We claim that momentum is conserved, yet most moving objects evk3q9kmuo0c2efjb o(zg o) 8*f6z8xcientually slow down and st 6*f9g uq oobm)2oxz ezi(8803fkjkccop. Explain.

When a person jumps from a tree to the ground, what happens to tgdtt9+b .zt hmz;r, /bhe momentum of the person upon strikim+, bgh;zdztttr. b 9/ng the ground?

When you release an inflated but untied balloon, why does it fly acro(pwsmlws0u98t v+v z; ss the room?t80(vzu ww;lsmp +9v s

It is said that in ancient times a rich man with a bag of gold coins frc 2zt+o, aprmj,au. 3lp5f v2aoze to death while stranpmlatu3c o.2pj+2 ,zraf5,va ded on a frozen lake. Because the ice was frictionless, he could not push himself to shore. What could he have done to save himself had he not been so miserly?

How can a rocket change direction when it is far outkqq g8 (a0m+ij in space and is essentially ikq0(q + gaj8min a vacuum?

According to Eq. 7–5, the longer the impact time of an impulse, the smaller th 8grnf,oi wh.7e 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 7frw .8nogi h,collision and reduce the possibility of fracture or death.

Cars used to be built as rigid as possible to grq 6b-v7 k, b6 6mqg6zeyz1wrwithstand collisions. Today, though, cars 6v q1 gwz-keb7,r q 6r6myz6bgare designed to have “crumple zones” that collapse upon impact. What is the advantage of this new design?

Why can a batter hit a pigsba +qrv7/d7ta.l)a tched baseball further than a ball tossed in the air byd g)tr /a7vs7 aq.+lba the batter?

Is it possible for an object to receive a larger impulse from ahi:peow+n*(q7p4h 2w h 2kpxi small force than from a large force? Explaino( * pwqhwpi22p ie:hk4xn+7 h.

A light object and a l3a69f8itipc0w:y bl,r as6xheavy object have the same kinetic energy. Which has the great83rsi9afxw0ylp,a t:b 6 icl6er momentum? Explain.

Describe a collision in which all kinetic energj /2yr1i1ufd7xwv y w+y is lost.

At a hydroelectric power plvd ydg w8f68a,ant, water is directed at high speed against turbine blades on an axle that turns an electric generator. For maximum power generatiofa 6gd88vdy,wn, 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 at aia)0 hots ,exys9d54ki3 cmp3 45 $^{\circ} $ angle as shown in Fig. below. What is the direction (a) of the change in momentum of the ball, (b) of the force on the wall?

A Superball is dropped from a height h onto a hard steel plate (fixed toan4o ,m29k:yzk.az p fyj3g(c 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 zk4 n23k( .a ,ycjpzgo y9fma:Earth as our system, during what parts of the process is momentum conserved? (c) Answer part (b) for a piece of putty that falls and sticks to the steel plate.

Why do you tend to lean backward when carrying a heavy loau)zs 4 gm.sy8sd in your arms?

Why is the CM of a 1-m length of pipe at its mid-point, whereas this is not truer f gp,lwxj8j4) )v/nb fo8j)vrxlnw ) j/,pg4fbr your arm or leg?

Show on a diagram how yiyl6wg3t g- :rour CM shifts when you change from a lying position to a sitting posit ril-g6 3w:gtyion.

If only an external force cuyl:eoy3z/u0q8 e go (an change the momentum of the center of mass of an object, how can the internal force of an engine accelerate a caru(le0y 83/y o:zguoqe?

A rocket following a paro8fm(- n, gjla s6n.xcabolic path through the air suddenly explodes into many pieces. What can you an 6lm, js8.-ncfg(xosay about the motion of this system of pieces?

