We claim that momentum isk5c6**r fdcej:g(cb j conserved, yet most moving objects eventually slow down and stop. Exj( b**djf :g6erc5c ckplain.

When a person jumps from a tree to the ground, what happens to the momentum on1u.ytnfmlw 88 mc;9. .kxppsf the pu. ;ynmlstxm1f pp.88.ckwn 9erson upon striking the ground?

When you release an inzp4 .dndh-;-p l0imfv flated but untied balloon, why does it fly across the room lid0zdm.4fv hn; pp--?

It is said that in ancient times a rich man with a bag of gold coins froze to f,rph e(-uj 4pdeath 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 h f-4ep (phruj,imself had he not been so miserly?

How can a rocket change direction when it is far out in spac/p1ng(yt g)etd2m yc3 e and is essentially in a vacuum?g/g)( 2c mytpye 31tnd

According to Eq. 7–5, the longer the impact tim8 t3 kqfb2(bdcofe49c 7/ukn,pyu a*ae of an impulse, the smaller the force can be for the same momento 9nau uccf /fy,b8(db2ea k3kqp4t7* um 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 collision and reduce the possibility of fracture or death.

Cars used to be built as rigid as possible to withstand collisions. Tolv x6ub:3 3pdcday, though, cars are designed to have “crumple zones” that collapse upon impldu3 p :36xbcvact. What is the advantage of this new design?

Why can a batter hit a pitched baseball further than a ball tossed in the air b3n )+c;;ltk+fly lci8 dj 1afqy ; aflcq3kd ++tc)linf 8y;j1l the batter?

Is it possible for anjr( lwu9f-hf+agqle ; pzy7gv,) ))ew object to receive a larger impulse from a small force than freggpl(yhvq z+)uff- 9 e war ,);)jwl7om a large force? Explain.

A light object and a heavy object have th naxql6/pb.b19qgrna6d +p+ le same kinetic energy. Which has the greater mlprx+aq1napq9 + b6./b6ndlg omentum? Explain.

Describe a collision in which all kinetic energy is lowc n2zdtrnt ld4/;/-ost.

At a hydroelectric power plant, water is directed at high speyx 3 /ean( okz60onqv;ed against turbine blades on an axle that turns an electric generator. For maximum power generation, x;akovy6 3o/zeqn0 (n 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 b -0 mymp(pa*d k93ocqat 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 droppep) 7x6zouoof eo.k5 )29e o)mza;wylu d from a height h onto a hard steel plate (fixed to the Earth), from which it rebounds at very nearly its original speed. (a) Is the momentum of the ball conserved during any part of this procke7f9oo65) u)eoao ;z2y w.)lzpox muess? (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 carrdshdud ootz34x e75az- ,g, 6kying a heavy load in your arms?

Why is the CM of a 1-m length of pi 1 1akxihg q;sl2xp/z;pe at its mid-point, whereas this is not true for your arx a;xh2gl ; k/iz1q1spm or leg?

Show on a diagram how 6z-unbqz vc bt:7q7hbc6u2 .myour CM shifts when you change from a lying position to a sitc 6u vub-z7q m.n:b2cq6 bz7thting position.

If only an external force can change the momentuaoem+cum 2q0d1q e5n( m of the center of mass of an object, how can the internal force of an engine accelerate2c+qn0 aum q(d1o5 eme a car?

A rocket following a parabok l:/ct.6nrm*3i-swmxfk+ k 2 ,-l5pqjokt s ilic path through the air suddenly explodes into many pieces. What can you say about the motion of this system of p.k ,-tqli lork 3xt 5+6kmsnpf2:mksi- jw /c*ieces?

