We claim that momentum is conserved, yet most movwh8yeg95 wnh-ing objects eventually slow down89yhwn-whg e 5 and stop. Explain.

When a person jumps fromnb6 ggvzf0a,5ag 0a2q a tree to the ground, what happens to the momentum of the person upon striking thq ,60g bgvfgaa0n 5za2e ground?

When you release an inflatlv4./mxa 14z7 ta8sjr amzw9eed but untied balloon, why does it fly across the room?lr9x a./jmes7zva1zt48 m aw4

It is said that in ancient times a0q1zi */bhukef2sb. d 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 not been so misers1u/d .ihqb2 b0k*ez fly?

How can a rocket change direction when it is far out in space and;7 /h2 dd4*j;w npubktfzzc2j is essentially in a vaczutd;2/27*b;p4djf jk zhw cnuum?

According to Eq. 7–5, the longer the impact time of an imp6w5 0m (3kaoxqdmvr;;i/c d qdulse, 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 collision5 r6c0o mdq/qamd;d w3 ivx;k( and reduce the possibility of fracture or death.

Cars used to be built as rigid2 uluc1h;li,n:b6 pn d as possible to withstand collisions. Today, though, cars are designed to have “crumple zones” that collapse upon i;pbi2 u hnn ,l6clud:1mpact. What is the advantage of this new design?

Why can a batter hit a pitched baseball further than a ball tossed in the . xrv y:hfznoj,q,n67l9yxp- air by the xl-p97noy,v: fyj.zqxr 6,hnbatter?

Is it possible for an object to receive a larger impulse from a smk7 73e6s re:knin kh;vall force than from a large force 7 khrni6;vk7 eks:3ne? Explain.

A light object and a heavy objeeu c0(h(d +r9d dfgju0ct have the same kinetic energy. Which has the greatd (h00 (ergf+dj9ducuer momentum? Explain.

Describe a collision in which all kinetic en m* ;cxv7x;qnqergy is lost.

At a hydroelectric power pl mcfcy6 jwer* sq:.z52ant, water is directed at high speed against turbine blades on an axle that turns an electyz5s*qw2:.rc ef6 jm cric 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 e2b5e 7 tcsjvwj9y6k9t 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 height h onto a hard steel plate (fixed to th 6f wk)jjbyo*5e 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 t6w*jboy)j fk5he 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:cpycxc94+)bciss7ji1podfx o 8 2 h) carrying a heavy load in your arms?

Why is the CM of a 1-m length of pipe at its mid-point, whereas , -7i.aoks (xo-ujccuthis is not true for your arm-uk- j,o(io. uccxa7 s or leg?

Show on a diagram how your CM shifts when you change fro:,2,auk3okggya8b aeax br 00m a lying position to a sitting pos,,by0u gabexa8g rk0 3oa a2k:ition.

If only an external force can change the momentumz(lh95l2 tbm0n grpd ) of the center of mass of an object, how can the internal force of an el5h0 dzg2b lr(m9p n)tngine accelerate a car?

A rocket following a parabolic path through the air suddenly explodes into mbo.8uhhc ip:5 any pieces. What can you say about the motion of thiu:c5o8b. hh pis system of pieces?

  What is the magnitude of the momentum of a 28-g sparrow *b (1cikmlfv+k 6 :ylzha8ks7flying with a speed of 87ilk:+zlcy1a kbhvkf ( m* 86s.4 m/s    $kg\;m/s$

  A constant friction force of 25 N acts on a 1 d,gx28k(i*pkhuiuzsy9. :s u5 5lsgp8r maq65-kg skier for 20 s. What is the skier’s change in v.uk(h2 s9ruys pig l*u, p8qg8ki1mz5 :dx5s aelocity?    m/s

  A 0.145-kg baseball pitched at 39 m/s is hit on nr */cvqz1dh/gz.t v6hzdy /w7+a 0sqa horizontal line drive straight vch0sz1nv7 d+r//z*q tdw6hzyag ./qback toward the pitcher 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 throw2 tdo22eu 5gvus a 6.40-kg package out horizontally with a speed of 10 m/s Fig. below Calculate the velocity of the boat immediately after, assuming it was initially at rest. The mass of the child is 26.0 kg, and uug222vd et5o that of the boat is 45.0 kg. Ignore water resistance. The velocity of the boat is    m/s

