We claim that momentum is conserved, yet most m1 1 dvjgv0ebv11v gkh.oving objects eventually slow down and stop. Explg1 db1vvhv0j kg1 .ev1ain.

When a person jumps from a tree to the ground, whmt3dq 6mw2kd, at happens to the momentum of the persdmk6qd,2 mw3ton upon striking the ground?

When you release an inflated but untied ak 3j5 e;z;nnuballoon, why does it fly across the room?nau n 5;ze;j3k

It is said that in ancient times +ycl7;j8 k( fybp v.uwa rich man with a bag of gold coins froze to death while stranded on a frozen lake. Because the ice was frictionless, he couldbfcy.wl;k7p jv+(8 yu 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 when8276e qml c 6vloh/,upzj kn4uxj2it(- s c4an it is far out in space and is essentially in a vac8,nzop mvl24 eh4-lcunia7qk2j6( us/ x 6 tjcuum?

According to Eq. 7–5, the longer the impact time of an impulsebo6p*n yla1 2a, 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 reduce thon6*2l ba ap1ye possibility of fracture or death.

Cars used to be built as rigid asoevf1(lmqbf a ,p /++l possible to withstand collisions. Today, though, cars are designed to have “crumple zones” that collapse upon impact. What is the advanm1fopa( +qfv/e bll+, tage of this new design?

Why can a batter hit a pitchev wchb2le.jml2,e8 t*v ppt17d baseball further than a ball tossed in the air by t2*e8pe2 j.lmb ,v t1h7 pcvlwthe batter?

Is it possible for an object to receiyaem8v3bpim6hew0 y:n;d07v c :m -vj ve a larger impulse from a small force than from a laea m 0myvvh y8cwim:; 076n-v:j3bpd erge force? Explain.

A light object and a )mf iawhe+(xh7/m2 5jl*dejf heavy object have the same kinetic energy. Which has the greater momwi)7(xj*ffh2 e le a+/m mhd5jentum? Explain.

Describe a collision in whotp/dizp r 53kvc6 ayw*33pj(ich all kinetic energy is lost.

At a hydroelectric power pl;t7lbq.0 aaw6vr,:y q)0u rskfv6r y7paibv *ant, water is directed at high speed against turbine blades on an axle that turns an electric geneqawy7pv0.auf:a trrl*b v6vi )r ;06, y7 bqksrator. For maximum power 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 a7irhl(g 5n1rakm2ko; wall at 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 hf3 t1v4yq u:os onto a hard steel plate (fixed to the Earth), from which it rebounds at very nearly its original speed. (a) Is the momentum of the ball conserved during any part of this process? (b) If we consider the ball and Earth as our system, duri:tfy 43ouq1vs ng 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 carry(n (hkjily v)h,b2urhr0;8 gcing a heavy load in your arms?

Why is the CM of a 1-m lck *vpbyj3fd(ep38p ,s31zq-.iscqsgx (yc6 ength of pipe at its mid-point, whereas this is not true for your arm or leg8s(i ,bf (cyjx1*3-e vq3q 6. y3gdkssc cpppz?

Show on a diagram how your CM shifts when you change from a lying positjykjo yta5 i k9lq:9ani4sk 785o2 y:jion to a sitting positiokjq:asoi724i j yl9t55ay 8j:9nykko n.

If only an external fors;;jxn/o e-xfce can change the momentum of the center of mass of an object, how can e o-jn; xx/sf;the internal force of an engine accelerate a car?

A rocket following a parabolic path thret 0p 82l ,9ghfqqsu,mough the air suddenly explodes into many pieces. What can s 8,lmupet f,q0g2q9hyou say about the motion of this system of pieces?

  What is the magnitude of the momentum of a 28-g sparro l4qlp1 :9s2lh 0uvlunw flying with a speed of $8.4 \; m/s$    $kg \; m/s$

  A constant friction force of 25 N acts on a 65-kg skier for 20 s. What is x 2 3ii lfgk+fvl.9,jiva87izthe skier’s change in velocgiv 98,2jf.3kvixif+ izla7l ity?    m/s

  A 0.145-kg baseball pitched at 39 m/s is hit on a ho 9d y36.njj )fgaww;dxbj0w6jrizontal line drive straight back toward the pitcbdf6xg j.;aw )w3 9 0jj6nydwjher 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 horizontl u. kmvec2z/rm 5 -hh8zds5o;ally with a speed of 10 m/s Fig. below Calculate the velocity of the boat im cr oh8m z5lz-e.;s5mdkuv2/hmediately after, assuming it was initially at rest. The mass of the child is 26.0 kg, and that of the boat is 45.0 kg. Ignore water resistance. The magnitude of the velocity of the boat is    m/s

