We claim that momentum is consevhb-eh ceg j)s+.s5fr)5k u4 erved, yet most moving objects eventually slow down and stop. uv-5srhb +5)se gc)hej.4 fek Explain.

When a person jumps from a tree to the ground, what happens to the moment p 0 ocs9.2gzqc.p5pg:g. n 9t1yzljuium of the person upncop 0g zpggj y q.l91s.t9z:ui5 2c.pon striking the ground?

When you release an inflated but untied balloon, why heanp ,rx 7l0t,cn bfc;0 h o6p1f:lr.does it fly across the room?0nrf0 xb plf ,poh, ;.7c tl1:6caernh

It is said that in ancient t6lonn - engikq2:/o z5imes a rich man with a bag of gold coins froze to death while stranded on a frozen lake. Because the ice was frictionless, he could not push himself to shore. What goolkneqz2i:n/56 -n could he have done to save himself had he not been so miserly?

How can a rocket change directioqkne+l ev2, c:n when it is far out in space and is essentially in a vaqkv+2 :e,l cencuum?

According to Eq. 7–5, the longer the impact time of an impi(k,6 p 2ssd8a d -6tjtxqob5 xqp3oq.ulse, the smaller the force can be for the same momentum change, and hence the smaller the deformation of the oo-bxo6 d ,ptqtsdqsqkx86 5aipj( 2.3 bject 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 built4z1)2;wfe sj, gm arnk as rigid as possible to withstand collisions. Today, though, cars are designs;a4fnz2)e,1grj wk med to have “crumple zones” that collapse upon impact. What is the advantage of this new design?

Why can a batter hit a pitched baseball further than a bxl z6f :u/ wlsd22ug(+4qy7zkiq(fq kall tossed in the air by the batter?k slf w7i6(u kqlq /: +z24fyduzq2x(g

Is it possible for an object to receive a larger impulse tj 3uixw 2pe7wx1;dt6 from a small force than from a lar3jexu6iw pw;7xt td12ge force? Explain.

A light object and a heavy object have the same kinetic eneizjui2/ewx8gvh /g j.7 o::db rgy. Which has the greater momentum? Expla: 2i8ugdz:v g/joxw/ie .hjb7in.

Describe a collision in which all kinetirq8 1ghr(qzjc c6) erqcrf*. 3c energy is lost.

At a hydroelectric power plant, water v4jbf zd3uyn/ice8tmfzf, /s50 :s g2is directed at high speed against turbine blades on an axle that turns an electric generatojugf tbz0cesd s4 /v, :nzm8352i f/yfr. 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 wall6kb: .guahxp49w ;rrej;d7gd at 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 from a heo4q rojx4w( c2p4 xu0bight 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 process? (b) If we consixw 4(u 4p jqrxoco4b20der 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 loadg- c l1sxtbf(8.fty, p in your arms?

Why is the CM of a 1-m length of pipe at its mid-p9/z ifdkyp9k(cd cb r*g671cwoint, whereas this is not true for your arm or 7*gbcy dp 6 /kdzwcick1fr(99leg?

Show on a diagram how your CM shifts when you change from a lying position to a3t:tim 2qv .ry mt: 2rt3 qv.iysitting position.

If only an external force can /t8 g6mgpkf4s change the momentum of the center of mass of an object, how can the internal 4spt8fg k/6g mforce of an engine accelerate a car?

A rocket following a parabolic path through the air skel c2wx-nbj *p p75buu94)a w1pz:iluddenly explodes into many pieces. What can ejuul*7)14iwp- 2bppabn9:5lckz wx you say about the motion of this system of pieces?

