We claim that momentum is conserved, yet most moving objects ev wwdw3m j8/x1wentually slow down and stop. Explainwdwwj /m3w8x1.

When a person jumps from a tree to the ground,1zr tt+m46o p. d:,:ndgcixb n what happens to the momentum of the c,b: do r. :1mxzng pi64dtnt+person upon striking the ground?

When you release an inflated but untied balloon, why does it fly across rs4w/ xnsh(9rn ybargeo93 39 the roomw sg9a9ber 3xs3ohnr4(9 /yrn ?

It is said that in ancient times a rich man with a bag of gold coins froze tovpr. hl-xmjqr* 65ii7:sh ag+ death while stranded on a frozen lake. Be5.rxamj*- ilpvhs :rghq i 6+7cause 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 it is far out tsu.r777. jrpp mbd c8in space and is essentially 7pbc. pdr.u7t rm7s8jin a vacuum?

According to Eq. 7–5, the longer the impact time of an impulse,8:lb-b4 :usbu3 zouzc 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 4zsz3buu:u8cb:lob -an automobile collision and reduce the possibility of fracture or death.

Cars used to be built as rigid as possible to withstand collisions. Tod j5:6xlb.35uty dysap ay, though, cars are designed to have “crumple zones” that collapse upon impact. What is the a5lydt63.sp5:y jax b udvantage of this new design?

Why can a batter hit a pitched baseball further than a ball tossed rjyx5apb.zh2723a ca in the air by the batter5 p2hjx aa2bc3r yaz7.?

Is it possible for an object to receive a larger impulse from a small r nh/yclfe8h7(bnwhzy9a,::force than from a large force? Exhbn ah9 wrhy,fcn(z :8e: /ly7plain.

A light object and a heavy object havrti2a6ayc)-n0f swq 6a y.2vfe the same kinetic energy. Which has the greater momentum? Explaa . )-n2yr2icyfa0s v6aqt6wfin.

Describe a collision in wo6rqtbfz xj8s)z7 :2so /yu /shich all kinetic energy is lost.

At a hydroelectric power plant, water is directed at5ioxiww 4.(lbf 5eoxhsfr +h03k4f 7n high speed against turbine blades oni w+rn7e b55 h3lf0ois44fhk(wxfo.x 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 wall a f/z6 r2i*a)6hxyubou t a 45 $^{\circ} $ angle as shown in Fig. 7–30. What is the direction (a) of the change in momentum of the ball, (b) of the force on the wall?

A Superball is dropped from a h9jx d gi6z91deeight h 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, during what parts of the process is momentum conserved? (c) Adg 96jz9dxei1nswer 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 in your arms? vq deuq/):th6

Why is the CM of a 1-m length of pipe at it2x,v yf faiuo,l 41x,fs mid-point, whereas this is not true for your a2xyx1fi vf4u,fla ,,orm or leg?

Show on a diagram how your CM shifts when you change from ad/ws3qs+e ,,* 2x ctxui toybw 1vx.wr7c1k8j lying position to a sitting position.yc xer+,ij8twc3/xuk1q ,t wx7wd.1b* svso2

If only an external force can change the momentum of the center of mas:u v-yvl7:bb6tq ;vy dfw3wu c-rqx-)s of an objec7bvv;wqbtuuc-q- dyw x)vy r -6f::l 3t, how can the internal force of an engine accelerate a car?

A rocket following a parabolic path thr-xk5 j agg4xu6ough the air suddenly explodes into many pieces. What can you say aboutuag6 k- 5xxg4j the motion of this system of pieces?

