We claim that momentum is conserved, yet moc;jz bv9atz -sk5 k9)ttlh m44fu..qxst moving objects eventually slow down anvz. mq.)fh; - 59tt4c9uak j4lxbkzstd stop. Explain.

When a person jumps from a tree to the ground, what happens to the momentuy )fskgc zn,1:m of the person upon strikzfc1s ),: knyging the ground?

When you release an inflated but untied balloon, why does it fn 5,6wx w,j2tfs liw96ewypm5ly across the room?nmlx ,y,wwf2569 ewj5is6 tw p

It is said that in ancient times a rich man with a bag of gold coins froze k.u3 9bjbx)g n1+kvfn2dlt:bto death while stranded on a frozen lake. Because the ice was frictionless, he could not push himself to shore. What could he have done to save himself had he not k:bbx dv 2 1lb+t)f9k 3njngu.been so miserly?

How can a rocket change da.eald xf1l mwq/ )+r*irection when it is far out in space and is essentially in a vacuum?f xa .dr+allm1*qwe/)

According to Eq. 7–5, the longer the impact time of an impulse, the wv z;vqmdb73f;piv09 r1w mx ne9b.y8 smaller the force can be for the same momentum change, and hence the smaller the deformation of the object on which the force acts. On this basis, explain the value of air bags, which are intended to inflate vbq 3b;97vv;i 9m .0xyfndz1wr8mwepduring an automobile collision and reduce the possibility of fracture or death.

Cars used to be built as rigid as possible to withstand collisiocz1ruezs9y5g v-i.vaq / 2h 4wns. Today, though, cars are designed to have “crumple zones” that collapse upon impact. Whag5.a zc91 rwui 2yqehz /sv4v-t is the advantage of this new design?

Why can a batter hit a pitched baseball further than a ball tossed inkodp+2 gy 1m3+2tav )chl:zgn the air by the batter?td:na zym2lgv 3 p)1h+k+ c2go

Is it possible for an object to receive a larger impulse from5f.a3sg(a3lhxrat rwe 64 zs; a small force than from a large force? Etg6fx ;a r35aerwh(z.a l4s 3sxplain.

A light object and a heavy object have the same kinetic energy. Which has thgg ra/z/5rlr:g s,ab4e greater momentum? Explarsrgag , a5:4zrg/b l/in.

Describe a collision in which all kinetic energyaf8,: rd /xrgiy(jki1 is lost.

At a hydroelectric power plant7rqhs5.qq (j; m 1oh3rsozfool4 :; ab, water is directed at high speed against turbine blades on an axle that turns an electric generator. For maximum power generation, should the turbine blades be designed so that the water is brought to a dead stoq; 3 7s:.5sqo4ohlrqbfh1z ;o( amrjop, or so that the water rebounds?

A squash ball hits a wall atv4dlim:,)a sj 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 wl;)qulrl :0;k6 k7py8ut7(ft ofz xh from a height h onto a hard steel plate (fixed to the Earth), from which it rebounds at very nearly ikz; h fqu8frxl (oy 7 7)6lut;lpkw:t0ts 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 l 5s*yqmu4vvzdf)txk(c m6- c5ean backward when carrying a heavy load in your arms?

Why is the CM of a 1-m length of pipe at its mid-point, whereas thi*ley l; j 69s2zvd wfns);+slis is not true for your ;;9zsllv inwf6 l)s*j2yesd+ arm or leg?

Show on a diagram how your CM shifts when you k(qio.in 1i)uva27w h change from a lying position to a ihin1(vqa) w2o 7i.uk sitting position.

If only an external force can change the momentumqfz7e bdy53l5 of the center of mass of an object, how can the internal force of an engine accelerate a cayf 3edq 75l5zbr?

A rocket following a parabolic path through the air suddenly explodes 7g k)*l,z tv+/u,spgtf usb7 sinto many pieces. What can you say about the motion of th)gts ,,su/+* pbgvz ufts7kl7 is system of pieces?

