We claim that momentum is conserved, yet most moving objects eventuallezeeh+z 2y- (hvjy573q /jjupy slow downjjeezy 5v yh 237(pej-+h/quz and stop. Explain.

When a person jumps from a tree to the ground, whrnxf8 . 5.6hqn5rszytja0(vny e /3dlat happens to the momentum of the person upon striking the ground6szrn 5 th l(v rd3xny5nq.fyaj8/e 0.?

When you release an inflated but untied balloon, e r7c:qz)trt q .c*u 5o-i9xzuwhy does it fly across the roomci) x9-u 7t5zuzrq qeo*cr:.t?

It is said that in ancdbz;l k3jx +p)ient times a rich man with a bag of gold coins froze to death while stranded on a frozen lake. Because the ice was frictionless, he could not push himself to shore. What cox b)j;z+l kd3puld 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 ft (4dpx4o +/:gb +ba3t akqnnand is essentially in3 pqbx atbnoad:4(k4nf+t /g+ a vacuum?

According to Eq. 7–5, the longer the impact time of 0loqr) 7 o3yix8pbf*ran impulse, the smaller the force can beq b ry8loi f3p*0)xr7o for the same momentum change, and hence the smaller the deformation of the object on which the force acts. On this basis, explain the value of air bags, which are intended to inflate during an automobile collision and reduce the possibility of fracture or death.

Cars used to be built as rigid as possible kl+. ex8:yivn/oak u0n3ww b8d(t-zm to withstand collisions. Today, though, cars are designediyno+3 /w(0e:8mk da-8nkblvxw t.u z to have “crumple zones” that collapse upon impact. What is the advantage of this new design?

Why can a batter hit a pitched baseball further than a ball toss:8gqsx1 )el,qwnq :gp ed in the air by the batq w 8gle1: ,)n:sqpqxgter?

Is it possible for an object to receive a larq. 2z(kjpwo )1srg: pbger impulse from a small force than from a large jr(.qp)z2g k pbw:1o sforce? Explain.

A light object and a heavy object have the same kinetic energy. Which5 g2sunq8b2 +dz, eaam has the greater momentum?+zusa m8qbe5 , ga2n2d Explain.

Describe a collision in which all kinetic energy is ld) + zk*keu)ryost.

At a hydroelectric power planz0 (iwo)kh cp7ot3mw*kzg(y+ t, water is directed at high speed against turbine blades on an axle that turns an electric generator. For maximum power generation, shouhc3(kw ymgp *t oiz7() kzwo+0ld the turbine blades be designed so that the water is brought to a dead stop, or so that the water rebounds?

A squash ball hits a wall .7 wza4b(1of 4cjgp 8mwifd b6nu3rc. at a 45 $^{\circ} $ angle as shown in Fig. 7–30. 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 ontops6)8+8gyh5jrc(cw bmt ;ssc a hard 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) for a piece of pu88smt5 css hry;bccjw 6+gp) (tty that falls and sticks to the steel plate.

Why do you tend to lean backward when carrying a heavy lo*i wfcn ;9diucyneu4+b06 e0vj-x dg)ad in your arms?

Why is the CM of a 1-m lengthy d7yv8z- thovcnn;r4.k f4iqq*da+2 of pipe at its mid-point, whereas this is not true for youi*;hko v7t2c8 y.n4ydf4qnzqv - ra+dr arm or leg?

Show on a diagram how your CM shifts when you change from a / ypzy(en(g* llying position to a sitt z ylge(npy/(*ing position.

If only an external fojk*k-qv 4nqif; 0jhwkq)-j -uqpl z47 rce can change the momentum of the center of mass of an object, how can th* kk;hk jqp -jzi0-qnv jwqu)474-fqle internal force of an engine accelerate a car?

A rocket following a parabolic path throuqhuz z3/djyu .ff2qo2zi 8g+ ;g7c5pcgh the air suddenly explodes into many pieces. What can you say about the motion of this qyi3 phu; 8zg q2gc.dozzfu+/7 25cjfsystem of pieces?