  Calculate the force exerted on a rocket, gimk( c5d7ha* bhven that the propelling gases are expell*m h5ab kd(c7hed at a rate of $1500 \; kg/s$ with a speed of $ 4\times10^{4 } \; m/s$ (at the moment of takeoff). F =    $\times 10^7 \; N$

  A 95-kg halfback movingt vdu ,u+:z/xy 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 alouzn; cuc0(7ckx m3 0ub4q u7;qddf 8jvne on alevel frictionless track with a constant speed of 18m/sz;u3 0cuqjc7qn;7dm8u fb4(cvkux 0d A 5350-kg load,initially at rest, is dropped onto the car. What will be the car’s new speed?    m/s

  A 9300-kg boxcar trava c.omo+8duq l6ils ;/eling 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 100km/h If the 1-l3al x;f bcn 1l(ltiair strikes a person at the rate of 40kg/s per square meter and is brought to rest, estimate the force of the wind on a person. Assume the persibllc-a ( x3;tln1f1l on 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 sw/oxt);dor: jz l-ks t-ml--opeed of 8.6m/s on a leveldjkr so-z:w mo--t)o /;lxt-l track. Snow begins to fall vertically and fills the car at a rate of 3.5kg/min Ignoring friction with the tracks, what is the speed of the car after 90.0 min?$\approx$    m/s

  An atomic nucleus inx7r6wpq vgs:z8r+ 2z pitially moving at 420m/s emits an alpha particle in the direction of its velocity, and the remaining nucleus slows to 350pz8prw26:x 7+q sr gzvm/s If the alpha particle has a mass of 4.0 u and the original nucleus has a mass of 222 u, what speed does the alpha particle have when it is emitted?    m/s

  A 23-g bullet traveling 230m ;gr2s 687)d4htd0t/o s mpr6ovefvbx/s penetrates a 2.0-kg block of wood and emerges cleanly at 170m/s If the block is stationary on a frictionless surface wht/gt ;dds fv)ov0 e7b8 o6r6smr2 xh4pen hit, how fast does it move after the bullet emerges?    m/s

  A 975-kg two-stage rocket is tra v;ce i1gz2z2ybfsz*i x 49oz,veling 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 travelin jo *q5ksqtyq2ivz( (1g in outer space with a velocity of 115m/s To alter 1v q5kis zty* j(qo(2qits 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 off the tee at a speed of 45m/s The golf cl o )vw.a.szu/vqj-pjv, :nc/mub was in contact with thezcs.pjo v.u:) ,/av vjmn/-qw 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 velocitt 74yvye 6d3kcwe4*pi)ffp8 )ki)ri f y of 8.5m/s and comes to rest in a time intervf)ic3i4ip k)*fd4vy8 ykr 7fpt e)w6eal 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 an4jxd7a.8+ rkp572ij+ is b avninwx1 id 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 inioee2h -g.rx . ,a6uwg charge of the crashworthiness 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 of impact until it is brought to rest. (a) Calculate the average force . .hr age-6iu2 xe,wogexerted 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 vfh- t:y+v(g pki c,u-to the east and is stopped in 0.75 s by a head-on tackle by a tai,:- vuy kh+(gtcp-fvckler 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 (mlvw d:7ov5.dwy9h53x ) dww/al 8ocosass 0.060 kg) points in the +x direction and is given by the graph of Fig. 7–33 as a function of time. Use graphical m):l5vdhlaww d/ .w 7ox5y dcoso8v3w9ethods to estimate
(a) the total impulse given the ball    N*s
(b) the velocity of the ball after being struck, assuming the ball is being served so it is nearly at rest initially.    m/s

  From what maximum height can a 75-kg person jump without breaking the lower lxr6 g+ y)zjzo6 2 1zo:kwsrevt 0i.vh-( yj;lleg 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 strengy:x ge +).ow rt0l zzvjk;i-y jr(zo16s62lh vth (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 directcx 4fs,qn g)31;ej wcrion) 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 1wr c;4sgcfq3)nexj, the 0.220-kg ball. $v'_A$    m/s  ----待选择----eastwest  $v'_B$    m/s  ----待选择----eastwest 

