We claim that momentum is conserved, yet most mosllh 1pj*s;qt/r, s: hving objects eventually slow down and/s:*hs;1tl,qs j hrp l stop. Explain.

When a person jumps from a tree to the gr(te tpjwt hqqc./+*3 o4bng3-7 dpvllound, what happens to the momentum of the person upon striking vjlq dh.tco73p g-3p w4t(qtl+en * b/the ground?

When you release an inflated but untied balloon, why does h ri*qt8g 7-jtit fly across the room - i7hg*rtt8qj?

It is said that in ancient times a sm j7ym9 o*,nck( :lmfrich man with a bag of gold coins froze to death while stranded on a frozen lake. Because the ice was frictionless, hem,o l9:(7fjc* ymkmns 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 space and is essentialpqz52t- 4* *;qd wzqfc0hizhe ly in a vacu*pzdetqz0;w5f -*2h zih q4c qum?

According to Eq. 7–5, the longer the impact time of an impulse, the smaller c 7 u )ll j5/m.4xbptbf1x/ezgthe force can be for the same momentum change, and hence the smaller the deformation of the object on which the force acts. On this basis, explain the value of air bb7c zj)/1gmbx/x5p.elf t ul 4ags, which are intended to inflate during an automobile collision and reduce the possibility of fracture or death.

Cars used to be built as,ne ppv2zy;k wjbis86/x,6gw rigid as possible to withstand collisions. Today, though, cars are designed to have “cyzj wns,/ew ,;6kipg xvpb826 rumple zones” that collapse upon impact. What is the advantage of this new design?

Why can a batter hit a pitched ba c)ix7zq, yvz2seball further than a ball tossed in the air by the batter?qzi vc7),2yzx

Is it possible for an object to receive a larger impulse jpsgvvj((q 3;6mv g7zga t /5cfrom a small force than fromg/ aqvg5tcjs(v;zj 3(6pgm7v a large force? Explain.

A light object and a heavy object have the same kinetic energy. Which has the gr)yjf6dj, krm8zz * .treater mom k,z6f ).j*jmy rr8tzdentum? Explain.

Describe a collision in9.r 5yzv g p8nb3-h2 v+jebvs/i:htxs which all kinetic energy is lost.

At a hydroelectric power is +8bes-j 6:wb )idxoplant, water is directed at high speed against turbine blades on an axle that turns an electric generator. For maximum power generation, shouldw6 :-+ise)i8bsjx obd the turbine blades be designed so that the water is brought to a dead stop, or so that the water rebounds?

A squash ball hits a wall at a yhq(6z ;ke*pf 45 $^{\circ} $ angle as shown in Fig. 7–30. What is the direction (a) of the change in momentum of the ball, (b) of the force on the wall?

A Superball is dropped from a height h onto a hard steel plate (fixedhs49*mha x+cnsx-r*xe vkb32 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 consider the ball and Earth as our system, during what parts of the process is momentum conserved? (c) Answer part (b) for a piece xs *xhkn9 42 +3vrecm*asx-hb of putty that falls and sticks to the steel plate.

Why do you tend to lean19bu+41fx 3ycrbmbw n backward when carrying a heavy load in your arms?

Why is the CM of a 1-m length of pipe at its mid-point, whereas this is kkx2g0q 0dn6xj uw+1anot true for yo0w+ju xqngd2 a6kk01xur arm or leg?

Show on a diagram how your CM u321a:1 wbzstofj67z w- qb6dksz,da shifts when you change from a lying position to a sitdtw -1kb bf uo66q7:2szsadj3wazz1 , ting position.

If only an external force can change the mom o3z 3a2pe+pdw6m dihk360jybxn qwnr4:m()sentum of the center of mass of an object, how can the internal force of an engine accelerate 3 kmje ib4m0zrxn wdns):opaqp(3hd2y+w 636 a car?

A rocket following a parabo81 a/ykb l(imblic path through the air suddenly explodes into many pieces. What can you say about the motalk yb( i1b8m/ion of this system of pieces?