  Calculate the force exert46v kkt+pjebk v wk*br2ge5.ea,s+/ ued on a rocket, given that the propelling gases are expelled at a rate of 1w+b+s/ 5,*4k v6e jv.bkp2rukegtaek 500kg/s with a speed of $ 4\times10^{4 }$ (at the moment of takeoff).$a\times10^7$ N a =   

  A 95-kg halfback moving at 4.1m/s onph/76kjh yjmvni+/gy9b a9s 8 an apparent breakaway for a touchdown is tackled from behind. When he was tackled by an 85-kg cornerback runni+ny6jm j b/9ksyav8h/9hg 7ipng 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 alone on alevel frictionless track 18omza ekkvw6tg /; .dwith a constant speed of 18m/s A 5350-kg load,initially at rest, is dropped onto thega /.kzemt;8 wk6ovd1 car. What will be the car’s new speed?    m/s

  A 9300-kg boxcar traveling at 15m/s strikes aiwq56sa073ym oom/ kw second boxcar at rest. The two stick tog5yk m7 36wiq/a0smwo oether and move off with a speed of 6m/s What is the mass of the second car?    m/s

  During a Chicago storm, winds can whip ,d *ld:.va :ti nby4o-8mekrrhorizontally at speeds of 100km/h If the air strikes a person at the rater lrk:*. bdv:aten -i4,m od8y of 40kg/s per square meter and is brought to rest, estimate the force of the wind on a person. Assume the person is 1.50 m high and 0.50 m wide. Compare to the typical maximum force of friction $\mu\approx1.0$ between the person and the ground, if the person has a mass of 70 kg.    N
$F_{on person}$  ----待选择----<> $F_{fr}$

  A 3800-kg open railroad car coasts agwg7q 8qs-ki0 long with a constant speed of 8.6m/s on a level track. Snow begins to fall verticask7q0 gi8gqw-lly 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 par1 8rkf jbf/6x6f ftzk2ticle in the direction /fk6 ffjr1x2kbz68t f 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 speed does the alpha particle have when it is emitted?    m/s

  A 23-g bullet traveling 230m/s penetrates a 2.0a -+ )b f4ha/lb; mqhmty7dq3zzg3v :o-kg block of wood and emerges cleanly at 170m/s If the block is stationary on a frictionless surface when hit, how fast does it move after the f:h l/vthgm bmoq-334 zbay;zad7)+qbullet emerges?    m/s

  A 975-kg two-stage rocket is nklv.7 6sbe::urp i*n0 xc t(ytraveling 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 veloci2kkskn .f-+ *p+ slqjaty of 115kj qak.f -knsp 2*+l+sm/s 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 0.045 kg is hit tabokm(2 a *x-..r pfgoff the tee at a speed of 45m/s The golf club was in contact with the ball fp -aa2m..*r(ogkxtb 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 to l;8i:; dojgslrest in a time interval of 8.0 ms. (a) What is the impulse given to l dio;8l js;g:the nail?    kg*m/s
(b) What is the average force acting on the nail?    N

  A tennis ball of mass m=0.06kg and speed v=o o)8+ wo4hi3vja,vpj25m/s strikes a wall at a 45 $^{\circ} $ angle and rebounds with the same speed at 45 $^{\circ} $ (Fig. 7–32). What is the impulse (magnitude and direction) given to the ball?   kg*m/s to the  ----待选择----leftright 

  You are the design engineer in charge of the crashwo(cut 6m e2cn/wrthiness of new automobile models. Cars are tested by smashing them into fixe2(w cnm6/tcu ed, massive barriers at 50km/h (30 mph). A new model of mass 1500 kg takes 0.15 s from the time of impact until it is brought to rest. (a) Calculate the average force exerted on the car by the barrier. $\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 e3vl mb2tws9fntxty:4n ,ca;*5e pw.yast and is stopped in 0.75 s by a head-on tackle by a ty e w3n:2fc,nbm x t5tapt;v* 9.l4ywsackler 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 0.0a(atle74c*v-fkk. vxu) -bb- bz1ri g60 kg) points in the +x direction and is given by the graph of Fig. 7–33 as a function of time. Usecb)ea*kv vbika. -ft 4u1-z-( xr 7lbg 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 withnxe, ,xazrdi)k6 abo n5:/g c-out breaking the lower leg bone of either leg? Ignore air resistance and assume the CM6,/:ge-, ) xraz5odxn a nkcib 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 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) wru/;vxbr04 e u- y /txcf(se3nith a speed of collides head-on with a 0.220-kg ball at rest. If the collision i ;tbyrxc (4x/nu /rvfus-e e03s perfectly elastic, what will be the speed and direction of each ball after the collision?Let A represent the 0.440-kg ball, and B represent the 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 eas3ighm8a;l 6v hd m5ja5t with 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 spa3ha;5vlmidm8jg h 56 eed 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 o-mcy f:ft: lj wq+or21f equal 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 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 op2-l jr1fwy o:qc :m+ftposite direction. ) v'$_A$ =    m/s v'$_B$ =    m/s