  A 0.450-kg ice puck, moving east with a speed of 3m/s has a hwn. ;lflzzyx.f 6q. g8ead-on collision with a 0.900-kg puck initially at rest. Assuming a perfectly elastic collision z86.gfq..zx fyw;lnl, 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 7z4eu vr s4psu+*r4i 4 y7:tnil7nlsgequal 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 collision?(Let A represent t s+t g7lrv4r 7u*penl4u: ns4z7iiy 4she 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 scrg,- 9j6ggkh b37,epjc yc+qlsm 40opeed 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 di43g0 sqp+ hkmoglceyc76-j,rbgjc9,rection 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 llcg1 prfqy+n0 *s 3:cwith a speed of 8.5m/s collides head-on and elastically with another ball ini0* slry 1:flgqc pn3+ctially at rest. Afterward the incoming softball bounces backward with a speed of 3.7m/s Calculate
(a) the velocity of the target ball after the collision    m/s
(b) the mass of the target ball.    kg
(Let A represent the moving softball, and let B represent the ball initially at rest.)

  Two bumper cars in an amusement park ride collide elhdxmra,v4q4u )don y 4lsf:4rt:y0 n0astically as one approaches the other directly from the rear (Fig.4y4 u)xy m l,d04s a:hrt0dfq:nnrvo4 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 elastic head-on collision with a second ball r)cltav/rca6i544a+u w3 *;x l eivb tinitially at rest. The second ball moves off with half the original speed of the first bal/aetbt)cwr iiau+a*xcr64543lvl v ;l.
(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 inclirn77r( frb ib3f+r1 wvne 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 higr+bnfr rwv7f7b3i( 1r h 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 object of massi q0jfz*/vs:k m$_A$ and velocity v$_A$ elastically striking a stationary object of mass head-on. (a) Show that the final velocities v'$_A$ and v'$_B$ are given by$v_{\mathrm{A}}^{\prime}=\left(\frac{m_{\mathrm{A}}-m_{\mathrm{B}}}{m_{\mathrm{A}}+m_{\mathrm{B}}}\right)\nu_{\mathrm{A}},v_{\mathrm{B}}^{\prime}=\left(\frac{2m_{\mathrm{A}}}{m_{\mathrm{A}}+m_{\mathrm{B}}}\right)\nu_{\mathrm{A}}.$(b) What happens in the extreme case when m$_A$ is much smaller than m$_B$ Cite a common example of this. (c) What happens in the extreme case when m$_A$ is much larger than m$_B$ Cite a common example of this. (d) What happens in the case when m$_A$=m$_B$ Cite a common example.

  In a ballistic pendulum experiment, projectile 1 results in a maximum heightwcs/i j9b j2use3j+u 1 h of the pendulum equal to 2.6 cm. A second projectile causes the the pen+ce32 /9 ijwsuj1usbjdulum 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 bur()-xb),mzyxqfo m 0 iries 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 horizontal components of the pendulum’s displacement.vertic(fib zo,r -q0 x)mmyx)al$\approx$    m horizontal =    m

(a) Derive a formula fouleo; a+fpj 4-r the 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 vo8 m22h/) pct r thxgjiaj3;2object, 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 piece2c)h 2iv m2ho3/t8; jgrpa xjt 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 into the rear end of a di;spkom)eh6:64zs k 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, calculates4isdkz: p)k 6;ehs6 om 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 rebounds to a ub3 ncxglyahy 5 f6e4sry8;6 6height of 1.20 m. Approximately how many rebounds will the ball make before losing 90% of iyg;a eu54nfr6 lyh8c6sb x6y3ts energy?   

A measure of inelasticity in a head-on collision of two objects n2sop;l.zk xw : w5/kc1b5vosis the coefficient of rest5bk2 .1/5oo pcwn; xswvk: lszitution, 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 mqa 9q 2qcg; hs3rml7+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, themg m27hq 3qr9 clq;+sa 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 t)tsjg0+cr/:sntl jw y 64q qh3he +x direction at 5.5m/s collides head-on with a 10.0-kg object mov0twh qq4 sr +:tjy3j sgc)n/l6ing in the -x direction at 4m/s Find the final velocity of each mass if:
(a) the objects stick together;   m/s
(b) the collision is elastic; v'$_A$ =    m/s v'$_B$ =    m/s
(c) the 15.0-kg object is at rest after the collision;   m/s ----待选择----not reasonable reasonable 
(d) the 10.0-kg object is at rest after the collision;   m/s ----待选择----not reasonable reasonable 
(e) the 15.0-kg object has a velocity of 4m/s in the -x direction after the collision. .   m/s ----待选择----not reasonable reasonable 
Are the results in (c), (d), and (e) “reasonable”? Explain
( Let A represent the 15.0-kg object, and let B represent the 10.0-kg object.)