  What is the magnitude of the momentum of a 28-g sparrow flying with a 9e lnzmc:*2 g 9kdpr)ospeed of $8.4 \; m/s$    $kg \; m/s$

  A constant friction force of 25 N acts on a 65-kg skier for4,n btewi(oxa2ei /z u9pfe72 20 s. What is the skier’sxpieeie72tu /azw(9b f 4o n,2 change in velocity?    m/s

  A 0.145-kg baseball pitched atrolo 37:hjnf ineue5v t h8(rilj /24+ 39 m/s is hit on a horizontal line drive straight back tr2n+/5l vune:3hhiilf8 (jo 7r jeo4toward 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 horizontally withqwi8s a)(r j3-,u3+ (( sgdp yzvckizk a speed of 10 m/s Fig. below Cigj zk,sqz(3cw) ui(d a 8y(rs+ k3pv-alculate the velocity of the boat immediately after, assuming it was initially at rest. The mass of the child is 26.0 kg, and that of the boat is 45.0 kg. Ignore water resistance. The magnitude of the velocity of the boat is    m/s

  Calculate the force exerted on a rocket, given that the propelgp; p:cmtus1x00* kmi ling gases are expelled at a0;xipm*cmu gkt10ps: 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 at -8m*/ 2kkil rurb,hyf$4.1 \; m/s$ on an apparent breakaway for a touchdown is tackled from behind. When he was tackled by an 85-kg cornerback running at $5.5 \; m/s$ in the same direction, what was their mutual speed immediately after the tackle?    $m/s$

  A 12,600-kg railroad car travels alone on alevel frictionless track w fsxb*g0//ne2sp3r v2akaa (tith a constant speed of 18m/s A 5350g av 2kbasa/r tsx2/( e30fp*n-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 atvy j/:y, )r0cy jeit6b $15 \; m/s$ 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 100f f69 qlatl33ajo+y i1km/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 atl9f33ya6l +jf1oq i 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 coasvx)3qa1;l4psv( y y dfts along with a constant speed of 8.6m/s on a level track. Snow begins to fall vertically and fills the car at a rate osy fpv a3v4lx1(q d);yf 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 4h:bpq2 a+n6gxzqf ,t7 20m/s emits an alpha particle in the direction of its velocity, and the remainingg7xq , aqpf+h6tz:n2b nucleus slows to 350m/s If 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 , tqfg*ts12twm3 u0 rw-w-u aw,6 qkukpenetrates a 2.0-kg block of wood and emerges cleanly at 170m/s If the block is stationary on tsqtkuuqg 3- twk0a,,u1* rmw 6fww2-a frictionless surface when hit, how fast does it move after the bullet emerges?    m/s

  A 975-kg two-stage r4vwpe 7dm sl 6 3ts1mmhp6rs4*ocket is 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 h ijeju2to ,6+in outer space with a velocity of 115m/s To alter its course by 35.ij2u6o, jeth+ 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/s The gm(5w;jne l : cpn)t,6zfkc0kg olf club was in(6zn ,pf; et nk g:wm)jc0k5cl 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 strik(q.7k,;yrva a7rzt;qgak 2vz es a nail at a velocity of 8.5m/s and comes to rest in a time interval of 8a;zz(v7t,gk;r v7y.qq2k ar a .0 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 andkg0 d ua4-b3f2 fgtaulz23y/y 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 charge of the crashworthiness of new )ah /t(-zqwgv+2bge )fb t0pkws 9lu-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 )0+gpb)-su 2vbq( katt fw-z le/hw9gs from 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 0.75l3zxtkc;b*2; aqwo8 p ztaf-) s by a head-8;)zz; akq3p *lfbwxaott2- con tackle by a tackler running due west. Calculate
(a) the original momentum of the fullback    kg*m/s
(b) the impulse exerted on the fullback    kg*m/s
(c) the impulse exerted on the tackler,    kg*m/s
(d) the average force exerted on the tackler.    N

  Suppose the force acting on a tennis ball (mass 0.060 kg) pointum+)r il-rip ,*j g 2zdvk6j9ms in the +x direction and is given by the graph of Fig. 7–33 as a function of time. Use graphical methods to estimate p) j,j mim9kgldvrriz-* +26u
(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 0m:)tbism gm) leg bone s:gm0mitm ) )bof 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 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 hfa/ -9p hpiz2of collides head-on with a 0.220-kg ball at rest. If the collision is perfectly elastic, what will be the speed and direction of each ball after the collision?Let A represent the 0.440-kg ball, and B represent t-2pzhhp/f 9i ahe 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 colli7 kbeow6:7/5 wgqhonqsion with a 0.900-kg puck initially at rest. Assuming a perfectly elastio:wqw hkg7q6n5/e7 o bc 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 ,okfz n .cf-k2undergo a 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 direction the positive direction. 2o.ckf,fnk -zLet 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 spqo9 t l, qsstta07+bw)ig(5zweed of 2.5m/s collides head-on with a 0.090-kg ball initially moving away from it at a speed of 1.15m/s Assuming a perfectly elastic collision, what are the speed and directl0) gat is 5w,t7 q9zbqo(ws+tion of each ball after the collision?(Let A represent the 0.060-kg tennis ball, and let B represent the 0.090-kg ball.)v'$_A$ =    m/s v'$_B$ =    m/s

