We claim that momentum is conservetkh)swm)yyu77 n ,t z:d, yet most moving objects eventually slow down anh ttz 77y:,suwn)m)kyd stop. Explain.

When a person jumps from a tree to the ground, what happens to the mqf b- *9pjhir5omentum of the person upon 5jp*fh i- 9brqstriking the ground?

When you release an inflated but untied balloon, wh ,, rxt.qkr; 8b ylhk60fcr;l -mjzw-ty does it fly across the room?t chmz-fqx0,86,lrj.-yr kwt ;r;klb

It is said that in ancient times a rich man with a bag of gold coins froze to 4-kqjr2yfcd97 tmj* cku irep:5.z e.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 hijmp tj.:zuecf2ydr 5*.k i 49qr- k7cemself had he not been so miserly?

How can a rocket chan4 c:8*dqomx opge direction when it is far out in space and is essentially in a vacuuo8p:mxo*qc d4 m?

According to Eq. 7–5, the long+kjau( t,cq i 9yet,nvmfe0)5er the impact time of an impulse, the smaller the force can be for the same momentum change, and hence the smaller the defora9e fc5(,jvq t0knitmu + ,y)emation of the object on which the force acts. On this basis, explain the value of air bags, which are intended to inflate during an automobile collision and reduce the possibility of fracture or death.

Cars used to be built as rigid as po2gp5chvonyex 5( (e:zssible to withstand collisions. Today, though, cars are designed to have “crumple zones” that collapse upon impact. What is the advantage of this new :h5 e(g np(xye5cz2ovdesign?

Why can a batter hit a pitched baseball further than a ball tossed in d; eifbx ps9,j1r scr;kmgh70ngi4* 3the air byer*xgg7;ci ;pmrbskis1 h093jdn 4f, the batter?

Is it possible for an object to receive a larger impxo 4wx g.n-agow10a+ sulse from a small force than from a osww+-g on 04xagax1 .large force? Explain.

A light object and a heavy object hag:u*n c4ii8rxve the same kinetic energy. Which has the gregr 48iui:c*xnater momentum? Explain.

Describe a collision in which all kinetic eb)cna;uy5 n*k nergy is lost.

At a hydroelectric power plant, water is directed at high speed agaid oun- rl sz901qjrsn*phl5ezm837/ cnst turbine blades on an axle that turns an electric generator. For maximum power generation, should the turbine blades be designed so that the water is brought to a dead stop, or so that the water rebosljdh /umnor5r9sl-3 p*nzz1eq087 c unds?

A squash ball hits a wall at a 1xca xdh4( ly j- d+b9eyw/r+q45 $^{\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 to th+s7:htp-eg aa e 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 aphg 7:a-es+tEarth 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 0sccx)gp/ b1con d8ot*nz1z ;load in your arms?

Why is the CM of a 1-m length of pipe at its mid-psmuh* y ji;(*lho13i qoint, whereas this is not true for your arm oqihi3yhjul(*sm ;1o* r leg?

Show on a diagram how your CM shifts wi5fxw ,cn0bg ;hen you change from a lying position to a sittfi 5 b,0wngxc;ing position.

If only an external force can change th2m 236kowotnx*y 8enx 9cqo6we momentum of the center of mass of an object, how can the ino 83oknnw txwo*q2xcye9m6 62 ternal force of an engine accelerate a car?

A rocket following a parabolic path throz0 b*nwmc -6dn,oecpo l3b 6m+ 0nbv2tugh the air suddenly explodes into many pieces. What can you say about the motion of this system 6+c 00ozbepnv*-nm3t6b ocd bwnl ,2m of pieces?