  What is the magnitude of the momggp. 4:xw.f haentum of a 28-g sparrow flying with a speed of 8:fxgpg hw 4..a.4 m/s    $kg\;m/s$

  A constant friction force of 25 N acts on a 65-kg skier for 20 s. eo3r*mcqr( a dbp9bq k1w4(0oWhat is the skier’ b dcepr(owr9mkq(q o4b130a*s change in velocity?    m/s

  A 0.145-kg baseball pitched at 39 mn 0y7gsbkr 4h4*zs m2n/s is hit on a horizontal line drive straight back toward the pitcher at 52m/s If the r442znhsngm 0*y k7sb 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 of0i 0d lpum)wr /f:jp)a 10 m/s Fig. below Calculate the velocity of the boat immediately after, assuming it was initially at rest. The mass of the child is 26.0 kg, and that of the boat is 45.0 kg. Ignore water /m0fj0dru )w:pal)pi resistance. The velocity of the boat is    m/s

  Calculate the force exerted on a rocket, given that the prorqk6:r;8dq6 +sd88i al egvzjpelling gases are expelled a886ierzvla s dk+;qgjqr: 8d6t a rate of 1500kg/s with a speed of $ 4\times10^{4 }$ (at the moment of takeoff).$a\times10^7$ N a =   

  A 95-kg halfback moving at 4.1m/s on an apparent breakaway for a to zqul(.3o hg c6l/by,auchdown is tackled from behind. When he was tackled by an 85-kg cornerq l 6ayz3.h(cl /,uobgback running at 5.5m/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 wicu1n )m9v)evsw;*h,g8d x/ s gfmz(gs th a constant speed of 18m/s A 5350-kg load,initially at rest,ns)*e;w v/m hvcg xsm1 sz9,) g8gd(fu is dropped onto the car. What will be the car’s new speed?    m/s

  A 9300-kg boxcar traveling at 15m/s strikes a second boxcar at rest. The two stiht9df +fmg5qm2..+ydf umu. *mtx0 rsck together and move off with a speed of 6m/s W.fmmf+d+xu.y9*uqg ft h2m 50rdms.that is the mass of the second car?    m/s

  During a Chicago storm, winds can whip horizontally at speeds(* v+)wty dneh of 100km/h If the air strikes a person at the rate of 40kg/s per square meter and is brought to rest, *d)tve h+n w(yestimate 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 railr6( rv 8ifvp6qg 2t+3qyge9o mooad car coasts along with a constant speed of 8.6m/s on a level track. S oq (vy6 +ogqe36i9rvp8t2gmfnow begins to fall vertically and fills the car at a rate of 3.5kg/min Ignoring friction with the tracks, what is the speed of the car after 90.0 min?$\approx$    m/s

  An atomic nucleus initially moving at 42.cy qrkh9/ls1 0m/s emits an alpha particle in the direction of its veloc/sl yq k.9hcr1ity, and the remaining 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 l2qg bj- 31nwdr9eiha2w3c72 dm;avl penetrates a 2.0-kg block of wood and emerges cleanly at 170m/s If the bl 9ml cjhve371g-nbdrq3 l 2a22dawi;w ock is stationary on a frictionless surface when hit, how fast does it move after the bullet emerges?    m/s

  A 975-kg two-stage rocket is traveling at a spee6ylq oenav;; v*8qg 2w24bqb jd 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 velociv-,h+w0vi*jl if+)nnc85wn f*enm xz ty of 115m/s To alter its c,z5n)i hen vjwl8*nc + 0-fixm nfv+w*ourse 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+. jkuz2oogh7x0 f/fk6,w tyj ;ogao* of 45m/s The golf club was in contact with the bal ;o0 k +fwyojgx2 o7tfkjg6aho./*z,u l 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 r.c z+,)fk o/qg*y01 yld suqynb.bp;fest in a time intervag/z1)cf0. *dlb yqp+.,ok y;y nqs ufbl of 8.0 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 and speed v=25m/s strikes wzl2 u t+a f27xf:n2ahz ss5+ia 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 automobilhnoy1) /61x lw jhc8fxe models. Cars are tested by smashing them into fixed, massive barriers at 50km/h (30 mph). A new model of mass 1500 kg takes 0.15 s from the time of impact until it is brought to rest. (a) Calculate the average force exerted on the car blx 6y1 hnwj1fx8)co/hy the barrier. $\approx$$a\times10^5$N a =   
(b) Calculate the average deceleration of the car.    m/$s^2$