  A radioactive nucleus at0kfnn:be tg5) rest decays into a second nucleus, an electron, and a neutrino. Thn)f0 bknget5 :e electron and neutrino are emitted at right angles and have momenta of $9.30\times10^{-23}kg\cdot m/s$ and $5.40\times10^{-23}\mathrm{~kg}\cdot\mathrm{m/s}$ respectively. What are the magnitude and direction of the momentum of the second (recoiling) nucleus?    $ \times10^{-22}$    $^{\circ} $ from the momentum of the electron

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

  Billiard ball A of mwfu(3oq9n+ ymd3;jcms e /,uiass $m_\mathrm{A}=0.400$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 inelas 9x+se9swy*d7 o v6ahatic collision between two objects of equal mass, each having initial speed the two move off sosy+*79a9x v6e dhaw together with speed v/3 What was the angle between their initial directions?    $^{\circ} $

  Two billiard balls of equal mass move at right obf 5.0-iud-ptiskbdwu 8/t 2 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 A ifpo2b/u8ds .5-i wutt-bdk0fter 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) weqh a-9 . 7pzow1qch6makes a perfectly elastic collision with another atom at rest. After the impact, the neon a7-cw 19 oqaez6hp .whqtom 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) makev-g:9fnuzkv t t,y6b2qpnz ; 1s a perfectly elastic collision with another atom at rest. After the impact, the neon atom travels away;9v2:tun-kygz 6 pt zvf ,q1bn 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 F apn,v;cki; )qig. 7–38. Specify relative to t;kiaqp)cnv, ; he left-hand 1.00-kg mass.    m

  The distance between a carb4eno1zju* ul4 phy+ u8iy6xa +on 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 fro e w(skl3m7vt,nt 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 thlev,7w(m s3 tke 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. Ipuib 6 5+vj.zlf three cars, each of mass 1200 kg, occupy its NE, SE, and SW corners, determine the CM o.i j uz+65pvblf the loaded ferryboat.$X_{CM}$ =    m $Y_{CM}$ =    m

  Three cubes, of side; ys p 9uq7lla z0.s:.p9 2ihhk.faxtms $l_0$,$2l_0$, 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 tkr9k /lhb u0 :ru+wrld4p7m1 of tomato paste (see Fig. 7–40), each of which is74rrmk /: hkrutudw9llpb1+0 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 tipping it.$X_{CM}$ =    l $Y_{CM}$ =    l

  A uniform circular plat e 8e mf )0v2z0/)ialbqkrs7rfe of radius 2R has a circular hole of radius R cut out of it. The center of the smaller circle is a distance 0.80 )0/iff8krme0ze)slra q v 72bR 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 prorlfyj,p( +dd 0a, (46bqqvregportions are the same as those in Table 7–1, and calculate the mass of one of your arl,+4j(qerqb0dy,d6 v fp (glegs.    kg

  Determine the CM of an outstretched arm using Table 7-h)sh u* a ph-df7 hmcc*w8uv9–1.   % 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 bent at l cugqhx(+s0hggg axz)d35./hlo)9na right angle. Assume that the person is 155 cm tall.9hxgn5+u.)l0d g gl3/zxh)q h oscg (a $X_{CM}$ =    cm $Y_{CM}$ =    cm

When a high jumper is in a position such that his arms and legs are hanging/yih ;o hs*a;twudewhre2)4 7 vertically, and his trunk and head are horizontai;)h2 dh*huy; est 74 warwo/el, 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 a2yqjvwiwiu;fg- 8( 1 zre $5.98\times10^{24}$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 a v4-un h2y+ 9wnu4glkman 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 mass w0 9ae*syn*y + iknj1r2.00 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 ab9sk* ya+* 1njre i0wynove the bottom of the handle is the point that will follow a parabolic trajectory?    cm

  A mallet consists of 8 zsg ,ie0fnjg/4b 7jfa uniform cylindrical head of mass 2.00 kg and a diameter 0.0800 m mounted on a uniform cylindrical handle of mass 0.5fe/0s78g4jg, fz inbj 00 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 Examplembsy f6q; +7n ny3p-co 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 g:vr87+ qaeeizef, )ognab( -mondola, 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 balloon. With what speed and direction (relative to Earth) does the balloon then move? What happe7eo - qemb,)agf rzv8+nai e:(ns if the passenger stops?