  A softball of mass 0.220 kg that is moving with a speedxv(c*r2) kw.roiwxg ; of 8.5m/s collides head-on and elastically with another ball initially at rest. Afterward the incoming softball bounces backward with a speed of xk)2 g;irv.ow( *c xrw3.7m/s Calculate
(a) the velocity of the target ball after the collision    m/s
(b) the mass of the target ball.    kg
(Let A represent the moving softball, and let B represent the ball initially at rest.)

  Two bumper cars in an amusement park ride collide elastically as one approache, /dqs8avitf6r+5t qz9nur( ss the other directly from the rear (Fig. 7–34). Car A has nvs5i+s(u9zafd68 tqrt/ , qr a mass of 450 kg and car B 550 kg, owing to differences in passenger mass. If car A approaches at 4.5m/s and car B is moving at 3.7m/s calculate
(a) their velocities after the collision v'$_A$ =    m/s v'$_B$ =    m/s
(b) the change in momentum of each.$\Delta p_{\mathrm{A}}$$\approx$    kg*m/s $\Delta p_{\mathrm{B}}$$\approx$    kg*m/s

  A 0.280-kg croquet ball makes an elastic head-on collio g;,rsc wm3i47bw y:qsion with a second ball initially at rest. The second ball moves w q7yg;s:wob,r m4 3cioff 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 frictionless incline a8:k2ti8 omhcbs 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 eac ibm8tc2koh:8 h 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 dh )t; xbo z.dduf) nu2*2vwn3object 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 gmcg c;t: bq/ch/g1/p3isk6fheight h of the pendulum equal to 2.6 cm. A second projectile causes the the pendulum to si:;1 p3gkcgcthqmf cg s/b//6wing 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 itsexn r5ozxq1fz2msr4,6 lf in a 3.6-kg pendulum hanging on a 2.8-m-long string, which makes the pendulum swing upward in an arc. Determine the vertical and horizontal cs1of,zxr 2x5nqm46z romponents of the pendulum’s displacement.vertical$\approx$    m horizontal =    m

(a) Derive a formula for the fraction of kinetic energy lost,-uuvp-pe3y p 6 $(\Delta\mathrm{KE/KE})$ for the ballistic pendulum collision of Example 7–10. (b) Evaluate for m=14g and M=380g

  An internal explosion breaks an object,vh;8c q4wtsf* 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, qsvh t;8c*f4w and B represent the lighter particle. ) KE'$_A$ =    J KE$_B$ =    J

  A 920-kg sports car collides into the rear end of a 230 +li ,keepnsp-j3uu9shl1j.k 4qq79w0-kg SUV stopped at a red light. The bumpers lock, the brakes are locked, and the two cars skid forward 2.8 m before stopping. The police officer, knowing that the coefficient of kinetic friction between tires and road is 0.80, calculates the speed of the sports car at h ji- 9.jl94ps7q3uuknklep ,+wqs e 1impact. What was that speed?(Let A represent the sports car, and B represent the SUV) $\approx$    m/s

  A ball is dropped from a heightz+d*it) d chhkph* v;dp*2o 0z of 1.50 m and rebounds to a height of 1.20 m. Approximately how many rebounds will the ball make before;hotd0cd 2pz vz*hi+hdp )**k losing 90% of its energy?   