  What is the magnitude of the momentum of a 28-g sparrow kisj e gi:-mc)na6u 1e3)dw2aflying with a speed of $8.4m/s$    $kgm/s$

  A constant friction force of 25 N acts on a 6b wpwdgo tbf2 ,52d/*,qwmz* jxui(2c5-kg skier for 20 s. What is the skier’s change *dj uq*fg5b 2i o(bxw22wp,mtdwzc,/ in velocity?    m/s

  A 0.145-kg baseball pit:.(,tbhw j.k 7z suticched at 39 m/s is hit on a horizontal line drive straight back toward the wu h7ij( tzkc,.: bts.pitcher at 52m/s If the contact time between bat and ball is $3\times {10}^{-3}$s calculate the average force between the ball and bat during contact.    N

  A child in a boat throws a 6.40-kg package out horizontally phc0 y*.a5az7a mgln+ 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 thah n5gaympc.*la7+az0 t 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 k6zt0ghhmp( m87+tk uthat the propelling gases are expelled at a rahtth0u+kmg ( m7z86k pte of $1500kg/s$ with a speed of $4\times {10}^{4}m/s$ (at the moment of takeoff). F =    $\times {10}^{7}N$

  A 95-kg halfback moviyi+,b i7mjl abi(g:xgo) (gi2ng at $4.1m/s$ on an apparent breakaway for a touchdown is tackled from behind. When he was tackled by an 85-kg cornerback running at $5.5m/s$ in the same direction, what was their mutual speed immediately after the tackle?    $m/s$

  A 12,600-kg railroad car travels alone on acfk w5* ws q td59wtm1(7swm2alevel frictionless track with a constant speed of 18m/s A 5350-kg load,initially at rest, is dropped onto tht(wd 5s9m swk2 cfw1aw57 m*tqe car. What will be the car’s new speed?    m/s

  A 9300-kg boxcar traveli)*6 spckn crbo48j-f tl/qj /ing at $15m/s$ strikes a second boxcar at rest. The two stick together and move off with a speed of $6m/s$ What is the mass of the second car?    $m/s$

  During a Chicago storm, winds can whip horizontally at speeds of 100a) jvfrv 9( lp2 y4cthfvl3o3;km/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 m lhr tf9y p;vv j)f43loa3vc(2aximum force of friction $\mu \approx 1.0$ between the person and the ground, if the person has a mass of 70 kg.    N
$F_{onperson}$  ----待选择----<> $F_{fr}$

  A 3800-kg open railroad car coasts along us4melk.e)ii/ tmz/b5.x -vwx 6oey j9a2 ,kowith a constant speed of 8.6m/s on a level track. Snow begins to fall vertically and fill6/jym k. wl.4e kioi e)a moz5-,sx/xet2vbu9s 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 initi pdflq 2l4(4f keukn;y c1ms;3ally moving at 420m/s emits an alpha particle in the direction of its velocity, and the remaining nucleus slows to 350m/s If the alpyf 2 su ne;m1f;qd4 lk3klpc(4ha particle has a mass of 4.0 u and the original nucleus has a mass of 222 u, what speed does the alpha particle have when it is emitted?    m/s

  A 23-g bullet traveling 230m/s penetrates a 2.0-kg block of wood and3 qob +chcdj5+ emerges cleanly at 170m/s If the block is sta+hbdcqo 3 c5j+tionary on a frictionless surface when hit, how fast does it move after the bullet emerges?    m/s

  A 975-kg two-stage rockjpjr 3g-8j ge4 f-n;4w diiz,bet is traveling at a speed of $5.80\times {10}^3\mathrm{m}/\mathrm{s}$ 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 $2.20\times {10}^3\mathrm{m}/\mathrm{s}$ 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? $v_A^{\prime }$   m/s  ----待选择----away from the Earthtowards the Earth  $v_B^{\prime }$   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? $a\times {10}^8$ a =    J

  A rocket of total mass 3180 kg is traveling in outer space with a velocity of 4m 1pdkun8+n7v kb+r j115m/s To alter its course by 35jru4 +8kmd+k7n pvn1b.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 of*y4+tidmmgi*1t ebr /ow;hzde (+ux0 f the tee at a speed of 45m/s The golf club was*4 we/x1zo*igd r;u(t y0+bm+idetmh in contact with the ball for $3.5\times {10}^{-3}$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 nay3(y xeq*0z*ng ;upguil at a velocity of 8.5m/s and comes to rest in a time interval of 8.0 ms. (a) What is the impulseep*gng30y( u*y; u xqz given to the nail?    kg*m/s
(b) What is the average force acting on the nail?    N