  An 0.145-kg baseball pitched h5 :rkw:q8g+ m4byge b,sw nj;f+x4goiorizontally at strikes a bat and is popped straight up to a height of 55.6 m. If the contact time is 1.4 ms, calculate the averag y;grfbx:+w isj g45be+ n k4mg:8,qowe force on the ball during the contact.    $^{\circ} $

  A rocket of mass m traveling with speed/ fv,w *(f) 4k vv8tt+hkln. 5ivmkfjy $v_0$ 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 totjs1 bhe:1978 xyjq-;bfvja. u4 za she corner pocket shot shown in Fig. 7–43. Relatih87xu1 ajsbsa9;tj f:v1e.y b 4qj z-ove 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? Give details.

  A 140-kg astronaut (including space suit) acquires a l ,ht(eb5i+/d55 c9zfw axhdc speed of 2.5m/s by pushing off with his legs from an 1800-kg space d cltchz(wb+/x955ia ,dh5efcapsule.
(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 kpr-b 0rf ;* vuzvh)1xmg and the other 80 kg, are initially at rest in outer space. They then push each othrup; * -r1zm)vvh bxf0er 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 collision with a second*)zfxh)u 5hzf ball (at rest) and rebounds in the opposite fzu)hzh )fx5*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 involving an automobzf:97 2-6bp(q yxms;e r)avooi7cnpqile accident. The accident involved car A of mass 1900 kg which crashed into stationary car B of mass 1100 kg. The driver of car A applied his brakes 15 m before he crashed into car B. After the collision, car A slid 18 m while car B slid 30 m. The coefficient of kinetic friction between the locked wheels and the road was measured to be 0.60. Show that thy7( q2m-o7x;fqr9 ipsz v6cp )aone:be 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 fli*r y z4yr7hj**pgpc3h ght of 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, what is the bounce height on thjpy7ph3 c*r*gyh 4rz*e 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 d.fc -tc1c* coxirectly above it. If the bullet has a mass of 29.0 g and a speed of 510m/so1ccc-.xtf c* how high will the block rise after the bullet becomes embedded in it?    m

  A 25-g bullet strike q2c rogo,* yl0+vyms5f4vf9y s and becomes embedded in a 1.35-kg block of wood placed on a horizontal surface just in front of the gun. If the coefficient o9yv lym+f5o42srv0 fc* gy, qof 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 7qgq+ k8u(cy hh rce5660 kg, sit in a rowboat of mass 80 kg. With the boat initially at rest, the two people, who have been sitting at opposite ends of the boat 3.2 m apart from each other, now exchange seats. How far and in what direction will the boc8+qg(hqe c u7 r6hy5kat move? The boat will move    towards the initial position of the 75 kg person(Round to two decimal places)

  A meteor whose mass was abouropqw-g2z /e+l eq41 ft $ 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 bro/ / z bbujfei bbvp8*.k+)z6iyken apart into two fragments by an explosion. One fragment acquires twice the kinetic energy of the other. What isbk+z /i)*6e b .pifvb8ub j/yz the ratio of their masses?   

  The force on a bullet is given by the form(4id:sx +e:oqy vt9g-u yt t-fwyq t2.ula 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 .d- lli7 x 2t+ko63cpmen7erb$m_A$ = 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 y* k k mr)j;zdrx9rh/(0,ycugparticle and a smaller nucleus. What will be the speed of this recoiling nucleus x dy )j;h,mcy(urk rzg/ r*90kif 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 ff0hnpua+c10j nd(z n9+*zqe n9p b;eh ired at an angle of 30 $^{\circ} $ to the horizon with a speed of 25m/s (Fig. 7–45). When it reaches the maximum height, it is hit from below by a 15-g pellet traveling vertically upward at a speed of 200m/s The pellet is embedded in the skeet.
(a) How much higher did the skeet go up?    m
(b) How much extra distance, $\Delta{x}$ does the skeet travel because of the collision? $\approx$   

  A block of mass m=2.2kg slides down a 7*48 sv/ izjv*p88(oommnfpodjx) f f 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 if1s(7u j:nt i0nn un. fciz7n-m it is to rebound from M, slide up the incline, stop, slide down the incline, and collide with M fitn70c.nn71( unu-in mjs z:again?    kg (Let A represent mass m, and B represent mass M.)

  The gravitational slingshot effect. Figure 7–47 shjqg 4)t5ram*xp 3h :opows the planet Saturn moving in the negative x directionpq3x) 5ptmr4j gaho *: 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