We claim that momentum is conserved, yet most moving objects et.ey;hym 7vhk.fm19i ventually slow down and sm7k vhey fy. im;.h1t9top. Explain.

When a person jumps from a tree to the ground, what hap6z+or d :elf +ddww-;hpens to the momentum of the person upon striking the grounr dw ze:h-;dwdfo+ +6ld?

When you release an inflated but untied balloon,8fpmk3tl:md.ls :av 0 why does it fly across the room?pav:0:mfkms t 3dl.8l

It is said that in ancient times a rich man with a bag of gold coins froze tmj-ouha1trp 50 - zr6*rwho n7o 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 ht7ano6--rm5pj zo rw0hu1*r been so miserly?

How can a rocket change direction when it is fybnix7svybmp3m ,i1 392*5uf quydq0d vp.f. ar out in space and is essentially in qbd.uf3u2.m 1fmvyy iq iyb79n,*3svxd pp50 a vacuum?

According to Eq. 7–5, the longer the impact l-/1osrjdqiwu.8a m)time of an impulse, the 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 during anm) - uqi.oarl/8dswj1 automobile collision and reduce the possibility of fracture or death.

Cars used to be built as rigid as p8/hyg,3 wefub 16*j7td g kicaossible to withstand collisions. Today, though, cars are designed to have “crumple zones” that collapse upon impact. What is the advantay83d /j tc7b6 kgf1w*i,egauhge of this new design?

Why can a batter hit a pitched nt+9nwuc7dd 8p kje30baseball further than a ball tossed in the air by tkd7 3cp0j 8+nnuetd9 whe batter?

Is it possible for an object to receive a larger impulse from a sm3t 45u0d sle1 bek.dfyall force than from a large fou0d t1dk y.b3efe4ls5rce? Explain.

A light object and a heavy object have the same kinetic energy. Which ha.qlsx)dc e: r; weag 95.bji7hs the greater momentum? Ex9x)ga.. ieqh ;5wbec d:lrs 7jplain.

Describe a collisionoi tiq)- n3 djb43q1yk in which all kinetic energy is lost.

At a hydroelectric power plant;r baoecz8.0xv3n ) bqg.pr z+, 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 dexa r.nz;)ro vb.p 80+bgzc3qe ad stop, or so that the water rebounds?

A squash ball hits a wall aw 4wqq;8ooq 0st 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 onto a hard steel plate (fixed to t 2ff:2a 0.nfw;pj8u,hwa xr dohe Earth), from which it rebounds at very nearly its original speed. (a) Is the momentum of the ball conserved 2;rx,pf2fjoandh:.8 0ua w f wduring any part of this process? (b) If we consider the ball and Earth as our system, during what parts of the process is momentum conserved? (c) Answer part (b) for a piece of putty that falls and sticks to the steel plate.

Why do you tend to lean backward when carrying a heavy load *lgeh m u kq7*d4;w(fdin your arms?

Why is the CM of a 1-m length of pipe at its mp+ hd t+g(9gybid-point, whereas this is not true f h (+btdgyp9g+or your arm or leg?

Show on a diagram how your CM shifts whe(pn xu ,5ijlr0n you change from a lying position to a sitting posit0,jr xpi(l5n uion.

If only an external force can cha y hh8)bq61 n,hs3ax9ficps8+bgl 1p mnge the momentum of the center of mass of an object, hy 8hgp9q 8xb)1hbs,3 lmf6 ic1h+anps ow can the internal force of an engine accelerate a car?

A rocket following a parabolic path through the air su:wasqq(2*.zo+9o hm1w l woyoodyx9/ ddenly explodes into many pieces. What can you sa (zq/ yyom9. dwooo1+ lh9a2xowqws:*y about the motion of this system of pieces?