  What is the magnitude of the momentum of a 28-g sparr+gk nrp ehn,fm2:i5*a ow flying with a speed of 8.+pehnf,r*mnag k:i5 2 4 m/s    $kg\;m/s$

  A constant friction force of 25 N acts on a 65-kg skier f1ve9nn+jmy q:91xs7ak lh q-ror 20 s. What is the sk1nr9+v-qn7q eh9 mlajyx1 k s:ier’s change in velocity?    m/s

  A 0.145-kg baseball pitched at 33/muw n en9w9y9 m/s is hit on a horizontal line drive straight back toward the pitcher at 52m/s If the contact tinn 9wyw/ e39mume between bat and ball is $3\times10^{-3}$s calculate the average force between the ball and bat during contact.    N

  A child in a boat throws a 6.40-k uan0(f:5hd4n/1 /iw iwfeiblvi k75f g 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 k 7b:n0hfd i/ufwii5 l45(ivn/a1wfeof the child is 26.0 kg, and that of the boat is 45.0 kg. Ignore water resistance. The velocity of the boat is    m/s

  Calculate the force exerted on a rocket, given that the proprcl7p-43eyh u7km x8kn)gqc(ukk k/) elling gases are expelled at a rate of 1500kg/s with a speed o/))-krle7xcn y8u7(uh kmgpqk 34kkc f $ 4\times10^{4 }$ (at the moment of takeoff).$a\times10^7$ N a =   

  A 95-kg halfback moving at 4.1m/s on an apparent breakaway for a tou l9)rliecy3 s/chdown is tackled from behind. When he was tackled by an 85-kg cornerback running at 5.5m/s in the same diic3ey 9sl)l/ rrection, what was their mutual speed immediately after the tackle?    m/s

  A 12,600-kg railroad car travels alone on alevel frictionless tracnwm,oq9)- z fnk 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 newfn9o) wzn ,mq- speed?    m/s

  A 9300-kg boxcar traveling at 15m/s strikes a second boxcar at rest. The t:t1zkb6hm c+s)0 apb owo stick to0zmohb6tb +)ac1:k spgether 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 speed+w:d)ay a o8- icfl-nds 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 0.5-+ao:wd n)la8i dfy-c 0 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 c1 s-1bs;: ug.p)h rgdryqs i.u(jzd6a ar 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 rh iz gq u;sy-j(purd)dsb1.: a 1.6sgthe tracks, what is the speed of the car after 90.0 min?$\approx$    m/s

  An atomic nucleus initially moving at 420m/s emits an a)d yo/o 8jdh9iicu 5:xlpha particle in the direction of its velocity, and the remaining nucleus slows to 350m/s If the alpha particle has a mass of 4.0 u and the original nucleus has a mass i d58u:o9xd jc yhi/o)of 222 u, what speed does the alpha particle have when it is emitted?    m/s

  A 23-g bullet traveling 230/diw sr8zna66 m/s penetrates a 2.0-kg block of wood and emerges cleanly at 170m/s If the block is stationary on a fz w6s/a8 i6rdnrictionless surface when hit, how fast does it move after the bullet emerges?    m/s

  A 975-kg two-stage rocket is f9ulg;0-q ey(ygbz:s 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 tra, kpvibmp00l 0veling in outer space with a velocity of 115m/pm, kv0p0li b0s To alter its course by 35.0 $^{\circ} $, its rockets can be fired briefly in a direction perpendicular to its original motion. If the rocket gases are expelled at a speed of 1750m/s how much mass must be expelled?    kg

  A golf ball of mass 0. eo67*mzn u q/wgdfw+ cy(1d/o/q ox1o045 kg is hit off the tee at a speed of 45m/s The golf club was in contact with tw7 oy/(o*dxqg c1qofou+6e1nw/d / zm he 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 veloe wruk8,vq+6ecity of 8.5m/s and comes to rest in a time interval of 8.0 msvku6,wq r8 e+e. (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 speed v=25m/s strikes a wall ;:.fgavb cin: 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 crashworthiness of new automobcw ome(f-omj n;x5-.uile models. Cars are tested by smashing them into fixed, massive barriers at 50km/h (30 mph). A new model of5(mwenj-c-o ;mufx. o mass 1500 kg takes 0.15 s from the time of impact until it is brought to rest. (a) Calculate the average force exerted on the car by the barrier. $\approx$$a\times10^5$N a =   
(b) Calculate the average deceleration of the car.    m/$s^2$

