We claim that momentum i1/8fwdoz,mjk0yp kf9d3b c +p s conserved, yet most moving objects eventually slow down and stop. Exp kp 8/9zf , k+dfpjwy0c3obd1mlain.

When a person jumps from a tree to th.-z hkewh6 5jbe ground, what happens to the momentum of the person upon striking thehb.z6ehkw 5j - ground?

When you release an .1imascc(p o*h lh4et*gp*j8inflated but untied balloon, why does it fly across the room?pi t *cm4o(*ce1l*a8.h hs jpg

It is said that in anci6r wh/0 bjg u6thmeegz6z 4;xvd89 0xqent times a rich man with a bag of gold coins froze to death whi0 06gqd9jehhrx 46bumz ze w6;8g /xvtle 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 miserly?

How can a rocket change direction when it is far out in spachr ydxw0eia-dv/r - z ;-6h;mce and is essentially in a vw-;hdzc hy rx0 dia-m;v/6e -racuum?

According to Eq. 7–5, the longer the impact time of an impulse, the smaller the /hjrbifh mrb8, *v+c. ijxm)5force can be for the same momentum change, and hence the s .*iv8b/,j mx+)bfcmhji rh 5rmaller 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 collision and reduce the possibility of fracture or death.

Cars used to be built as rigid as possible to withstand coe0 t nprsi43 m.d4r20dddik,jllisions. Today, though, cars are designed to have “crumple zones” that collapse upon impact. What is the ad msj di0k3pi4 r04detddr2,n.vantage of this new design?

Why can a batter hit a pitched baseball further than a ball tossed in the *igx:b:pd4hjdo:75 w(mf bv sair by thsd:hg * 7:vjpxbifod(4 wm5b:e batter?

Is it possible for an object to receive a larger impulse from a small force than(qlbr1w w h7n5q8a c5h from a large force? Explai5b cqnr57qalwh w1(8 hn.

A light object and a heavy object have th8zi 9b k13ogywe same kinetic energy. Which has the greater momentumz3i1b9wy kog8 ? Explain.

Describe a collision in which all kinetic ene.:n;u y6t:sxdfelg6 u rgy is lost.

At a hydroelectric power:fu sloy,/a 7r plant, water is directed at high speed against turbine bladyrl,7ousf :/a es on an axle that turns an electric generator. For maximum power generation, should the turbine blades be designed so that the water is brought to a dead stop, or so that the water rebounds?

A squash ball hits a wall a rf 9fhw 8abyvz)f,*2at a 45 $^{\circ} $ angle as shown in Fig. below. What is the direction (a) of the change in momentum of the ball, (b) of the force on the wall?

A Superball is dropped fr0;d i vs5b+hudom a height h onto a hard steel plate (fixed to the Earth), from which it reboundsds5u; hdi vb+0 at very nearly its original speed. (a) Is the momentum of the ball conserved during any part of this process? (b) If we consider the ball and Earth as our system, during what parts of the process is momentum conserved? (c) 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 load zqzq63icnwzry lzv djn18 1) 0g*p- +min your arms?

Why is the CM of a 1-m length of pipe at its mid-point,v+8)2:mzpey.pwz y p ki6dp2d whereas this is not true for your p 8pdzzi2kyep ydw 6v+2.p :)marm or leg?

Show on a diagram how your CM shifts when l7/t3a - s6lgms 9snhhyou change from a lying position to a ta ms /lh-glssh7n6 39sitting position.

If only an external force can ch.9b;+nbp 3 cj 3v1n3o cvlelrpange the momentum of the center of mass of an object, how can the internal force of 9rb b3cnvc+j ovp.p; nel13l3an engine accelerate a car?

A rocket following a parm8 wh5 kcisa2:abolic path through the air suddenly explodes into many pieces. What can you say about the motiahmsk:wc 258 ion of this system of pieces?

