We claim that momentum is conserved, yet most moving ol h3.j*pn iky 8am+4wlbjects eventually slow down and3m+.alk 8in*4jypwh l stop. Explain.

When a person jumps from a tree to the ground, what happens to the momentum of h78mrsrpjg( : the persjmhrg:sr87p( on upon striking the ground?

When you release an inflated but untied balloon, wnpypaxqc7+r b2*rh(c+ 1fco ry)9 kvf pr5u 0,hy does it fly across the room?+91o0q, f 2nry bcapprc7+r5pr f(*ukvxyhc)

It is said that in ancient times a rich man witn- wx ql5p9fmf1jt 2+kh 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 could he have done to save himself had he nxp 2nwf j9 t-5kf+ml1qot been so miserly?

How can a rocket change direcztr -chge e3 y5q2;nd2tion when it is far out in space and is essentially in a vacuum?eydc t 3h2-g;nq5 rze2

According to Eq. 7–5, the mpv ep/s2ao4g oft57k*v3z- v longer the impact 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 t7pofz*em/pvk53v2 v g ao4-sof 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 tq*v- whb7x 5peo withstand collisions. Today, though, cars are designed to have “crumple zones” t wq bh5exp*7v-hat collapse upon impact. What is the advantage of this new design?

Why can a batter hit a pitched baseball further than a aze bi0;ob( 5 aw3ehhoz8r( .xball tossed in the air by the batoazbh.3(5b 0 ar wh;e8e(xizoter?

Is it possible for an object to receive a larger impulse from a small fos7i pxnt r35g5rce than fro3 xri7s5tng5 pm a large force? Explain.

A light object and a heavy object halxh-m;vl v3 z 31*kuomve the same kinetic energy. Which has the greater mome *;uv 3mhx l-vmk1l3ozntum? Explain.

Describe a collision 7 vw/1 qwgn c.zpm.(aa6u5pgj in which all kinetic energy is lost.

At a hydroelectric power plant, water is direct++iggtwqg- 8u5kq8 edg*: lx ned at high speed against turbine blades on an axle that turns an electric generator. For maximum power kqnwg:t l8*gu++i5xdqg 8 eg-generation, should 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 at aeh:vs 1mu:f8r 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 (fix/k i1m7pdfib,tur1h.u 57 rtxed to the Earth), from which it rebounds at very nearly its original speed. (a) Is the momentum of the ball c7d rft1h5.r /, u7ip kbmi1tuxonserved 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 lean backw0)a xhws*o d 2pf)d3wiard when carrying a heavy load in your arms?

Why is the CM of a 1-m length of pipe at its mid-point,ag (9n3 a+nph92wcewd whereas this is not true forwn2 9agh 3 9ea(wc+pdn your arm or leg?

Show on a diagram how your CM shifts when you change from a x+qc 9 xer )tal.:1uyhlying position to a sitting poxq chye .):9xt+lar1 usition.

If only an external force can change the momentum of the center of mej 5n4 afo)7tqass of an object, how can the interna 75f)aton4e qjl force of an engine accelerate a car?

A rocket following a parabolic path through the air suddenly+5lk/.vhctc9 nvzny-a,z(vo explodes into many pieces. What can you say about the motion of this system of pieces?. vvzk (cv+59acn,tzno- y/ hl

  What is the magnitude of the momentum of a 28-g spa.n gibvhv/3 8urrow flying with a speed of 8.4 m/s8 ni.buv3vh/ g    $kg\;m/s$

  A constant friction force of 25 N acts on a 65-kg skier for 20 s. Wj 6ydbr1zs9,w1unr 80.i hwyuhat is the skier’s change in velocb9rw,hr isy6u1 j.yuw01n8 dzity?    m/s

  A 0.145-kg baseball pitched at 39 m/s iwp fhr39zmj m) pb7l)e+nqt 36s hit on a horizontal line drive straight back toward the pitcher at 52m/s If the contact time between bat and ba+ 37pj em9lwp)f bht) 6nqz3rmll is $3\times10^{-3}$s calculate the average force between the ball and bat during contact.    N

  A child in a boat thoso/ 1(b ;oyowa5z0i nrows a 6.40-kg package out horizontally with a speed of 10 m/s Fig. below Calculate the velocity of the boat immediately after, assuming it was initially at rest. The mass of the child is 26.0 kg, and that of the boat is 45.0/50 (o1wo yi;sonza ob kg. Ignore water resistance. The velocity of the boat is    m/s