  What is the magnitude of the momentum of a 28-g sparrow ft+xqu2;rp/ q 0ogq)uvlying with a speed of 8.4 m/s)o purqx;utqgq0+2 /v    $kg\;m/s$

  A constant friction force of 25 N acts on a 65-kg skier for iv5f5klf zr,yyuqqm-/1 vh6 )20 s. What is the skier’s changeq1ffk /-v5 )im5y zlryqvu,6h in velocity?    m/s

  A 0.145-kg baseball pitched at 39 m/s is hit on a horizontal line/z)wryamy8ex:sef4 3l :4qws drive straight back toward the pitcheqy 3 ) a4zy:mr4l8wsfee wxs:/r 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 horizonta2 qj;d j8puao-szc28i lly with a speed of 10 m/s Fig. below Calculate the velocity of the boat immediately after, assuming it was initially at rest. The mass of the child is 26.0 kg, and that of the boat is 45.0 kiuzjs-2q 8 d8 ocpja;2g. Ignore water resistance. The velocity of the boat is    m/s

  Calculate the force exerted on a rocket, given that the propelling gases are e8v-wm qd13yiigp s45lxpelled at a rate of 1500kg/s5vsq i43g1-8yd wlpmi with a speed of $ 4\times10^{4 }$ (at the moment of takeoff).$a\times10^7$ N a =   

  A 95-kg halfback moving at 4.1m/s on an apparent breakaway for al7 nth0 ctyoqdppi u;9r6)/ 3h touchdown is tackled from behind. When he was tackled by an 85-kg copnc0 /y 3tiot7)p9; hlhud qr6rnerback running at 5.5m/s in the same direction, what was their mutual speed immediately after the tackle?    m/s

  A 12,600-kg railroad car travels alond 7p8)ad fm)usjdo5 c:6:lv hrm/.ha ve on alevel frictionless track with a constant speed of 18m/s A 5350-kg load,initially at rest, is dropped onto the car. What will be the car’s new speed?:8v dm)h)ap su: 7 dvramjc 5/ho6fl.d    m/s

  A 9300-kg boxcar traveling at 15m/s strikes fk/uyht*v5xuhd,++ e a second boxcar at rest. The two stick together and move off with a speed of 6m/s What is the maskh+ +v/thud,e* f uyx5s of the second car?    m/s

  During a Chicago storm, winds can whip horizontally at speeds of 100km/h 2wybu ;r 6*z) 5vv7mm4wfcba oIf 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 a person. Assume the pc v*4ywv)ma bw2zf;6 b5om ru7erson 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 constantjf,1 )t4 .cjksrtfd oaa, o5+a speed of 8.6m/s on a level track. Snow begins to fall vertically and fills the car at a rate of 3.5kg/min Ignoring friction with the tracka,,5d)f j4takj1t f ao.+oc rss, 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 partaz;v 5lm0dv+z )nh4 sx9sx eh5icle in the direction of its velocity, and the5sxh+ ldv450);s hvzz ax9nme 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 speed does the alpha particle have when it is emitted?    m/s

  A 23-g bullet traveling 230m/s penetrates a 2.0-kg block of wood anmy13y ql h w(wfl7hy4 bq74bh0d emerges cleanly at 170m/s If the block is stationary on a frictionless surface when hit, h(ll hb74hqw0w41mf 7 yy3 ybhqow fast does it move after the bullet emerges?    m/s

  A 975-kg two-stage rockegxe(k9ir 8fcnw03 t qzp;ep36t is traveling at a speed of $5.80\times10^3\mathrm{~m/s}$ with respect to Earth when a pre-designed explosion separates the rocket into two sections of equal mass that then move at a speed of $2.20\times10^3\mathrm{~m/s}$ relative to each other along the original line of motion. Let “A” represent the upper stage (that moves away faster) and “B” represent the lower stage.
(a) What are the speed and direction of each section (relative to Earth) after the explosion? $v'_A$   m/s  ----待选择----away from the Earthtowards the Earth  $v'_B$   m/s  ----待选择----away from the Earthtowards the Earth 
(b) How much energy was supplied by the explosion? [Hint: What is the change in KE as a result of the explosion? $a\times10^8$ a =    J

  A rocket of total mass 3180 kg is traveling in ou+2a* 0gpggqa rter space with a velocity of 115m/gg 0+pqa2r*gas To 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 0.0of :c*lzlz la f2c*(lp6 fu(k945 kg is hit off the tee at a speed of 45m/s The golf club wasa(9f2kczpllu f 6col* l(: f*z in contact with the ball for $3.5\times10^{-3}$s Find (a) the impulse imparted to the golf ball,    kg*m/s
(b) the average force exerted on the ball by the golf club.    N