  A 95-kg fullback is runnx/3h:8ao q-ayusgu 3king at 4m/s to the east and is stopped in 0.75 s by a head-on tackle by a tackler rua3-uk:ua/yh g 3qxo s8nning 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 2 : 8whhfoo+fki 2qs5l. zb9grtennis ball (mass 0.060 kg) points in the +x direction and is given by the graph of Fo92 8gr5owk lfizfh:s.bh 2q +ig. 7–33 as a function of time. Use graphical methods to estimate
(a) the total impulse given the ball    N*s
(b) the velocity of the ball after being struck, assuming the ball is being served so it is nearly at rest initially.    m/s

  From what maximum height can a 75:;0 e0c ziwawl-kg person jump without breaking the lower leg bone of either leg? Ignore air resistance and assume the CM of the person moves a distance of 0.60 m from the standing to the seated position (that is, in breaking c0:awz;iwle 0 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 of ctuqkae ;y93* jwsf)) dollides head-on with a 03 ead9)qsykfj w; )u*t.220-kg ball at rest. If the collision is perfectly elastic, what will be the speed and direction of each ball after the collision?Let A represent the 0.440-kg ball, and B represent the 0.220-kg ball. $v'_A$    m/s  ----待选择----eastwest  $v'_B$    m/s  ----待选择----eastwest 

  A 0.450-kg ice puck, moving east with a speed of 3m/s has a head-opnu:d/fu 5m,x n collision with a 0.900-kg pu:/5unupd mx f,ck initially at rest. Assuming 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 und ,4ylpubz2i/plb95l.zg y/jz ergo 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.Let B represent the ball moving at 3yj.p g zbp/lylz uli95/z b24,.00 m/s in the opposite direction. ) v'$_A$ =    m/s v'$_B$ =    m/s

  A 0.060-kg tennis ball, movi:s+ f;2hcbpm eqlpmp(, ax )l9ng with a speed 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 direction of each ball after the collision?(Let A represent the 0.060-kg tennis ball, and let B represent the 0.090-kg ep+am ;lsp:pbm l 29q,fc)xh(ball.)v'$_A$ =    m/s v'$_B$ =    m/s

  A softball of mass 0.220 kg that is moving with a speed of 8.5m/s co,kqvz4*kndie;b0a m*3t 5 wbfllides head-on and elas,qt*vf3;m4d w 50 iaz kbe*bkntically with another ball initially at rest. Afterward the incoming softball bounces backward with a speed of 3.7m/s Calculate
(a) the velocity of the target ball after the collision    m/s
(b) the mass of the target ball.    kg
(Let A represent the moving softball, and let B represent the ball initially at rest.)

  Two bumper cars in an amusement park ride collide elastical0 l(mmrlpbk.q n8asd/m h: 0m4ly as one approaches the other directly from the rear (Fig. 7–34). Car A has a mass of 450 kg and car B 550 kg, owing to differences in passenger mass. If car A approaches at 4.5m/s and car B is moving at 3.7m/s c.hk n:sambml qdmlr(/4 800mpalculate
(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 j c 1-bfuz 7-so,rdj2on,r(jlcollision with a second ball initially at rest. The second ball moves off witho-(j,7d -ojurbcjlfzr 2 n1,s 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 incli u l 4qz)fo:3y czw/exfea(m2:ne as shown in Fig. 7–35, and elastically strikes another cube a)e/azfz2 cfq4 wmxuoy:l(: 3et 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: Both leave the incline moving horizontally.]$\Delta x_{m}$$\approx$    m $\Delta x_{M}$$\approx$    m

ake the general case o9ry.)mdg xk21wkmst) f an object 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 fy bucv4. onl3.v w(u1experiment, projectile 1 results in a maximum height h of the penduv n3fucu(y1w bl o.v.4lum equal to 2.6 cm. A second projectile causes the the 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 buri gzlt sdo:2sln+/wy8k wh9q; .es itself in a 3.6-kg pendulum hanging on a 2.8-m-long string, which makes the penduluz.ds qghnll y+ otw98:;/s2wkm swing upward in an arc. Determine the vertical and horizontal components of the pendulum’s displacement.vertical$\approx$    m horizontal =    m