  What is the magnitude of the momentum of a 28-g sparrow flyixnu7m6en*f4vi 8yv 5c ng with a speed of $8.4 \; m/s$    $kg \; m/s$

  A constant friction force of 8pob9yg h6*rg+ /uucz 25 N acts on a 65-kg skier for 20 s. What is the skier’uhp9r6 *cgb8+gz yo/us change in velocity?    m/s

  A 0.145-kg baseball pitched at 39 m/s is hit on a horizontal line px 0i8t zecj8dmv x:9)drive straight back toward the pitcher at 52m/s If the contact time between bat and ball ist)98pmc0j id ezx8x:v $3\times10^{-3}$s calculate the average force between the ball and bat during contact.    N

  A child in a boat throws a 6.40-kg packa7kh 9nmhvl(w)m *e8t78q)ld ukl (j33ginw k ege out horizontally with a speed of 10 m/s Fig. below Calculate the veloc8*u 7jd(w tn9 vn(im eq 7gkkmw83)hll hel)3kity of the boat immediately after, assuming it was initially at rest. The mass of the child is 26.0 kg, and that of the boat is 45.0 kg. Ignore water resistance. The magnitude of the velocity of the boat is    m/s

  Calculate the force exerted on a rocket, given tha(0ss tv(umzv 52h1r uyt the propelling gases are expelled at a r1hy 5sv0 vrmu2u((zt sate 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 movi :e3g cgnc7*ey5a 3nkz4 ic5rlng 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 alonmof(l,+becb.+ xql t dpj42- ee on alevel frictionless track with a constant speed of 18m/s A 5350-kg load,initially at rest, is dropped onto the car. What will be the car’s new ce+(o. bl 4ptb +ed2qjf-l,xmspeed?    m/s

  A 9300-kg boxcar traveling at 82h zeg7 ,xiyt$15 \; m/s$ 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, lqs7gyb/it bz ;uwzwy 6),j 75winds can whip horizontally at speeds of 100km/h If the air strikes a pi7,zyu5/tyj7;g l)sq b6bwwzerson 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 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 consta z*n.ql-bj 5gant speed of 8.6m/s on a level track. Snow begins to fall vertically and f gq la5n-.*zjbills 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 initigy( arptzy2p97xm3; 4p rfbe,ally moving at 420m/s emits an alpha particle in the direction of its velocity, and the remainin g4r,myy e3atppf 7z r;(bx2p9g 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 pec th)/8l)*kt4j zyskzdqz :x 6netrates a 2.0-kg block of wood and emerges cleanly at 170m/s If the block is s qck6:zj) y h tzx8/ks4*z)dlttationary on a frictionless surface when hit, how fast does it move after the bullet emerges?    m/s

  A 975-kg two-stage rocket is w+ f1qap,uxjz*w 5 um/traveling at a speed of $5.80\times10^3\mathrm{~m/s}$ with respect to Earth when a pre-designed explosion separates the rocket into two sections of equal mass that then move at a speed of $2.20\times10^3\mathrm{~m/s}$ relative to each other along the original line of motion. Let “A” represent the upper stage (that moves away faster) and “B” represent the lower stage.
(a) What are the speed and direction of each section (relative to Earth) after the explosion? $v'_A$   m/s  ----待选择----away from the Earthtowards the Earth  $v'_B$   m/s  ----待选择----away from the Earthtowards the Earth 
(b) How much energy was supplied by the explosion? [Hint: What is the change in KE as a result of the explosion? $a\times10^8$ a =    J

  A rocket of total mass 31 e )qzur x1m*uxog2,d)80 kg is traveling in outer space with a velocity of 115m/s To alter its course by *u1 )d,uqmz2 eg x)xro35.0 $^{\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 4hhx,9a dtts.2e 295 7xlps rda5m/s The golf club was x2s sa l7,d 5dtxhrep2ta 9h.9in contact with the ball for $3.5\times10^{-3}$s Find (a) the impulse imparted to the golf ball,    kg*m/s
(b) the average force exerted on the ball by the golf club.    N

  A 12-kg hammer strikes a nail at a velocity of 8.5m/s and co)i6 :tp.4v)yk :vk sf f7h.t .*satwou8jh ncomes to rest in a time interval of 8.0 y8s.tu:k ns . of vw4 ot6*v7t.k:cfhjiahp))ms. (a) 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+esud,b7l b1 r speed v=25m/s strikes a wall at a 45 $^{\circ} $ angle and rebounds with the same speed at 45 $^{\circ} $ (Fig. 7–32). What is the impulse (magnitude and direction) given to the ball?   kg*m/s to the  ----待选择----leftright 