  What is the magnitude of the momentum of a 28-g sparrow flying with a s:flwv1j ;(k op9flnfx k0ctd94- cm6 ht2go e,peed of $8.4 \; m/s$    $kg \; m/s$

  A constant friction force )a)t 9l yo m4pe)msfy4of 25 N acts on a 65-kg skier for 20 s. What is the skier’s change in ve )9ftesp y)olm4ay) 4mlocity?    m/s

  A 0.145-kg baseball pitched aw0c,* lbya+wl6 vh9q ice6oslwo:j+1 t 39 m/s is hit on a horizontal line drive straight back toward the pitcher at 52m/s If the contact timeh+vljl cww 91sy*l0c6awb :6qo eoi, + 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 ad f7b1ylye6)7czvx(6.40-kg package out horizontally with a speed of 10 m/s Fig. below Calculate the velocity of the boat immediately after, assuming it was initially at rest. The mass of the child is 26.0 kg, and that of the boat is 45.0 kg. Ignore w6)ebvalcx77(fd 1yy z ater resistance. The magnitude of the velocity of the boat is    m/s

  Calculate the force exerted on a rocket, given that the fw:: 3/qc(oqesuw ylypp/;w lya3l, , ve3h0hpropelling gases are expelled at ae3;, u ( wv,:l3lq/h/3 l:hw ao0fwcye yspyqp 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 movinms1 clnqm1s 7mec)n)to 30pk,a b/(ahpr+ s0r g 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 on alevel frictionless track (smn. blf x.t v6oo:del73ko8.g0fmmwith a constant speed of 18m/l0 gonlsktmm.vo78f:ofm(3 b .. edx6s A 5350-kg load,initially at rest, is dropped onto the car. What will be the car’s new speed?    m/s

  A 9300-kg boxcar traveling9 k sa(b0lwx+kr+4fez 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, wx r:b , l: sw)mmjc3l4p2f8fkginds can whip horizontally at speeds of 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 l3ffb r4lwm k:)msx8 p2:c jg,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 ca 2f1:vf+h vsw2,dqqhc r coasts along with a constant speed of 8.6m/s on a level track. Snow begins to fall vertically and fills the car at a rate of 3.5kg/min Ignoring friction with the tracks, wqd2sv cq,f12vfw:+hh hat is the speed of the car after 90.0 min?$\approx$    m/s

  An atomic nucleus initially moving at 420m/s emits an alpha partikg.5kwiyyul8ce6*prhd ,w 42 cle in the direction of its velocity, and the remaining nucleus slows to 350m/s If the alpha particle has a m.e gi6 2hp5k* wudlwy,rk 48cyass 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 pe8 jzqwyd hnm79 ha* b-n/2plu3netrates a 2.0-kg block of wood and emerges cleanly at 170m/s If the block is stationary on a frictionless surface wh h -apq y*/zw7h2nlj d9u83mbnen hit, how fast does it move after the bullet emerges?    m/s

  A 975-kg two-stage rq f9* :j4rsdfx xur0hpj. +fc3ocket is traveling at a speed of $5.80\times10^3\mathrm{~m/s}$ with respect to Earth when a pre-designed explosion separates the rocket into two sections of equal mass that then move at a speed of $2.20\times10^3\mathrm{~m/s}$ relative to each other along the original line of motion. Let “A” represent the upper stage (that moves away faster) and “B” represent the lower stage.
(a) What are the speed and direction of each section (relative to Earth) after the explosion? $v'_A$   m/s  ----待选择----away from the Earthtowards the Earth  $v'_B$   m/s  ----待选择----away from the Earthtowards the Earth 
(b) How much energy was supplied by the explosion? [Hint: What is the change in KE as a result of the explosion? $a\times10^8$ a =    J

  A rocket of total mass 3180 kg is y4rsq;j21ejc xme08v traveling in outer space with a velocity of 115m/s To alter its course by 3ce1 sv2jery8jm 4;qx05.0 $^{\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 Thj6cimuu. q; *77uh vpk :df4efe golf club ke* 76 f7vpj4: ufhu cmi.d;quwas in contact with the ball for $3.5\times10^{-3}$s Find (a) the impulse imparted to the golf ball,    kg*m/s
(b) the average force exerted on the ball by the golf club.    N