  A tennis ball of mass m=0.06kg and speed v=25m/s strikefqwe1 . 5hcfq: itto 6(*hnm1gs 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 engi*p720qc 0ot xtkoyqr)neer in charge of the crashworthiness of new automobile models. Cars are tested by smashing them into fixed, massive barriers at 50km/h (30 mph). A new model of mass 1500 kg takes 0.15 s from the time of impact until it is brought to rest. (a) Calculate the average force exerted on the car by the ba)t qrxtk qo*7o 02cyp0rrier. $\approx$$a\times {10}^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 hezmp(w o82zald/s4xx (loluia*l.6o6 8l.o (4x i lp/6(uox2swzlmodaaz6l* ad-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 (mass 0.060 k dccs41sxw*o t12ayqyenx 1) ;g) points in the +x direction and is given by the graph of Fig. 7–33 as a function o1sc;qxx1e4sc) y t*wodna2 y 1f 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-k2i nnhmy 2*f,zg person jump without breaking the lower leg bone of either leg? Ignore ai z,i2h*fmn 2ynr 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 $170\times {10}^6\mathrm{N}/{\mathrm{m}}^2$ and its smallest cross-sectional area is $2.5\times {10}^{-4}{m}^2$ [Hint: Do not try this experimentally.]    m

  A ball of mass 0.440 kg m;txey8om ,b .ioving east (+x direction) with a speed of collides head-on with a 0.220-kg bax;o y8i, mte.bll 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. $v_A^{\prime }$    m/s  ----待选择----eastwest  $v_B^{\prime }$    m/s  ----待选择----eastwest 

  A 0.450-kg ice puck, moving east with c1a:vs: m a fhl0sgt)/ 1ku4ova 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 collision?Let A represent the 0.450-kg puck, and let B represent the 0.900-kg puck.o0):4ksfalvcs:v1a1/m uht g 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 elmnm*dx0wo vgx-(f *d7astic 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 thdxgfm n* mw7o-(0v*xd at 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 co/d6y:xvq wmfu3211rxvc 0r hs)sm j+b llides head-on with a 0.090-kg ball initially moving away from it at a speed ofwhru:16 /1cxsmd yfqj)m0xv3 br2+s v 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 witk q*h(*i ghja7h 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 spekiq **h7gj(ahed 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 elastically as one apprs-10gct tt ( a-00(oykuvdeuroaches the other directly from the rear (Fig. 7–34). Car A has a mass of 450 kg and car B 55-g e0( d0a0 k(tcyrou1vt-s ut0 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.$\mathrm{\Delta }{p}_{\mathrm{A}}$$\approx$    kg*m/s $\mathrm{\Delta }{p}_{\mathrm{B}}$$\approx$    kg*m/s

  A 0.280-kg croquet ball pzps01d ykdgz:)ve) / *hxrr( makes an elastic head-on collision with a second ball initially at1*epvrhx/rs))p( d zd k y0:zg 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 $(\mathrm{\Delta }\mathrm{kE}/\mathrm{KE})$ gets transferred to the second ball?   

  In a physics lab, a cube slides down a frictionless incline as shown in 47e +vnw7gu1qvlm.ouFig. 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 7qm vuo.+17wu4gne l vis 90 cm off the floor, where does each cube land? [Hint: Both leave the incline moving horizontally.]$\mathrm{\Delta }{x}_m$$\approx$    m $\mathrm{\Delta }{x}_M$$\approx$    m

ake the general case biz93pi y2wu aq62 5i32djqgkuuke .q ,7wb;iof an 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, pp9 l yd8pa5t+ :5jsl6ub+lxmyrojectile 1 results in a maximum height h of the pendulum equal to 2.6 cm. A second projectile causes the the pendulum +m :lxb+68s9yl dpta5ulypj5to 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 q;*+,uwhij4nl,qcbo in a 3.6-kg pendulum hanging on a 2.8-m-ln ,h+ j;boiqlc wqu*,4ong string, which makes the pendulum 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 +1)xqwbazidgof ,rwh9a3 *l8 kinetic energy lost, $(\mathrm{\Delta }\mathrm{KE}/\mathrm{KE})$ 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 piecfo(+s n8hx5l4 d w;stfes, one 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, andf+fhxont 4 wsld;5s8( B represent the lighter particle. ) KE'${}_A$ =    J KE${}_B$ =    J