  What is the magnitude of the momentum of a 28-g sparrow flying with yd1j1c 2wzgb- )gc2 vbhbkh.9a speed of $8.4 \; m/s$    $kg \; m/s$

  A constant friction force of 25 N acts on a 65-kg skier6h /m h,inedg9j fe1051qy gmj for 20 s. What is the skier’s qgnhhm im1g,5j0 e9f61/ jde ychange in velocity?    m/s

  A 0.145-kg baseball pitched at 39 m/s is hi.z zrr z 3t4,kkufpc.3t on a horizontal line drive straight back toward the pitcher at 52m/s If the contact time betwe zu.z,.3rpzrkk t4c3fen bat and ball is $3\times10^{-3}$s calculate the average force between the ball and bat during contact.    N

  A child in a boat throws a 6.40-kg package out horizontally with a speo4ncs9:ky o tv-u- *wied of 10 m/s Fig. below Calculate the velocity of the boat immediately after, assuming it was initially at rest. The mass of the chs:4koc9voin-*t wu -y ild 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 exeuu / pa)gke5wjgg3d/9rted on a rocket, given that the propelling gases are expelled at eu93 w5 kjg )dg/agu/pa rate of $1500 \; kg/s$ with a speed of $ 4\times10^{4 } \; m/s$ (at the moment of takeoff). F =    $\times 10^7 \; N$

  A 95-kg halfback movingk/b lx95mv;bu0 :7mpqop +bv j 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 t)z+(aia rcrf7zpy0;ra5-3q s1c , vyoc 1dz oon alevel frictionless track with a constant speed of 18m/s A 5350-kg load,initially at qca,35as- f11)+; oarvpyy (zoi ccdz0 z7rrtrest, is dropped onto the car. What will be the car’s new speed?    m/s

  A 9300-kg boxcar trav;q:*owq0 )py/v * klqfx zdm)neling at $15 \; m/s$ strikes a second boxcar at rest. The two stick together and move off with a speed of $6 \; m/s$ What is the mass of the second car?    $m/s$

  During a Chicago storm, winds can 5ttmo;/)ht zkwhip horizontally at speeds of 100km/h If the air strikes a person at the rate of 40kg/s per square meter anmhttz;k/o 5)t d is brought to rest, estimate the force of the wind on a person. Assume the person is 1.50 m high and 0.50 m wide. Compare to the typical maximum force of friction $\mu\approx1.0$ between the person and the ground, if the person has a mass of 70 kg.    N
$F_{on person}$  ----待选择----<> $F_{fr}$

  A 3800-kg open railroad car coasts along with a constant speed of 8.6mw6,lkf7-dj8 1jtmu j-lf vnxw/: hse6 /s on a level track. Snow begins to fall verti 7d-wm,lfk -1u8nw evs: 6 fxh6jtljj/cally 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 ewsn+0 c5src4w jr*8x tmits an alpha particle in the direction of its velocity, and the remaining nucleus slows 08rc*w+s snt 4xj5w crto 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 travel6ru /y2osfrx .ing 230m/s penetrates a 2.0-kg block of wood and emerges cleanly at 1xfror s6y2.u /70m/s If the block 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 is traveling hu, r9uopu(2t3 wa1cx 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 traveli/ar9biz ew- m:ng in outer space with a velocity of 115m/s To alter iei-9 baz/ r:mwts course by 35.0 $^{\circ} $, its rockets can be fired briefly in a direction perpendicular to its original motion. If the rocket gases are expelled at a speed of 1750m/s how much mass must be expelled?    kg

  A golf ball of mass 0.045 kg is hit off the tee at a speed of 45m/s The golfvq; e:opq( ,+vb+rgtr club was in contact with the ball; q og+v ptv,b+qre:(r 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 at3q l hgjf( hxl+z(1(du a velocity of 8.5m/s and comes to rest in a time interval of 8.0 ms. (a)zh(xu 3 q(jflg+lh1d( What is the impulse given to the nail?    kg*m/s
(b) What is the average force acting on the nail?    N

