We claim that momentum is conserved, yet most moving obj fji )xzl445r2j,c/hj s0 snhjects eventually slow down and stop. Explains0zix 2h,c4sj/ h 54) rfjljjn.

When a person jumps from a tree toj(f8og-gv2zs wag r+t. +;pdc the ground, what happens to the momentum of the person upon striking thea2g zcpgg.8v( or++; - tjswdf ground?

When you release an inflated but untied balloon, why does it fly acros,b/lf tkwq /dp 5bf ;rrd1p;*ss the roompl*ft q5p/r1,b d;rfbw k /s;d?

It is said that in ancient times a rich man with a;r(iw5cz vjd4 bag of gold coins froze to death whilvrij (4;d 5wzce 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 been so miserly?

How can a rocket change direction when*iuwdiz2 xgw4)jqyn*t 9*+r 6nur6l b it is far out in space and is essentially z62+unu jdiw 4n )b*l**wyr rgq9t6 ixin a vacuum?

According to Eq. 7–5, the lv+hl;p )6 mhjkonger 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 of air bags, which are intended to inflate during an automobile collision and r h+mpj;)6 vhkleduce the possibility of fracture or death.

Cars used to be built as rigid as possible to withstand collisions. Todajtwrf2pzc+,tbj) z9 y2 ns2e .y, though, cars are jtrfz2cp2)y,b 2stznj.9e+ w designed 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 tossed in the air cez4 4d(m,c mykmvl:- by the batter?c k,m -mmvcz4 y4(l:ed

Is it possible for an object to r9,;ocnyb g ,uqp1 k6ou(u mb1ueceive a larger impulse from a small force than fcb9ugb,o6nuuo(m;,y q1 kpu 1rom a large force? Explain.

A light object and a heavy object have the same kinetic energyycl5/o 1u7dz *6u hpwi. Which has the greater momentum? Exp 5d*h/c 16wuziyl u7oplain.

Describe a collision in which all kinq 0zjz6 afo7e0etic energy is lost.

At a hydroelectric power plan,+hs:ivr z f-sv,s 7dzt, water is directed at high speed against turbine blades on an axle that turns an electric generator. For maximum power generation, should the tzvh+iz s,-ss 7 ,rfv:durbine 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 a f(hq dygx/8meo1m1f6 t a 45 $^{\circ} $ angle as shown in Fig. below. What is the direction (a) of the change in momentum of the ball, (b) of the force on the wall?

A Superball is dropped from a height h onto a hard steel plate (fixed to the Ea):+dl7cv.(po.c kub qxhs(sn rth), from which it rebounds lsu khc + bp v)((7xs:.n.coqdat 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 putty that falls and sticks to the steel plate.

Why do you tend to lean backward when carrying a heavy load z pm4rf 9. k+18clx 1mo+:elijj7gvlnin your arms?

Why is the CM of a 1-m length of pipe at its mid-point, whereas t 0p v rgfnaw,:upqhsn*k (+7o-r0l wc3his is not true for younr07g wfa*(0hrl3- nuv : s+qpw,op kcr arm or leg?

Show on a diagram how your CM shifts when you change from a lying pk. ,3dsddt b5 *v,omxwom3*tbfm)xj2 osition to a sitting pommkd,) *jvxdo,3ft t. do s b3b*52wxmsition.

If only an external force can chnrh2 .(1pg:dtn*awy.-p0nw xkiclb 3ange the momentum of the center of mass of an object, how can the internal force of 2n:(* .w3.yc-rpnkdl pn 1tiha bgwx0an engine accelerate a car?

A rocket following a parabolic path through the air sny oz xa6 6o+e3yc4ft,qybn :/uddenly explodes into many pbnqon3+ cyoa :y46f ,z/yx6teieces. What can you say about the motion of this system of pieces?