  What is the magnitude of the momentum of a 28-g sparrow flyi +va:pq-9p h 6;fnbzymng with a speed of $8.4 \; m/s$    $kg \; m/s$

  A constant friction force of 25 N acts on a 65-kg skier for 20 su+qdz z*kvr-tw t 54.q. What is the skiert 4uv5qzw+dqtr*-. zk ’s change in velocity?    m/s

  A 0.145-kg baseball pitched at 39 m/s px;/ 5e 9.uwucn p2dmcv.ps9jis hit on a horizontal line drive straight bj;d. npp 95w.vu9sx2pcm/eu cack 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 throws a 6.40d0ug.j4 gmup9-kg package out horizontally with a speed of 10 m/s Fig. below Calculate the velocity of the boat immediately a.ju4pd0 9ggmufter, assuming it was initially at rest. The mass of the child is 26.0 kg, and that of the boat is 45.0 kg. Ignore water resistance. The magnitude of the velocity of the boat is    m/s

  Calculate the force exerted on a rocket, given that the propellg*+ k 89tqn6f+ekgk)gm4 bx eling gases are expelled at a rate of b4g8eg6 e*gk9 fmtqxkl)n+ k+$1500 \; kg/s$ with a speed of $ 4\times10^{4 } \; m/s$ (at the moment of takeoff). F =    $\times 10^7 \; N$

  A 95-kg halfback moving n n,qfhmoj2o2p,x8 j9at $4.1 \; m/s$ on an apparent breakaway for a touchdown is tackled from behind. When he was tackled by an 85-kg cornerback running at $5.5 \; m/s$ in the same direction, what was their mutual speed immediately after the tackle?    $m/s$

  A 12,600-kg railroad car travels alone on alevel frictionless tjr,ytej6pb* 4rack with a constant speed of 18m/s A 5350-kg loe y tjp64*jb,rad,initially at rest, is dropped onto the car. What will be the car’s new speed?    m/s

  A 9300-kg boxcar traveling at il4v.922vxmi d ex(p-ys uqx;sg+c/l $15 \; m/s$ strikes a second boxcar at rest. The two stick together and move off with a speed of $6 \; m/s$ What is the mass of the second car?    $m/s$

  During a Chicago storm, winds can whip horizontally at speeds od k3 u hemyx3*bi)-;qnf 100km/h If the air strikes a person at the rate of 40kg/s per square meter and is brought to rest, estimate the force of the wind on a person. Assume the person is 1.50 m high and 0.50 m wide. Compare to the typical x-i;k bqumh3)e3*dny 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 8.6ma)2gtmvr)rb5 1bu7r d/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 tracks, what is the speed of the car a 2u1bm7rv5tr)a r bgd)fter 90.0 min?$\approx$    m/s

  An atomic nucleus initialjhv5q(gqx tx(/0u3i4 jpx(e.kme4iyu i.;culy moving at 420m/s emits an alpha particle in the direction of its velocity, and the remaining nucleus slows to 350m/s If the alpha particle h ( ihxtvq(x44( qjpi/yxe3.u5 eg kcjuum;.i0as 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-kgc+qy3o,f ) jsv;nvp2x ,kd1lqfm.v q8er ; q,u block of wood and emerges cleanly at 170m/s If the block is stationary on a frictionless surface when hit, how fast dq 18vf+ upmx,nj.,q;2vvy q f,lk3sec r qo);does it move after the bullet emerges?    m/s

  A 975-kg two-stage rocket is traveling at a spm3( )beqkic ,xeed 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:j1b 3dfizo(4p7yu xx is traveling in outer space with a velocity of 115m/s To alter 3yxud(ob4i 1jz:f7 px 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 off the tee at a speed of 45m/s The d (n*yhvg *:hxogdkg+ o: : .qsl2ydr3golf club was in contact with the balln.r*s xovg2 +(q :*ddlgyhhgd ::oy 3k 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/ x*m ztum+33ue 0zz9cgdoh)n*s and comes to rest in a time interval of 8.0 ms. (a) W)z dmghun c*3t9 zme3+0z x*uohat 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 spee zwtcpd+2.rz 8d 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 enginthvhoh y(l0siu*w 35t;isagg-mnee5 2 6 95n peer in charge of the crashworthiness of new automobile models. Cars are tested by smashing them into fixed, massiv -i0wutpg h*m;o( elsv5sne5iya56n 32h9h tge 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 east and is stopped in 0.75 s by a h bpj2s8s+pg a l8)m 7o5c-*h khafinc,eadp2i8ms-knpsaf)7g a5,+ obch*h clj 8-on tackle by a tackler running due west. Calculate
(a) the original momentum of the fullback    kg*m/s
(b) the impulse exerted on the fullback    kg*m/s
(c) the impulse exerted on the tackler,    kg*m/s
(d) the average force exerted on the tackler.    N