  A tennis ball of mass m=0.06kg and speed v=25m/s st5w(nwma ;+jq4v p kl3hrikes 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 chargezbq+1flreo au6g u.*nzwbqk(lx4 .3* of the crashworthiness of new automobile models. Cars are tested by smashing them into fixed, massive barriers at 50km/h (30 mph). A new model of mass 1500 kg takes 0.15 s from the time of impact until it is bro k4o*.aqweng(fu x1zlrl + ubz36bq* .ught 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 i xrg,2r-i0yjat 4m/s to the east and is stopped in 0.75 s by a head-on tackle by a tackler running due west. Calculate ygi i r2jr-,0x
(a) the original momentum of the fullback    kg*m/s
(b) the impulse exerted on the fullback    kg*m/s
(c) the impulse exerted on the tackler,    kg*m/s
(d) the average force exerted on the tackler.    N

  Suppose the force acting on a tennis ball (mass 0.060 kg) points in the +jux :s4y*bhn 2x direction and is given by the graph of Fi4*x j2bnhysu:g. 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 breaking the lowerbm,qbn)pn8 5;i ps,ft leg bone of either leg? Ignore air resistance and assume the CM of the person moves a distance of 0.60 m from the standing to the seated position (that is, in breaking the fall). Assume the breaking strength (force per unit q8)t p,fi5nb,n;psb marea) 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 colc y,l0s)ic pn1lides head-on with a 0.220-kg ball at rest. If the collision is perfectly elastic, what will be the speed and directionc ip1 clyn,s)0 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, mqu zx7/ -xbw: b5y *3/wk q5hnbj-opffoving east with a speed of 3m/s has a head-on collision with a 0.900-kg puckxxy-/z fp f jhkqwn/5wb*:bu-37bq5o 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-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 elastic gdaf mg3 95e*ehead-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 d ma5e fg*e93gB 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 wit.9rab -i6tubm h a 0.090-kg ball initially moving away from it at a speed of 1.15m/s Assuming a perfecbt . 6br9ia-umtly 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 1bvopirmi*) nm g:6 d;a speed of 8.5m/s collides head-on and elastically with another6mor* id)png : ;mv1bi ball 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 parkq42gs o aaf7v(47f6y -y f,kc1gco nnh ride collide 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 oyffnsv7a6ngfy 7ghck2co , a4(4q - 1mass. If car A approaches at 4.5m/s and car B is moving at 3.7m/s calculate
(a) their velocities after the collision v'$_A$ =    m/s v'$_B$ =    m/s
(b) the change in momentum of each.$\Delta p_{\mathrm{A}}$$\approx$    kg*m/s $\Delta p_{\mathrm{B}}$$\approx$    kg*m/s

  A 0.280-kg croquet ball makes an elastic head-ob*imn0i;(f pi n collision with a second ball initially at rest. The second ball moves off with half the original speed of the firstpi0nbf*m i;i( 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 ab58*anj 8evhk/sf sw1 q th2uf 14f+lxs 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 movingt uh+f 1sf 2se /fa85hvwj q8kbl1*x4n horizontally.]$\Delta x_{m}$$\approx$    m $\Delta x_{M}$$\approx$    m

ake the general case of ab yn .vw;kan9up1 h,q:n 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 experiment,+xtn 5 f0yieijj,x6jx ;l+wr7 projectile 1 results in a maximum height h of the pendulum equa+f65ixxj,jinr0 +xy ;wjl et7l to 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 a 3.6-kg pendulum hanginpr fs( lmj.o3 ;88z cqubapk1/g on a 2.8-m-long string, which makes the pendulum swing upward in an arc. Determine the vertical and horizontal components of the pendulum’sr z1jkupm 8lopq(cfa;. s/38b displacement.vertical$\approx$    m horizontal =    m