  Calculate the force exerted on a rocket, given that the propelling gases are*4d /xs ydgu dcu.;t4-ch(dh d )ai8im expelled at us4*t -xida /h.yg;d4 m d8hid)uc(cda 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 h-0, sj 9tq qc m+jx)o6e*ht(x.qyw1bp z.chnon 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 speed immediately after the tackthx -0 qsxcne)hjq * j.,qh c.t916(mzowb+ yple?    m/s

  A 12,600-kg railroad car travels alone on alevel fricw kzk0k7ryi:tsp6(cldau2.x0 hx88 rtionless track with a constant speed of 18m/s A 5350-kg load,initially at rest, is dropped ont0dzk6k u: al7x0t 8c2ip8h x(kw.rr syo the car. What will be the car’s new speed?    m/s

  A 9300-kg boxcar traveling at 15m/s strikes a second boijdt-p 09 rsdz 2 l+wn38z5cg w1ik-njxcar at rest. The two stick together and move off with a speed of 6m/s What is the mass 290 gpcz n8rwi3j1wdt -+5-sjzi ld knof the second car?    m/s

  During a Chicago storm, winds can whip horizontally at speedsli 8 4dt5rxxa9 of 100km/h If the air strikes a person at the rate of 40kg/s per square meter and is brought to58idxt l9ra4x rest, estimate the force of the wind on a person. Assume the person is 1.50 m high and 0.50 m wide. Compare to the typical maximum force of friction $\mu\approx1.0$ between the person and the ground, if the person has a mass of 70 kg.    N
$F_{on person}$  ----待选择----<> $F_{fr}$

  A 3800-kg open railroad car coasts along with a constant speed of 8.6m/s on 6za +,1olahte kn-8apa level track. Snow begins to fall vertically and fills the car at a rate of 3.5kg/min Ignoring friction with the tracn8 +-a1 ezl,ataohkp6ks, what is the speed of the car after 90.0 min?$\approx$    m/s

  An atomic nucleus initially mov iv k/fvvlspr0z8o1+*6u5wpe2 k3ndping at 420m/s emits an 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 o we*pr/oi pz052lkp6u v f k38dns+1vvriginal 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 bloc ;qk sy(di6 n zgvf*y3t,f):it9epa 2ik of wood and emerges cleanly at 170m/s If the block ipsiytneqat9fki,6 (yz id;)23v :g f* s 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 speedxz)zdsi:9gx e:s f7 o5 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 ishozj+ c8 7*ybku5ps7c+/rqa w traveling in outer space with a velocity of 115m/s To alter +cb7w/ zp*hroycauk 8qsj +7 5its course by 35.0 $^{\circ} $, its rockets can be fired briefly in a direction perpendicular to its original motion. If the rocket gases are expelled at a speed of 1750m/s how much mass must be expelled?    kg

  A golf ball of mass 0.045 kg is hit offjx. :txe/i +i/pkr;ua txvn23 the tee at a speed of 45m/s The golf club was in contactujii/n3taptekv ;rx.x+:2x/ with the ball for $3.5\times10^{-3}$s Find (a) the impulse imparted to the golf ball,    kg*m/s
(b) the average force exerted on the ball by the golf club.    N

  A 12-kg hammer strikes a nail at a velocity od7m0m yphf fx*4nm;r/ f 8.5m/s and comes to rest in a time 0/f7 yn;m4xmf*rm hdpinterval 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 a wall 6eyp noue2z;s wcti38( 7o6hd/s;ogs 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 ni 3+ xd;etq-h00dwjexew automobile models. Cars are tested by smashing them into fixed, massive barriers at 50km/h (30 mph). A new model of mass 1500 kg takes 0.15 s from the time of impact until it is brought to rest. (a) Calculate the average force exerted on the car by the barrier. x;ewddx3 e+0jt i0q-h $\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 0.75 s-rx7qv42 jvji by a head-on tackle by a tackj427qrv-vj xi ler 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) points r* rt*ahm)r/ i4p hz9bin the +x direction and is given by the graph of Fig. 7–33 as a function of /rt)rm b a*9irzp*hh4 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 heigh.phf,;ibqm- 2hmzix(t can a 75-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 stan x-h,m(.p fz2;b himiqding 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 dirn,idgive5 g9)79liip ection) with a speed of collides head-on with a 0.220-kg ball at rest. If the collision is perfectly elastic, what will be the speed and direction of each ball after the collision?p)vlni 99eig7ii,5 dg 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 spzr5 k4r-qph lc,6 wbt2eed of 3m/s has a head-on collision with a 0.900-kg puck initially at rest. Assuming a perfectly elastic collision, what will be the speed and direction of each object after the collision?Let A represent the 0.450-kg puck, and let B representr,5qp26w l4c-tkh rbz the 0.900-kg puck. v'$_A$ =    m/s ----待选择----eastwest  v'$_B$ =    m/s ----待选择----eastwest 