  What is the magnitude of the momentum of a 28-g sparrow flying with a fsez o.mawx mpg jrz2/g j59jd14 +5q:x-t)vaspeed of $8.4 \; m/s$    $kg \; m/s$

  A constant friction force of 25 N acts on a 65-kg skier for 2cbre1n (+ :9s1 um.qcib*g q2ixmsi7b0 s. What is the skier’s change in g+c*9b1ib:2e.m17(c rm qisxiu bq nsvelocity?    m/s

  A 0.145-kg baseball pitched at 39 m/s is hit on a hor: ;*vcz 6bjarjizontal line drive straight back toward the pitcher at 52m/s If the contact time bea*j6c zvj:; rbtween 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 so: yiyg 9fcb;g m6 p(ltfs/51with a speed of 10 m/:6 o(p9y f1mygt sg l5f/bsi;cs 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 resistance. The magnitude of the velocity of the boat is    m/s

  Calculate the force exej(r,mi n*u1/zkzrc *z 4l.puf rted on a rocket, given that the propelling gases are expelled at a rlm4.c/ nz uk rpj 1*zf*zir(u,ate of $1500 \; kg/s$ with a speed of $ 4\times10^{4 } \; m/s$ (at the moment of takeoff). F =    $\times 10^7 \; N$

  A 95-kg halfback moving uqx25z,f +(teky(rpfct4omq;5 *su n at $4.1 \; m/s$ on an apparent breakaway for a touchdown is tackled from behind. When he was tackled by an 85-kg cornerback running at $5.5 \; m/s$ in the same direction, what was their mutual speed immediately after the tackle?    $m/s$

  A 12,600-kg railroad car travels alone on alevel frictionless track zmhfk +t4(wo di4o -e3with a constant speed of 18m/s A 5350-kg load,initially at rest, is dropped onto the car. What will be thihe m-kto3zo+ (4fd4 we car’s new speed?    m/s

  A 9300-kg boxcar trave0j5 k6zdakl ay;(c +liling at $15 \; m/s$ strikes a second boxcar at rest. The two stick together and move off with a speed of $6 \; m/s$ What is the mass of the second car?    $m/s$

  During a Chicago storm, winds can whip horizontally at speeds of dl6ar( .z*e x /paqv3cly/s8n 100km/h If the air strikes a person at the rate of 40kg/s qc(y/.*3dla6 zn8 x/as lpr veper square meter and is brought to rest, estimate the force of the wind on a person. Assume the person is 1.50 m high and 0.50 m wide. Compare to the typical maximum force of friction $\mu\approx1.0$ between the person and the ground, if the person has a mass of 70 kg.    N
$F_{on person}$  ----待选择----<> $F_{fr}$

  A 3800-kg open railroad car coasts along with a constant speed ofc sc8l2 o .bzm:uuf;d;uy .e:v 8.6m/s on a level track. Snow begins to fall vertically and fills the car at a rate of 3.5kg/ms. 8v;cdful ozu;2me. ucyb::in Ignoring friction with the tracks, what is the speed of the car after 90.0 min?$\approx$    m/s

  An atomic nucleus initially moving a5n-oz ;hx :oz: bisn(ct 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 original nucleus has a mass of 222 u, what speeb o(nzcsz;:i n5o:-xhd 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 wood and emerges c snv4f9 21fcv(oe gd+p2t*u bqleanly at 170m/s If the block is1f4c2u+9o(bn*pq e 2sgdt vfv 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 ilo/m2g yz1, pg*1k*ne lz,n jat 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 velocity of;e de/pruhqw xl 046, )c1seth 115m/s Tx 04e )1q/hwc6pdee,rht;ls u o alter its course by 35.0 $^{\circ} $, its rockets can be fired briefly in a direction perpendicular to its original motion. If the rocket gases are expelled at a speed of 1750m/s how much mass must be expelled?    kg

  A golf ball of mass 0.045 kg isin/m 0e exl6vnla17/ k hit off the tee at a speed of 45m/s The golf club was in //7a kexl0mnen6v1 licontact 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+ kjf+lxk.)o a velocity of 8.5m/s and comes to rest in a time intervaxfk).o kla+ j+l 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.d)uok*u+m r6hr doxbq93hxv+t 55i0e06kg and speed v=25m/s strikes a wall at a 45 $^{\circ} $ angle and rebounds with the same speed at 45 $^{\circ} $ (Fig. 7–32). What is the impulse (magnitude and direction) given to the ball?   kg*m/s to the  ----待选择----leftright 