(a) Derive a formula 71mz drj,1md+j a8.lo bz, kpwfor 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 brcmmis (-n5r9e3+bo mcy. dh9d eaks an object, initially at rest, into two pieces, one of which has 1.5 times the mass of the other. If 7500 J were released in the explosion, how mu +be 9(n shoic-.d9 mm3rdmc5ych 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 collides into the rear end of a 2300-kg SUrfw +1i7i;; xjau 6ikcV 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 speed of the sports car at impact. What was that speed?(Let A represent the sports car, and B repri+iw67rfa1uk i; xjc;esent the SUV) $\approx$    m/s

  A ball is dropped from a f8 +k52ak awwdr)yoj(fd /s7i height of 1.50 m and rebounds to a height of 1.20 m. Approximately how many rebounds will the balff w 5j(kw/di2ko+a8 )7drsa yl make before losing 90% of its energy?   

A measure of inelasticity in a head-on collision of two objects is the coj c.4vl: sbl1a1.hhng7x o4bs efficient of restitution, e, defined s1l.bb :n4h ljgh.v1s x47a coas$e=\frac{\nu_\mathrm{A}^{\prime}-\nu_\mathrm{B}^{\prime}}{\nu_\mathrm{B}-\nu_\mathrm{A}},$
where $\nu_\mathrm{A}^{\prime}-\nu_\mathrm{B}^{\prime}$ is the relative velocity of the two objects after the collision and $\nu_\mathrm{B}-\nu_\mathrm{A}$ is their relative velocity before it.
(a) Show that e=1 for a perfectly elastic collision, and e=0 for a completely inelastic collision.
(b) A simple method for measuring the coefficient of restitution for an object colliding with a very hard surface like steel is to drop the object onto a heavy steel plate, as shown in Fig. 7–36. Determine a formula for e in terms of the original height h and the maximum height h’ reached after one collision.

  A wooden block is cut into two pieces, one with three times the mass o+;alo lx+ hmk*8xxph8f 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 x;x+ xl+8ho*8pkamhlthe ratio of distances each block travels? ----待选择----1/91/101/81/6 

  A 15.0-kg object moving in the +x direcrnjqq jd1z lw .op26-2tion at 5.5m/s collides head-on with a 10.0-kg object moving in the -x direction at 4m/s Find the final velocity of each-jq. 22 ojdp61 nrzqlw 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 det6bfp9 czw 8 2*rozbzb7md 5cu r*a84mcays into a second nucleus, an electron, and a neutrino. The electron and neutrino are emitted at right anglesbo57t4u* *p8m8abbdcrzzm29 cr6fw z 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 massq61m-2,mqwvk ,a bf ha $m_\mathrm{A}=0.400$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 in rvgl(u/h sn,n:qym 4,elastic collision between two objects of equal mass, each ha,/uqs4grml(,yh n :nv ving 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 mass move at right angles and meet a(r q1ryh: +pnst 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 directq h(1+prsyr n:ion 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 coll*rqgy qegr ++;ision with another atom at rest. After the impact, the neon atom travels away at a 55+g qgr*yr;eq+ .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 x9vbhd ep)z6)6- kca8gv0ah qatom at rest. After the impact, the neon atom travels away at a 55.6x )v 60 hzv-g6d8)bq paa9echk $^{\circ} $ angle from its original direction and the unknown atom travels away at a -50 $^{\circ} $ angle. What is the mass (in u) of the unknown atom? [Hint: You can use the law of sines.](Let A represent the incoming neon atom, and B represent the target atom) $m_B$   u

  Find the center of mass of the three-mass system shus d438lcc+q ,vk(l wkown in Fig. 7–38. Specify relative to the left-hand 1.00-kg mass kd4cc3 (8l,svulwkq +.    m

  The distance between a carbon atom (3 .yi;1k7f(un mona xl$m_{\mathrm{C}}=12\mathrm{u}$) and an oxygen atom ($m_{\mathrm{O}}=16\mathrm{u}$) in the CO molecule is $1.13\times10^{-10}$m How far from the carbon atom is the center of mass of the molecule?    $\times10^{-11}$m