  A 0.060-kg tennis ball, moving wlj gzxy /n(i(728ywro ith a speed of 2.5m/s collides head-on with a 0.090-kg ball initially moving away from it at a speed of 1.15m/s Assuming a perfectly elastic collision, what are the speed and direction of each ball after the collision?(Let A repgiwzyo(/ 7r(y8lx 2jn resent 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 72rhksvg t4h: 8.5m/s collides head-on and elastically with another ball initially at rest. Afterward the incoming softball bouncer7sh4vkg:h2 t s 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 coz e:s6iu 48abrllide elastically as one approaches the other directly from the rear (Fig. 7–34). Car A has a mass of 450 kg and car B 550 kg, owing to differences in passenger mass. If car A approaches at 4.5m/s and car B is moving at 3.7m/s calculr:4 beua6s8ziate
(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 h4 a2s;z: c-ovrgs nnk+ 5-qqjjead-on collision with a second ball initially at rest. The second ball moves off with haqc+s 4jnqn: ;z2jg vk-ar5-so lf 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 incli ci0d2c)kdzw u2vk7:jne as shown in Fig. 7–35, and elastically strikes 0cd2)vk:w 7cui 2zdkj 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 object of mar o:pfew .u0.rss 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 8 ,i*dqwj-ssr, projectile 1 results in a maximum height h of the pendulum equal rjd *,wiqs- s8to 2.6 cm. A 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 buries itself in c 3z)ueuyr8c ;ba xx** lvw3k0a 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 rbv cxe3 0x3ca8klz;ywu**u ) components of the pendulum’s displacement.vertical$\approx$    m horizontal =    m

(a) Derive a formula for the fraction of kinetic energbjr5j3r2tqur 9b ys+v o re230y 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 wd-szn h*yr,-mf(8jyk+it. yvk d,5b rest, into two pieces, one of which has 1.5 tiw iky5bhf k djns t8r-.zm,y(d-,+ *yvmes the mass of the other. If 7500 J were released in the explosion, how much kinetic energy did each piece acquire? (Let A represent the heavier particle, and B represent the lighter particle. ) KE'$_A$ =    J KE$_B$ =    J

  A 920-kg sports car c+jairc smjc211 u0rw :ollides into the rear end of a 2300-kg SUV stopped at a red light. The bumpers lock, the brakes are locked, and the two cars skid forward 2.8 m before stopping. The police officer, knowing that the coefficient of kinetic friction between tires and road is 0.80, calculates the spw :cj+ rsri0 um2c11ajeed 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 -acd k5qmp6c.of 1.50 m and rebounds to a height of 1.20 m. Approximately .p5c -ackdq6 mhow many rebounds will the ball make before losing 90% of its energy?   

A measure of inelasticity ins/g-c9my .9)hd)fgb(wjev 1*u klzm xa/ho,z a head-on collision of two objects is the coefficient of restitution, e, defined 9*/fmhj)9yb ceh gd-)zol,/ x (mvw k.suagz 1as$e=\frac{\nu_\mathrm{A}^{\prime}-\nu_\mathrm{B}^{\prime}}{\nu_\mathrm{B}-\nu_\mathrm{A}},$
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 5/mdk g5jctd. 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 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 trave5kjg5d./ctmd ls? ----待选择----1/91/101/81/6 

  A 15.0-kg object moving in the +x direction at 5.5m/s c ,h6w;rwx l;o5x+-fl9 jp e .glxia4wrollides head-on with a 10.0-kg object moving in the -x direction at 4m/s Find the final velocity of eacri 5hjlxeop;.+gf, 4 - lw6wlx;awrx9h 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 secon bdh;p5eiv,o +d nucleus, an electron, and a neutrino. The elehpbo, ;e+iv d5ctron 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 mass9ys jv +oepa*e,9 e7bk $m_\mathrm{A}=0.400$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 bebt.xuzfx x:s5051at ms,lr *mtween two objects of equal mass, each havinb50 t*ufm1txs ,sx:x zl5m.rag initial speed the two move off together with speed v/3 What was the angle between their initial directions?    $^{\circ} $