  Suppose the force acting on a tennis ball (masrnc(b dqvnfkl o.y3 :wj,;2 1v8 bfjs0s 0.060 kg) points in the +x direction and is given by the graph of Fig. 7–33 as0 w(,b. v; n sj1nkfdcfy qlvj3rob:82 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 lower 4jvk mu1 bn,l1leg bone of either leg? Ignore air resistancb 1n4jku,1m lve 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 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 u2koe)b;0 jkc(+x direction) with a speed of collides head-on with a 0.220-kg ball at rest. If the collision is perfectly elastic, what will be the speed and direction of each ball after the collision?Let A represento;c2b eukj)0k 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 e 4:ajiiip5nj- ast 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 speed and direction of each object after the colj 4p-n:ai5iijlision?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 ma4q mo( f+296hkxxy0mqcp atg -ss 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 directioc6 x (4qqmphfoy+-mx ak02gt9n.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, moup7wevc5 r(+4ox 4dckving with 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 Ass+ cu oxw(rdp4v5k4ec 7uming a perfectly elastic collision, what are the speed and direction of each ball after the collision?(Let A represent the 0.060-kg tennis ball, and let B represent the 0.090-kg ball.)v'$_A$ =    m/s v'$_B$ =    m/s

  A softball of mass 0.220 kg that is moving withwx(5acly892sjcfg i; a speed of 8.5m/s collides head-on and elastically with another ball initially at rest. Afterward the incoming softball bounces backward with a speed of 3.2x;(jylfcc 5g8 9iwsa7m/s Calculate
(a) the velocity of the target ball after the collision    m/s
(b) the mass of the target ball.    kg
(Let A represent the moving softball, and let B represent the ball initially at rest.)

  Two bumper cars in an amusement park ride collide elastically as one approachvx;ku)ei6 g/f es 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 / )eifuvk6; xgB is moving at 3.7m/s calculate
(a) their velocities after the collision v'$_A$ =    m/s v'$_B$ =    m/s
(b) the change in momentum of each.$\Delta p_{\mathrm{A}}$$\approx$    kg*m/s $\Delta p_{\mathrm{B}}$$\approx$    kg*m/s

  A 0.280-kg croquet ball makes an elastic head-on collision with a seco 9779e p*9xd zxzkwsxynd ball initially at rest. The second ball moves off with half the original speed of tz *ysdp7 x9zw799xexkhe 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 frivvi , duf2;8;wtt nq6cctionless incline 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 e cfv,td2n6;i vwt q8u;ach 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 ma)*s;p8i 6 d.h u7iszztze;idiss 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 exrg1np( ewll +rvxpv9es812h 6periment, projectile 1 results in a maximum height h of the pendulum equal xp w8vl(gl1n ree26v h91spr+ 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 un69a(d*hy m- iatve+ hanging on a 2.8-m-long string, which makes the pendulum swing upward in an arc. Dete6y *vah+tn9a(d meiu-rmine the vertical and horizontal components of the pendulum’s displacement.vertical$\approx$    m horizontal =    m

(a) Derive a formula for the fraction of kineti(nw*( 2mn;kjsr nf 40hl pj(fuc 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, initiloo1q ew.ke *,ally at rest, into two pieces, one of which has 1.5 times the mass of the othee*o .k,qlew1or. 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 collides into the rear end of a luiw; vo+d*w-2300-kg SUV stopped at a red light. The bumpers lock, the brakes are locked, and the two cars skid*wu;d wilo v-+ 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 represent the SUV) $\approx$    m/s

  A ball is dropped from a height of 1.50 m and rebounds to/)eef mtgywhx85k 36 yajs :s8 a height of 1.20 m. Approximately how many rebounds will the ball make before losing)hs sg txjye56fk83a/eyw8: m 90% of its energy?   