  A 12-kg hammer strikes a nail at a velocity of 8.5m/s and comes to/ml-s tzw +(li rest in a time interval of 8.0 ms. (a) What is the impulse given to the tz(-li/ m+lwsnail?    kg*m/s
(b) What is the average force acting on the nail?    N

  A tennis ball of mass m=0.06kg and spej0rq lti bu (7a5u0x qb59ygg;.icc+ced 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 of the crashworthi6pf ho3y7 vph kt)hz+5ness of new automobile models. Cars are tested by smashing them into fixed, massive bapo5h+7y) tp zkh6hfv3 rriers 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 tbtkvd9 -i/iro10 ee(3 cw4z oghe east and is stopped in 0.75 s by a head-on tackle by a tackler running due west. Calculatee(wd iok vo 4 0r3-gti/1zbec9
(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 0.0603)j p4)gi zc. -4c(zlewmz,ijyw b3pj kg) points in the +x direction and is given by the graph of Fig. 7–33 as a function of time. Use graphical4,yc)3ipw4jc jbp( l -mz .gzej3)w iz 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 perarabyk.qzeg 9 s 763z+son jump without breaking the lower leg bone of either z. a6+br z7yk9 egq3asleg? 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 area) of bone is $170\times10^6\mathrm{~N/m^2}$ and its smallest cross-sectional area is $2.5\times10^{-4}m^2$ [Hint: Do not try this experimentally.]    m

  A ball of mass 0.440 kg moving east (+x direction) with a s5ycq4rs uy 8l(peed of collides head-on with a 0.c 5 yu4qys(rl8220-kg ball at rest. If the collision is perfectly elastic, what will be the speed and direction of each ball after the collision?Let A represent the 0.440-kg ball, and 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, movinah /5g*efo bj.g east 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 jeo*ha/. g5bf 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 head-on ct-3r/u )*3xczg j(tvwkh( mcaqd2u -p ollision. 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?(Le j3 u-uwm*kctp3aqx2d ((-/)ghvzcrtt 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, movii(s1 lp 0x8zxth tb9;sng 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 Assuming a perfectly elastic collision, what are the89 (hss0xpt l 1itb;zx 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 kgsb8, /ttcexuq o)3h -z+rnfh7 that is moving with a speed of 8.5m/s collides head-c8fho ,ut3n7 zq)bhx+s-e /rton and elastically with another 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 ride collide el4:xjkigw. : yea 5:: q,rugr rpo7fby.astically as one approaches the other directly from the rea5a:jg:kyrer q p:4yrx7fb, o.iw :g.ur (Fig. 7–34). Car A has a mass of 450 kg and car B 550 kg, owing to differences in passenger mass. If car A approaches at 4.5m/s and car B is moving at 3.7m/s calculate
(a) their velocities after the collision v'$_A$ =    m/s v'$_B$ =    m/s
(b) the change in momentum of each.$\Delta p_{\mathrm{A}}$$\approx$    kg*m/s $\Delta p_{\mathrm{B}}$$\approx$    kg*m/s

  A 0.280-kg croquet ball makes an er7) lon bqr3( 6nt /amono)y/clastic head-on collision with a second ball initirco)q3 /roy tn/7a (l)nb6nomally at rest. The second ball moves off with half the original speed of the first ball.
(a) What is the mass of the second ball?    kg
(b) What fraction of the original kinetic energy $(\Delta\mathrm{kE/KE})$ gets transferred to the second ball?   