A measure of inelasticity in a head-on collision of two objectn9 )6x0bdse x48 vypahs is the coefficient of restitution, e)s0n xh 8yev94d bap6x, 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 os,gzm1j1t2trer0 4le h, vz3pf 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- 30 ee,4z1 m,ttpr lsghjzrv21surfaced 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 hlv8rom-he(-jg3jy -: rjbt n)gy. gc/ ead-on with a 10.0-kg object moving in the -x directig:y 8v- m hy-beo-g lrjj ()g/jr.cnt3on 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 er42u)zm abby6bb 7f14ll b* zglectron, and a neutrino. The electron and neutrino are emitted at right angles and have momenta bbz2g l 7f)yba r *m4bblu14z6of $9.30\times10^{-23}kg\cdot m/s$ 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 mye.t2n) *ems vass $m_\mathrm{A}=0.400$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 k yk 51d*yyz:v (h5xp or-p:ohcollision between two objects of equal mass, each having initial speed the two move off together with speed v/3 Wpyo5 y * xyvk rd-:p1zh:kh5(ohat was the angle between their initial directions?    $^{\circ} $

  Two billiard balls of equal mass move at right angles and meet zp m6 (nkmc)+kuo20z kat the origin of an xy coordinate system. Ball A is moving upward along the y axis at 2m/s and ball B is moving to the right along the x axis with speed 3.7m/s After the collision, assumed elastic, ball B is moving along the positive y axis (Fig. 7–37). What is the fo2kum+( 0zpkm6k) z ncinal 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 collision with aj4v)(gypba+(cul 7 cq nother atom at rest. After the impact, the neon atom travb )+ac 4 vu7cyl((qjgpels 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 bki )jga zi*ep) d*(7sanother atom at rest. After the impactakbsgjz *(7id*epi)), 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 system show ak2 8an47embrn in Fig. 7–38. Specify relative to the left-h82m7k aaen4 rband 1.00-kg mass.    m

  The distance between lz - xpkn;z3r-)*c iiia 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 behind the front s6o . v-e8jdutof 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 - ejsv6duot.8 the front of the car, and three people sit in the back seat 3.90 m from the front? Assume that each person has a mass of 70.0 kg.    m

  A square uniform raft,he 1m1g7y8zyddjs7 . m 18 m by 18 m, of mass 6800 kg, is used as a ferryboat. If three cars, each of mass 1200 kg, occupy its NE, SE, ady dm8 z7gymj7hs11.end SW corners, determine the CM of the loaded ferryboat.$X_{CM}$ =    m $Y_{CM}$ =    m

  Three cubes, of sidesk0nhllp/ bb(hvxs,: 4 $l_0$,$2l_0$, 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*kin/ej46p 52y3e h emvbg ar6 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 ogre6 2 5jeaibe vn*34p6 ykh/mperator 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.z*f;lw-t n* bp qt.iz cut out of it. The cent.bt;tz.pn zl*qfw i- *er 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 center of mass of the plate? [Hint: Try subtraction.]   R

  Assume that your proportions are the same as those in Table 7–s ei3 3.ara0ww1, and calculate the mass of one of youaaei30r.ww3 s r legs.    kg

  Determine the CM of an outstretched arm using Tablnc 68- fxt9vg,wj207f1f+pdeu p,1 tbnjktwm e 7–1.   % of the person's height along the line from the shoulder to the hand

  Use Table 7–1 to calculate thecu5; t;,uaqv g position of the CM of an arm bent at a right angle. Assume that the person is 15,;uqa ;tv ucg55 cm tall. $X_{CM}$ =    cm $Y_{CM}$ =    cm

When a high jumper is in a position suc+3pm/jvn*ac z h that his arms and legs are hanging vertically, and his trunk anp vazmc*n+ 3/jd 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 Mo tsl7ir,6gu*4( hz b gqf;pj7bon 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 ap4w6l8q,0v5)w o wez/ukqk x ggart 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 and3; rco4xt; khgj 2oek1 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 poink ; hojc2txk;eo3 41rgt that will follow a parabolic trajectory?    cm

  A mallet consists of a uniform cylindrical head of mass 2.00 ke)w36gv0zl *+d q z,tjl zqfj-g 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 tl zvw*z ,djtlq+g3 ze 0-f6q)jhe point that will follow a parabolic trajectory?    d    d

  (a) Suppose that in Exampl( 2u;p ye0chhpe 7–14 (Fig. 7–29), $m_{II}$=3$m_{I}$ Where then would $m_{II}$ land?    d(Round to two decimal places)
(b) What if $m_{I}$=3$m_{II}$    d

A helium balloon and its gondola, of mass M, are in the air and sta20mnqpsr4o6lj5abt 0x e(tk (tionary 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 speeqtmox2( ks (5bjt e40l6rp an0d 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 st)8jx4 ;hq5;r9 nrl2hvndwvl pji2r e7raight up to a height of 55.6 m. If the contact time is 1.4 ms, calculate the average fh8w xlqdj4rrl ;ire 25) nh2;7p9nvvjorce on the ball during the contact.    $^{\circ} $