  A 920-kg sports car collides into the rear enzrfj jl z5t4p;+k.ow8d of a 2300-kg SUV stopped at a red light. The bumpers lock, the 5 zjptr zwl. 8;4jko+fbrakes are locked, and the two cars skid forward 2.8 m before stopping. The police officer, knowing that the coefficient of kinetic friction between tires and road is 0.80, calculates the speed of the sports car at impact. What was that speed?(Let A represent the sports car, and B represent the SUV) $\approx$    m/s

  A ball is dropped from a height of 1.50 m and rebounds to a heightji1g5 fopxuch4 7v f:2 5+vkcc of 1.20 m. Approximately how5iv:x1pc u j5hcc7gv2f+4okf many rebounds will the ball make before losing 90% of its energy?   

A measure of inelasticity in a head-on collision of two ob: k91iey9 ( xzbvxrw,tjects is the coefficient of res 9i:wkvbt9xe (, zrx1ytitution, 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 into two pieces, one with three times the mass of the othev ,fs(- /otuojr. 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 i,o svuo-(f jt/s 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- kj+ypelcl.h a(-1(nton with a 10.0-kg object moving in the -x direction at 4m/s Find the final velocity of each mass ifhp(l .t (nle-a+ cj1ky:
(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 r1l pa yak8*ov;est decays into a second nucleus, an electron, and a neutrino. The electron and neutrino are emitted atav a ok1lp*;y8 right angles and have momenta of $9.30\times {10}^{-23}kg\cdot m/s$ and $5.40\times {10}^{-23}\mathrm{kg}\cdot \mathrm{m}/\mathrm{s}$ respectively. What are the magnitude and direction of the momentum of the second (recoiling) nucleus?    $\times {10}^{-22}$    ${}^{\circ }$ from the momentum of the electron

  An eagle ($m_{\mathrm{A}}=4.3\mathrm{kg}$) moving with speed ${\nu }_{\mathrm{A}}=7.8\mathrm{m}/\mathrm{s}$ is on a collision course with a second eagle ($m_{\mathrm{B}}=5.6\mathrm{kg}$) moving at ${\nu }_{\mathrm{B}}=10.2\mathrm{m}/\mathrm{s}$ 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 ; iae) 4ke8u s.bjgl:g$m_{\mathrm{A}}=0.400$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 eq9h p zpd9r7 5bc9gozaath-d, 3ual mass, each having initial spez9h, ddh grpo 7t9p9zcb5aa-3ed the two move off together with speed v/3 What was the angle between their initial directions?    ${}^{\circ }$

  Two billiard balls of equal mass move xng/:+3 )hvii -cm we yv5)hpqat right angles and meet at the origin of an xy coordinate system. Ball A is moving upward along the y axis at 2m/s and ball B is moving to the right along the x axis with speed 3.7m/s After the collision, assumed elastic, ball B is moving along the positive y axis (Fig. 7–37). What is the final direction of ball A and what are their two hih/)m)q np-eg 3ywcv5xi:v+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 wirt -ypn.-j h-yth another atom at res tn.--yyh -pjrt. 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 pe4j d; e39kcorlrfectly elastic collision with another atom at rest. After the iml 9e4roc d;j3kpact, 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 system shown in Fig. 7–38vfkp su5jg5aw2 c(s54. Specify relative to the left-h2 wp5 5jacv5 (sg4kfusand 1.00-kg mass.    m

  The distance betweenpb; (e:0tuxp c a carbon atom ($m_{\mathrm{C}}=12\mathrm{u}$) and an oxygen atom ($m_{\mathrm{O}}=16\mathrm{u}$) in the CO molecule is $1.13\times {10}^{-10}$m How far from the carbon atom is the center of mass of the molecule?    $\times {10}^{-11}$m

  The CM of an empty 1050-y,wvx 0e6+rdn kg car is 2.50 m behind the front of the car. How far from the front of the car will the CM be when two peopleey, xr6vd nw0+ 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, *4-:udmng*9rv ypi h*rdvs6 h18 m by 18 m, of mass 6800 kg, is used as a ferryboat. If three cars,yud vrhm6: *h- **pvs4rnd g9i each 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 sidesb mnya9fjm3z. vs 83,d $l_0$,$2l_0$, 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) palleo v8d);sc4+gyma jb9a t has a load of identical cases of tomato paste (see Fig. 7–40), each of which is a cube of length l. Find the center of gravity in the horizontal plane, so that the crd9a;+cyo vsmgajb4)8ane operator can pick up the load without tipping it.$X_{CM}$ =    l $Y_{CM}$ =    l