  A 12-kg hammer strikes a nail at a velocity of 8.5m/s and comes t; 0segt u;v+alo rest in a time interval of 8.0 ms. (a) What is the impulse given to the nat ;vag +sleu;0il?    kg*m/s
(b) What is the average force acting on the nail?    N

  A tennis ball of mass m=0.06kg and speed2wsmwsnf0 0dk 0bt6;h 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 o )rdm i3vqie29f the crashworthiness of new automobile models. Cars are tested by smashing them into fixed, massive barriers at 39rqm 2v) idei50km/h (30 mph). A new model of mass 1500 kg takes 0.15 s from the time of impact until it is brought to rest. (a) Calculate the average force exerted on the car by the barrier. $\approx$$a\times10^5$N a =   
(b) Calculate the average deceleration of the car.    m/$s^2$

  A 95-kg fullback is running at 4m/s to the east and is stopped in 0.75 s bydbuh39cvz x13 -i0qbx. dmw 5w a head-on tackle by aw 3.d3qx1h0-bmvxz 9w5c iubd 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 -qwhf wr5hr5m :x*kv8in the +x direction and is 8 rkqfh5wh:mxw v- *r5given by the graph of Fig. 7–33 as a function of time. Use graphical methods to estimate
(a) the total impulse given the ball    N*s
(b) the velocity of the ball after being struck, assuming the ball is being served so it is nearly at rest initially.    m/s

  From what maximum height can a 75-kg person jump without brea +kc4 fvv5;4xin :+hbnuu/ urgking 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). Assnnv r +u i+hufvc54; x4/ub:kgume the breaking strength (force per unit area) of bone is $170\times10^6\mathrm{~N/m^2}$ and its smallest cross-sectional area is $2.5\times10^{-4}m^2$ [Hint: Do not try this experimentally.]    m

  A ball of mass 0.440 kg moving east (+x direction) with a speed of collidb-9kjri-k jghm) ) j6des 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 hjjr )i6g-k- 9 km)djbB 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 wit.u k- lhqwc:9vh a speed of 3m/s has a head-on collision with a 0.900-kg puck initially at rest. Assuming a perfectly elastic collision, what will be the speed and direction of each object after the collision?Let A represent the 0.450-kg puck, and let B represent the 0.900-k.hqkl-cv9:u wg puck. v'$_A$ =    m/s ----待选择----eastwest  v'$_B$ =    m/s ----待选择----eastwest 

  Two billiard balls of eqjmno**oauj2 2 ual mass undergo a perfectly elastic head-on collision. If one ball’s initial speed was 2m/s and the other’s was 3m/s inj*2j 2 no*mauo the opposite direction, what will be their speeds after the collision?(Let A represent the ball moving at 2.00 m/s, and call that direction the positive direction.Let B represent the ball moving at 3.00 m/s in the opposite direction. ) v'$_A$ =    m/s v'$_B$ =    m/s

  A 0.060-kg tennis ball, moving with a speed of 2.5m/s collides head-on dq-qgw jxa4-/with a 0.090-kg ball initially moving away from it at a speed of 1.15m/s Assuming a per-x-a jq4wdg /qfectly 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,lig.t :x h rg/,cw aas4. 2se4gdnwn- with a speed of 8.5m/s collides head-on and elastically with another ball initially at rest. Afterward the incoming ni4w- sg2hgg/ :aaw4t..s,n,xd cl resoftball 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 ewq4o 4zbnnll n4)ly 20lastically as one approaches the w ny42 n4q4b)l0nzoll other directly from the rear (Fig. 7–34). Car A has a mass of 450 kg and car B 550 kg, owing to differences in passenger 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 .:d2aw ohh zqc)6w,prmakes an elastic head-on collision with a second ball initially at rest. Tha2r, )qdh.:h pz6wo cwe 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 5f.vvr ya0zx* as shown in Fig. 7–35, and elastically strikes another cube at the bottom that is only one-half its mass. If the incline is 30 cm high and the table is 90 cm off the floor, where does each cube land? [Hint: Both leave the incline moxz5.r 0 *fayvvving horizontally.]$\Delta x_{m}$$\approx$    m $\Delta x_{M}$$\approx$    m