  A 95-kg fullback is running at 4m/s to the east and is stoppey jh56zlw bw6:d in 0.75 s by a head-on tackle by a tackler running due west. Calculaw bjw566hl:yz te
(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 6 ,whahe9ux, -zng opf6xd.y. 6oo g*ndirection and is given by the graph of Fig. 7–33 as a f6gyo. x6oud ,enp n.9-zghfh ,w6*oaxunction of time. Use graphical methods to estimate
(a) the total impulse given the ball    N*s
(b) the velocity of the ball after being struck, assuming the ball is being served so it is nearly at rest initially.    m/s

  From what maximum height can at6:uap2 h jgcbrk15cb;uuf4- 75-kg person jump without breaking the lower leg bone of either leg? Ignore air resistance and assume the CM of the person moves a distance of 0.60 m from the standing to the seated position (that is, in breaking the fall). Assume the breaking strength (force per unit area) of bone 4ubacp2btr;u5 hf:cuj6kg -1 is $170\times10^6\mathrm{~N/m^2}$ and its smallest cross-sectional area is $2.5\times10^{-4}m^2$ [Hint: Do not try this experimentally.]    m

  A ball of mass 0.440 kg moving east (+x direction) with a speed of co.+r;aj5;jc,fv xv i( e iajz9fllides head-on with a 0.220-kg ball at rest. If the collision is perfectly elastic, what will be the speed and dir (ai5a9;cf jv.ifjzxv;j+ ,erection 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 b+8nkbxr1g 7.es zz/ least with a speed of 3m/s has a head-on collision witln8ke/1bx +b zg7.srzh 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. v'$_A$ =    m/s ----待选择----eastwest  v'$_B$ =    m/s ----待选择----eastwest 

  Two billiard balls of equal mass undergo a peri+bme .d ef:r-wp ;j,qfectly elastic head-on collision. If one ball’s initial speed was 2m/s and the other’s was 3m/s in the opposite direction, what will be their speeds after the collision?(Let A represent the ball moving at 2.00 m/s, and call that direction the positive direction.Let B represent the ball moving at 3.00 m/s in the oppmpqr:bj fe+di,-.w;eosite direction. ) v'$_A$ =    m/s v'$_B$ =    m/s

  A 0.060-kg tennis ball, mov6dsj .jtlj+i 9ing with a speed of 2.5m/s collides head-on with a 0.090-kg ball initially moving away fro 6djsil+9 jj.tm it at a 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 speqpj /co,x,*al(- hou led of 8.5m/s collides head-on and elastically with another ball initially at rest. Afterward the incoming softball bounces backward with a x,-/alop(uj lqh,oc *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 elastically as ondacsn -/ati5.e approaches the other directly from the rear (Fig. 7–34). Car A has a mass of 450 kg and car B 550 kg, owing to differences in passenger mass. If car A/dsa .n-ac it5 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 collin; ap3-p4fzpssion with a second ball initially at rest. The second ball moves of3a -;fpsn4zppf 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 j/)hp wpgp:3w i7 m*uwqt6 ne,down a frictionless incline as shown in Fig. 7–35, and elastically strikes another cube at the bottom that is only*htjn7 im/wg )eq wp6upw 3:,p 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 mas,7 ;np*pxkqri*mwl0 rs 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) h5fpuivyzpa c)bkw4qr;q)+ z) 28 lveight h of the pendulum equapz)q af8+b45kp rw )q ivzy);v)2culh l 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 n9cs 5b i *qx kh7;s(h3kcn;vq230m/s buries itself in a 3.6-kg pendulum hanging on a 2.8-m-long string, which mas h37*khc 59cnvq( qi n;;sbxkkes 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 cqw ((esh nr88of kinetic energy lost, $(\Delta\mathrm{KE/KE})$ for the ballistic pendulum collision of Example 7–10. (b) Evaluate for m=14g and M=380g