  You are the design engineer in charge of the crashworthiness of new automdm8xeq+)3 mye-tuk*2+b e1z h ogg0 amobile models. Cars are tested by smashing them into fixed, massive barriers at 50km/h (30 mph). A new model of mass 1500 1e uxog a+tmeqmy2h+m*8b-e)3z gd0kkg 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. $\approx$$a\times10^5$N a =   
(b) Calculate the average deceleration of the car.    m/$s^2$

  A 95-kg fullback is runningdm,x cpapuyr 6/8/*gk at 4m/s to the east and is stopped in 0.75 s by a head-on tackle byugk d8*6 /rxmpa /pcy, 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) points in i-+ fed9zvu(1iz aqt+ny-qxk;ep +)95ktpn qthe +x direction and is given by the graph of Fig. 7–33 as a function of time. Use graphical methods top un e1+ q5kfq p9eikx;y+ znvq9azi-t+-dt() estimate
(a) the total impulse given the ball    N*s
(b) the velocity of the ball after being struck, assuming the ball is being served so it is nearly at rest initially.    m/s

  From what maximum height can a 75-kg person jump without br+k8yk3h qgfepyw b*.2w ))dikeaking the lower leg bone of either leg? Ignore air resistance and assume the CM of the person moves a distance of 0.60 m from the standing to the seated position (that is, in breaking the fall). Assume the breaking strek+2w ye8pbi*q) y).ghk3dwf k ngth (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 direcvr88k72dgbz 4 bl-zu ation) 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?Let A represent the 0.440-kg ball, and B represent the k-2u7dvglr bz88 4a zb0.220-kg ball. $v'_A$    m/s  ----待选择----eastwest  $v'_B$    m/s  ----待选择----eastwest 

  A 0.450-kg ice puck, movin: jgy+lw) ktus:ffxfe, - c.b,g east with a speed of 3m/s has a head-on collision with a 0.900-kg puck initially at rest. +ef-.fsl:, :,gu jcywft)kbxAssuming 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 equalkr91 vc ,ml3wgmg;2ef)9xv yv mass undergo 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 co v9 cmgrekvy,1wxg;ml 3)29 fvllision?(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:m7 lvkh0y6y w 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 collision6lymy7w hk0v :?(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 movin,m0ff hc9li o5g with a speed of 8.5m/s collides head-on and elastically with another ball initially at rest. Afterward thef 9,i5lmch 0of 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 elastically as oneeh j * t215a2n/pocw9b olsxx4v9b0ab approaches the other directly froms v/* b a ho42ap9bxc9e0j1 b25wlnotx 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 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 elbrjh,up- - 7ykastic head-on collision with a second ball initially at rest. The second ball moves o- y-j7purkbh,ff 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 asrz2o. tym qkwbz2( 8x8 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 2b(tx2w.8y zqmzo8 r kis 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 object of ifdq. ft* / 49afkp,aqtd +r z*z*sw+imass 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 resoau 74 h q)ha/pm7d/anults in a maximum height h of the pendulum equal to 2.6 cm. A second projectile causes the the pendulum to swing twice u oadh/n 7ma7qp4/ h)aas 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 buriesl)egixpd ,dp/j*su-6 itself in a 3.6-kg pendulum hanging on a 2.8-m-gudp,xi/6*) p-elsdjlong string, which makes the pendulum 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 qywz zpn06 0s a7,w yzvwvm990of 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 objg5*oj)m ++jit/c7il shsk vl0ect, initially at rest, into two pieces, one of which has 1.5 times the mass of the other. If 7500 J were released in the explosion, how much kinetic energy did each piece acquire? (Let A represent the heavier particle, and B represet)/0i+lockj*sv+ jlih 5sgm 7 nt the lighter particle. ) KE'$_A$ =    J KE$_B$ =    J

  A 920-kg sports car collides into the rear end of a 2300-kg SUV stopped at a re lg0 fl(:0se /z uzqs3v*yzt2gd light. The bumpers lock, the brakes are locked, allu3t y sv:egzzq*0(/g0sf 2z nd 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 heighzi8b 4e ,;e+6ovvyx:tsp z( 8bef sk-rt of 1.50 m and rebounds to a height of 1.20 m. Approximately how many rebounds will the ball make before losing 90% of 8s (yb48es,6o b+kz ; :-vpzi tevrfxeits energy?   

