We claim that momentum is conserved, yet most moving oq7 1wt pqb4ge 3g:rpbdssdq s;d+b+ 9;bjects eventually slow down and stop. E;de:tbsp ddbqg 3b qr1w97;s 4+ +qgspxplain.

When a person jumps from a tree to the ground, what happens to the mom9// 5oropsywb79b dpgs;4 ykventum of the pe;/vpy swrob 9k5gd/4po sy9 7brson upon striking the ground?

When you release an inv;5 mj,oyubx28yk3p nc44fjkflated but untied balloon, why does it fly across the room?j4 f2ocj k 8 4m5nvpbyxy,uk3;

It is said that in ancient time;tc 1id5/uq y pkce2cbdqc(r*:iun2 5s a rich man with a bag of gold coins froze to death while stranded on a frozen lake. Because the ice was frictionless, he could not push himself to shore. What could he have done to save himself had he notidc ; nb2i*uypcc c5:dqu/k2e15(trq been so miserly?

How can a rocket change directiobx+o, pw mp t:1rqc5.vn when it is far out in space and is essentially in a vb qwop,:x.t +cm1pvr5 acuum?

According to Eq. 7–5, the longeu,k)ihpok:ytef( d2t6jd.ky w;g6 u0r 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 a6 kyt:e; y 0).pwgfh( jtdi2douk6uk ,re intended to inflate during an automobile collision and reduce the possibility of fracture or death.

Cars used to be built as rigid a70,arm r6gtgtr ,vib+s possible to withstand collisions. Today, though, cars are designed to have “crumple zones” that collapse upon impact. What is the advantage +rv g,7arb 0tmr6 g,tiof this new design?

Why can a batter hit a pitched baseball furty a)/+pqh2:ms5dlmo jdvt,m 4her than a ball tossed in the air by the 5:t2m+)y,voad/mlj sh qdm4 pbatter?

Is it possible for an object to receive a larger impulse from a small force thau/:k9uq(c,i6h 2, mlln gs mein from a large2km6, hc (/ii:,n s q9euglulm force? Explain.

A light object and a heavy object ha5aj1;i.;yklksvs,u*8c 2ume :s e 0w qjlc,mmve the same kinetic energy. Which has the greater momentum? Explainck,0yl l5ve s,asum s8 ;u; 12wmkec*ji.qmj :.

Describe a collision in which aojrwnb3wz( *0 ll kinetic energy is lost.

At a hydroelectric pow0naiak ubdtt.v)edx*(l5wo1 :* ee *eer plant, water is directed at high speed against turbine bladesxi ** td te) eeva w(d1:b.nuao5e0l*k on an axle that turns an electric generator. For maximum power generation, should the turbine blades be designed so that the water is brought to a dead stop, or so that the water rebounds?

A squash ball hits a wa mp6)ekg989nyvos bf6ll 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 h onto a h n) d t qj58znu+spavpo5i:t-,ard 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 consi in,t8- ojd p:s u5t5qa+n)zvpder 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,m-0q:ydip eu5ay /mf3 o a,qn carrying a heavy load in your arms?

Why is the CM of a 1-m length of pipe aiwbj-f 5o 5s9bt its mid-point, whereas this is not true for yowb5bi f -sj5o9ur arm or leg?

Show on a diagram how your CM shifts when you change from a lying position*byzh;;ca1m -syewq ey,g 5x4 to a sitting position. ,g5s qh;*1 bac4yyxm;we -zey

If only an external force can change therw ih+yx896qgsiun 2j+vb - m. momentum of the center of mass of an objecbn++9xr-humi 86s j2yi gq.vw t, how can the internal force of an engine accelerate a car?

A rocket following a parabolic path through thed ot2*w2n o (b6 p6moafjrac18 air suddenly explodes into many pib 62ctm6o(a npd82j fw aro*1oeces. What can you say about the motion of this system of pieces?