  An internal explosion ubzex hpxwl 6x*o q9q(d*n3(7 7iz k9ybreaks an object, initially at rest, into two pieces, one of which has 1.5 times the mass wx*eq (q9lz(ix9o7xdzp* b6 7un3khy 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. ) KE'$_A$ =    J KE$_B$ =    J

  A 920-kg sports car collides into the rear end of a 2300-kg SUV;( 3e(f 8 qawyb :jlctta/kg*t stopped at a red light. The bumpers lock, the brakes are lo:jtey/3;bwlgc f(* attak8 q(cked, 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 frof s fs(.:jvd(gm a height of 1.50 m and rebounds to a height of 1.20 m. Approximately how many rs.(vjfdf (s:gebounds will the ball make before losing 90% of its energy?   

A measure of inelasticity i7 -pxuksb5 im(3 hte-qn a head-on collision of two objects is the coefficient of res-ksp7hibmt(q- 3e5u xtitution, 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 thel.e( j+c;c ibl 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-surfaceic.lb+e lc;j( d 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 5.5 zfa*l.rb* k-nrp /px6m/s collides head-on with a 10.0-kg object moving in the -x direction anrbpk-lz*. /*xpf 6r 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 second nucleus, an electron+ 1 izgan( cd,kzfw++bngo2 p+, and a neutrino. The electron and da+gwcfn+, k(1 p g+2izo+znbneutrino are emitted at right angles and have momenta of $9.30\times10^{-23}kg\cdot m/s$ and $5.40\times10^{-23}\mathrm{~kg}\cdot\mathrm{m/s}$ respectively. What are the magnitude and direction of the momentum of the second (recoiling) nucleus?    $ \times10^{-22}$    $^{\circ} $ from the momentum of the electron

  An eagle ($m_{\mathrm{A}}=4.3\mathrm{kg}$) moving with speed $\nu_\mathrm{A}=7.8\mathrm{~m/s}$ is on a collision course with a second eagle ($m_{\mathrm{B}}=5.6\mathrm{kg}$) moving at $\nu_{\mathrm{B}}=10.2\mathrm{m/s}$ in a direction perpendicular to the first. After they collide, they hold onto one another. In what direction, and with what speed, are they moving after the collision? v =    m/s $\theta$ =    $^{\circ} $ rel. to eagle  ----待选择----AB 

  Billiard ball A of m( +rf)uutp/+3 e+ *ez whjnmzcass $m_\mathrm{A}=0.400$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 collisisrt*. +l08gsd) ,e6u afc nwrion between two objects of equal mass, each having initial speed the two move off together with speed v/3 What sfd ur tra*8,lc0 6.si)e+nwgwas the angle between their initial directions?    $^{\circ} $

  Two billiard balls of equal mass move at right angles and meet at the orji5.4y0/nwj wgo+cs -kq/u x 5bge(tp igin 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 twocsx/5 obt 4gwj 5. q-jnpk0w giye(u+/ 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 anoth;eecl /pm7cz)16s mjlwxs1 :y er atom at rest. After the impact, the neon atom trav6j7mc 1)se pemcl x/1z:sywl;els away at a 55.6 $^{\circ} $ angle from its original direction and the unknown atom travels away at a -50 $^{\circ} $ angle. What is the mass (in u) of the unknown atom? [Hint: You can use the law of sines.](Let A represent the incoming neon atom, and B represent the target atom) $m_B$   u

  A neon atom (m=20u) makes a perfectly elastic coym.hpv 8;0c,*b oqtm rllision with another atom at rest. After the impamhvq,b0 co t8*;ym.p rct, 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 oq 4w us0fx,ngvp9gf (4f the three-mass system shown in Fig. 7–38. Specify relative to theu 04 xf w9gq(s4v,gpnf left-hand 1.00-kg mass.    m