(a) Derive a formula for the fraction of kinetic energy lost, co4wz x+kg(:l zh(6rf$(\Delta\mathrm{KE/KE})$ 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 rest5g9,xv): obf 7 p/ia bszh)hp cusmh02, into two pieces, one of which has 1.5 times the mass of the other. If 7500 J were released in the explosion, how much kinetic energy did each piece acquire? (Let A represent the heavier particle, and B represent thfsihg ap0bp):sb,mh )x9 5v2 hc u/z7oe lighter particle. ) KE'$_A$ =    J KE$_B$ =    J

  A 920-kg sports car collides iwb/pxyp3) wo plhbz. v5b9)0cnto the rear end of a 2300-kg SUV stopped at a red light. The vob.bp ppw0bh) y39l)zcw x 5/bumpers lock, the brakes are locked, and the two cars skid forward 2.8 m before stopping. The police officer, knowing that the coefficient of kinetic friction between tires and road is 0.80, calculates the speed of the sports car at impact. What was that speed?(Let A represent the sports car, and B represent the SUV) $\approx$    m/s

  A ball is dropped from a height of 1.50 m and reboun+i1,t*( myg ;nloq3 j uswf2kwds to a height of 1.20 m. Approximately how mamq,g;2s1 j3 o *+yl(tifwkuwnny rebounds will the ball make before losing 90% of its energy?   

A measure of inelasticity in a head-on collision of two objects*px 7tf1+jt/- xy lv+eklfd 3n is the coefficient of restitujdyf3 ptnxf el /7txlk*++- v1tion, 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 tim wu +n)brd2qn+5tfzgk91ss m3es 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 exp1nsd mgb)n+25fwz9qst ruk+3 lodes, 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 direl53+p e3:a8gpzq i 0z7zxy zoxction at 5.5m/s collides head-on with a 10.0-kg obj7zxg30 +i e:x zz85l poqzy3apect moving in the -x direction at 4m/s Find the final velocity of each mass if:
(a) the objects stick together;   m/s
(b) the collision is elastic; v'$_A$ =    m/s v'$_B$ =    m/s
(c) the 15.0-kg object is at rest after the collision;   m/s ----待选择----not reasonable reasonable 
(d) the 10.0-kg object is at rest after the collision;   m/s ----待选择----not reasonable reasonable 
(e) the 15.0-kg object has a velocity of 4m/s in the -x direction after the collision. .   m/s ----待选择----not reasonable reasonable 
Are the results in (c), (d), and (e) “reasonable”? Explain
( Let A represent the 15.0-kg object, and let B represent the 10.0-kg object.)

  A radioactive nucleus at rest decays into a second nucleus, 4gl veo5l)5 kzan electron, and a neutrino. The4ol 5lvgz5k)e electron and neutrino are emitted at right angles and have momenta of $9.30\times10^{-23}kg\cdot m/s$ and $5.40\times10^{-23}\mathrm{~kg}\cdot\mathrm{m/s}$ respectively. What are the magnitude and direction of the momentum of the second (recoiling) nucleus?    $ \times10^{-22}$    $^{\circ} $ from the momentum of the electron

  An eagle ($m_{\mathrm{A}}=4.3\mathrm{kg}$) moving with speed $\nu_\mathrm{A}=7.8\mathrm{~m/s}$ is on a collision course with a second eagle ($m_{\mathrm{B}}=5.6\mathrm{kg}$) moving at $\nu_{\mathrm{B}}=10.2\mathrm{m/s}$ in a direction perpendicular to the first. After they collide, they hold onto one another. In what direction, and with what speed, are they moving after the collision? v =    m/s $\theta$ =    $^{\circ} $ rel. to eagle  ----待选择----AB 

  Billiard ball A of mass6ub 36vp.jyau ca:lp ( $m_\mathrm{A}=0.400$kg moving with speed $\nu_\mathrm{A}=1.80$m/s strikes ball B, initially at rest, of mass $m_\mathrm{B}=0.500$kg As a result of the collision, ball A is deflected off at an angle of 30.0 $^{\circ} $ with a speed $\nu_\mathrm{A}^{\prime}=1.10$m/s (a) Taking the x axis to be the original direction of motion of ball A, write down the equations expressing the conservation of momentum for the components in the x and y directions separately. (b) Solve these equations for the speed v'$_B$ and angle $\theta_{\mathrm{B}}$ of ball B. Do not assume the collision is elastic. $\theta_{\mathrm{B}}$ =    $^{\circ} $ v'$_B$ =    m/s