A measure of inelasticity in a head-on collision of two objectsdu, w.ow48xs4d1ykcc is the coefficient of restitution, e, defwk4 dy,d.xcw 1sou8c4 ined as$e=\frac{\nu_\mathrm{A}^{\prime}-\nu_\mathrm{B}^{\prime}}{\nu_\mathrm{B}-\nu_\mathrm{A}},$
where $\nu_\mathrm{A}^{\prime}-\nu_\mathrm{B}^{\prime}$ is the relative velocity of the two objects after the collision and $\nu_\mathrm{B}-\nu_\mathrm{A}$ is their relative velocity before it.
(a) Show that e=1 for a perfectly elastic collision, and e=0 for a completely inelastic collision.
(b) A simple method for measuring the coefficient of restitution for an object colliding with a very hard surface like steel is to drop the object onto a heavy steel plate, as shown in Fig. 7–36. Determine a formula for e in terms of the original height h and the maximum height h’ reached after one collision.

  A wooden block is cut into two pieces, one with three times :c7tpc76 mip hthe 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 sltm:7ip 76 hccpide 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 directiof52(qz p3i9q t*v kbpkn at 5.5m/s collides head-on with a 10.0-kg object moving in thkq 23k fvb*q( tp95izpe -x direction at 4m/s Find the final velocity of each mass if:
(a) the objects stick together;   m/s
(b) the collision is elastic; v'$_A$ =    m/s v'$_B$ =    m/s
(c) the 15.0-kg object is at rest after the collision;   m/s ----待选择----not reasonable reasonable 
(d) the 10.0-kg object is at rest after the collision;   m/s ----待选择----not reasonable reasonable 
(e) the 15.0-kg object has a velocity of 4m/s in the -x direction after the collision. .   m/s ----待选择----not reasonable reasonable 
Are the results in (c), (d), and (e) “reasonable”? Explain
( Let A represent the 15.0-kg object, and let B represent the 10.0-kg object.)

  A radioactive nucleus at rest dsbf u++* m,kkdecays into a second nucleus, an electron, and a neutrino. The electron kd ,*us++bfkm 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 masn-oyd ws67 k6z7d 7lsms $m_\mathrm{A}=0.400$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 between two objects of j,kb)+s gssrhs58zp, equal mass, each having initial speed the two g rsszshpb+)k, 8 sj,5move 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 at the origin1c , 3rjkie9rd 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 coe r ij9crk3d,1llision, assumed elastic, ball B is moving along the positive y axis (Fig. 7–37). What is the final direction of ball A and what are their two speeds? direction of ball A is  ----待选择----x directionx direction v'$_A$ =    m/s v'$_B$ =    m/s

  A neon atom (m=20u) makes a perfectly elastic collision with another atz/r,3d k ,jhgi yw1jh3p.l i5gom at rest. After the impact, the neon atom tjhwh,p3i yk1./d r35gi, jglzravels away at a 55.6 $^{\circ} $ angle from its original direction and the unknown atom travels away at a -50 $^{\circ} $ angle. What is the mass (in u) of the unknown atom? [Hint: You can use the law of sines.](Let A represent the incoming neon atom, and B represent the target atom) $m_B$   u

  A neon atom (m=20u) makes a perfectly elastic collision wiqnbhz(9-g . yjth another atom at rest. After the impact, the neon atyzh9(bj-.q gnom 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 system shown in Fig. 7–38. Su/k2w/ux9we4bw f k:fpecify relative to the left-hand 1.00-kg b/ 2ukxw:/fu 4w9efwkmass.    m

  The distance between a e 4; ,eluqw tlkv2d4cqg,; yd/w)j h6scarbon atom ($m_{\mathrm{C}}=12\mathrm{u}$) and an oxygen atom ($m_{\mathrm{O}}=16\mathrm{u}$) in the CO molecule is $1.13\times10^{-10}$m How far from the carbon atom is the center of mass of the molecule?    $\times10^{-11}$m

  The CM of an empty 1050-kg car is 2.50 m behind theaq xs -4) ebrq-hth /myr fus.(sfc27: front of the car. How far from the front of the carh-7 :csq4rae sh ufs2q/-b( t.fr x)my 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 kg.    m