  A uniform circular plao4ipvrs+dr6u 6 sc0p2te of radius 2R has a circular hole of radius R cut out of it. The center of the smaller circle is a dvi 62+s046 d cuprrospistance 0.80R from 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 proportions are the same as thogeg0t 9e:n g:b6egj0mse in Table 7–1, and calculate the mass of one :6mj g0:g 9eeegbgnt 0of your legs.    kg

  Determine the CM of an outstretched - v9ra:ho0 -xkxz4n*kctmp.k 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 bent at a ioio;e px7i(zth)y 6 ac06js)yzsv)* right angle. Assume that to pycs)z;s i)xy*hie76 j o()av 6zi0the person is 155 cm tall. $X_{CM}$ =    cm $Y_{CM}$ =    cm

When a high jumper is in a position such that /2 d 2fwi,a4nh0f:df:x n; qrb(hlvvxhis 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 outside the body? Use Tanvra2 fh:0dbxnd hil4 ,; (xfq 2:/fwvble 7–1.

The masses of the Earth and Moon are 7nlde i26n4fzq p kk3)g 1jst+$5.98\times {10}^{24}$kg and $7.35\times {10}^{22}$kg respectively, and their centers are separated by $3.84\times {10}^8$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 qr temcnvg8-ho(4x)4pb lx2 7kz j(f( on frictionless ice.
(a) How far from the woman is their CM?    m from the woman
(b) If each holds one end of a rope, and the man pulls on the rope so that he moves 2.5 m, how far from the woman will he be now?    m
(c) How far will the man have moved when he collides with the woman? He has moved    m from his original position

  A mallet consists of a uniform cygas3yofv:xsm- ;:t /w b+abx +lindrical 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 is the point that wibw gs:+bma;xto:/ vx sa-fy 3+ll follow a parabolic trajectory?    cm

  A mallet consists of a uniform cylindrical head of mass 2.00 kg and a diame068x(w9twh p 9 4joov6lgddaster 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 tos40aoo69dl9 h6g jxvww8p(ts dsed, spinning, into the air, how far above the bottom of the handle is the point that will follow a parabolic trajectory?    d    d

  (a) Suppose that in Example 7–14 (Fig. 7–29),,.g/rylv o gx.9g8tr/rh1 ben5pa ;oy $m_{II}$=3$m_I$ Where then would $m_{II}$ land?    d(Round to two decimal places)
(b) What if $m_I$=3$m_{II}$    d

A helium balloon and its gondola, of mass M, are in the air and statio3f*)j zgyje7qv5 7 lwbnary with respect to the ground. A passenger, of mass m, then climbs out and slides down a rope with speed measured with respect to t wz )gj*37ebyqvjf l75he 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 pitcheo5-6 )e(daqr x6c yfl+ us;kwvca0h5id 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 thehr6s5ovlyu(fcx5-+6 dcaw k ) 0i a;qe contact.    ${}^{\circ }$

  A rocket of mass m travelin.bwidk5(z og nw;: t,-fnb+uzg 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 is fac 6sb-gp fwy8:j7j;lmhed with the corner pocket shot shown in Fig. 7–43. Relative dimensions are also shown. Shou: jw;b j-h7p8ysgflm6 ld 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) acalflrqn6 b(zsm,hve,m:*d j: )6gqn4 quires a speed of 2.5m/s by pushing off with his legs from an 1800-kg space aes ,lg v)b 4,:nqm: (fzmd66jrnlqh*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 63jfn t6v- g/o-dp- qln0 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 hasnqfn-lt6 v3jpdg - /o- moved 12 m?    m

  A ball of mass m makes a head-on elas hggqap76,e5q pfw*q4tic collision with a second ball (at rest) and rebounds in the opposite directhpq7p45gq qg 6wfae,*ion 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 expert witness in a court case invol/j5oo u9axy7c ving 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 measured to be 0.60. Show that the driver of car A was exceeding the 55-mph (90km/h) speed limit before x u/o9acoy7 5japplying the brakes.    mi/h

A golf ball rolls off the top of a flight of concrete steps of tbz 4gd)r65t imotal vertical heigid4 brzmt5 )6ght 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 reaches the bottom of the stairs?