  The CM of an empty 1050-kg car is 2.50 m bexqdu/4dzohr1 ff 8e9 -hind 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 th - qd/1fxuof9rezhd84e 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 ujf (aee 7so)oxu mi)lj4k;vra 26-n,ssed as a ferryboat. If three cars, each of mass 1200 kg, occupy its Nlr e6(7o 2fsu,e;kam sa)njoj-v) i4xE, SE, and SW corners, determine the CM of the loaded ferryboat.$X_{CM}$ =    m $Y_{CM}$ =    m

  Three cubes, of sides )4unz vc.*uwa$l_0$,$2l_0$, 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 ly(pt7zw.dn z-nka0b 5oad 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 horizontal plane, so that the crane operator can pick up the load without tippingntz0w5(a z7 d.k ynb-p it.$X_{CM}$ =    l $Y_{CM}$ =    l

  A uniform circular plate*o qqzqg6 ;t40v;fdl u of radius 2R has a circular hole of radius R cut out of it. The center of the smaller circle is a distance 0.80R from th;t d*qq;vzouqf6 4g0le center C of the larger circle, Fig. 7–41. What is the position of the center of mass of the plate? [Hint: Try subtraction.]   R

  Assume that your proportions are the same as those in Tad1 u6 b. pme.kz:r,ipp8 zwhp3ble 7–1, and calculate the rp z6pb,mkp 1d. p ueziw.83:hmass of one of your legs.    kg

  Determine the CM of an outstretched ar1vf /61joybt3; dtyf tm 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 rik(* q1;wyw ii8mk4wzjght angle. Assume that the person is 155 cm t8mz;w kkwj ( y*iq14wiall. $X_{CM}$ =    cm $Y_{CM}$ =    cm

When a high jumper is in a position such that his arms and legs are h)*)kqx( u6 gvhn sooo,anging 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 the bodhsx o )vg,*ou6k )nqo(y? Use Table 7–1.

The masses of the Earth and hd .j5ax uf8vuck1i-/Moon 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 ;7-a94fuqr wupq uzg+rf)szk/; l7tg80-kg man stand 10.0 m apart on frictionless ice.
(a) How far from the woman is their CM?    m from the woman
(b) If each holds one end of a rope, and the man pulls on the rope so that he moves 2.5 m, how far from the woman will he be now?    m
(c) How far will the man have moved when he collides with the woman? He has moved    m from his original position

  A mallet consists of a uniform cylindrical head of mass 2.00 kg ad;v8, oiddpcii k7c 2 qkg7 +v3zu:9atnd 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 bot9t8q,i7u;ivo i3dcdpkk+:z7gdvc 2 a tom of the handle is the point that will follow a parabolic trajectory?    cm

  A mallet consists of a uniform cylindrical head of mass 2.0l4rq9idi 4l:n g enwrx7-gn160 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.ilnx :n1erg4lgi9r6 7w nqd-4 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 Exampvrc:- g :iio9o(hpv x5le 7–14 (Fig. 7–29), $m_{II}$=3$m_{I}$ Where then would $m_{II}$ land?    d(Round to two decimal places)
(b) What if $m_{I}$=3$m_{II}$    d

A helium balloon and its gondola, of mass M, are in thezd97bxf5*4ag t,e5 kpq a;tan air and stationary with respect to the ground. A passenger, of mass m, then climbs out and slides down a rope with speed measured with respect to the balloon. With what speed and direction (rep dx,a7fqa 9 aezkb;g5tn4* t5lative to Earth) does the balloon then move? What happens if the passenger stops?