  Two billiard balls of equal m 2nbqe5*o(iu tl9;gnx w n6yb.ass move 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 .ib6xn 9ng loewyt* uq2(b ;n5the 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) m6m0e9cetqg vg,o- o( zwbqd,8akes a perfectly elastic collision with another atom at rest. A,om zgbgvoe(ec9q wt6 08 -,qdfter the impact, the neon atom travels away at a 55.6 $^{\circ} $ angle from its original direction and the unknown atom travels away at a -50 $^{\circ} $ angle. What is the mass (in u) of the unknown atom? [Hint: You can use the law of sines.](Let A represent the incoming neon atom, and B represent the target atom) $m_B$   u

  A neon atom (m=20u) makes a perfectuqsgg gf:s()8i x1g,ply elastic collision with another atom at rest. After the impacts8 g) iug(s:gfqxg1p, , the neon atom travels away at a 55.6 $^{\circ} $ angle from its original direction and the unknown atom travels away at a -50 $^{\circ} $ angle. What is the mass (in u) of the unknown atom? [Hint: You can use the law of sines.](Let A represent the incoming neon atom, and B represent the target atom) $m_B$   u

  Find the center of mass of the thry jfe6flv.2b b kqp8p r0w nx),8bs85dee-mass system shown in Fig. 7–38. Specify relativf y f6 .,r b2e88dn p)q5xwvpb80sjkble to the left-hand 1.00-kg mass.    m

  The distance between a cab u*l yqt-*0ik+inif,rbon 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 ckh7.k 6r5giv .5s9fruvc7gwk ar 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 seat 3.90 m from the front? Assume that each person has a mass of 70.0 kg67vk w5. fvsu5i97kgrghc rk ..    m

  A square uniform raft, 18 m by 18 m, of mass 68so.dmz,l( n7:w5 6 igng sg*sc00 kg, is used as a ferryboat. If three cars, each of mass 1200 kg, occupy itsgl g:w s(di67z o5s nmc*,ns.g NE, SE, and SW corners, determine the CM of the loaded ferryboat.$X_{CM}$ =    m $Y_{CM}$ =    m

  Three cubes, of sidesg+hiwz: x3p2a $l_0$,$2l_0$, 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 ident5hk7h)vm+ eqz,sg) bgs h+au 4ical cases 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 ph 7q hs4h5+)kb)g,zu mae+vsgick up the load without tipping it.$X_{CM}$ =    l $Y_{CM}$ =    l

  A uniform circular plate of radius 2R has a circudhey( bk/7, xvlar hole of radius R cut out of it. The center of the smaller circle is a distance 0.80R from the center C of th(/ed7h,xv kyb e larger circle, Fig. 7–41. What is the position of the center of mass of the plate? [Hint: Try subtraction.]   R

  Assume that your proportions are the same as those in Taxyd/cdz /3uzic w:45 yrjf7 f-ble 7–1, and calculate the mass of one of your legsf-3zy xujd45 c7ywc/r/zi:fd.    kg

  Determine the CM of an outstretched arm a92aofsoi aw v g4p;;atxb9 2)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 a/, ukvwr yl *dk9 m9zx1bes*-ob99hpt rm bent at a right angle. Assume that the person is 155 cm tall k/zwe*hyb9sxk9 9, u9plvmdt - rb1*o. $X_{CM}$ =    cm $Y_{CM}$ =    cm

When a high jumper is in a position such that his arvi ox+29bu0lnms and legs are hanging vertically, and his trunk and head are horizontal, cal+9 uxi2obl0 nvculate 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 x:iqn1m:i z6 haaf:afsuhb,4*5hs; o 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 frictionless ice: (gnecn 0qwfw+xx59 h.
(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 2.03-s q7.1jy aq;g6d o 9nawqety0 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 ts y9716.w jqaen;tyqq3ogd a- he handle is the point that will follow a parabolic trajectory?    cm

  A mallet consists of a uniform cylindrical head of mass 2.00 vift g0i*9 f,omd9g+gkg and a diameter 0.0800 m mounted on a uniform cylindrical handle of mass 0.500 kg and length ,ifgggm+* d990v ftio0.240 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 Example 7–14 (Fig. 7–29),7p +tqos ,dql*)5wsjq $m_{II}$=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 stat+a *pk2mc8iv7vc2b dl8 vw 6zbionary with respect to vdcbv+86ab8 2 iv*2p7k wc mzlthe 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 happens if the passenger stops?