  After a completely inelastic collision between two objects of equal mass, eachgiu0qcjc* a c.b-4z. d;nkulk1 f9or( having initial speed the two move off together with speed v/3 What was the angle betwzo i0.c cuajk c (kfulnbd94.*g;1 -qreen their initial directions?    $^{\circ} $

  Two billiard balls of equal mass.s vlmrjd5mc c r,(yn7mhk:.8 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, assumed 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 speekh ry m.7(m:vjmrlsc,c.n 85dds? 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 wiws8ayz vg ax ivd4+617th another atom at rest. After the impact, the neon atom travels away at a 55dv6v7ya18wig axzs 4 +.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 another atom -mjq* w fnvg)v9:wu (lat rest. After the impact, the neon atom travels9)( :v*jf lwwnvq-gm u 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 shown in Fig. 7–38. Specify relahx ajc lz:7;0ative thajcl7;az: 0x o the left-hand 1.00-kg mass.    m

  The distance between a carbon atomiqfzwr313an; +lv 1(wdq4uu zw l p8.s ($m_{\mathrm{C}}=12\mathrm{u}$) and an oxygen atom ($m_{\mathrm{O}}=16\mathrm{u}$) in the CO molecule is $1.13\times10^{-10}$m How far from the carbon atom is the center of mass of the molecule?    $\times10^{-11}$m

  The CM of an empty 1050-kg car is 2.50 m behind the front of upg, i nl,t0frw wf:74e23 hqgthe car. How far from the front of the car will the CM be when two people sit in the front seat 2.80 m from the front of the car, and three people sit in the back seat 3.90 m from the front? Assume that each person has a mae:h,fu3ni t 407w,qp lrgwfg 2ss of 70.0 kg.    m

  A square uniform raft, 18 m by 18 m, of mass 6800 kg, is used a (e3gol8ov e ,hfb9uqo77 8inas a ferryboat. If three cars,fhngbqoa98vi3 (oe ,e7u8 7 ol each of mass 1200 kg, occupy its NE, SE, and SW corners, determine the CM of the loaded ferryboat.$X_{CM}$ =    m $Y_{CM}$ =    m

  Three cubes, of sidespy:*o(cbgsz 8 $l_0$,$2l_0$, 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 ofgcn ldsa4)4k9 n-0mb89wewgu 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 operatwl08g k- gu nm4ane9)4scwb9dor 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 out vj4g ..y5zdfjef -+,+mq p8/zrkrix pof it. The center of the smaller circle is a distance 0.80R from the center C of the larger circle5++pdf,qx8/vgkzj-r. .re4i zjpf y m, Fig. 7–41. What is the position of the center of mass of the plate? [Hint: Try subtraction.]   R

  Assume that your proportio5 8)oilxj( b zj3uvma/ns are the same as those in Table 7–1, and calculate the mass of one(zmv3 juoa lx5i8b)j/ of your legs.    kg

  Determine the CM of an outstretched arm usingf(e w 5h9 *.mljoh+lbm 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 ngzim4g 3,ny3d19 kcgCM of an arm bent at a right angl3gnn ,km1zgi4y dg39ce. Assume 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 hanging zizu7uvb) a m uify/9/os8y)50f .kz bvertically, and his trunk and heuvyza. )7o /b8syu9b5 f)/ui0z ifkzmad 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 Eartgz 7/+myowg,69 r e-gr, )hwvk qfsnx;h 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 ntdl r 7ln-;9sddkne6-,4us usb y v-/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 cylindb4wc00 5j bjsl fob:x-rical 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 the point that wbb0f4c jxwj05s-ol b:ill follow a parabolic trajectory?    cm

  A mallet consists of a uniform cylindrical head of mass 2.00 kgv t7+d,hj5tedpj6alj l-an: g-im2 t2 and a diameter 0.0800 m mounted on a uniform cylindrical handle of mass 0.500 kg and length 0.240 m, as lt l 75+-eni 2pjt dd2jv jah:g-ma,6tshown in Fig. 7–42. If this mallet is tossed, spinning, into the air, how far above the bottom of the handle is the point that will follow a parabolic trajectory?    d    d