  Two billiard balls of equal mass undergo a perfectly elastic headhz fn8llf:3ur* )f bfysj;1z 2-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 the b* )ufsr:fz3lyjnl hz8;1f2f ir speeds after the collision?(Let A represent the ball moving at 2.00 m/s, and call that direction the positive direction.Let B represent the ball moving at 3.00 m/s in the opposite direction. ) v'$_A$ =    m/s v'$_B$ =    m/s

  A 0.060-kg tennis ball, moving with a speed of 2.5m/s collides head-on with a 0yo)yxc()r )pd .090-k)pc ))yr(d yxog 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 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. 5p88xr c,rzsg5x zjxj /pn/ullides head-on and elastically with another ball initially at rest. Afterward the incoming softball bounces backward with a speed of 3.7m/s C .px55zs g,nruj jrxx8zp8/ /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 elastic-o;8s d sjok,y*8lkju+ jsv0 s. 5xcbwally 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 masxys+s0.jk k ovw,j 8lub;c 5*so-8j dss. If car A approaches at 4.5m/s and car B is moving at 3.7m/s calculate
(a) their velocities after the collision v'$_A$ =    m/s v'$_B$ =    m/s
(b) the change in momentum of each.$\Delta p_{\mathrm{A}}$$\approx$    kg*m/s $\Delta p_{\mathrm{B}}$$\approx$    kg*m/s

  A 0.280-kg croquet ball makes an elastic head-on collision with a second bal/wk/*c a nh*z5drr:ynl initially at rest. *nc/*k nrr5dyz:ah /w The second ball 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 frictionless incline as show,;8mlegz bw r)n in Fig. 7–35, and elastically strikes another cube at the bottom that is only one-half its e; grb8,lw) mzmass. If the incline is 30 cm high and the table is 90 cm off the floor, where does each cube land? [Hint: Both leave the incline moving horizontally.]$\Delta x_{m}$$\approx$    m $\Delta x_{M}$$\approx$    m

ake the general case of an(b3b5e9k7ymydeul go7 .r. dq va4 3gi 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 pendulk * owly;fpjz; limt oqr3/9lsp()q63 um experiment, projectile 1 results in a maximum height h of the pendulum equal to 2.6 cm. A second projectile causes the the pendulqloplpy* zw3 sk6m);fr; /(3qtolj 9ium 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 trnr/ ) xr.dd d2sr-(buwuko2 g:aveling 230m/s buries itself 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 h/o(d 2rr)wxn2brd.s-uk d :gu orizontal components of the pendulum’s displacement.vertical$\approx$    m horizontal =    m

(a) Derive a formula for therr0ht6aemocwe3(io6+,4 xy o7 9ivc f fraction of kinetic energy lost, $(\Delta\mathrm{KE/KE})$ for the ballistic pendulum collision of Example 7–10. (b) Evaluate for m=14g and M=380g

  An internal explosion breaks an object, initially at rest, into jkjm/yku;t e)ye0o d-ps.6 mn;e/ dg9 two pieces, one of wdsm)de ee ;otyp/-kn/k9j j. u;60mg yhich 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 the lighter particle. ) KE'$_A$ =    J KE$_B$ =    J

  A 920-kg sports car collides i2d dqw h/vey5hv16 r/jnto 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 sto/h hqd1 v5/d2rwy je6vpping. 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 7 (saz9/zajvlrebounds to a height of 1.20 m. Approximately how many rebounds will the ball make before az97 (j s/lazvlosing 90% of its energy?   

