components of the pendulum’s displacement.vertical$\approx$    m horizontal =    m

(a) Derive a formula for thh3y x0du uppbsv8 u17ug83l0me fraction 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 breaks an object, initially at rest, intkshqz5 dmtaw8 paqb m-j495(-o 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 eneptb(qh 5z8qm-kad5 j9w4s-ma rgy did each piece acquire? (Let A represent the heavier particle, and B represent the lighter particle. ) KE'$_A$ =    J KE$_B$ =    J

  A 920-kg sports car collides into the rear end of a 2300-kg SUV stopped at a re/*57bs0spehot l jay1 d light. The bumpers lock, the brakes are locked, and y hp7alt *0o1ssbj5e/ 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 he* qoge4 tr+(zvight of 1.20 m. Approximately how many rebounds will the ball make b(o 4vgqe zrt*+efore losing 90% of its energy?   

A measure of inelasticity in a head-on collision of two objects is the coefficc)bfo34 c dtg0ient of resti)t3o cgfc40bd 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 three times jz17fcvfs.c8 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 ofj 1sf7z. c8fcv distances each block travels? ----待选择----1/91/101/81/6 

  A 15.0-kg object moving in the +x direckr0/bd* zd f4zj )9eyf7b8m 3-shgpmntion at 5.5m/s collides head-on with a 10.0-kg object movinge/d8d hbfzkjm0fb-3m rp4syz 7*gn9 ) 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 seco y4j-zj kma 2w9od-ys*nd nucleus, an electron, and a neutrino. The electron and neutrino are emj*w ydm-soa9y -jz4 2kitted 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 mass8 heoovamy 4n8 1q/;ms -8beobnrat(* $m_\mathrm{A}=0.400$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 betwep kc ar7md)l/0: ,ans9lzy /apen two objects of equal mass, each having initial speed the two move o p9rc ld0n),mz pk/:yaa7 /alsff together with speed v/3 What was the angle between their initial directions?    $^{\circ} $

  Two billiard balls of;xfc z c1.sr4ox8r tq( equal mass move at right angles and meet 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, assumqr8t; .ox(x4zf1src c ed elastic, ball B is moving along the positive y axis (Fig. 7–37). What is the final direction of ball A and what are their two speeds? direction of ball A is  ----待选择----x directionx direction v'$_A$ =    m/s v'$_B$ =    m/s

  A neon atom (m=20u) makes a perfectly elastic 23 iz) +(fm:bym 3ft6nxzpq vocollision with another atom at rest. After the impact, thf:(6)x2pzz3ovyn itf q m b+3me 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

  A neon atom (m=20u) makes a perfectly elastic c) hpny98eutwk( n :o k.. hxo4n4 miv8zqv38zgollision with another atom at rest. After the impact, the neon atom travels atgqo8eon: xz4 h yhv.9u8 pz) mn(v3n 4w.kik8way at a 55.6 $^{\circ} $ angle from its original direction and the unknown atom travels away at a -50 $^{\circ} $ angle. What is the mass (in u) of the unknown atom? [Hint: You can use the law of sines.](Let A represent the incoming neon atom, and B represent the target atom) $m_B$   u

  Find the center of mass of the three-mass system shown in 4 hl1 kqn jq yc)b8iklumqe0s:k ;u435Fig. 7–38. Specify relative to the lef4 n35uykih 0:4c eqk mkj;qluq8b)ls 1t-hand 1.00-kg mass.    m

  The distance between a cez 14+ra qs nai.40scparbon 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 ooi,+k,elt 2 ecar 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 t+, k2oo,etl iehe 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 ;r r9nmb-5y (i7 :7gurof le0v:shppo a ferryboat. If three cars, each of mass 1200 k e pnv:is7ho 50 :mlr( b7-gypu9rfor;g, occupy its NE, SE, and SW corners, determine the CM of the loaded ferryboat.$X_{CM}$ =    m $Y_{CM}$ =    m

  Three cubes, of sideo30mh16ghb qi b895poq kajr2s $l_0$,$2l_0$, 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 tomato paste (see Fig. *f hc9:mbl9q 3bapb+z 7–40), each of which is a cube of length l. Find the center of gravity in the horiz9b*+3fb c p9q almzb:hontal plane, so that the crane operator can pick up the load without tipping it.$X_{CM}$ =    l $Y_{CM}$ =    l

  A uniform circular platjke6ce cc7i: )v(xb4 fn jri*.k,z6ife of radius 2R has a circular hole of radius R cut out of it. The center of the smaller circle is a distance 0.80R from the center C of the larger c* (cxj4v,cfcbr7ek n6:6.j )iefik i zircle, Fig. 7–41. What is the position of the center of mass of the plate? [Hint: Try subtraction.]   R

  Assume that your propo;o 97fd j.lqwprtions are the same as those in Table 7–1, and calculate the mass of one olo9q;.fd7jwp f your legs.    kg

  Determine the CM of anmlpj723c6r i (y(rby v outstretched 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 thy 9ln9. 31c gwnuln-qn-qm 1qae position of the CM of an arm bent at a right angle. Assume that the y193u-.-nan gm nq 1qnlq9wcl person is 155 cm tall. $X_{CM}$ =    cm $Y_{CM}$ =    cm

When a high jumper is in a zf:/ez u35yt pb0hnr*v wjx)/position such that his arms and legs are hanging vertically, and his trunk and head are horizontal, calculate how far below the torsozn0tryf*3 bexv)u/zw j :p5/h’s median line the CM will be. Will this CM be outside the body? Use Table 7–1.