  You are the design engineer in charge ofzv.+yi *q0eol the crashworthiness of new automobile models. Cars are tested by smashing them into fixe q*o vez.y+l0id, 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 ety-s di *7q*qiast and is stopped in 0.75 s by a head-on tackle by a tackler running due west. Calculate d iqy-q**s 7ti
(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 +x d a8i65jyo-ew1hx su96zs+ aaxirection and is given by the graph of Fig. 7–33 as a function of time. Use grap 966es5a-xy jso haaix8+z1uw hical 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 lb+ nkhotw7vmz69 cz9 9ower leg bone of either leg? Ignore air resistance and assume the CM of the person moves a distance of 0.60 m from the so t khzwmzc9b+n7v 699tanding 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 directnj kg6nv qgj79g,8(quion) with a speed of collides head-on with a 0.220-kg ball at rest. If the collision is perfectly elastic, what wil6 qgg8gn9 jj nu,q7vk(l 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 east with a speed of 3m/s has a head-on colli-lsed,70wdjyx2r xy;p,gy, ision 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 colliixys,ryl dgpew,y 2;7-d,j x0sion?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 by.mss(l48,, 9gqbz 3n ppuk csb.pg2equal mass undergo a perfectly elastic head-on collision. If one ball’s initp.pz4 ,yqum 2gls 8,bnbpb c(ks.39 sgial 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 opposite direction. ) v'$_A$ =    m/s v'$_B$ =    m/s

  A 0.060-kg tennis ball, moving with a speed of 2.5m/s fl5fz 5s 9ma-8qdxhl)collides head-on with a 0.090-kg ball initially moving away from it at l9 axfmz)s5ld8h5f -qa speed of 1.15m/s Assuming a perfectly elastic collision, what are the speed and direction of each ball after the collision?(Let A represent the 0.060-kg tennis ball, and let B represent the 0.090-kg ball.)v'$_A$ =    m/s v'$_B$ =    m/s

  A softball of mass 0.220 kg that is moving with a speed of 8.5m/s cold x8+9qvqym: tlides head-on and elastically with anothe 9d+:qy8xmt qvr 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 park g9 dl 6uydx7y1ride collide elastically as one approaches the other directly from the rear (Fig. 7–34). Car A has a mass of 450 6dx 1ydl u79gykg and car B 550 kg, owing to differences in passenger mass. If car A approaches at 4.5m/s and car B is moving at 3.7m/s calculate
(a) their velocities after the collision v'$_A$ =    m/s v'$_B$ =    m/s
(b) the change in momentum of each.$\Delta p_{\mathrm{A}}$$\approx$    kg*m/s $\Delta p_{\mathrm{B}}$$\approx$    kg*m/s

  A 0.280-kg croquet ball makes an elastic head-on collisio0( y wrkwj7t4f;jrjq,e o(wl 6n with a second ball initially at rest. The second ball moves off with half the o(r 4e( ,ww rky0jtj7woqlf;j 6riginal 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 frictionp /;+bfwbilww qhv),/ nl ;da+x62rslless incline as shown in Fig. 7–35, and elastically strikesl;w;sfnpx 2qrbv+,wa + /ld )6 lbi/wh 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 mass 2lhpjo;*,a dz m$_A$ and velocity v$_A$ elastically striking a stationary object of mass head-on. (a) Show that the final velocities v'$_A$ and v'$_B$ are given by$v_{\mathrm{A}}^{\prime}=\left(\frac{m_{\mathrm{A}}-m_{\mathrm{B}}}{m_{\mathrm{A}}+m_{\mathrm{B}}}\right)\nu_{\mathrm{A}},v_{\mathrm{B}}^{\prime}=\left(\frac{2m_{\mathrm{A}}}{m_{\mathrm{A}}+m_{\mathrm{B}}}\right)\nu_{\mathrm{A}}.$(b) What happens in the extreme case when m$_A$ is much smaller than m$_B$ Cite a common example of this. (c) What happens in the extreme case when m$_A$ is much larger than m$_B$ Cite a common example of this. (d) What happens in the case when m$_A$=m$_B$ Cite a common example.