ake the general case of an,eagoj-d,u q+-y(. r lt6eg os object of mass m$_A$ and velocity v$_A$ elastically striking a stationary object of mass head-on. (a) Show that the final velocities v'$_A$ and v'$_B$ are given by$v_{\mathrm{A}}^{\prime}=\left(\frac{m_{\mathrm{A}}-m_{\mathrm{B}}}{m_{\mathrm{A}}+m_{\mathrm{B}}}\right)\nu_{\mathrm{A}},v_{\mathrm{B}}^{\prime}=\left(\frac{2m_{\mathrm{A}}}{m_{\mathrm{A}}+m_{\mathrm{B}}}\right)\nu_{\mathrm{A}}.$(b) What happens in the extreme case when m$_A$ is much smaller than m$_B$ Cite a common example of this. (c) What happens in the extreme case when m$_A$ is much larger than m$_B$ Cite a common example of this. (d) What happens in the case when m$_A$=m$_B$ Cite a common example.

  In a ballistic pendulum experimentj s;( . * a(tabioh5m(wl5itxt, projectile 1 results in a maximum height h of the pendulum equal to 2.6 cm. A second projectile caus(j.x*5mai((ohltab s5ttwi;es the the pendulum to swing twice as high, $h_2=5.2\mathrm{cm}$ The second projectile was how many times faster than the first? $v_1$ =    $v_2$ ([color=rgba(0, 0, 0, 0.85)]Round to three decimal places)

  A 28-g rifle bullet traveling 230m/s buries itself in a 3.6-kg pendulu/a,g 4e1nxbrr 8nqmxll;n:p; m hanging on a 2.8-m-long string, which makes the pendu l14;xr:pml8/ nqr ,ne;anbgxlum 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 for4)1 sr*uv(znnvmeca9q4s2 mwg qt 9o0 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 object, initially at rest, intoj+)7gq5jvhkk.e y o; b dp-+xj 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 energj o j+gjhkb7yp -+ex;kdv.q)5 y did each piece acquire? (Let A represent the heavier particle, and B represent the lighter particle. ) KE'$_A$ =    J KE$_B$ =    J

  A 920-kg sports car collides into the rear end of a 2300-kg SUV stoppe c9vpob3 hu9c:d at a red light. The bumpers lock, the brakes are locked, and the two cars skid forward 2.8 m before stopping. The police officer, knowing that the coefficient of kinetic friction between tires and road is 0.80, calculates the speedvc39po b:u9hc 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 andyl3-. cxj.ioj rebounds to a height of 1.20 m. Approximately how many rebounds will the ball make before losing 90% of itl .i.yxj jo3c-s energy?   

A measure of inelasticity in a head-on co-fkgz 8u7fg.2ga hp on 3us(,zllision of two objects is the coefficient of restitution, ehga gg 2,uf8-k37 sonzupz.f(, 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 q-6c oq3r 1hcds x*6wz7q6ikiwith three times the mass of the other. A de 7* ocq1 xqcq3 hdkiriw66z-s6pression is made in both faces of the cut, so that a firecracker can be placed in it with the block reassembled. The reassembled block is set on a rough-surfaced table, and the fuse is lit. When the firecracker explodes, the two blocks separate and 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 directiqmm5izf69qtpvi/ t5; on at 5.5m/s collides head-on with a 10.0-kg object moving in the -x direction at 4m/s Find thmt/iq5ft 5v6qmpi ;9ze 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 nucleus, an elect/yv 3xnjzj+xj p6vt 19ron, and a neutrino. The electron and neutrino are emitted ty 1x+zjxjv 6vpn/ j93at 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 mat(lsbq244u n+rja +plss $m_\mathrm{A}=0.400$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 betwz va5+n zn og4bqducn,,h)/ -feen two objects of equal mass, each having +f/gb, zd,qnn hocuavnz4-) 5initial speed the two move off together with speed v/3 What was the angle between their initial directions?    $^{\circ} $

  Two billiard balls of equal mass move at right angles and0 tz2k0wa8vuy.hg5h d4h 1ro n 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 finalzd1.yrohh 4nh 52ukw8v 0a0t g direction of ball A and what are their two speeds? direction of ball A is  ----待选择----x directionx direction v'$_A$ =    m/s v'$_B$ =    m/s