  What is the magnitude7uw crf,rt2nug 3 s8;t of the momentum of a 28-g sparrow flying with a speed of $8.4 \; m/s$    $kg \; m/s$

  A constant friction force of 25 N acts on alha be ;v vv,o;q78jg)-4qxma 65-kg skier for 20 s. What is the skier’svqx-eglmv ;qvbajh ;a 4)87 ,o change in velocity?    m/s

  A 0.145-kg baseball pitched at 39 m/s isi nqzjn+h3pq;x-0/h v vb4t brb a-82k hit on a horizontal line drive straight back toward the pitcher at 52m/s If the contact time between bat and bzxr-p+nbj2hh 4qiq/v0b -8k ;tbv3anall is $3\times10^{-3}$s calculate the average force between the ball and bat during contact.    N

  A child in a boat throws a 6.40-kg package out horizontally with a speed of 10 w3o .k gdz -vzk/b;kkn/)m*s)edz9crm/s Fig. below Calculate the velocit.*;9r )enkw z/ dvgs)-bkdz /ozkkc 3my 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 exerted on a rocket, given that the propelling gas *8u hx vwtz2+mvza8t;es are expelled at a ra*xt8m2t; vvahu +z z8wte 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 movingxyoj(7 hdwhg*3 5dz2+n9qbuc 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 tra7ka./ /kzqz ddck with a constant speed of 18m/s A 5350-kg load,indqk /.z/ zad7kitially at rest, is dropped onto the car. What will be the car’s new speed?    m/s

  A 9300-kg boxcar traveling at vy: gbi 0v gxwoggx;qh;+c 6,wy 2e*8j$15 \; m/s$ 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 speed ou hll5e/oymyn9s)wq9xfd6u cag;j; j5.7+y s of 100km/h If the air strikes a person at the rate of 40kg/s per square meter and is brought to rest, estimate the force of the wind on aqw.ln/ +sc 556dgj ;7hauxmo ojly9)e;y9fyu 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 a leip) 54p,snspy.4i ba.afliw*8 st +hh *was 8sipbs 4i4h.p5n. hy)p+i,atlfvel 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 initially moving at 420m/s emits an alpha parti ( rwpb4zym45pcle 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 spee wrp5pzy4m4b (d 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 r gg0jj-7h yt9*d5uhi and emerges cleanly at 170m/s If the blockh9*jru-g0dji 5h yg7 t is stationary on a frictionless surface when hit, how fast does it move after the bullet emerges?    m/s

  A 975-kg two-stage rocket isxbm( tb45o m;s traveling at a speed of $5.80\times10^3\mathrm{~m/s}$ with respect to Earth when a pre-designed explosion separates the rocket into two sections of equal mass that then move at a speed of $2.20\times10^3\mathrm{~m/s}$ relative to each other along the original line of motion. Let “A” represent the upper stage (that moves away faster) and “B” represent the lower stage.
(a) What are the speed and direction of each section (relative to Earth) after the explosion? $v'_A$   m/s  ----待选择----away from the Earthtowards the Earth  $v'_B$   m/s  ----待选择----away from the Earthtowards the Earth 
(b) How much energy was supplied by the explosion? [Hint: What is the change in KE as a result of the explosion? $a\times10^8$ a =    J

  A rocket of total mass 3180 kg is traveling in outer space with a velocity of n9l:w1s2) rug1hogpc 115m/s To alter its course by29oh :gw11u g) rnpcsl 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 ud -;pb h+dxyomxuk3/k 195neof 45m/s The golf club was in contact wit hd-un3x5p9/odkb1;ym x+uek h 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 aj(gkeg 23g( ap,cy9ya velocity of 8.5m/s and comes to rest in a time interval of 8.0 ms. (a) What is the impulse given to the nayga 3gck9j(,eyg2(p ail?    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 l8+f2p8bui ax 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 crash 6fhx,xwh9 .;mutf5 xzworthiness 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 9 hhf; xztf5x6m,u.xw it is brought to rest. (a) Calculate the average force exerted on the car by the barrier. $\approx$$a\times10^5$N a =   
(b) Calculate the average deceleration of the car.    m/$s^2$

  A 95-kg fullback is running at 4m/s to thewc iir9/p3c:l east and is stopped in 0.75 s by a head-on 39:iwlip cc r/tackle by a tackler running due west. Calculate
(a) the original momentum of the fullback    kg*m/s
(b) the impulse exerted on the fullback    kg*m/s
(c) the impulse exerted on the tackler,    kg*m/s
(d) the average force exerted on the tackler.    N