  In a ballistic pendulum experiment, projectile 1 results in a maxirdm+/1gr:;p - ng 8myhv6x xwamum height h of the pendulu8r1xhgy;a:v x -p+d6rgmwn/m m equal 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 buri: s:f knpxlkz94jkh 85es itself in a 3.6-kg pendulum hanging on a 2.8-m-long string, which makes the pjk k::h4 pfl8snk5 z9xendulum swing upward in an arc. Determine the vertical and horizontal components of the pendulum’s displacement.vertical$\approx$    m horizontal =    m

(a) Derive a formula for the fraction of kinetic energy lo olsno5;q :okwo.7lg .st, $(\Delta\mathrm{KE/KE})$ for the ballistic pendulum collision of Example 7–10. (b) Evaluate for m=14g and M=380g

  An internal explosion breaks an object, initially at rest, into two pieces, onf4*/o o4 (frw ylsfvu5e of which has 1.5 times the mass of the other. If 7500 J were released in the explosion, how much kinetic energy did each piece acquire? (Let A represent the heavier particle, and B represent the lighter particle. ) ysf4ru*f5 ov lw(o4/ fKE'$_A$ =    J KE$_B$ =    J

  A 920-kg sports car collides into the rear end of a 2300-kg SUV stopped at a rux4a tcof,t0pk17 g y)ed 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 41 7g 0cuo xy)pkfta,tfriction 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 a h0t(+vxz; iatnd rebounds to a height of 1.20 m. Approximately how many rebounds will the ball make before losing ;va+(0txzih t 90% of its energy?   

A measure of inelasticity in a head-onl e xs1,1x2crvznm 0 :g/d6+qcc u+ 4hgqmyw;w collision of two objects is the coefficient of restgcq2+ev;c x4 wlmq ,:/uh0mwds czx6g 1rny1 +itution, e, defined as$e=\frac{\nu_\mathrm{A}^{\prime}-\nu_\mathrm{B}^{\prime}}{\nu_\mathrm{B}-\nu_\mathrm{A}},$
where $\nu_\mathrm{A}^{\prime}-\nu_\mathrm{B}^{\prime}$ is the relative velocity of the two objects after the collision and $\nu_\mathrm{B}-\nu_\mathrm{A}$ is their relative velocity before it.
(a) Show that e=1 for a perfectly elastic collision, and e=0 for a completely inelastic collision.
(b) A simple method for measuring the coefficient of restitution for an object colliding with a very hard surface like steel is to drop the object onto a heavy steel plate, as shown in Fig. 7–36. Determine a formula for e in terms of the original height h and the maximum height h’ reached after one collision.

  A wooden block is cut vr(gj.e7huq + dz+ lv6into two pieces, one with three times the mass of the other. A de( r. g6ejvu7d+ h+zlqvpression is made in both faces of the cut, so that a firecracker can be placed in it with the block reassembled. The reassembled block is set on a rough-surfaced table, and the fuse is lit. When the firecracker explodes, the two blocks separate and slide apart. What is the ratio of distances each block travels? ----待选择----1/91/101/81/6 

  A 15.0-kg object moving in the +x direction at 5.5m/s collides head-on wi 9ux4;he v+uxsth a 10.0-kg object moving in the -x direction at 4m/s Find the final velocity of each mass ifus h+xxe v9;u4:
(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 u2vi qi5onx(0j6 b9rh t dul-fg5cpb8z1 / +nlinto a second nucleus, an electron, and a neutrino. The electron and neutrino are emitted at right angles and ha5z 2jl5 to+n9qgp /b(cxunbfuhi-vl rd160i8ve 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 mass u6qvg2oz2z4z $m_\mathrm{A}=0.400$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 bx-pi /qlgw17u etween two objects of equal mass, each having initial speed the two move off together with speed v/3 What was t-ix7wpq 1/g luhe angle between their initial directions?    $^{\circ} $

  Two billiard balls of equal mass move at rigrnr9f9 jmo:/nzbln1+ ht angles and meet at the origin of an xy coordinate system. Ball A is moving upward along the y axis at 2m/s and ball B is moving to the right along the x axis with speed 3.7m/s After the collision, assumed elastic, ball B is moving along the positive y axis (Fig. 7–37). What is the final dijnrn fn b9+ol1 :mr9/zrection 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 at;a;i;p*bwp2 q ub5acfom at reswf5ip ;a;qp ;ub2cab *t. After 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 per hg2 bivt+k;26qska5p fectly elastic collision with another atom at rest. After the impact, the neon atom travels away vkb+p g2iq s62a ;5thkat 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/ nzu8ayo4qv8. Specify relative to the left-hand 1.0qn8ouy/a vz840-kg mass.    m