  (a) Suppose that in Example 7–14 (Fig. 7–p6xvi mdat2 us:p4oen8g o-y/8 4zbx+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 t7v p(obkrk 5:tejviub 3+op1(he air and stationary with respect to the ground. A:vkv( koob7 b5 p+ip1 e(u3jtr 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 andwfrcr 1gv/bi, a,0 n(r is popped straight up to a heig rfar,,c/01w( bgrv niht of 55.6 m. If the contact time is 1.4 ms, calculate the average force on the ball during the contact.    $^{\circ} $

  A rocket of mass m traveling with speedr 1h7y4aon e-(g*c bpg+tpru m*xyx;5 $v_0$ 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 shown0k w1(i;c- ly2qep-1hu ynhpa in Fig. 7–43. Relative dimensions are also shown. Should the player be worried about this being a “scratch shot,” in which the c1upn2l;e-ya qpyhi( hc 0w-1 kue ball will also fall into a pocket? Give details.

  A 140-kg astronaut (including space suit) acquires a speed of 2li4iqjyqxnaf 8.;v ;j96y:cd.5m/s by pushing off with his legs fro9xy6v;ij8 ynfdc : a;ql qi4.jm 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 anif2tn(j 9vrh2 c1trm4yi 1(ond the other 80 kg, are initially at rest in outer space. They then push each other apart. How far apart are they when the lightn i r 21tvmirct1h2y4(jonf 9(er astronaut has moved 12 m?    m

  A ball of mass m makes a head-on icanc yx+3cm;o b5.g(elastic collision with a second ball (at rest) and rebounds in the oci5xc+mb onyc3ga(;.pposite direction with a speed equal to one-fourth its original speed. What is the mass of the second ball? $m_B$ =    $m_A$(Round to two decimal places)

  You have been hired as an expert witness in a cvwy )oi,p6d,j ourt case involving an automobile accident. The accident involved car A of mass 1900 kg which crashejd6i, ,yow )vpd 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 brakes.    mi/h

A golf ball rolls off the top of a flight of concrete steps of total vertic2x bgrd,2 rz0aal 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 are perfectly elastic, what is the bounce height on the fourth bounce when the ball reaches the bottom of th, 20dbzr ga2rxe stairs?

  A bullet is fired vert3 tllbheulb sut ;v858q.g97dically into a 1.40-kg block of wood at rest directly above it. If the bullet has a mass of 29.0 g and a speed of 510m/s how high will the block rise after the bullet be8u 38 bt5.s 9dlugvhbl qe7;tlcomes embedded in it?    m

  A 25-g bullet strikes and becomes e+ko h-v5jwx -kmbedded in a 1.35-kg block of wood placed on a kxkw + -ohj-5vhorizontal surface just in front of the gun. If the coefficient of kinetic friction between the block and the surface is 0.25, and the impact drives the block a distance of 9.5 m before it comes to rest, what was the muzzle speed of the bullet?    m/s

  Two people, one of mass 75 kg and the other of maop4g nu (pdu+4ss 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 directionpg4udpo (u+4n 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 p:55afy4c uq+*7u j1 hdnpdqb was 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 two fragments by*s0e dqa;dq/ u an explosion. One fragm; d0udq*sq a/eent acquires twice the kinetic energy of the other. What is the ratio of their masses?   

  The force on a bullet is given by thev xc( k/sodclz8s6 *u5 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 j5j;qf xs51 bvs;g:uh$m_A$ = 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 radioa2ixaf*p gijlw l4xx4k46gp4 ) ctively into an alpha particle and a smaller nucleus. What will be the speed of this recoiling nucleus if the speed of the alpha px4 4xi jl*fkp)4 6wxliagg42particle 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 f-aa+jbs/c1r3x8wi 7 pp f.idat 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 slidkws/bd tjva,, mkf nc)2 s8a43es 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),r j*z;s1cl no, what is the upper limit on mass m if it is to rebound fr*j o 1n,rl;sczom M, slide up the incline, stop, slide down the incline, and collide with M again?    kg (Let A represent mass m, and B represent mass M.)

  The gravitational slingshot effect. Figure 7–47 shows the planet Saturn0t ew :/:f1ta2:lctb- gwtwg z moving in the negative x direction at its orbital speed (with respect to g0 t2lc- t: t1::aw/eg ftwwzbthe 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