  Suppose the force acting on a tennis ball (mass 0.0 +c .aq0002a:3alm)nekxjea / q cnlni60 kg) points in the +x direction and is given by the graph of Fig. 7–33 as a function 2aikq:a n3n0.a0l)x/qae mcl j +cn0e of time. Use graphical methods to estimate
(a) the total impulse given the ball    N*s
(b) the velocity of the ball after being struck, assuming the ball is being served so it is nearly at rest initially.    m/s

  From what maximum height can a 75-kg person jump without breaking the lower nl)* :jf r7an3mi9,cxqd9 vaz leg bone of either leg? Ignore air resistance and assume the CM of the person ,7q n )93mjv:ldraz*ci9xfanmoves a distance of 0.60 m from the standing 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 direction) with a spe1/ 8r11t ijtinohxk7red 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 collisk 1hi187otntrj 1/i xrion?Let A represent the 0.440-kg ball, and B represent the 0.220-kg ball. $v'_A$    m/s  ----待选择----eastwest  $v'_B$    m/s  ----待选择----eastwest 

  A 0.450-kg ice puck, moving east with a speed of 3m/s has a head-on collision wh ppevf4 2:sa3) qpoc-ith a 0.900-kg puck initially at rest. Assp a-ofes4 q 2:hpvp)3cuming a perfectly elastic collision, what will be the speed and direction of each object after the collision?Let A represent the 0.450-kg puck, and let B represent the 0.900-kg puck. v'$_A$ =    m/s ----待选择----eastwest  v'$_B$ =    m/s ----待选择----eastwest 

  Two billiard balls of equal mass undergo a perfectly elmaqsd/ 9yd -dt8t 4j5mastic 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?(Lemy94/ 8d-jads5 ttmqdt 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 collidecf11buk0q b vxxch;c+4 i6 2afs head-on with a 0.090-kg ball initially moving away from it at a1 k a+iqc;vch14cbff2 u6xbx0 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 8.5me7o7p 3rpf0l5nr i/f;pqwg2t /s collides head-on and elastically with another b p2ilrepr7t 3/0;fof7qngp5 wall initially at rest. Afterward the incoming softball bounces backward with a speed of 3.7m/s Calculate
(a) the velocity of the target ball after the collision    m/s
(b) the mass of the target ball.    kg
(Let A represent the moving softball, and let B represent the ball initially at rest.)

  Two bumper cars in an amusement park ride collide elastically as one appr72kv g+-ae lxvoaches the other directly vxg e-+avl72 kfrom 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 elasti n4mmmnp *.e(dx 3454y0brc ox qbdsr2c head-on collision with a second ball initially at rest. Them44p.rbcbm2no*r0 msq4 d5 3eyn xx d( 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 shown in (w,o:;ud grc k.fajhms6fw;o4 kmv(+ Fig. 7–35, and elastically som(m6s (g;:f j,fw.+ v;huoac w4dkk rtrikes another cube at the bottom that is only one-half its mass. If the incline is 30 cm high and the table is 90 cm off the floor, 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 obl 1e61ktzl2ftkhm,a6,nj .dehy +,e cject of mass m$_A$ and velocity v$_A$ elastically striking a stationary object of mass head-on. (a) Show that the final velocities v'$_A$ and v'$_B$ are given by$v_{\mathrm{A}}^{\prime}=\left(\frac{m_{\mathrm{A}}-m_{\mathrm{B}}}{m_{\mathrm{A}}+m_{\mathrm{B}}}\right)\nu_{\mathrm{A}},v_{\mathrm{B}}^{\prime}=\left(\frac{2m_{\mathrm{A}}}{m_{\mathrm{A}}+m_{\mathrm{B}}}\right)\nu_{\mathrm{A}}.$(b) What happens in the extreme case when m$_A$ is much smaller than m$_B$ Cite a common example of this. (c) What happens in the extreme case when m$_A$ is much larger than m$_B$ Cite a common example of this. (d) What happens in the case when m$_A$=m$_B$ Cite a common example.