A measure of inelasticity in a head-on collision of sr4 suzvp+19e5zcjs2 /*rxqz two objects is the coefficient o 4ru25sx*z+9 psczq je/zsv 1rf restitution, e, defined as$e=\frac{\nu_\mathrm{A}^{\prime}-\nu_\mathrm{B}^{\prime}}{\nu_\mathrm{B}-\nu_\mathrm{A}},$
where $\nu_\mathrm{A}^{\prime}-\nu_\mathrm{B}^{\prime}$ is the relative velocity of the two objects after the collision and $\nu_\mathrm{B}-\nu_\mathrm{A}$ is their relative velocity before it.
(a) Show that e=1 for a perfectly elastic collision, and e=0 for a completely inelastic collision.
(b) A simple method for measuring the coefficient of restitution for an object colliding with a very hard surface like steel is to drop the object onto a heavy steel plate, as shown in Fig. 7–36. Determine a formula for e in terms of the original height h and the maximum height h’ reached after one collision.

  A wooden block is cut into two pieces, one with three times the mass of the othel5gav9lu2,zch3 cu6q r. A depression is made in both faces of the cut, so thatcl3v hcq a,5gu92 zlu6 a firecracker can be placed in it with the block reassembled. The reassembled block is set on a rough-surfaced table, and the fuse is lit. When the firecracker explodes, the two blocks separate and slide apart. What is the ratio of distances each block travels? ----待选择----1/91/101/81/6 

  A 15.0-kg object moving in the +x dgo:b : j .cu2fvd.zxz6irection 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 :bjx2guv 6:df co.zz. 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 d ru i3xsvj2)/;wteuy8zsne1 (ecays into a second nucleus, an electron, and a neutrino. T se3wv)u81xtisru 2; jnyze /(he 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 ma9z*pgp/7nlnk d4 nn ;pss $m_\mathrm{A}=0.400$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 betweenc( mmero9r(- i two objects of equal mass, each having initial speed the twomm9cri(er-o( move off together with speed v/3 What was the angle between their initial directions?    $^{\circ} $

  Two billiard balls of equal mass move ap *r*8toacw j-t 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 * pcwr-a8 ot*j(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 another2w rxj6k8 lcyv(f5 2dc atom at rest. After the impact, the neon atom tr5 22v wcd(yjf6cr8klxavels 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 (c nye5ay +hbz r68dl9 lf;6 fvbx,v/yjs;p h,another atom at rest. After the imcsj6ep,8yv5yy ,(d bbf fva6xr+; z/hh ;n9ll pact, the neon atom travels away at a 55.6 $^{\circ} $ angle from its original direction and the unknown atom travels away at a -50 $^{\circ} $ angle. What is the mass (in u) of the unknown atom? [Hint: You can use the law of sines.](Let A represent the incoming neon atom, and B represent the target atom) $m_B$   u

  Find the center of mass of the three-mass system v 28i bc.osot6shown in Fig. 7–38. Specify relative to the left-hand 1.00 bis8ov .t26co-kg mass.    m

  The distance between a cajw s3-gwq 49qqrbon atom ($m_{\mathrm{C}}=12\mathrm{u}$) and an oxygen atom ($m_{\mathrm{O}}=16\mathrm{u}$) in the CO molecule is $1.13\times10^{-10}$m How far from the carbon atom is the center of mass of the molecule?    $\times10^{-11}$m

  The CM of an empty 1050-kg car is 2.50 m behind the front j;51kt/. csvl d*3u,erei*fyhar tg4 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 three people sit in the back seat 3.90 m from the front? Assume that each person.lts rfrhave i4g/y* 3 1j*;cd,utek5 has a mass of 70.0 kg.    m

  A square uniform raft, 18 m by 18 m, of mass 6800 kg, is used6t97qtlq ;rql as a ferryboat. If three cars, each of mass 1200 kg, occupy qq79lrq 6 tl;tits NE, SE, and SW corners, determine the CM of the loaded ferryboat.$X_{CM}$ =    m $Y_{CM}$ =    m