  The distance between a carbon atomx *tjcdc jf5* u,9fd6i ($m_{\mathrm{C}}=12\mathrm{u}$) 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 the car. How far fx;.h5rcod4p(( vuih d rom 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 fr.(d (i ;xpd c4hvhrou5om 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 useyc6 wln;ai+h 3d as a ferryboat. If three cars, each of mass 1200 kg, occupy its NE, SE, +w ha6y3 c;ilnand SW corners, determine the CM of the loaded ferryboat.$X_{CM}$ =    m $Y_{CM}$ =    m

  Three cubes, of sides(odj etb,oo+z7 dy8;m $l_0$,$2l_0$, 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 tomato past3o7uj. o ov,kzg i8 3*hfbirc0e (see Fig. 7–40), each of which is a cube of length l. Find the center of gravity iv oziiob .g0 rkc,fjo3783h*un 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 9s 3cv:9jto)e p4h. nfedi9af2R has a circular hole of radius R cut out of it. The center of the smaller circle is a distance 0.80R fr vhpecenida )9 f .:sjf9t394oom 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 those in Table 7–1, and calculab:ad 0a lsa3(tte the mas3lsd a a0ab(:ts of one of your legs.    kg

  Determine the CM of an outkdgx 5skx espwx9 7wx92,3v1nstretched 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 -af n/so s2roqx+kqw/l9o- (h at a right angle. Assume that the person is 155 cm t9wla s+-q(onqf-2ks o/xro/ h all. $X_{CM}$ =    cm $Y_{CM}$ =    cm

When a high jumper is ia e;y ;gin4vh5n a position 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 the CM will be. W5;gi en4 ahvy;ill this CM be outside the body? Use Table 7–1.

The masses of the Earth a b0 b41,cywe w,-y)e1kn .axdsbxxf6pnd 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-k pqj8zw: 4x8sqg man stand 10.0 m apart on frictionless ice.
(a) How far from the woman is their CM?    m from the woman
(b) If each holds one end of a rope, and the man pulls on the rope so that he moves 2.5 m, how far from the woman will he be now?    m
(c) How far will the man have moved when he collides with the woman? He has moved    m from his original position

  A mallet consists of a uniform cylindricam7c l((6gjqvp- d8td tlo yaax4x;2(rl 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. 7–4pa26l yd t7v4 ma c(g;-x8lroj(dxt(q2. If this mallet is tossed, spinning, into the air, how far above the bottom of the handle is the point that will follow a parabolic trajectory?    cm

  A mallet consists of a uniform cylindrical head of magqz x,jryo1 (b;dz9 *v- sosn(ss 2.00 kg and a diameter 0.0800 m mounted on a uniform cylindrical handle of mass 0.500 kg and leng(yj *,ns1osgbvzz-o;x dr q9(th 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 will follow a parabolic trajectory?    d    d

  (a) Suppose that in Example 7–14 (Fig. 7:l.(hw+ g q z*/ivobde–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, ofjmk3z z2f arm75o1cx3a/(nr b sudp.* mass M, are in the air and stationary with respect to the ground. A passenger, of mass m, then climbs out and slides down a rope with speed measured with respect to the balloon. With what speed and direction (relative zo(5*mfak 2rbza 3p3njrdxs7.1u m/c to Earth) does the balloon then move? What happens if the passenger stops?

  An 0.145-kg baseball pitched horizontally at strikes a bat t hj,215wi zerand 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 th, t2j1iz5w rehe contact.    $^{\circ} $

  A rocket of mass m traveling with speed ievo);ww,,h 4uh fgs6 $v_0$ 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 lvl0oh*ec o54g)pdu)g 3t zm(corner pocket shot shown in Fig. 7–43. Rel*o5 (gvo4cghlpuz0l ed) m3t)ative dimensions 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 2.5m/s by pushfvmj* 4b* .axting off with his legs from an 1800-kg space*4afb.mj vxt * 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 kg, are initially at 0f3za,fxahw l,, 3ax urest in a3x a, xaw fl0hf,3z,uouter 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 rest) jqkx)c us50: ba8vw+rand rebounds in the opposite direction with a speed equal to one-fourth its original speed. What is the mass o)wxc+8ak5 qs 0ujvb:rf the second ball? $m_B$ =    $m_A$(Round to two decimal places)

  You have been hired as an expert witnes yf3ds59a;h hhs in a court case involving an automobile accident. The accif3 y 9s;hhadh5dent 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 applying the brakes.    mi/h

A golf ball rolls off the top of a flight of concrete steps of 6ou r9n ojwz,8fwtx 31total 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 when the ball reaches thrf9w wn8jx out3,1z 6oe bottom of the stairs?