  In a ballistic pendulum experiment, projectile 1 results in a maximumoo0ca. +1( puufmw; t3f4qh 2mqm 6glw height h of the pendulum equal to 2.6 cm. pq3w0;.1 c 4uff+g w6hm mtqlauoom(2A second projectile causes the the pendulum to swing twice as high, $h_2=5.2\mathrm{cm}$ The second projectile was how many times faster than the first? $v_1$ =    $v_2$ ([color=rgba(0, 0, 0, 0.85)]Round to three decimal places)

  A 28-g rifle bullet traveling 230m/s b7.6drrssh t; yuries itself in a 3.6-kg pendulum hanging on a 2.8-m-long string, which makes the pendulum swing upward in an arc. Deterr .s;s7yd6 hrtmine the vertical and horizontal components of the pendulum’s displacement.vertical$\approx$    m horizontal =    m

(a) Derive a formula for the fraction of kinetix8meo+dv rmu3 9 r5(edt-0whcc 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 -pih4sj. /zb.k v44v.drqddbq/1hw qrest, into two pieces, one of which has 1.5 times the mass of the other. If 7500 J were released in the explosion, how much kinetic energy did each piece acquire? (Let A represent the heavier particle, and B represent the lighter particle. ) KE'4qkr.h/-b vq s1p/hw4i b4j.dd qdzv. $_A$ =    J KE$_B$ =    J

  A 920-kg sports car collides into the rear end oe:n/k a ql7eo,f a 2300-kg SUV stopped at a red light. The bumpers lock, the brakes are locked, and the two cars skid forward 2.8 m before stopping. The police officere 7lk,:naoe q/, 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 rebounds to a height of 1.20 m. n.3 )jnj45 xcx2f awqiApproximately how many rebounds will the ball make before losing 90% of its ex xajcw5qf34.ij) n 2nnergy?   

A measure of inelasticity in a head-on collision of two objec s3ul,qj0 2z kb8:m,sd hhdqc:h9/etq ts is the coefficient of restitution, e, defined asmd9qsq/k:jhutz08 3,scl , hbe2h:qd$e=\frac{\nu_\mathrm{A}^{\prime}-\nu_\mathrm{B}^{\prime}}{\nu_\mathrm{B}-\nu_\mathrm{A}},$
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 cutwt(u4i jq7xb .zjib 9.kq92nz into two pieces, one with three times 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 rxz .z.i9uj2nqqbk9ji 47 wtb(eassembled. 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 direction at 5.5m/s cb 0-b3s( orc;1 rg 5 cgqvv2bq1tfnxw3ollides head-on with a 10.0-kg object moving in thxgv11bsrq -2 5ct03bn gq ;(cbr ovw3fe -x direction at 4m/s Find the final velocity of each mass if:
(a) the objects stick together;   m/s
(b) the collision is elastic; v'$_A$ =    m/s v'$_B$ =    m/s
(c) the 15.0-kg object is at rest after the collision;   m/s ----待选择----not reasonable reasonable 
(d) the 10.0-kg object is at rest after the collision;   m/s ----待选择----not reasonable reasonable 
(e) the 15.0-kg object has a velocity of 4m/s in the -x direction after the collision. .   m/s ----待选择----not reasonable reasonable 
Are the results in (c), (d), and (e) “reasonable”? Explain
( Let A represent the 15.0-kg object, and let B represent the 10.0-kg object.)

  A radioactive nucleus at rest decays into a second nuc6 iwel u9hs-uq+m/y/:eh1qosleus, an electron, and a neutrino. The electron and neutrino are emq :19w uqy leoe/i6s /hmh-s+uitted 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 mase8*b 46fjh/ f/nu 9zgouwka(ws $m_\mathrm{A}=0.400$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 inelaste6 o6sr flzs(hkfw*wc ;v+o )3ic collision between two objects of equal mass, each having initial speed the two move off together with speed v/3 What was t vc66(of3esw)+k;f lshwr*zo he angle between their initial directions?    $^{\circ} $