  The distance between tf 5tha4o0ihi**d0ns a carbon atom ($m_{\mathrm{C}}=12\mathrm{u}$) and an oxygen atom ($m_{\mathrm{O}}=16\mathrm{u}$) in the CO molecule is $1.13\times10^{-10}$m How far from the carbon atom is the center of mass of the molecule?    $\times10^{-11}$m

  The CM of an empty 1050-kg car is 2.50 m behind the front o34nx+9yfjp u rf 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 mxj fr9 uy34pn+ass of 70.0 kg.    m

  A square uniform raft, 18 m by 18 m, of mass 6xq97-kpwhf wvd5agjvn5 :+9 u800 kg, is used as a ferryboat. If three cars, each of mass 1200 kg, occupy its NE, SE, and SW corners, uw 5-kv7a+jxh5: vf n9w9gp qddetermine the CM of the loaded ferryboat.$X_{CM}$ =    m $Y_{CM}$ =    m

  Three cubes, of sides n(4k)w cyd+ym $l_0$,$2l_0$, 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 cases of tomrhujqs bov, *dd,2+z0q z,c3oato paste (see Fig. 7–40), each of which is a cube of length l. Find the center o,zqh,rjc uv32 d,+sd*oqo 0 zbf gravity in the horizontal plane, so that the crane operator can pick up the load without tipping it.$X_{CM}$ =    l $Y_{CM}$ =    l

  A uniform circular plate of radius 2R has a circular hole of radius R cufzcj49,rwlw dd (bf;,t out of it. The center of the smaller circle is a distance 0.80R fwl,zb f4;fj,crw (dd9rom the center C of the larger circle, Fig. 7–41. What is the position of the center of mass of the plate? [Hint: Try subtraction.]   R

  Assume that your proporb9vojslw; 7n 7tions are the same as those in Table 7–1, and calculate the mass of one of b j7vw9 7lo;snyour legs.    kg

  Determine the CM of an outstretcx0-q/( hssq smhed arm using Table 7–1.   % of the person's height along the line from the shoulder to the hand

  Use Table 7–1 to calculate the position of thec5(arqhlix78evy p7(6l2ex i x3b 6ca CM of an arm bent at a right angle. Assume that the person is 155 2 e76q 63(axrlylx5cp vh ei 87aix(bccm tall. $X_{CM}$ =    cm $Y_{CM}$ =    cm

When a high jumper is in a positionw efkzw/ qv-(xms6g 61 such that his arms and legs are hanging vertically, and his trunk and head are horizontal, calculate how far below the torso’s median line thew x6kzw m -1/ef(g6svq CM will be. Will this CM be outside the body? Use Table 7–1.

The masses of the Earth anvbms)x 9qmo6bm7, 1hl1 dgs/n d 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 80 l :y7)dfu q4 rj;yn3oxjm/.if-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 unifor 5 .5k cfk*)nqmkkly:wm 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 thisklyq: )nk.5kmk5wc*f mallet is tossed, spinning, into the air, how far above the bottom of the handle is the point that will follow a parabolic trajectory?    cm

  A mallet consists of a uniform cylindrical head of mass 4e- dv j fj*3;etwz,wx3di.qvxq.3 mu 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 ieqqvwvtd34z df mu. e,3.*;i x3-xwj js 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.kx+k9wc3du h9g+ kka 4 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, ar eh4crl d+je-27p ;alie in the air and stationary with respect to the ground. A passenger, o2h;elrij+e dpa 7c4-lf 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 pitc+*f0drx9rd xohed horizontally 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 force on the ball during the 90dd+*frrxo x contact.    $^{\circ} $

  A rocket of mass m travelingmftqm+p.:c g3f k c mse12,od9 with speed $v_0$ along the x axis suddenly shoots out fuel, equal to one-third of its mass, parallel to the y axis (perpendicular to the rocket as seen from the ground) with speed 2$v_0$ Give the components of the final velocity of the rocket.$P_x$: v'$_x$=    $v_0$
$P_y$: v'$_y$=    $v_0$

A novice pool player 7j q izsfo-o)uli1 2d4is faced with 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,i ozo1ifsjl2u)4 7 d-q” in which the cue ball will also fall into a pocket? Give details.