  What is the magnitude of the momentum of a 28-g sparrow flying with a speed ofxse3 ehfjl mj45h f)da*4 m8t1 815femxhltdjh*s83 m)4 je4f a.4 m/s    $kg\;m/s$

  A constant friction force of 25 N acts on a 65-k/zak6 x z 3gxd6w:.saug skier for 20 s. What is the skix gd .u:z6aka63s/xz wer’s change in velocity?    m/s

  A 0.145-kg baseball pitched at 39 m/s is hit on a horizontal line drive st)gdpsga cj0yq qkq0. :2-ku2mraight back toward the pitchqa2ds0 u. kk:gjqy0 m g-qc)p2er 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 ;0tyh r z f* *:mhndsazw;on)+horizontally with a speed of 10 m/s Fig. below Calculate the velocity of theafh ztwo;d; m0 *rn+n)*s: yhz 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 velocity of the boat is    m/s

  Calculate the force exerted on a rocket, given that the propelling gk064pzvq zk5 sases are expelled at a rate of 150pksz5 z6k0q4 v0kg/s with a speed of $ 4\times10^{4 }$ (at the moment of takeoff).$a\times10^7$ N a =   

  A 95-kg halfback moving at ) hd4v *bhe- q99fprla 0.dafi4.1m/s on an apparent breakaway for a touchdown is tackled from behind. When he was tackled by an 85-kg cornerback running at 5.5m/s in the same direction, what was their mutual spp*)bdf9e aq 9id-va4. hf0lrheed immediately after the tackle?    m/s

  A 12,600-kg railroad car travels alone on alegb.*odhi) ffhn;:2kn r)d va.tk, :usvel frictionless track with a constant speed of 18m/s A 5350-kg load,initially at rest, is dropped onto the car. What will be the car’s nv.h :bhfds)*dn k;an.t:)fu rg 2oi,kew speed?    m/s

  A 9300-kg boxcar traveling at 3 3pv.z f,x qrqxgvp+(15m/s strikes a second boxcar at rest. The two stick together and move off with a speed of+ 3,x rvvqz3.pqxg(fp 6m/s What is the mass of the second car?    m/s

  During a Chicago storm, winds can whip horizontally at speep o-ry ,oa;gako*+ey7ds of 100km/h If the air strikes a person at the rate o7o y* +; g-oaayrk,poef 40kg/s per square meter and is brought to rest, estimate the force of the wind on a person. Assume the person is 1.50 m high and 0.50 m wide. Compare to the typical 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 y1 humm g1cz/r(4-kr2m. vyjw r)cx s(car coasts 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 of 3.5kg/min Ignoring friction with the tracks, what ivmr12)1m um(-jk zcr4c/wxy( s yhr.gs the speed of the car after 90.0 min?$\approx$    m/s

  An atomic nucleus initially moving at 420m/s emits anup+;w+ rpgqcx.2.3*q shv .ykc kl* br alpha particle 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 v.cp*wy+3 l *bqkc;h+ 2urx.q pksgr. nucleus has a mass of 222 u, what speed does the alpha particle have when it is emitted?    m/s

  A 23-g bullet traveling 230m/s penetrates a 2.0-kg block of woommk jy03 *p)qvk i,ed a1y32djd and emerges cleanly at 170m/s If the block is stationary on a frictionless surface when hit, how fast does it move a d0*eji pm3qk3yj 2,)dyvakm 1fter the bullet emerges?    m/s