  Two billiard balls of equal mass moi0ctu4 v3tq0tve at right angles and meet at the origin of an xy coordinate system. Ball A is moving upward along the y axis at 2m/s and ball B is moving to the right along the x axis with speed 3.7m/s After the collision, assumed elastic, ball B is moving along the positive y axis (Fig. 7–37). What is the final direction of ball A anvqtc4u3 t0ti 0d 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 ayz:2t3o,c23zzrp cz d m wwg)*nother atom at rest. After the impact, the neon atom t :*cz32zpo wr cgy3 mzzwtd,)2ravels 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 another atom atz-f)-7z em23t 8v n) zlkfuzih rest. After the impact, the neonl8 -e)zf n3zf7)mtvh k -i2zuz 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-mas i)fc)ef88u drs system shown in Fig. 7–38. Specify relifru8ce)) df8 ative to the left-hand 1.00-kg mass.    m

  The distance between 8 wgmy z.)6cppa 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 105p1zl6ac nvbk 6*iiv:80-kg car is 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 three people sit in the back li iv zvp8*k6a 1:cb6nseat 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 ferry/la -xo hvm rt+0 3,jno1:inbga)b8paboat. If three cars, each of mass 1200 kg, occupy its NE, SE, and SW corners, determine the CM of the la1t:-r08jaavbo)x3p +mnl,g/h bo inoaded ferryboat.$X_{CM}$ =    m $Y_{CM}$ =    m

  Three cubes, of sides t:xh, l0c3sa wvf5 q:q$l_0$,$2l_0$, 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 camtw10 ;iq5;jtajc b/eses of tomato paste (see Fig. 7–40), each of which is a cube of length l. Find the center of gravity in the horizontal plane, so that the crane operator can p; eqt1m;/5ajj iwtb0c ick up the load without tipping it.$X_{CM}$ =    l $Y_{CM}$ =    l

  A uniform circular plate of radius 2R has a circular hole of radius R cut ouguoseo j:(wn 25jw;6f t 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 the position of the center of mass 5e jojf:gs(2wno; 6uwof the plate? [Hint: Try subtraction.]   R

  Assume that your proportions are the69 :wiout1nzl same as those in Table 7–1, and calculate the mass of one of youlzwio91 t6un:r legs.    kg

  Determine the CM of an oe907tx x bk2 3/,n(tww1ehu6smuz w tbutstretched arm using Table 7–1.   % of the person's height along the line from the shoulder to the hand

  Use Table 7–1 to calculate the position of the CM of an arm bent at a rigf q;cxh9jlu/6j 02 zpxht angle. Assumezxl/j;jq90 hc2 6x puf 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 arez+zlw j ig5/7h hanging vertically, and his trunk and head are horizontal, calculate how far below the torso’s median line the CM will be. Will this CM be outside t+z/lwizg75jh he body? Use Table 7–1.

The masses of the Earth and Moon are9wne, x 0( lq 4g*ty-wr5w/rs3pf vyf9zqo l8j $5.98\times10^{24}$kg and $7.35\times10^{22}$kg respectively, and their centers are separated by $3.84\times10^{8}$m (a) Where is the CM of this system located? (b) What can you say about the motion of the Earth–Moon system about the Sun, and of the Earth and Moon separately about the Sun?

  A 55-kg woman and an 80-kg man stand 10.0 m apart on frictionlka u10 z67o5mji+nv-z3 ichom ess 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 la+ imptq 1 (u)bz/xj;mass 2.00 kg and a diameter 0.0800 m mounted on a uniform cylindrical handle of mass 0.500 kg and length 0.2( p baxzt;iujq/1l+ m)40 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 a uniform cylindrical head of m5p:rx0zmyc dayas-h spwo/cqe37 0:+ass 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 i-hpa/ oy x:0 zd r3+m7syw0qa5:scecps the point that will follow a parabolic trajectory?    d    d

  (a) Suppose that in Example 7–14 (Fig. 7–29)xm; a8d1)a, xkq,ncb ,p8umug, $m_{II}$=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 air and statios/(:oyi wyr25f ddm 5mjv9h1wnary with respect to the gr y hyms2(mv1 5drowfi5:j 9w/dound. 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 happens if the passenger stops?