  A 140-kg astronaut (including space suit) acquires a speed of 2.5k9jg x(0v-33 pksob cym/s by pushing off with his legs from an 1800-kg spac(30byo 9-kg v3sckjxpe 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 and the other 80 kge+qn2ttjoj 3:ct if8cqfm*8 1, are initially at rest in outer space. They then pmje:c *f1 oitt2tj3n 8q +q8cfush 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 collisiopno3*s qg-b0 xn with a second ball (at rest) and rebounds in po nxq- sgb3*0the opposite direction with a speed equal to one-fourth its original speed. What is the mass of the second ball? $m_B$ =    $m_A$(Round to two decimal places)

  You have been hired as an exp xc5v:a,dyzk5 ert witness in a court case involving an automobile accident. The accident involve5,c:xvya5 d kzd car A of mass 1900 kg which crashed into stationary car B of mass 1100 kg. The driver of car A applied his brakes 15 m before he crashed into car B. After the collision, car A slid 18 m while car B slid 30 m. The coefficient of kinetic friction between the locked wheels and the road was measured to be 0.60. Show that 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 total vertical hefi9no*xx6-s r ot(dk1ight 4.00 m. The ball hits four times on the way down, each time striking the horizontal part of a different step 1.0 m lower. If all collisions are perfectly elastic, what is the bounce height on the fourth bounce when the ball reaco ( 6fxr9xs-kdon*i t1hes the bottom of the stairs?

  A bullet is fired vertically into a 1.40-kg block of wood at 2 p:x4x n6dpnq.y8vvycts 4 y5sd4bt.rest directly above it. If the bullet has a mass of 29.0 g and a speed of 510m/s how high will the block rise after the bullet becomesv nxy:4pdv pd4q6sy5 cn2bx .4. 8stty embedded in it?    m

  A 25-g bullet strikes and becomes embedded in a 1bsj64gn3ic1/ y7w/kd n: xbvj.35-kg block of wood placed on a horizontal surface just in front of the cv1j 6kjs4 by:7n3ixd //gn bwgun. 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 zw nw4fx/v9(z75 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 and in what directi vf w9wxzn(/4zon 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 w7 rm0 ao(j aop)fqb6j,as 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 ty zb-bi j5un4+e1m6 vfrq+9s kwo fragments by an explosion. One fragment acquires twice the kinetic energy of the other. What is the ratio j6-uiy v9smb+1k5f neqrbz +4 of their masses?   

  The force on a bullet is given by the formula F = 580- y(1 l4c-b5k6bd jgjlx1rs p9q( $1.8 \times10^{ 5}$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 x x6appy ue;) v*d*d.r$m_A$ = 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 decaysnl )(m e 8ysf4v1pny34r )ohyn radioactively into an alpha particle and a smaller nucleus. What will be the speed of this recoiling nucleus if the sp8)) 3m np4 ynosvn4ylehr(1fyeed 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 targe3wlnk;5m k t:kt) 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 dz(0q6 ,,rx3j9qwo q whs)fwz town 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;iw5s4 y. fuae–46), what is the upper limit on mass m if it is to rebound from M, slide up the incline, stop, slide down the incline, andaes wf;. 45iyu 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 Saturn m5 0q t dni.,y/;wtaltnoving in the negative x /. wqdt;t a5n 0tl,iyndirection at its orbital speed (with respect to the Sun) of 9.6km/s The mass of Saturn is $5.69 \times10^{ 26}$kg A spacecraft with mass 825 kg approaches Saturn. When far from Saturn, it moves in the direction at 10.4km/s The gravitational attraction of Saturn (a conservative force) acting on the spacecraft causes it to swing around the planet (orbit shown as dashed line) and head off in the opposite direction. Estimate the final speed of the spacecraft after it is far enough away to be considered free of Saturn’s gravitational pull.    km/s