  Three cubes, of sidesvv + / m89dpbrjc*;rol $l_0$,$2l_0$, 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 tomat g0tqs0:av:c3wzn um7zr+ /p go 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 thezgcu0v3g:rqn7 w m+: szt 0pa/ crane operator can pick up the load without tipping it.$X_{CM}$ =    l $Y_{CM}$ =    l

  A uniform circular plazpwqoz s*.wbs* .trx imfp2k82l/a :m d/(o ,cte of radius 2R has a circular hole of radius R cut out of i/kcbm*rp.w8f( o.s px,:zlid s*mwa2z/2qtot. The center of the smaller circle is a distance 0.80R from the center C of the larger circle, Fig. 7–41. What is the position of the center of mass of the plate? [Hint: Try subtraction.]   R

  Assume that your proportions are the same as those in Table 7–1,6fkd6zykr6dsos3c v l7n8klkj 17n2, and calculate the mass of one of your legflls638ynkcn2v kk67ks 16,zo drd 7js.    kg

  Determine the CM of an outstretched ar5jg4x5qyhzu) m 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 o3 gsvem3a1u1of the CM of an arm bent at a right angles31maug3o ve1. 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 veru/ 9 ka+w2yvjqtically, and his trunk and head areu j/yvak9w2q + 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 Moo,nil bbk ii wgu 7x;1g(vl((y2n 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 apa*7uw1an3,* cufmv+ xybgr,h r rt 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 u3o sk(l9 hzj3l6jx( mzniform cylindrical head of mass 2.00 kg and a diameter 0.0800 m mounted on a uniform cylindrical handle of mass 0.500 kg and length 0.2o3j (sxhm6ljl k (93zz40 m, as shown in Fig. 7–42. If this mallet is tossed, spinning, into the air, how far above the bottom of the handle is the point that will follow a parabolic trajectory?    cm

  A mallet consists of 6x8hbu-pm3 sr5i t0q il;h;xcr 36 di1piu:pea uniform cylindrical head of mass 2.00 kg and a diameter 0.0800 m mounted on a uniform cylindrical handle of mass 0.500 kg and length 0.240 m, as shown in Fig. 7–42. If this mallet is tossed, spinning, into the air, how far above the bottom of the handle is the point that will i pr;m6u5i8ushxq6 td pi:rpb3x -ie1;hl c03follow a parabolic trajectory?    d    d

  (a) Suppose that in Example 7–14 (Fixrs40d7+tfu tn ( xr)kg. 7–29), $m_{II}$=3$m_{I}$ Where then would $m_{II}$ land?    d(Round to two decimal places)
(b) What if $m_{I}$=3$m_{II}$    d

A helium balloon and its gondola, of mass M, are in the ai ;6 2:do8his woxxu2yer 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 wha8d2xy6ih2u;:wose o x t 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 strike9v6l( 0 mjlgs2simuk tpy9y/3s a bat and is popped straight up to a height of 55.6 m. If the contact time is 1.4 ms, calc il s 0vk9sl9tymy(mu6j2/gp 3ulate the average force on the ball during the contact.    $^{\circ} $

  A rocket of mass m traveling wiy24i ,mx ry)uv,hh ;ieth speed $v_0$ along the x axis suddenly shoots out fuel, equal to one-third of its mass, parallel to the y axis (perpendicular to the rocket as seen from the ground) with speed 2$v_0$ Give the components of the final velocity of the rocket.$P_x$: v'$_x$=    $v_0$
$P_y$: v'$_y$=    $v_0$

A novice pool player is faced with the corner pocket shot shown in Fig. 7–43. ( infmsk+( ef4Relative dimensions are also shown. Should the player be worried aboumi+fn(e fk4s( t this being a “scratch shot,” in which the cue ball will also fall into a pocket? Give details.