  A neon atom (m=20u) makes a perfectly elastic collision with another atom at nufsx-i*(f.d /-jyn wrest. After the impact, the neon atom traveli u j/(*nsdywn-f-. xfs 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 t31kv.z6p0h3wrjb7zw ,n u,ao t q4d ia perfectly elastic collision with another atom at rest. After the impact, th 3,1 zn.d iak4oz07t6uvpww, 3rhtqbje 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 n0nsgn,f,(f wsystem shown in Fig. 7–38. Specify relative to the left-hand 1.nfgw( nn,f 0,s00-kg mass.    m

  The distance between a carbo-/u jglsb j1v 7q5xf)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:q1z*hzc/( h yftnnb ( 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 s(b* nhh:1q (c/fzyznt it in the back seat 3.90 m from the front? Assume that each person has a mass of 70.0 kg.    m

  A square uniform raft, 18 m by 18 m, of ma.vgl-at+-pli:at n l: ss 6800 kg, is used as a ferryboat. If three cars, each of mass 1200 kg, occupy its NE, SE, anill.+--ltv nt :pga:a d SW corners, determine the CM of the loaded ferryboat.$X_{CM}$ =    m $Y_{CM}$ =    m

  Three cubes, of sides n 7 qvg03bct a gee10;l(h)hws$l_0$,$2l_0$, 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) palletjp+49z c/nto ui a (kwd4uewl m3v/;n: has a load of identical cases of tomato paste (see Fig. 7–40), each of which is a cube of length l. Find the center of gravity in the ( n/9uw ceiadp4+ lkn;mwoz3t4 uj /:vhorizontal plane, so that the crane operator can pick up the load without tipping it.$X_{CM}$ =    l $Y_{CM}$ =    l

  A uniform circular plate of radius 2R has a circular hole of radius R rfk02-ij24gmr6j -l ( kmr s,.v chw mybm7o)dcut out of ii(70b)dgfmrw .v j64,rry k-2sojmc mk2 -hlmt. 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 tho- 7es6 ahqj::ymjrq++xy: g.li ghfi2se in Table 7–1, and calculate thshyyqg-6 x:.fag:ie2qjrj+i 7l:+h me mass of one of your legs.    kg

  Determine the CM of an outstretched arm using Table3mze)68 oatv.p6te6 eptb bs3 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 right a t:9yc.4pzrniq. s ok;loe+p.ngle. Assume that the person is 155 cm tal;z.pk:osytcr.4o il en.+qp9l. $X_{CM}$ =    cm $Y_{CM}$ =    cm

When a high jumper iszc94uzdg biay ))ewys bp5)) 4 in a position such that his arms and legs are hanging vertically, and 5)ep s cz)9 44)bzubigyyda)whis trunk and head are 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 Moontetm+,p )x8 ul 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 apart on fricti:z o+7x/vj )wh.pnnrf onless ice.
(a) How far from the woman is their CM?    m from the woman
(b) If each holds one end of a rope, and the man pulls on the rope so that he moves 2.5 m, how far from the woman will he be now?    m
(c) How far will the man have moved when he collides with the woman? He has moved    m from his original position

  A mallet consists of a uniform cylindrical head of mass 2.00 kg and a diamewt xx9+,gc5qk ter 0.0800 m mounted on a uniform cylindrical h95xw cgkt+ qx,andle 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 follow a parabolic trajectory?    cm

  A mallet consists of a uniform cylindrical head of mass 2.00 kg and a diamebx5b .0y efmo5ter 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, intoxf50 5e.ybmbo 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 Example 7–14 (Fig. 7–29), ux4qmjzg2;7ealm o k;m2u k1;$m_{II}$=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 an9lypn1 ; (0 ca34jfl4ifk sna9f7cqgid 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? What4cfilp9n1( a3fjs gla q 4;79fynk0ci happens if the passenger stops?