  An 0.145-kg baseball pitched horizontally at stryrbws6) e7r.likes a bat and is popped straight up to a height of 55.6 m. If the contact time is 1.4 ms, calculateyerwrl.7b6 s) the average force on the ball during the contact.    $^{\circ} $

  A rocket of mass m travw(iu5z6 ayu.f eling 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 shown i yepd.6 irzks,ht6g:x95o)q b n Fig. 7–43. Relative dimensions are also shown. Should the player be worried about this being a “scratch shot,” in whic y6sghteoz rx5pq. ,9:6i bd)kh the cue ball will also fall into a pocket? Give details.

  A 140-kg astronaut (including space suit) acquire xo3m2. yermbnu90m;gs a speed of 2.5m/s by pushing off with his legs from an 1800-kg space cap09 ;om nuby.m32g rxmesule.
(a) What is the change in speed of the space capsule?    m/s
(b) If the push lasts 0.40 s, what is the average force exerted on the astronaut by the space capsule? As the reference frame, use the position of the space capsule before the push.    N

  Two astronauts, one of mass 60 kg and the other 80 k) e+dq p t6wf(xc)+yqbg, are initially at rest in outer space. They then push each other apart. How far apart are they qx+wy d+fqct) b(p)e6when the lighter astronaut has moved 12 m?    m

  A ball of mass m makes a head-on ela z6 koyy91uj9f:c b4bwt 7yac/stic collision with a second ball (at rest) and rebounds in the opposite direction wit91t7:fy96c uab /bykwyzco j 4h 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 exq opc ep;22obviw*71-2zikxepert witness in a court case involving an automobile accident. The accident involved car A of mass 1900 kg which crashed into stationary car B of mass 1100 kg. The driver of car A applied his brakes 15 m before he crashed into car B. After the collision, car A slid 18 m while car B slid 30 m. The coefficient of kinetic friction between the locked wheels and the road was measured to be 0.60. Show that th2 ;iw1 v *qeok2zx2i -7oebpcpe 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 tohuuib bnu9;,/ p of a flight 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 col/uuhu9n,b ;b ilisions 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 directlyxgw y5hyw 0bu7k+cn jfb 80d4+ above it. If the bullet has a mass of 29.0 g and a speed of 510m/s how hiybj 4+chn+8k07wud gxy f5b0w gh will the block rise after the bullet becomes embedded in it?    m

  A 25-g bullet strikes and becomes embedded /c ej)d.d1mqq zq12eo in a 1.35-kg block of wood placed on a horizontal surface just in front of the gun. If the coefficient of kinetic friction between the block and the surface is 0.25, and the impact drives the block a distance of 9.5 m before it com2ej.zocm q1 /)dqq e1des to rest, what was the muzzle speed of the bullet?    m/s

  Two people, one of mass 75 kg u lx(s *r8s4yband 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 direction will the boat move? The boat will muy( 4rs8xs *blove    towards the initial position of the 75 kg person(Round to two decimal places)

  A meteor whose mass was abouk5f2hh 5;lvlng 00 :a4uernewo t/( wut $ 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 explosk j ek pnc-w0cql8i()4ion. One fragment acquires twice the kinetic energy of the other. What is the ratio of their masseswkjqnc )04 -ec(li8 pk?   

  The force on a bullet is given by the formula F = 5ml9m1 ;q:+g* lkwtigwbqg8/ po 89kg t80-( $1.8 \times10^{ 5}$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 masseszyv t8c)f5 ug( $m_A$ = 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 akr,i7yih1eusake ( 4*aces7n *e88mvn alpha particle and a smaller nucleus. What will be 71kh84isaem*ec av u(r, *nk7e sye8ithe 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 targek 7viys le coh7wck8o4 q-(e,;t) is fired 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 30.0i 3b( ez(7h,ghulpbpk73 gg0z cz)ps + $^{\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)uej;t y6j9z.x u*ci z on mass m if it is to rebound from M, slide up the incline, stop, slide down the incline, and collide wi .t 6jzcy); ue9xij*uzth M again?    kg (Let A represent mass m, and B represent mass M.)

  The gravitational slingshot effect. Figure 7–47 shows tn. l* fzz9nuk9he planet Saturn moving in the negative x direction at its orbital speed (with respect to the Sun) of 9.6km/s Th*9nu. lf9zzkne 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