  A 975-kg two-stage rocz+ug(c8f u0c81i i b kua;ko4kzf*t uh6-a nv4ket 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 in outer space with a v6p )b2e2jl0 m*0hhxui m fou0xelocity of 115m/s To alter 0h0j)ub 62x0 m*pl2 ofmxeihuits 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 kfd(6lv::;e55suc tu 8wkt ie is hit off the tee at a speed of 45m/s The golf club was ut;c65vt8s eu :kwf: de(kli 5in 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 vs6rg*imlzx:-1pz8q kl4/ btielocity of 8.5m/s and comes to rest in a time interval of 8.0 ms. (a) What is the impulse given tbpzl 4kzgrs-imq txi l168* /:o 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 g06dl fhiwck;o: 8 j4sstrikes 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 v l03gg)zjlo +of new automobile models. Cars are tested by smashing them into fixed, massive barriers at 50km/h (30 mph). A new model of mass 1500 kg takes 0.15 s from the time gj+lzl3 0vog)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 *ffw;v ;lrd)et d83gq to the east and is stopped in 0.75 s by a head*vd);f ;frtg le3qwd8 -on 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(surry:;/x 4.bkz k)j,vc/c i(wetxg) points in the +x direction and is given by the grks.z)b k4rwtejr: ( u,/y;i g (vccxx/aph of Fig. 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 8x m6,rmxw7 qb75-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 i w6x,8qrmm b7xs, 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 of colltfq1dvorwf29l-)k wn+6bszg 0let(s 7(4i in ides head-otn i-f7r9) w2(t(e4 1wf0z6 gvsbln+sidlqkon 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 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 (/:a u3kokxj 2jhs.xewith a speed of 3m/s has a head-on collision with a 0.900-kg puck initially at rest. Assuming a perfectly elastic collision, what will be the speed ke2x h:j.o sj(akux 3/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 perf + r qqkffo4):gc)av*dectly 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 tdq *a4:)ckvo +frgf)qhe 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 1 z:p joq:io- xjj1j0hb*dit(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 tennt: jio b1qh1j*:zxi od-j 0(pjis 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 5 6 +nqm 4;3hlixfiuhp,u zlzmp0,7qnthat is moving with a speed of 8.5m/s collides head-on and elastically with another ball initially at rest. Afterward the incoming softball bounceph+47hzu nfxzuqn ,i0 pq,l53; m6mlis 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 shgim c a-hs:ly1b9, b2 bs**bride collide elastically as one approaches the other directly from the rear (Fig. 7–34). Car A has a mass of 450 kg and car B 550 kg, owing to differences in passenge:bmghc*syb , ab i*91h- s2slbr 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 .zd-lxl1hj; lx2j m /thead-on collision with a second ball initially at rest. The second bal2md l;l l1h/xjz x-tj.l moves 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 frictionle(yeq*psnsm /0ss 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(sn* y0eq/mp s, where does each cube land? [Hint: Both leave the incline moving horizontally.]$\Delta x_{m}$$\approx$    m $\Delta x_{M}$$\approx$    m

ake the general case of xg 7ss:-xg(z) odlw4aan 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 experiment, projectile 1 results inq zsom(tun0jg8x1 9)/-ctauk a maximum height h of the pendulum equq(k08tg-m u )js cnoxua1t/9z al 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 buries itself in a 3.6-kg p38v w bpbgbmppz +1+ u/y24tzrendulum hanging on a 2.8-m-long string, which makes the pendulum swing upward in an arc. Determine the vertical and horizontal components of the pmz v2g1u3b +zbyb ptr/+8pw4 pendulum’s displacement.vertical$\approx$    m horizontal =    m

(a) Derive a formula for the fraction oau 3 ok+e2ous:f 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, k :jufw8 d5p0ou a9 sdm1aw28ointo two pieces, one of which has 1.5 times the mass d9ma suf 1w:2jpa8 u5o od08wkof the other. If 7500 J were released in the explosion, how much kinetic energy did each piece acquire? (Let A represent the heavier particle, and B represent the lighter particle. ) KE'$_A$ =    J KE$_B$ =    J

  A 920-kg sports car collides in1j*k /vz c)yeato the rear end of a 2300-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 impact. 1/zj) c*aekyv 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 j66c2yh5tym-sgblyf 5t +tf4)y3xo z1.50 m and rebounds to a height of 1.20 m. Approximately how many rebounds will the ball make before losing 90% of its energy?5gy6x jfct by5 y-l3t)+ys2hot mz64f   

A measure of inelasticity in a head-on collision of two objects* oz;v mo wq fmw,d(gq,mk7m5: is the coefficient of restitution, e, de:qf;d,zwmmk (vq,go* w 57mmofined 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 g1/a;a ) t omx4nbu3ghk+-xmbof 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 firem ) ;akb- 1/tnoxh3gxmbaug+4cracker explodes, the two blocks separate and slide apart. What is the ratio of distances each block travels? ----待选择----1/91/101/81/6 