  In a physics lab, a cube slides down a frictionless incline as shown in r3g 4xqvvy6m lox)5lv:w4 n5jFig. 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 inclq 4g6yvv 5l5lr )wmxovnj34x: ine moving horizontally.]$\Delta x_{m}$$\approx$    m $\Delta x_{M}$$\approx$    m

ake the general case of an 1;r) ,th0xop5enc lli 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, projectile 1 results in a maximum h(0uh bh *y w0fvhl rhp15a*b4ceight h of the pendulum equal tpwuc5r 01* b(0hbvhh yl* fah4o 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 * eocylt)ub yml:scb fzc+q;5ss);7.traveling 230m/s buries itself in a 3.6-kg pendulum hanging on a 2.8-m-long string, which makes the pendulum swing upward in an arc. Determine the vertical and horizontal;c ob) lq+zbcfty:s7 5msc lsu ).ey;* components of the pendulum’s displacement.vertical$\approx$    m horizontal =    m

(a) Derive a formula for the fraction of kinetic energy lost):3 ctqh n vj,rr4swg5.dv3vn , $(\Delta\mathrm{KE/KE})$ 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,vr5 f+g2 -;ezdyaa5yq into two pieces, one of which has 1.5 times the mass of the other. If 7500 J were released in the explosion, how mug+;a dyya5 rv-5qfe 2zch 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 if4+-ahx:w +q4rezn m into the rear end of a 2300-kg SUV stopped at a red light. The bumpers lock, the brakes are locked, and the two cars skid forward 2.8 m before stopping. The police officer, knowing that the coefficient of kinetic friction between tires and road is 0.80, calculates the speed of the sports car at impact. What was that speed?(Let A repx +w+q-z fmr4ia4: henresent the sports car, and B represent the SUV) $\approx$    m/s

  A ball is dropped from a height of 1.50 m ansd e(+rys4g j 37s)nzcd rebounds to a height of 1.20 m. Approximately h4 rsgzn) 73j +sec(dsyow many rebounds will the ball make before losing 90% of its energy?   

A measure of inelasticity in a head-on collision of two objects is .)e)q0/ nznb6nhhk xw:c+e5qsuznm +the coefficient of restitution, e, d5hzn:qneq 6)0bnzs w+ e+/m.ncx)uhk efined 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-e(tuh wxli9( with three times the mass of the other. A depression is made in both faces of the cut, so that a firecracker can be placed in it with the block reassembled. The reassembled block is set on a rough-surfaced table, and the fuse is lit. When the firecracker explodes, the two blocks separate and slide apart. What is the ratio of dist-li(xu eth9(wances each block travels? ----待选择----1/91/101/81/6 

  A 15.0-kg object moving in the +x direction at 5)eb vub0a*n;0e iqex-i oh/nqh3 nl) :.5m/s collides head-on with a 10.0-kg object moving ;*h vnbbeineqihqe)3n:a u ) 0-/0xloin the -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 decays into a 0x n1.h42d ;iufaawjesecond nucleus, an electron, and a neutrino. The electron and neutrino are emitted at rigu xa4dj2f10; ani. hweht 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 mass mv w3zi 02wjy1$m_\mathrm{A}=0.400$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 obx56xh ik6-uke jects of equal mass, each having initial speed the two move off together with speed v/3 What was the angle between th65xk- kux i6eheir initial directions?    $^{\circ} $

  Two billiard balls of equal mass move at right angles4ngciqt7yy,p*lb: 7 y91pn; uoga z8a 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 ugn,y qtypbla;8 *7c17z o4pgyn :9aito 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 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 e2)ddkt3fi ji +liqtkcwv)o3q1 ep9;v 8o+3zolastic collision with another atom at rest. After the impal1i+ fvqod2;od)wtc89ev3 p3 oii3qktz)+jk ct, 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 perf jv+lpn*vo.uc3p;o .oectly elastic collision with another atom at rest. After the impaj;3v cov pun+l.o*.opct, the neon atom travels away at a 55.6 $^{\circ} $ angle from its original direction and the unknown atom travels away at a -50 $^{\circ} $ angle. What is the mass (in u) of the unknown atom? [Hint: You can use the law of sines.](Let A represent the incoming neon atom, and B represent the target atom) $m_B$   u

  Find the center of mass of the three-mass /8+3y8f xkkjrm+ pn 7on9r kp:9gcuii system shown in Fig. 7–38. Specify relative to the l7rkng9/f mki3+oxy8u + 9nk r:8pjpiceft-hand 1.00-kg mass.    m