The masses of the Earuh gh0y20,xe 9j t8cmzth and Moon are $5.98\times10^{24}$kg and $7.35\times10^{22}$kg respectively, and their centers are separated by $3.84\times10^{8}$m (a) Where is the CM of this system located? (b) What can you say about the motion of the Earth–Moon system about the Sun, and of the Earth and Moon separately about the Sun?

  A 55-kg woman and an 80-kg man stand 10.0 m apart on frictio o8dp *dhwrt(bgni9 2 igrn*6 7uy+g-nnless 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 diameter(fbo/*r pfspa32 g-()ijax kq 0.0800 m mounted on a uniform cylindrical hi ofpps* ar-b q)(fx/kj23(agandle 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 unifornrtq(iu: y:br i60qj:m cylindrical head of mass 2.00 kg and a diameter 0.0800 m mounted on a uniform cylindrical handle of mass 0.500 kg and length 0.240 m, as shown in Fig. 7–42. If this mallet is tossed, spinning, into the air, how far above the bottom of the handle is theru: i:britj6 (q0nq:y point that will follow a parabolic trajectory?    d    d

  (a) Suppose that in Example 7–14 (Fig. 7–29)1qwmo f i9 v6l6vz34yw, $m_{II}$=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 masyp 3 .f-jxg)hms M, are in the air and stationary with respect to the ground )mx-h.gpjfy 3. 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 strikes a bat and is popped stn*0s nmlz/ycj4/ u-lpraight up to a height of 5m n-z*n/l j04lc/usy p5.6 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 traveli)3 +npm 6dzfkh ss(gv0fll4 e5kw,c n(ng 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 wifilyq-, 8gs0 kth the corner pocket shot shown in Fig. 7–43. Relative dimensions are also shown. Should the player be worried about this being a “scratch shot,” in w-fs,ig 8yk ql0hich the cue ball will also fall into a pocket? Give details.

  A 140-kg astronaut (including space suit) acquireu;l tdp lh5a1)s a speed of 2.5m/s by pushing o1 )al ;uld5thpff with his 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 and the other 80 kg, are initially at rfkg )+f;ick )xl8apl 2est in outer space. They then push each other apart. How far apart are they when the lighter astronaut has movilg 8+fakfl;k )2x c)ped 12 m?    m

  A ball of mass m makes a head-on elastic collision with a second f f3wx6.e0 tnwball (at rest) and rebounds in the opposite direction with a speed equal to one-fourth its original speed. What is the mass of t3ff.xww0t 6n ehe second ball? $m_B$ =    $m_A$(Round to two decimal places)

  You have been hired as an expert witness in a court case involvispfx cd3yl/ek*e,c slb93- ;ang 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 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 brac9e3yp k *l-se s;/,xl3bfadckes.    mi/h

A golf ball rolls off the t a;-9 snp0yzjy 3erla6op of a flight of concrete steps of total vertical height 4.00 m. The ball hits four times on the way down, each time striking the horizontal part of a different step 1.0 m lower. If ;lyyz -p3n 06 ara9sjeall 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 1.4tiq4-wr+z4c d;ue)zx0-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 acxdz; 4ieu) q-wtz 4+rfter the bullet becomes embedded in it?    m

  A 25-g bullet strikes and becomes e2r w)5;bnzl )f(fv cvsmbedded in a 1.35-kg block of wood placed on a horizontal 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 bef2ls()wvvrfcz 5;b)nf ore 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 ma+b k(zxx3f wmrp;aw 9g---ppsss 60 kg, sit in a rowboat of mass 80 kg. With ;xkpf(w - 3m 9wasgpzpx+- r-bthe 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 boat will move    towards the initial position of the 75 kg person(Round to two decimal places)

  A meteor whose mass was abouidhi7xdlw y n8rqu+: 30 vql(7t $ 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 sudacecq9js ;(v-;tti) o denly broken apart into two fragments by an explosion. One fragment acquires twice the kinetic energy of the other. Wh; q)osccv i9-t(e; tjaat is the ratio of their masses?   

  The force on a bullet is given by the formu rtfgx+9+u9:vs g.a,:w ini utla 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(jd t bfq09 bifm/,ge4 $m_A$ = 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 rww; q,tfquv79j4+ ix+5sg jdz est decays radioactively into an alpha particle and a smaller nucleus. What will be the speed of this recq,tfwv759 wi+ 4qdgx jjzu+s;oiling 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 3rusa7qrn o/d qxw lbkqdsbg2 669 wa;*63q9vtarget) 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 9eaba7gvkdv t zitl:(80zg+0 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 limis )qtcnnv7/a5*x tz y)t on mass m if it is to rebound from M, slide up the incline, stop, slide down the incline, ans acqz5t7vn*))nt xy/ d collide with M again?    kg (Let A represent mass m, and B represent mass M.)

  The gravitational slingshot effect. Figug62y9 den4nz x apr0/nre 7–47 shows the planet Saturn moving in the negative x direction at its orbital speed (with respect to the Sun) of 9.6km/s The mass of Saturn isnn p9 a6rg2ey/xz4 dn0 $5.69 \times10^{ 26}$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