  A bullet is fired vertically into a 1.40-kg block of wood0nkomljxi e9r;f1 , u8ppj- 5e at rest directly above it. If the bullet has a mass of 29.0 g and a speed of 510o-e0 8x;ulj,n1 jkp em5r9pif m/s how high will the block rise after the bullet becomes embedded in it?    m

  A 25-g bullet strikes and bm wevd / :y.rnrz.*uh -x)sdx b9x-v(qecomes 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 0.25, and the impact drives the block a distance of 9.5 m before it comes to rest, what was the muzzle speed of wh.d :x -vm / xun v*e-)b(rzdsyq.xr9the bullet?    m/s

  Two people, one of mass 75 kg and the other of mass 60 kg,aw7,2a8kw8r0 dyg y;gvt xac 7 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 02wac7gr7kdv8aywy a8,x t; gwhat 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 :*jd +zordl*qbh48 tg about $ 1\times10^{ 8}$kg struck the Earth ($m_E$=$6 \times10^{ 24}$kg) with a speed of about 15km/s and came to rest in the Earth.
(a) What was the Earth’s recoil speed?    $ \times10^{-13 }$m/s
(b) What fraction of the meteor’s kinetic energy was transformed to kinetic energy of the Earth?    $ \times10^{ -17}$
(c) By how much did the Earth’s kinetic energy change as a result of this collision?    J

  An object at rest is suddenly broken apart into two fragments by an exp(y/redhq0c/og,2 s m ylosion. One fragment acquires twice the kinetic ,gro d(yshq02ecy // menergy of the other. What is the ratio of their masses?   

  The force on a bullet is given by thebnwa.mg6;amm,d: y4 t formula F = 580-( $1.8 \times10^{ 5}$t) over the time interval t=0 to t = $3.0 \times10^{-3 }$s In this formula, t is in seconds and F is in newtons.
(a) Plot a graph of F vs. t for t=0 to t=3.0ms
(b) Estimate, using graphical methods, the impulse given the bullet.    N*s
(c) If the bullet achieves a speed of 220m/s as a result of this impulse, given to it in the barrel of a gun, what must its mass be?    kg

  Two balls, of masses axb29-im78i e7i7yv8fph fwi $m_A$ = 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 i( akx*ppvn*a. nto an alpha particle and a smaller nucleuskapn(.x p* av*. What will be the speed of this recoiling nucleus if the speed of the alpha particle is $ 3.8\times10^{5 }$m/s Assume the recoiling nucleus has a mass 57 times greater than that of the alpha particle.    m/s

  A 0.25-kg skeet (clay target) 8ac 1noo vku,a it l);-qc.e5.qg 3aldis fired at an angle of 30 $^{\circ} $ to the horizon with a speed of 25m/s (Fig. 7–45). When it reaches the maximum height, it is hit from below by a 15-g pellet traveling vertically upward at a speed of 200m/s The pellet is embedded in the skeet.
(a) How much higher did the skeet go up?    m
(b) How much extra distance, $\Delta{x}$ does the skeet travel because of the collision? $\approx$   

  A block of mass m=2.2kg slides down a ievt6b6nfpco:47d kp) us y :bz26vl3 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 the upper limit on mass m if itqcgo 3c g c)r3hp1gf85 is to rebound from M, slide up the incline, stop,c f 5q hpggc)331cgor8 slide down the incline, and collide with M again?    kg (Let A represent mass m, and B represent mass M.)

  The gravitational slin*a.; m fqosxz+ aw-gqd(;7 vzpm8i/bigshot effect. Figure 7–47 shows the planet Saturn moving in the negative x direction at its orbital speed (with respect to the Sun) of 9.6km/s The mass of Saturmo g+f8ipv .q-amqixa*zz 7s;dw(/ b;n 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