  The distance between a carb y;l5ru2 /d/q1fe trduon 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 of th 7e:ao+e 6kowge car. How far from the fronek oeaow+7g: 6t of the car will the CM be when two people sit in the front seat 2.80 m from the front of the car, and three people sit in the back seat 3.90 m from the front? Assume that each person has a mass of 70.0 kg.    m

  A square uniform raft, 18 m by 18 m, of mass 6800 kg, is use9jp(q j2kypy 16oawt: d as a ferryboat. If three cars, each 16pq2ptwyk:j (ayjo9 of mass 1200 kg, occupy its NE, SE, and SW corners, determine the CM of the loaded ferryboat.$X_{CM}$ =    m $Y_{CM}$ =    m

  Three cubes, of sides ma/ d- vb1u/alq2dea p9m*k90cu o)vw$l_0$,$2l_0$, 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,n oi zu jmk*tu l5x h/h6;i*hxxy,:e( 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 pix hmhu ;xj /lek,tzyu,(xi*5i n*ho: 6ck up the load without tipping it.$X_{CM}$ =    l $Y_{CM}$ =    l

  A uniform circular plate of radius 2R hf7n jo5f h uxp 9f e:s6p3c;r3sq:crzcz6mo.5as a circular hole of radius R cut out of it. The center of the smaller circle is a distance 0.80R from the center C of the lasr. oc3nzx5o :rs56uf6ef cjp fm7;p:3qh z9c rger 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 Table 7–1, ib-ri 2cg0f :l4a ,w+lpa r1lhand calculate the mass of one of your li -la:4f1r i,gcbr0wp2 llh a+egs.    kg

  Determine the CM of ankwo ax d:10avz /s-;vg outstretched 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 the CM of an arm i4,fu6q4z ogp bent at a right angle. Assume that the personfo4q p4iu6, gz is 155 cm tall. $X_{CM}$ =    cm $Y_{CM}$ =    cm

When a high jumper is in a position such that hiom,f )0 cwkum)s arms and legs are hanging 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 o) k0)f wm,moucutside the body? Use Table 7–1.

The masses of the Earth jd3e6.0 of iqqand 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-kg man stand 10.0 m apart on fri9zdz hq2*nw)uv91cf 63 q usbcctionless 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 cylindgte -pt2t3zx( u ( nfqb3dp3)prical 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 the air, how far above the bottom of the handle) 3tpub-tgppqdn3( e 32ztfx( is the point that will follow a parabolic trajectory?    cm

  A mallet consists of a uniform cylindrical head of mass 2.00 kcnj4u3y8;xm * m a2eskg 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 malleu c3e8m2;k*4 njmasxy t is tossed, spinning, into the air, how far above the bottom of the handle is the point that will follow a parabolic trajectory?    d    d

  (a) Suppose that in Example 7–po y7:t vzf4ds7 ;zxf/ *5gb4ar 7smbn14 (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 the air efqvei0uq)d+x; w +r,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 (relative to Earth) does the balloon then move? What h;r)0 vw,ex+d +fq qieuappens if the passenger stops?

  An 0.145-kg baseball pitched horizontally at strikes a bat and is p4wg o wya-r-t nmo9lhd ajuco3f217 81opped straigh-adgln3oyf14m9ota-8jwh w17 2 u crot 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 contact.    $^{\circ} $

  A rocket of mass m traveling with sp5ax)d;o t0/d lu+mv3 cb6yqbq eed $v_0$ along the x axis suddenly shoots out fuel, equal to one-third of its mass, parallel to the y axis (perpendicular to the rocket as seen from the ground) with speed 2$v_0$ Give the components of the final velocity of the rocket.$P_x$: v'$_x$=    $v_0$
$P_y$: v'$_y$=    $v_0$

A novice pool player is faced with the corner pocket shot shown in Fig. es pg(,cj7e b .rd uksk-+,j7t7–43. Relative dimeb7+(kcg.dtpsk7j sj ee, -ru ,nsions are also shown. Should the player be worried about this being a “scratch shot,” in which the cue ball will also fall into a pocket? Give details.