  A 15.0-kg object moving in the +x direction at 5.5m/s collides head-on m0x3d ;y3 ,wlbcnic.n) xby1b .n4h kpwith a 10.0-kg object moving in the -x direction at 4m/s Find the final velocity of each mc;n.y4x)y i,bpb n.kb hd03n3lwmc1x ass 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 electron, t7k5 q20m cc*slnmm 1rand a neutrino. The electron and neutrino are emitted at right angles and ham*7 5 0mn1tscqkmcrl2ve 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 mf5z;z oj4ujh+ ass $m_\mathrm{A}=0.400$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 ine41nq*u 8 lugjolastic collision between two objects of equal mass, each having initial speed the two move off together with speed v/3 What was the angquo un* 84jgl1le between their initial directions?    $^{\circ} $

  Two billiard balls of91-nru0mj alq )g- xy; nfbcv)be85 zkjrl45p 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 em q80k55) ylv-b4lzf bc)xr1u-ngan p9 r ;jjspeed 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 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 another 4)mrbl0r;rzy-lp-v p 7v4l vyq/jc-p atom at rest. After the impact, the neonmp z-vyv-q7r;p /r)lvyllb4 0-prj4 c 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 e 51ovwqtgjrkdd 57tf*/ vu6+hlastic collision with another atom at rest. After the impact, the neon atom tr 1/6dhuk+rtvqv wj57 *gdto5favels 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. Specifrdpry66qv 1d2n48 cppy relative to tc4 2r6 pvry68dpd np1qhe left-hand 1.00-kg mass.    m

  The distance between a carbon a)d //hxpa)eqltom ($m_{\mathrm{C}}=12\mathrm{u}$) 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 car6s 2.06z/ffajlcbdnl is 2.50 m behind the front of the car. How far from the front of the car will tfld/ .z602fajnb csl6he 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 mass of 70.0 kg.    m

  A square uniform raft, 18 m by 18 m, of mass 6800 kg, is used as a ferryboat. I uwfoxh4 l5 k8m :4/oadzci7j+f three cars, each of mass 1200 kg, ow4 +fk:oi4zjm xo c dlu5ha78/ccupy its NE, SE, and SW corners, determine the CM of the loaded ferryboat.$X_{CM}$ =    m $Y_{CM}$ =    m

  Three cubes, of sidesd.bk r xdoi4)vvjvrc8/77h 5dud ,;sp $l_0$,$2l_0$, 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 (se68 5s gabn8tbre Fig. 7–40), each of which is a cube of length l. Find the center of gravity in the horizontal plane, so that the crane operator can pick up the load without ti6sgab8 tbrn 85pping it.$X_{CM}$ =    l $Y_{CM}$ =    l

  A uniform circular plate of radius 2R has a circular hole of radius R cut o9-; pwap 7 fw6,xx2lbnnx 0dawut of it. The center of the smalwbx0, ;796w l-paxfpxda 2n wnler 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 7–1,ld30i t9dl gf 6i5-atv and calculate the mass of one of youradv9t i - 5llg6tdif03 legs.    kg

  Determine the CM of an outstr3 ug;f5: yn)r2+t1hy c:w kdm4cc sxjaetched arm using Table 7–1.   % of the person's height along the line from the shoulder to the hand

  Use Table 7–1 to calculate the position of the CM of an arm am o)k)c:qn,nvsw w9; bent at a right angle. Asq , )wwks9:)mncvo;an sume that the person is 155 cm tall. $X_{CM}$ =    cm $Y_{CM}$ =    cm

When a high jumper is in a positio2 r tdxzb)hi/+;d gn3j mc+5ivn such that his arms and legs are hanging vertically, and his trunk and head are hori)dzr/ c ;ix+ hgiv2mjtb5dn +3zontal, 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 Moon are(*qxsva pn xx/w,m.+ kxsi3c1 $5.98\times10^{24}$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 mxcza3 sg- s0p(r(. wtfrictionless 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 ancva8 - /:ao.ejhcx0liyzi7k5 d 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 t.aiz: v8oi/5yaexh- ccl 70 kjhe bottom of the handle is the point that will follow a parabolic trajectory?    cm