A measure of inelasticity in a head-on collision of twod..x+e o) zqco objects is the coefficient of restitution, e, defi+x eqo)..odz cned 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 pfdghtrtuxg(;v0**9 the mass of the other. A depression is made in both faces of the cut, so that a firecracker can be placed in it with the block reassembled. The reassembled block is set on a rough-surfaced table, and the fuse is lit. When the firecracker explodes, the two blocks separate and slid 9f*h0rpdugxt(vt; *g e 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 ;n4itz;zg )tsnb*i cakr s1kb3u,4o0 +x direction at 5.5m/s collides head-on with a 10.0-kg object moving in the -x direction at 4m/s Find the final velocity of each mass ,urnzncbb 4ask si*;ot01 g;4k z3ti) 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-am y,2l vjeup(r/zw2 decays into a second nucleus, an electron, and a neutrino. The uz jv2pa(wel2, r/m-yelectron 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 mass am9jf6) ;ks,pxs l*mi $m_\mathrm{A}=0.400$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 com .n33au uqfa, k2adk8t-g tm5llision between two objects of equal mass, each having initial speed the two move off together with speedd3.nk mq3u - ,8mktatg5af a2u v/3 What was the angle between their initial directions?    $^{\circ} $

  Two billiard balls of equal mab 2b(n-p2e.q wi7fyx yss move at right angles and meet at the origin of an xy coordinate system. Ball A is moving upward aly(y 2 x.iq fp2nbb7-weong 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 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 colli2ees;8(d -ztz suo y ufia082bsion with another atom at rest. After the impac0bai2zzyd ;t 2 us8(eeo-fu8 st, 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

  A neon atom (m=20u) makes a perfectly elastic collision with a2,b-h/buqxx8r-c xn ut76cw tnother atom at rest.b2,rh nxw- ut 6t ubq8c7/x-cx After the impact, 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 o(.i90 qacand66qu j c)mzzzg8f the three-mass system shown in Fig. 7–38. Specify relative jz 0)96 uda6cqg mncq8zzi(.a to the left-hand 1.00-kg mass.    m

  The distance between 9d5)h py ufg/la 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 iigu, t:s7 hbb*s 2.50 m behind the front of the car. How far from the front of the car will the CM be when two people sit in the front seat 2.80 m from the front of the car, and tihgb7 *b:ut ,shree 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. Ifo,nu)8x+g aunlu irb z:r:k2 6w l+p,w three cars, each of mass 1200wualun+:ou2 b+k 8 x6,prgzn :,lr)wi kg, occupy its NE, SE, and SW corners, determine the CM of the loaded ferryboat.$X_{CM}$ =    m $Y_{CM}$ =    m

  Three cubes, of side6* kmeo4pl3/4i+w h6 jc gqtaas $l_0$,$2l_0$, 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 l smahf385d gv+ev81jxoad of identical cases of tomato paste (see Fig. 7–40), each of which is a cube of length l. Find the cent 8xse8 vm+afvgdhj135er of gravity in the horizontal plane, so that the crane operator can pick up the load without tipping it.$X_{CM}$ =    l $Y_{CM}$ =    l

  A uniform circular plate of radius 2R has a circular hole ofkjb). yj+f7yv-:upeg radius R cut out of it. The center of the smaller circle is a distance 0.80R from the center C of the larger circle, Fig. 7–41. What is vbf+ )u.pjej7 -yy: gkthe position of the center of mass of the plate? [Hint: Try subtraction.]   R

  Assume that your proportions are the same as those in Table 7–1, and calcula/x w;jp1 m8 emz5kb4rmzahr)y3g+*m tte the mas ztmryxj84;h 5g 1km+am*eb m)p3 rw/zs of one of your legs.    kg

  Determine the CM of a;*2 dw0xn5zn d mkp5hbn outstretched arm using Table 7–1.   % of the person's height along the line from the shoulder to the hand

  Use Table 7–1 to calculate the position of the CM of an arrd: +yh l:hjgyw 1iyb+0l1p* cm bent at a right angle. Assy1+rly+hh0bpjdg l 1::w y*ciume 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 v p3tezcw :z-w kz+;z-rertically, and his trunk and head akz wzwte+:crp;z --3zre 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 2 s)z6o iojy,nMoon 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-fwch) m2gl b9dg3:j n74xng.n kg man stand 10.0 m apart on frictionless ice.
(a) How far from the woman is their CM?    m from the woman
(b) If each holds one end of a rope, and the man pulls on the rope so that he moves 2.5 m, how far from the woman will he be now?    m
(c) How far will the man have moved when he collides with the woman? He has moved    m from his original position

  A mallet consists of a uniform cylindrical head of maht.aq6 :xinr, ss 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 bottn x.r,h:6itaqom of the handle is the point that will follow a parabolic trajectory?    cm

  A mallet consists of a uniform cylindrical head of mass 2.00( y5bz+)b ;g rmjw ;ttonyg)c: 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 thano: y();rttzjy+5m gwg b )bc;t will follow a parabolic trajectory?    d    d

  (a) Suppose that in Example 7–14u m)*bmmfvd.mxpt+ 84 (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 ia;-cx5c/ 1;t:ip :jcq pavlxbts gondola, of mass M, 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 ba l;qt5 vpa ;:c-/ccx1axi:j pblloon. With what speed and direction (relative to Earth) does the balloon then move? What happens if the passenger stops?