  A 140-kg astronaut (including space suit) acquires a speed of j-v*m4l 7gkh):fldwx 2.5m/s by pushing off with his legs from an 1800-kg spacjfl:7 kx)wl- gdm* vh4e 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 ac.i;clwl t4 ;and the other 80 kg, are initially at rest in outilt. wl ;;4ccaer space. 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 elastic collision with a second ball (at -3ane8sni)b3y5hyd7mt j q 0w rest) and rebounds in the opposite direction with a speed equal to one-fourth its original spee3 a)8qh jnybsne3-0dy5tim7wd. What is the mass of the second ball? $m_B$ =    $m_A$(Round to two decimal places)

  You have been hired as an expert witness in a court case involving an automobi 6orkdb8p ztdh5c7abwrc.a 3 gil4**4le 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 rzib t *4 8bag6.*lca3w kpodhcr75d415 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 cr qr0i;p6e sjwbc812ha -m aaej/2iq4oncrete steps of total vertical height 4.00 m. The ball hits four times on the way down, each time striking the horizontal part of a different step 1.0 m lower. If all collisions are perfectly elastic, what is the bounce height on the fourth bounce whj1mai20 6ia /ws-p erjh8b ;2cqaq4eren the ball reaches the bottom of the stairs?

  A bullet is fired vertically into a 1.40-kg block 4b(iz lcmk:: de:rvp*hja or;/ /xm7qof wood at 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 becomes embedd;hz/ v ma qpd/ro(e lb:m:c7kr4x:*jied in it?    m

  A 25-g bullet strikes and becomes embedded in (mmgi/c6b2pn a 1.35-kg block of wood placed on a horizontal surface just in front of the gun. If the coefficient of kinetic friction between the block and the surface is 0.25, and the impact drives the bli2n bcpmg(m 6/ock 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+ shzuxsu 0k.5, 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 dir+zh5k usu.x0 section will the boat move? The boat will move    towards the initial position of the 75 kg person(Round to two decimal places)

  A meteor whose mass was aboutluj5-8 m+ .kkba)g lzl $ 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 isidhw3 5(cv tbz4.hkju(b:7zk suddenly broken apart into two fragments by an explosion. One fragment acquires5dk. cw (khz(43bjiz7uhv :bt twice the kinetic energy of the other. What is the ratio of their masses?   

  The force on a bullet is given by the formula Fkcfmxb- **sj 5h8xyu3 s 2sw0i = 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 0q;qy xel7yns 8 f,l0t$m_A$ = 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 radioactively f4 yltzc)w+ -zinto an alpha particle and a smaller nucleus. What will be the s4+ z )cwz-fyltpeed 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) i2f- ei 40eehdrzc-u mwu;, 2fjs 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 wegzl ppmbb1 sm/ 78ym,g+8r ;a 30.0 $^{\circ} $ incline which is 3.60 m high. At the bottom, it strikes a block of mass M=7kg which is at rest on a horizontal surface, Fig. 7–46. (Assume a smooth transition at the bottom of the incline.) If the collision is elastic, and friction can be ignored, determine
(a) the speeds of the two blocks after the collision,v'$_A$ =    m/s v'$_B$ =    m/s
(b) how far back up the incline the smaller mass will go. $\approx$   (Round to the nearest integer) (Let A represent mass m, and B represent mass M.)

  In Problem 79 (Fig. 7–46), what is the2 mv/n 04t w/q,jkb7xwle d5lv upper limit on mass m if it is to rebound from M, slide upjvv/mq/nkl d450 ebw ,t27xwl 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 7–47 shows the planet Saturn moc 1nq0yk apm; 6 )scvr)t6 ekb8ydz4a3ving in the negative x direction at its orbital speed (with respect to the Sun) of 9.16nd cqa)y t) yc ev4bamz0;86k skp3r6km/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