  An 0.145-kg baseball pitched horizontally at strikes a bat aju-cziig w p:k(a7 cj97n9 3bs:/ihhcnd is popped straight up to a height of 55.6 m. h9 jcg77 c:iinjsu3-k bph(z: /awic9If the contact time is 1.4 ms, calculate the average force on the ball during the contact.    $^{\circ} $

  A rocket of mass m traveling withh0j mvtu:rv)cjujbjt f7fy-,z+ )8 8i 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 shz0jh)j mf9 p4 a0tu2bqown in Fig. 7–43. Relative dimensions are also shown. Should the player be worried about this being a “scra00fjtu4q hm) j9zpb2 atch shot,” in which the cue ball will also fall into a pocket? Give details.

  A 140-kg astronaut (including space suit) acekq6n l(2t 6*vy:dv7 eb9jymvquires a speed of 2.5m/s by pushing off with his legs from ne2 y(l6edt 9v: qvv*j6mby7kan 1800-kg space capsule.
(a) What is the change in speed of the space capsule?    m/s
(b) If the push lasts 0.40 s, what is the average force exerted on the astronaut by the space capsule? As the reference frame, use the position of the space capsule before the push.    N

  Two astronauts, one of mass 60 kg a a2u bw0z;zt4and the other 80 kg, are initially at rest in outer space. They then puuz4;a zawt 2b0sh each other 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 cmry09p//p ( 2cxkv fo1n- hnypollision with a second ball (at rest) and rebounds in the opposite direction with a p/0hkvonfmpr y /( 1nxy9cp-2 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 aw775 a af6zxxb 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 sl7bx7fx za56 waid 18 m while car B slid 30 m. The coefficient of kinetic friction between the locked wheels and the road was measured to be 0.60. Show that the driver of car A was exceeding the 55-mph (90km/h) speed limit before applying the brakes.    mi/h

A golf ball rolls off the top of a flight of concrete steps of wqzeji5v y3,,ii empc6)i0 /bm (;kjxtotal 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 collisij/mkemypw6(5z ;0iv qc,i) iix jeb 3,ons 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 o:l a tq/xmox- dp2:r)ef wood at rest directly above it. If the bm:xre l/pdxq:-)o a2tullet has a mass of 29.0 g and a speed of 510m/s how high will the block rise after the bullet becomes embedded in it?    m

  A 25-g bullet strikes and g2;w6rdrr.s gbecomes embedded 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 b wg;gsrr2 .6rdefore it comes to rest, what was the muzzle speed of the bullet?    m/s

  Two people, one of mass 75 kg and the other of mass 60 kg, sit in a rowboat o rv2h6r + cs/sh5c0rctf mass 80 0csrr/5r6tchs2 +hv ckg. 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 move    towards the initial position of the 75 kg person(Round to two decimal places)

  A meteor whose mass was mpabz 38*2mpa, pm(2l(a r7 f /vlx a/w,swypiabout $ 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 ina/g ,0om(ho)b5r d 3yjie5 tmbto two fragments by an explosion. One frrdi 0/)tobme jba5,oh5y 3 m(gagment acquires twice the kinetic energy of the other. What is the ratio of their masses?   

  The force on a bullet is given bz6gwvuf of1c42 ehz(+ pnan8 xtx.;f 0y 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 cx) u1z;mm gotvr a36x5e )/zh ;)cdrc$m_A$ = 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 dewg549 , mbnixrq6 kwv8x:x zi3cays radioactively into an alpha particle and a smaller nucleus. What will be the speed ovxwri8g 9 : 6xniwmkb ,x35z4qf 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) q, *4btyqdil/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 30.0ql 9n8*+p q8 (b ueqvp-pykzi) $^{\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 if it is to re /irjqq49+iod v kjlch(z*c.4bound from M, slide up the incline, stop, slidk.dv 4 (4 qj/9jr iio*hqcz+lce down the incline, and collide with M again?    kg (Let A represent mass m, and B represent mass M.)

  The gravitational slingshvvkpl )cxh8.,epv mel2i+ . t(ot effect. Figure 7–47 shows the planet Saturn moving in the negative x direction at its orbital speed (with respect to the Sun) +elv c.v)xl i t(hpv. p,e8m2kof 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