  An 0.145-kg baseball pitched horizontally at strikes a bat and is popped stra3-x4a8:tcjyfn yr sp. ight up to a height of 55.6 m. If the contact time is 1.4 ms, calculate the averagex n-4:8rtj.cy3s pyaf force on the ball during the contact.    $^{\circ} $

  A rocket of mass m traveling wit8 0ns xa(l xrwmx b2y6ez4,ys;h 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. 7–434ibysgk7 ;.th. Relative dimensions are al sky ;it7b4.ghso 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 speed of 2.5m/s by pu+x 8w8g ijx+zb-/ +4 zp/thfdlvflri 0shing off with his legs from an 1800-kg space f/xlid- 0w vi ++h8j48xz+gf/tbrplzcapsule.
(a) What is the change in speed of the space capsule?    m/s
(b) If the push lasts 0.40 s, what is the average force exerted on the astronaut by the space capsule? As the reference frame, use the position of the space capsule before the push.    N

  Two astronauts, one of mass 60 kg and the other 80 kg, are in5g oubyz:i08/x9qkpnitially at rest in outer space. They then push each other apart. How far apart are they when the lighter astronaut has movzx k85g ui:p0oy 9/nqbed 12 m?    m

  A ball of mass m makes a head-on elastic collision with a second ball (at q/0fpg f.mc 7g :-qjy9lztdb)i f ty;.rest) and rebounds in y 7zf-f:mpq)b /ygfgj;i0 c tt.q9dl.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 inl8nj7 qj --e c;nzwsy9 a court case involving an automobile accident. The accident involved car A of mass 1900 kwn- j ;zcy8jq sne-7l9g 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 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 y8mya 1,b1vp5lz*xb(*dn8 rwn t82se lcen;q 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 collisions are perfectly elastic, what is the bounce height on the fourth bounce when the ball reaches the botl8*wlqn88 sz *a,y ncpn2rde51vb y(x;bm e1ttom of the stairs?

  A bullet is fired vertically into a 1.40-kg block of wood at rest directly abovayllm9 q dse8w0+ b19he it. If the bullet has a mass of 29.0 g and a speed of 510m/s how high will the block rise after tmqaw e90l+ydb 8hl1s9he bullet becomes embedded in it?    m

  A 25-g bullet strikes and becomes embedded in a 1.35-kg block of wood p l:d(kf:z)r pf*. . azxziz*vilaced 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 comes to rest, what was the muzzle speed: d)krz.f*xalf*zzzv (iip :. of the bullet?    m/s

  Two people, one of mass 75 kg and the other of mass 60 kg, sit in a rowboat of zy wrgind,49*;r,qfvmass 80 kg. With the boat initially at resz9;v*i ,fw 4ry rqdg,nt, 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 move    towards the initial position of the 75 kg person(Round to two decimal places)

  A meteor whose mass waq5 ;a .x/52maluy knt47aswpjs about $ 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 suzcjy wqy 0i+)0ddenly broken apart into two fragments by an explosion. One frq z+c)yy00iwjagment acquires twice the kinetic energy of the other. What is the ratio of their masses?   

  The force on a bullet is given*at2i ..1ohpul le0k tthh+*m 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 k- mc,g22hbv1a6ep dr $m_A$ = 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 decarv(v,)q4 +sxffgts4r ys radioactively into an alpha particle and a smaller nucleus. What will be the speefvvgr,+t44rs ) qsx( fd of this recoiling nucleus if the speed of the alpha particle is $ 3.8\times10^{5 }$m/s Assume the recoiling nucleus has a mass 57 times greater than that of the alpha particle.    m/s

  A 0.25-kg skeet (clay target) is fired at an anglexxnido dj; yy sax:4.zfd:( 16 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=2.20b/ wq+eesvon)r d(6v 4-adkxkg slides 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)x cwb. diw s+y cun.hc8(hg ,z,di*4;h, what is the upper limit on mass m if it is to rebound from M, slide up the incline, stop, slide down the incline, and c.d84 dbyw h,cic;(zxh,g wu+n s*chi.ollide with M again?    kg (Let A represent mass m, and B represent mass M.)

  The gravitational slingshot effect. Figure 7–47 shb/ njko/1l+gg ows the planet Saturn moving in the negative x direction at its orbita+1kj //lo gbgnl 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