  A square uniform raftpwtw4+6y 2xb j ewy395fd8llg, 18 m by 18 m, of mass 6800 kg, is used as a ferryboat. If three cars, each of mass 1200 kg, occupy iwb3j85dwll e9f+gtw p246yy xts NE, SE, and SW corners, determine the CM of the loaded ferryboat.$X_{CM}$ =    m $Y_{CM}$ =    m

  Three cubes, of sided)d.lcr ,4 sx/dxriz,cbk-1es $l_0$,$2l_0$, and $3l_0$ are placed next to one another (in contact) with their centers along a straight line and the $l=2l_{0}$ cube in the center (Fig. 7–39). What is the position, along this line, of the CM of this system? Assume the cubes are made of the same uniform material. $X_{CM}$ =    $l_0$ from the  ----待选择----leftright  edge of the smallest cube

  A (lightweight) pallet has a load of identical ccji ;dewv 9-:cq581jjbo*jki ases 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 without95 jbc;djckij* 1j :8v weoq-i tipping it.$X_{CM}$ =    l $Y_{CM}$ =    l

  A uniform circular plate of radius kk x(wq1l wd242R has a circular hole of radius R cut out of it. The center of the smaller circle is a distance 0.80R from the center C1dx4k w2wl kq( 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 qwy/ edgfhv/nx1*1*z in Table 7–1, and calculate the mass of one of your legfg1/*n*/1z qhxde yvw s.    kg

  Determine the CM of an outstretched arm using Tz -5o23szm apqk-funkn h;, 3fable 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 j.ftgp37u.hte f hg )2of an arm bent at a right angle. Assume that the person is 155 cm tall3tf 2hg.)h fup.e7gjt. $X_{CM}$ =    cm $Y_{CM}$ =    cm

When a high jumper is in a position such that his arms and legs are han l 6 muo)seff8sh7k3x/ging 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 body? Use Tabll 78ef6s x)fhuko/3 mse 7–1.

The masses of the Earth and Moon a1cld z+ qrt91,ljxn,z re $5.98\times10^{24}$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 apartr1y agr:ui8p3 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 ux5c 6d 7(rsql3h9klj jniform cylindrical head of mass 2.00 kg and a diameter 0.0800 m mounted on a uniform cylindrical handle of mass 0.500 kg and length 0.240 m, as shown in Fig. 7–42. If this mallet is tossed, spinning, into thd7kjlrl6(5q j s3h9c xe air, how far above the bottom of the handle is the point that will follow a parabolic trajectory?    cm

  A mallet consists of a uniformhv: 8ovo6;:w+7t2 oogxmn ,.zwmrt nx cylindrical head of mass 2.00 kg and a diameter 0.0800 m mounted on a uniform cylindrical handle of mass 0.500 kg and length 0.240 m, as shown in Fig. 7–42. If this mallet is tosseo o:ozmx.rh 8ngv 2t:ov6t7,n;m+wwx d, 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 Examp9men/u-y ck8 k a atq,n7fl ct7e:2uq+le 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 gjutynq+;r: qso7 r59rondola, of mass M, are in the air and stationary with respect to the ground. A passenger, of mass m, then climbs out and slides down a rope with speed measured with respect to the balloon. With what speed and dijs7tyr:9+o;ru5 qr qnrection (relative to Earth) does the balloon then move? What happens if the passenger stops?

  An 0.145-kg baseball pitched horizontlux*p0rl//:(acqi 9wumx7q l ally at strikes a bat and is popped straight up to a height of 55.6 m. If the contact time is 1.4 ms, calculate the average /ucxpm*: uxq0wl( r/iq79lalforce on the ball during the contact.    $^{\circ} $

  A rocket of mass m traveling with speedq5s*crrr.da 0 $v_0$ 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 with2ie 09,mjxy gq the corner pocket shot shown in Fig. 7–43. Relative dimensions are also shown. Should the player be worried about this being a “scratch shot,” in which the cue bay 92g,x jqi0emll will also fall into a pocket? Give details.