  A 140-kg astronaut (including space suit) acquires a sped-jsglb 1k(k*p. 6foeed of 2.5m/s by pushing off with his d6l pj fbk .g*(oe1sk-legs from an 1800-kg space capsule.
(a) What is the change in speed of the space capsule?    m/s
(b) If the push lasts 0.40 s, what is the average force exerted on the astronaut by the space capsule? As the reference frame, use the position of the space capsule before the push.    N

  Two astronauts, one o4sbb7wp) jbngs c (;n1f mass 60 kg and the other 80 kg, are initially at rest in outer space. They then push each other apgbjb (n p;714 sw)bcnsart. How far apart are they when the lighter astronaut has moved 12 m?    m

  A ball of mass m makes a head-on elastic hfrt1)5+j6 xykpc6wacollision with a second ball (at rest) and rebounds ih+6afkxw5)cj p 6yt 1rn 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 as an expert witness in a court case involx:e,(np 8af/ z-esm 6uri 9kpwving an automobile accident. The accident involved car A of mass 1900 kg which cr6n ae,m/sr8-kpwu(x z:i ef9pashed 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 ofzq+mngm*hn1.u nn5w o a +08f7gbu;au concrete steps of total vertical height 4.00 m. The ball hits four times on the way down, each time striking the horizontal part of a different step 1.0 m lower. If all collisions are perfectly elastic, wha7an+ zuu nf. nao8n+ 5mmq;hw0g 1gu*bt is the bounce height on the fourth bounce when the ball reaches the bottom of the stairs?

  A bullet is fired vertically into a 1.40anu35 0u 5f:wnpqute ;-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 becu0n5uq wfe n5t:p; 3auomes embedded in it?    m

  A 25-g bullet strikes and becomes embedded in a 1.y 9i/8s*cy 1zn) w*ci2e09iyqgwwsp:i 1png c35-kg block of wood placed on a horizontal surface just in *is ccc1nw 9)yg*q/ s 0peyiy8 9:ngzwpi1 iw2front 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 mass 60 kg ..h(j0 mz0.op4n fo1p6qqm 9vll bmgt, 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 o hgm0op(l..6pnqjzvf.tb40ml mq9 13.2 m apart from each other, now exchange seats. How far and in what direction will the boat move? The boat will move    towards the initial position of the 75 kg person(Round to two decimal places)

  A meteor whose mass was aboutgrxnqeo z8f *0 zuck)3,t-( xt $ 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 qyr5- 5rd, ,hqej 6bomfragments by an explosion. Onehrqmb,6q5-, jo5ryd e fragment acquires twice the kinetic energy of the other. What is the ratio of their masses?   

  The force on a bullet is gi 4(k1ccidu r/tven by the formula F = 580-( $1.8 \times10^{ 5}$t) over the time interval t=0 to t = $3.0 \times10^{-3 }$s In this formula, t is in seconds and F is in newtons.
(a) Plot a graph of F vs. t for t=0 to t=3.0ms
(b) Estimate, using graphical methods, the impulse given the bullet.    N*s
(c) If the bullet achieves a speed of 220m/s as a result of this impulse, given to it in the barrel of a gun, what must its mass be?    kg

  Two balls, of masses dcnak-pamlllo3pcj2fz s5 m60+r79, $m_A$ = 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 radioactirv qe 6dg+6hg5vely into an alpha particle and a smaller nucleus. What will be the speed of this recoiling nucleus if the speed of thdegvq 56g+rh 6e 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 anho,9j,t7uk bd 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 sfkxg1z:zo 96 w45 )deqy6l lmtlides down a 30.0 $^{\circ} $ incline which is 3.60 m high. At the bottom, it strikes a block of mass M=7kg which is at rest on a horizontal surface, Fig. 7–46. (Assume a smooth transition at the bottom of the incline.) If the collision is elastic, and friction can be ignored, determine
(a) the speeds of the two blocks after the collision,v'$_A$ =    m/s v'$_B$ =    m/s
(b) how far back up the incline the smaller mass will go. $\approx$   (Round to the nearest integer) (Let A represent mass m, and B represent mass M.)

  In Problem 79 (Fig. 7–46), what is the upper limit on mase;zqutf(x8 f+ s m if it is to rebound from M, slide up the incline, stop, slide down the incline, and c;ue fxqf(+tz8 ollide with M again?    kg (Let A represent mass m, and B represent mass M.)

  The gravitational slingshot effect. Figure 7 8ovqfc klhf7 j,(hep/vf)of-0 qe45q –47 shows the planet Saturn moving in the negative x direction at its orbital speed (with respect to the Sun) of 9.6km/s The mass of Saturn isqvj f 0 7 phqoeo,q8k(el4-h)5f c/fvf $5.69 \times10^{ 26}$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