  An 0.145-kg baseball pitched horizontally at strikes a bat and is po-9e pq. zgm 2+hxf(uqh glyy (ck32v(bpped straight up to a height of 55.c hl -pfy(zg+2qv ( 9(uxmg.hqe2k3 yb6 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 trave4m:.vk;oj0e vka ay*fling 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 shods ru4q+ lux) k8q*ot.wn in Fig. 7–43. Relative dimensions are also shown. Should the player be worried about this being a “scratc8*r4+o. qx)tqk usdluh shot,” in which the cue ball will also fall into a pocket? Give details.

  A 140-kg astronaut (including spazlfnl26m w- a)ce suit) acquires a speed of 2.5m/s by pushing off with his legs from an 1800-kg space la l2n-f6wmz)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 6 na,620ay )wh7ge(+du x kaqna0 kg and the other 80 kg, are initially at rest in outer space. They then push each other apart. How far 0a ay+n)(7anu2 qwxa ged,6h kapart are they when the lighter astronaut has moved 12 m?    m

  A ball of mass m makes a head-on elastic coll 0b4y trirpm7:s+ l9oaision 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 se+rrtso7mp:4l09 iaby cond ball? $m_B$ =    $m_A$(Round to two decimal places)

  You have been hired as an expert witness in a court case inbs:na y4x.5l c1nk+iw volving 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 141a n:b+s 5.cwnlykix8 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 smuv3 ylt-h.7 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 1.3y.- ulsm vh7t0 m lower. If all collisions are perfectly elastic, what is the bounce height on the fourth bounce when the ball reaches the bottom of the stairs?

  A bullet is fired vertically into a 1.40-kg block of wood at rest directcdx .oi;6:li( qbgu: fxlis4zd;f+4dly above it.;;x b+6c(si :i qflfglid:.od44d ux z 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 embedded in it?    m

  A 25-g bullet strikes and bec u/xlxy+-jed6jo )u0 domes embedded in a 1.35-kg block of wood placed on a hor/j + 6lxo)ujdduex y0-izontal 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 masc-d dn/u/c))p kil-iys 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 direcccp/-) u-id y)dik/lntion 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 j( zre ns3(r-f,zu 3myd8;cy4.rrk tbabout $ 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 exp00*i gu ksigffs(7k,dtw k;.glosion. One fragment acquires0sgksf,* g0.t;i k(fwg i7u dk twice the kinetic energy of the other. What is the ratio of their masses?   

  The force on a bullet is given by the formula F = 5b s44z; 5qjborr ee0r,bhxb-3.m /aeh80-( $1.8 \times10^{ 5}$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-d0 xusxnjm9dm+mm a1cd 66v0 $m_A$ = 40g and $m_B$ = 60g are suspended as shown in Fig. 7–44. The lighter ball is pulled away to a 60$^{\circ} $ angle with the vertical and released.
(a) What is the velocity of the lighter ball before impact?$\approx$    m/s
(b) What is the velocity of each ball after the elastic collision?v'$_A$ $\approx$    m/s v'$_B$ $\approx$    m/s(Round to two decimal places)
(c) What will be the maximum height of each ball after the elastic collision?    m

  An atomic nucleus at rest decays radioactively into an alpha particle and a smcep8xv --oy e7aller nucleus. Whatc- -7xp8v yoee will be the speed of this recoiling 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 angle o,d)+ qr alks2tununtp6z,6e6 f 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 slides0oq dhd.ot*2j 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), whax ss 1:7flb:v .wea9mjt is the upper limit on mass m if it is to rebound from M, slide up the incline, stosve:9.s:l 1j7fm axbwp, 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 pl + bcvcjib-d9v8ca5jg zu my4bv+8p**anet Saturn moving in the negative x direction at its orbitalb pu-z**cc9 d 4bcv amjg j5vy+iv+88b 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