  A rocket of mass m travelin g2thp4,r+7ryepo sfs9 ys x7/g 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 corner pocket shot shown in Fig. 7–43ks gq0;oi2b,k . Relative dimensions are also shown. Should the player be worried about this being a “scratch shot,”qi2k;s b0ko, g 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 pk) :ag 7j q29xdbe+xv fx)cm+iushing off with hij)+7mg2cq9)ei xvf x xdbak:+s 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* .txjwabc f+eyb5 yy)ai4/4w 80 kg, are initially at rest in outer space. They then push each other apart. How far apart are they when the lighter astronaut has movief5a. /yc4 j xwtaw+4*yybb)ed 12 m?    m

  A ball of mass m makeseehu 8- j,pkm6 a head-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 the second ball? m6ee-upk h8j,$m_B$ =    $m_A$(Round to two decimal places)

  You have been hired as an e otf n0 cm3j :7nbnn.ll(5-ylhxpert witness in a court case involving an automobile accident. The accident involved car A of mass 1900 kg which crashed into stationary car B of mass 1100 kg. The driver of car A applied his brakes 15 m before he crashed into car B. After 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 tc jybm-hnn lnnl3.07ol5:(f before applying the brakes.    mi/h

A golf ball rolls off the top of a flight of concrete steps of total rk9vqrkmez)*-a yw+ * vertical height 4.00 m. The ball hits four times on the way down, each time striking the horizontal part of a different step 1.0 m lower. If all collisions ar mwr9qv-e k+a)kzyr* *e 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 va 3ezxsuw5a x8) 68ae8: ujbjwood at rest directly above it. If the bullet has a mass of 29.0 g and a speed of 510m/s how high will the block rise after the bullet becomj8vxzjas8u) a b 86ewaxe:u35es embedded in it?    m

  A 25-g bullet strikes and becomesylxyipoewf: 0merxx,df/ e+- g2/n4j/ +x9ga embedded 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 be:niwp+0gf +my ,ye/-4 xrxfde o/x2 9jgla/xetween 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 m7u)pcx/;ts )i3m lej fzw,d 7pass 75 kg and the other of mass 60 kg, sit in a rowboat of mass 80 kg. With the boat initially at rest, the two people, who have been sitting at opposite ends of the boat 3.2 m apart from each other, now exchange seats. How far and in what direction will theepcjp ,7 xl7mw)uf /d;)tz3is 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 about cspe /7p46 sjx4sl5obj wb v66$ 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 ispwy 4:ycb:jj- pj)q 5d suddenly broken apart into two fragments by an explosion. One fragment acquires twice the kinetic energy of the other. What is the ratio of their mw:d jj-y ycpp4:b )q5jasses?   

  The force on a bullet is givs)-*mpy t;b dvp ung.2dn:1 /aztlz c:en 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 masses pcbd / c.+d :lev)qy:glbt ;y;.me:qw $m_A$ = 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 ine)kb3 pn8a5wi *19h(knb aeeeto an alpha particle and a smaller nucleus. What will be the speed of this raa)n3eknkibpe ewe(* 1 h59b8ecoiling 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 target) is fired at an angl pfhku hbu6 ztx i 0;vwn;12k3w191nzse 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 uin ser1r.t:y evlhn, k0.s/5$^{\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 ljh7n0zd/x .y rimit on mass m if it is to rebound from M, slide up the incline, stop, sli0hjx/.d zr 7nyde down the incline, and collide with M again?    kg (Let A represent mass m, and B represent mass M.)

  The gravitational slingshot effect. Figure 7–63 av+1 ( d+jyln h+rn*qstnnh47 shows the planet Saturn moving in the negar3+d *hnthj1n+6vq(ln+any s tive x direction at its orbital speed (with respect to the Sun) of 9.6km/s The mass of Saturn is $5.69 \times10^{ 26}$kg A spacecraft with mass 825 kg approaches Saturn. When far from Saturn, it moves in the direction at 10.4km/s The gravitational attraction of Saturn (a conservative force) acting on the spacecraft causes it to swing around the planet (orbit shown as dashed line) and head off in the opposite direction. Estimate the final speed of the spacecraft after it is far enough away to be considered free of Saturn’s gravitational pull.    km/s