  A 140-kg astronaut (including sp; iql 3mqd)d7pn2uns3p;r( l)v+ydis y+0x pjace suit) acquires a speed of 2.5m/s by pushing off wins3qy rp m+) yu 732;p0l didvp;jx)n+l dq(sith his legs from 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 ,4tg knjt5l:s.1jh48byv.gqf f6f d0t9wh nqof mass 60 kg and the other 80 kg, are initially at rest in outer space. They then push each other apart. How far apart are they when the lighter astronaut has mo9f8 t5,nfv:klgqg. hwd 60btsj14hq. t4 nfj yved 12 m?    m

  A ball of mass m makes a head-on elastic collisionjurpr50 ba r/r ix8(n7 with a second ball (at rest) and rebounds in the opposite direction with a speed equal to one-fourth its original spee/5 rp0b x8urjnir(r a7d. What is the mass of the second ball? $m_B$ =    $m_A$(Round to two decimal places)

  You have been hired as an expert wiqg (uf+ byqdo) nurlbk /.mo(1/m(:votness in a court case involving an automobile accident. The accident involved car A of mass 1900 kg which crashed into stationary car B of mass 1100 kg. The driver of car A applied his brakes 15 m before he crashed into car B. After the collision, car A slid 18 m while car B slid 30 m. The coefficient of kinetic friction between the locked wheels and the road was mea/gu .fbv1lo+qud o)okr/ y(mb(n:m(qsured 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 oft+95 ss i7cbrfex hj:be81*bhf the top of a flight of concrete steps of total vertical height 4.00 m. The ball hits four times on the way down, each time scsh bjxbsf5:8 r 9hetbe*7i1+triking 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 bottom of the stairs?

  A bullet is fired vertically into a 1.40-kg block of wood at restne3lh4f l3i ia2q7fv .od mpt9:e2 dz-a nji-9 directly above it. If the bullet has a mass of 29.0 g and 2iznf9depda-hi alq.j:4tlfm9 o32n 7-iev3a speed of 510m/s how high will the block rise after the bullet becomes embedded in it?    m

  A 25-g bullet strikes and becomesag5 z+es* myn)1u ew)pj wtps 3m/ml/( embedded in a 1.35-kg block of wood placed on a horizontal surface just in front of the gun. If the coefficielety )5ps1sg/jwm *nm /ez3pm u) (w+ant 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 xdrksbv4(al3m * ;y r675 kg and the other of mass 60 kg, sit in a rowboat of mass 80 kg. With the boat initially at rest, the two people, who have been sitting at opposite ends of the boat 3.2 m apart from each other, now exchange seats. How far blsrm4 3y*d;v6 x r(kaand 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 wasb)w-/)) ir 0 bqnznlbc v-b6xs 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 broken apart into two qr0oi sk81+k 7oqxrx (fragments by an explosion. One fragment acquires 7x8 xriqk qs+(1ook0rtwice the kinetic energy of the other. What is the ratio of their masses?   

  The force on a bullet is given by the formula F = 580-hw(j cio-gl u7:ov dwb)-yr( ,do f58q( $1.8 \times10^{ 5}$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 44tvav bb,n2b gt0 k;g$m_A$ = 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 dec45 0m *lnyovqn *f+vwzays radioactively into an alpha particle and a smalleo +mw fl5yqnv0 zn*4v*r nucleus. 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 .k bt2vq2 ngcnv6o:5r 0kgdxo.7 7 dhytarget) 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 30.0gn50 s80sm afp)+pipu $^{\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 onw - kk;y(uj+l5w.) zlucmvji0 mass m if it is to rebound from M, slide up the incline, stop, slide down the incli-k wkvlwjiul)j (0;cu.mz5y+ ne, and collide with M again?    kg (Let A represent mass m, and B represent mass M.)

  The gravitational slingshot effect. Figure 7–47 shows the planet Saturikif1 emxmmk1 aq1c .7,:bgo1-h go.j n moving in the negative x direction at its orbital speed (with respectofjmchk7 1.1q1bik ema .imxg o1-:,g 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