  A bullet is fired vertically into a 1.10kfz wgn.*z/aj- loy40-kg block of wood at rest directly above it. If the bullet has a mass of 29.0 naj/w.0-z1 z yokfgl *g and a speed of 510m/s how high will the block rise after the bullet becomes embedded in it?    m

  A 25-g bullet strikes anma*xo+kt) g q3d becomes embedded in a 1.35-kg block of wood placed on a horizontal surface just in front of the gun. If the coefficient of kinetic friction between the block and the surface is 0.2*k)xm+gq a ot35, and the impact drives the block a distance of 9.5 m before it comes to rest, what was the muzzle speed of the bullet?    m/s

  Two people, one of mass 75 kg and the other of mass 60 kg, sit in a rowbocfp)-/j b sdp4 1lrsn/at of mass 80 kg. Wi 4f /sp-pd/r)sc1jln bth the boat initially at rest, the two people, who have been sitting at opposite ends of the boat 3.2 m apart from each other, now exchange seats. How far and in what direction will the boat move? The boat will move    towards the initial position of the 75 kg person(Round to two decimal places)

  A meteor whose mass was about wu9ty+ pf;nts6:9n fs$1\times {10}^8$kg struck the Earth ($m_E$=$6\times {10}^{24}$kg) with a speed of about 15km/s and came to rest in the Earth.
(a) What was the Earth’s recoil speed?    $\times {10}^{-13}$m/s
(b) What fraction of the meteor’s kinetic energy was transformed to kinetic energy of the Earth?    $\times {10}^{-17}$
(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 fmfyzgdco ,hn2,zt8yx7 njov/ 7c*h*3 ragments by an explosion. One fragment acquires *,27ct3zjvo8/mghy z xdcfon7yn,* h twice the kinetic energy of the other. What is the ratio of their masses?   

  The force on a bullet quxb) (: pptk.is given by the formula F = 580-( $1.8\times {10}^5$t) over the time interval t=0 to t = $3.0\times {10}^{-3}$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 km( 1 0,vus,v griez. z,cuw:x$m_A$ = 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 into an alpha particle and a w (zv o5 c7wg8bs:z0fmsmaller nucleus. What will be the speed of this recoiling nuczsf7 gbm c8wwz5v:o (0leus if the speed of the alpha particle is $3.8\times {10}^5$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.gxst qhj46upz(k2rxcq/a* )u 6cof ro9: 4z t) 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, $\mathrm{\Delta }x$ does the skeet travel because of the collision? $\approx$   

  A block of mass m=2.2kgoc+u: d8 :gop,o enk:a;n ffo- slides down a 30.0 ${}^{\circ }$ incline which is 3.60 m high. At the bottom, it strikes a block of mass M=7kg which is at rest on a horizontal surface, Fig. 7–46. (Assume a smooth transition at the bottom of the incline.) If the collision is elastic, and friction can be ignored, determine
(a) the speeds of the two blocks after the collision,v'${}_A$ =    m/s v'${}_B$ =    m/s
(b) how far back up the incline the smaller mass will go. $\approx$   (Round to the nearest integer) (Let A represent mass m, and B represent mass M.)

  In Problem 79 (Fig. 7–46), wh6 sg66 hrafh5)f+ inqeat is the upper limit on mass m if it is to rebound from M, slide up the incline, stop, slide down the incline, and collide wig5 6)n fh6rs a+fq6heith M again?    kg (Let A represent mass m, and B represent mass M.)

  The gravitational slingshot effect. Figure 7–47 shows the planet Sy7ls*: rsfe 2c1 2nxtoaturn moving in the negative x direction at its orbital speed (with respect to the Sun) of 9.6km/s T1:*fnsx 2 7tl 2ryeocshe mass of Saturn is $5.69\times {10}^{26}$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