  A mallet consists of zbuqyv;. -r fbo- 6 u7b.3miczz/jnl4tg(h4ja uniform cylindrical head of mass 2.00 kg and a diameter 0.0800 m mounted on a uniform cylindrical handle ovj bzlzic b(jn q4 f.zg ;uy-.r437btu-6/hmof 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?    d    d

  (a) Suppose that in Exampjdmr3 t6z (ec.l-/)exzv rq3wle 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 M7p lhkms kroy/23 wwqg7x3(1c , are in the air and stationary with respect to the ground. A passenger, of mass m, then climbs out and slides down a rope with speed measured with respect to the balloon. With whatg kqs omkh7/p(2c3x7y rw3w1 l 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 poppimy9;l t+1cel(cyn clv*w, :m s4p5mqed straight up to a height of 55.6 m. If the+: 4tq*y(lsmcmi51 plly9 wm,cc; vne contact time is 1.4 ms, calculate the average force on the ball during the contact.    $^{\circ} $

  A rocket of mass m traveling wi ;+es9rwdsdx3rb2q)y th 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 t i*ml7n.-8rlj- m(b j7tjvjla9lsxtm6 db 8t3he 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 which the cue ball will also fall into a pocket? Givet 7a3m *bjj8lb8t9 .rtlmmdv s6- liln(jj -7x details.

  A 140-kg astronaut (including space suit) ,rxi3yb) kh tl dvc9p+ql-m46acquires a speed of 2.5m/s by pushing off with his legs frlv9-qx6r+ch t ,dmpi 4lky)3bom 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 aipz 2oyiw e4pyeg3llr m.bo* y6*7i.*t rest in outer space. They thygi*i r 3l7 p.m4.* eo*yb6ipeoylw 2zen push each other apart. How far apart are they when the lighter astronaut has moved 12 m?    m

  A ball of mass m makes a head-on elastic gaq/ a7z+e:2ahq w3 eocollision with a second ball (at rest) 7 z3q:o ageqeah/2 w+aand rebounds in the opposite 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 a.4ss wa.t srv7sqw. 6ksy,m)wn ,d9hvs an expert 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 dmw w ,n)..vv7 9 hsawqs. tks6ss4,yrthe 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 cca)b8 lq cri.jrf6t +.oncrete 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 all collisions are perfectly elastic, what is the bounce height on the fourth bounce cir)68j.c .q+ lb tfrawhen the ball reaches the bottom of the stairs?

  A bullet is fired vertically into a 1.40-kg blockf.4m( za3zwnbnnr/ i - 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 becomes ezw z4i mba-n3.n/nrf( mbedded in it?    m

  A 25-g bullet strikes and becomes embedded in a4 de jl*m74yt)-e,(yk crrrx h 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 ireek4x* r7l, yct )jyh4- md(rs 0.25, and the impact drives the block a distance of 9.5 m before it comes to rest, what was the muzzle speed of the bullet?    m/s

  Two people, one of mass 75 kg and the other of mass 60 kg, sit in a row() s uqc2d)oicboat 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 qi c (2s)uc)doand 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 aboub bnybj3xs989 )x6 rjht $ 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 an expno57edc:t -ok losion. One fragment acquires twice the kinetic energy of the otht5:nco o7dk- eer. What is the ratio of their masses?   

  The force on a bullet is given by the formula F 1w98on8wzgsf = 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 massesrruu ec hrsq:7,)mbl1uz. 4w/ $m_A$ = 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 decaydqqmi6 7ex,1ac gykq;4 lw5g3s radioactively into an alpha particle and a smaller nucleus. What will be the speed of this recoiling n 6wakm d173g5q i;lcge,y4 qxqucleus 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 angle of 30a5pox a5/5 flnak,nl 4 $^{\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 dow i3ugq8lck xn5 m4z:6kn 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 limit on mass m if it is to r5hziwo17 f q3jebound from M, slide1wiq fjz75h3o 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 pic9 9* mvuojyu2) +5oz/qyovhlanet Saturn moving in ti yz/uqco)o 5hvv2 u9+m *j9yohe negative 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