  An 0.145-kg baseball pitched (r.xc1 ggkk+ nhorizontally at strikes a bat and is popped straight up to a height of 55.6 m. If the contact time is 1.4 ms, calck.nc rg1g (kx+ulate the average force on the ball during the contact.    $^{\circ} $

  A rocket of mass m traveling wit(w :(ywbf dzmqt(c)-dh 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 :q2 :ym5jpp7 fxn1gh bwith the corner pocket shot shown in Fig. 7–43. Relative dimensions are also show75b1f :ghq:m ypxjn2pn. 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 pud.g ye 7w-ak.jshing off with his legs from w.7gy-kjea d .an 1800-kg space capsule.
(a) What is the change in speed of the space capsule?    m/s
(b) If the push lasts 0.40 s, what is the average force exerted on the astronaut by the space capsule? As the reference frame, use the position of the space capsule before the push.    N

  Two astronauts, one of mass 60x:kkn:i,y: )nvpwb b)u+ 4bby kg and the other 80 kg, are initially at rest in outer sp:i::ky ) vynpkb4 +,bbwubn )xace. They then push 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 elascc qys,z41 db-tic collision with a second ball (at rest) and rebounds in the opposite direction with a speed equal to one-fourth its original speed. What is the mass of the second ball? ycdq s-1z,4cb$m_B$ =    $m_A$(Round to two decimal places)

  You have been hired as an expert witness in a couqzg,1 ibkfi)9u)-bk;hbg xyy-6 r7 iyrt 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 g)q-yikb 9- r,u;xyyzfk7h bib i)1g6m before he crashed into car B. After the collision, car A slid 18 m while car B slid 30 m. The coefficient of kinetic friction between the locked wheels and the road was measured to be 0.60. Show that the driver of car A was exceeding the 55-mph (90km/h) speed limit before applying the brakes.    mi/h

A golf ball rolls off the top of a flight of concrete steps of tota 1gta2 spa f ur+w0tvd8n;ja4v9bc13il vertical height 4.00 m. The ball hits four times on the way down, each time striking the horizontal part of a different ste w3g9 1c8+tvbf4jvniadtrupas1 a; 02p 1.0 m lower. If all collisions 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 r9-rcmi ,li(dwest directly above it. If the bullet has a mass of 29.0 g and a speed of 510m/s ho c (diwlmri,-9w high will the block rise after the bullet becomes embedded in it?    m

  A 25-g bullet strikes and becomk,a ;pv detzv3eg s:(7 h/,uf0hsx-vhes embedded in a 1.35-kg block of wood placed on a horizontal surface just in front of fp, hh sxht;u gsz:3eae(0,v-dv/vk7 the gun. If the coefficient of kinetic friction between the block and the surface is 0.25, and the impact drives the block a distance of 9.5 m before it comes to rest, what was the muzzle speed of the bullet?    m/s

  Two people, one of mass 75 kg and the other of mass 60 kg, sit in a rowboat ofd r4,h72-svi;hrp on d8sarc6 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 willrv 8 ia4h6dp,sh- drco2s r7n; move    towards the initial position of the 75 kg person(Round to two decimal places)

  A meteor whose mass was rmzkva1gl5 p4 jzgxbh,+-ln o9am;9: 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 suddenly brokestnet,ag9)f lx91f8 yn apart into two fragments by an explosion. One fragment acquires twice the kinetic energy of the other. What is the ratio of theen)y9s1ff9t a,xt l8gir masses?   

  The force on a bullet is givengq wjj09v gm)4 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 ogrt0 g(1i7vm;yuyr* $m_A$ = 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 radioavq3r/+ kqgv cd aol:-(t y7zz;h dqh,)ctively into an alpha particle and a smaller nucle vd:r7q(l;g,zqvh-yodktzc)3h q + /aus. What will be the 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 target) is fired 4fasq r;3fmc: 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 efy a.0*v. xhgb:scv.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. 7–46q(zcmntd 2+h( idxp)(7dg pe0), what is the upper limit on mass m if it is to rebound from M, sl(7de )(c z+ngit0m (2dxpdhq pide up the incline, stop, slide down the incline, and collide with M again?    kg (Let A represent mass m, and B represent mass M.)

  The gravitational slingshot effect. Figure 7–/go 8p5vmsp 7n47 shows the planet Saturn moving in the negative x direction at its orbital speed (5s o/gpnvm 7p8with 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