We claim that momentum is conserved, yet most moagcj nd23 i2h2ving objects eventually slow down and stop. Exp 22hni 3gda2jclain.

When a person jumps from a tree to the ground, what hbodkod* ux*9xyq:x **appens to the momentum of the person upon striking the ground**ybx9x:xk* od* o qud?

When you release an inflated but un6wvsk ,8xi2e stied balloon, why does it fly across the roomx2,swv 6sei k8?

It is said that in ancient times a ridt:8jv(( csi jch man with a bag of gold coins froze to death while stranded on a frozen lake. Because the ice was frictionless, he could not pudc:tj i8jv ((ssh himself to shore. What could he have done to save himself had he not been so miserly?

How can a rocket change directio 9mc9(sinu2 ;e3cm, .yzzy sbjay3:unn when it is far out in space and is essentially in a vaceimyj3(u3nzsbums :c ya,9y2 n ; 9cz.uum?

According to Eq. 7–5, the longer the impact time o q9ung6guj kygw+7jl7 j,s9c0dx4k , af an impulse, the smaller the force can be for the same jgag u7dkq6jusxwcj4k 7+,,g 9lyn9 0 momentum 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. Today, thoshp mhyqi)uf0) w .2v6ugh, cars are designed to havef60 y h2ps.uvmhwqi)) “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 ball tossed in the 1s2arqrpij6g3) ,x:ktzsti 5air by the gqj:si )6t,r13a5kri pxt2s zbatter?

Is it possible for an object to0)x3i8krdq 0etr6by7 mptb ,n receive a larger impulse from a small force than frrpqkbm)0 7,de 06r8bt nyx3tiom a large force? Explain.

A light object and a heavy object have the same kinetic energy. Which has t(2u hgu8+arpw)jo* z whe greater momentu wj 28wpuragu) (*zo+hm? Explain.

Describe a collision in which all kine+t yhbs( v4c)ftic energy is lost.

At a hydroelectric power plant, water is directed at high speed ao4gz w0(lb*y)o7 fan kgainst turbine blades on an axle that turns an electric generator. For maximum power generation, should the turbine blades be designed so that the water is brought to a dead 04*zkfy nolo7g wa)b(stop, or so that the water rebounds?

A squash ball hits a wall at a 4rh +p85r-g(,q kh9 gp7dqjzct no +op95 $^{\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 droppl0: a:eh5htaoed 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 process? (b) If we consider the bheah05::ao t lall 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 t:8 )qhtx;1kol35c vrkn n)yja heavy load in your arms?

Why is the CM of a 1-m length of pipe at its mid-poin x/l fbm,m5 zvhs+.d0izg8;n d. kcw6ht, whereas this is not true for your arm or legl, 56v; zg/..+d zwxnf08bc dm sikmhh?

Show on a diagram how yohzw5gp mpd98 1ur CM shifts when you change from a lying position to a sitting pompp z185d w9ghsition.

If only an external force can change the momentum of the centf:c o ywinygp33*8 u3aer of mass of an object, how can the internal force of an engine accelerauia 3wo:3 p*gyy8n c3fte a car?

A rocket following a parabolic path through the air suddenluh ucg q3/6vgr,;i;yc y explodes into many pieces. What can you say about the motion of t3 ; rggv;qhi/y,uc6uchis system of pieces?

  What is the magnitude of the momentum of a 28-g sparrow flying with a vperr72xp5n)speed of 8rn)5pvepr2x 7 .4 m/s    $kg\;m/s$

  A constant friction force of 25 N acts wee6plg 97mokumpa :3x. ee/*on a 65-kg skier for 20 s. What is the skier’s change in a/ * mmoek9g.l3u7:w6e pe expvelocity?    m/s

  A 0.145-kg baseball pitched at 39 m/s is hit on a horizontal line drive str u3 1q74twsl1mcbvx m46uln h4aight back toward th61 xb cwsh3t7nql lu41u4vm4 me pitcher at 52m/s If the contact time between bat and ball is $3\times10^{-3}$s calculate the average force between the ball and bat during contact.    N

  A child in a boat throws a 6.4 xinj b 0.k+r( tov3q*z. 5vldp;kf.lo0-kg package out horizontally with a speed of 10 m/s Fig. below Calculate the velocity of .dlp z(rvk5i. fj*.;3n b0vol+tqko x the boat immediately after, assuming it was initially at rest. The mass of the child is 26.0 kg, and that of the boat is 45.0 kg. Ignore water resistance. The velocity of the boat is    m/s

  Calculate the force exerted on a rocket, given that the p+m; 0d xfxmdrvi/iv1;ropelling gases are expelled avx;;di1rv m0if/mx+d t a rate of 1500kg/s with a speed of $ 4\times10^{4 }$ (at the moment of takeoff).$a\times10^7$ N a =   

  A 95-kg halfback moving at 4.1m/nn n/ts 3,bxvsu1mi4, s on an apparent breakaway for a touchdown is tackled from behind. When he was tackl13ss v,nubn4/inm tx ,ed 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 alevel frictionless trlb4t,3b2(+u*tpwn: jq gd je back with a constanub(j ,:2ebdqg+tnlb tw4j *3pt speed of 18m/s 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 traveling at 15m/s8q(llw hc*9 nm strikes a second boxcar at rest. The two stick together and move off with a speed of 6m/*lc9qw(n m 8hls What is the mass of the second car?    m/s

  During a Chicago storm, winds can whip horizontalsw ajyw8a27ji)sihya73 m;8b )-qkhely at speeds of 100km/h If the air strikes a p;w7 ) k ii)83sajahsw2hj8-em yab7qyerson at the rate of 40kg/s per square meter and is brought to rest, estimate the force of the wind on a person. Assume the person is 1.50 m high and 0.50 m wide. Compare to the typical maximum force of friction $\mu\approx1.0$ between the person and the ground, if the person has a mass of 70 kg.    N
$F_{on person}$  ----待选择----<> $F_{fr}$

  A 3800-kg open railroad car coasts along wz)hxtcg90 v/ pith a constant speed of 8.6m/s on a level track. Snow begins to fall vertically and fills the ca9ht)v/x 0c gpzr 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 initially moving7kb2iri .oi6kz+zjw pi/3 6z g at 420m/s emits an alpha particle in the direction of its velocity, and the remaining nucleus slows to 350m/s If the alpha particle h2ii6 +i/.zjkwbzgzro k67 3ipas 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 penetratesy dj )b6f7yzpxm3,3 6 ygcp5zb a 2.0-kg block of wood and emerges cleanl56 g y3mp f6jdc,7zyx3)ybzb py at 170m/s If the block is stationary on a frictionless surface when hit, how fast does it move after the bullet emerges?    m/s

  A 975-kg two-stage rocket is hw/-+x ood*n6 l /lvcqtraveling 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 tv+*ctjiw.z:9x7hbo,i ecr ha3; hl;is traveling in outer space with a velocity of 115m/s T.z ih rac;*c;tboiw ,x:v+l het7h 39jo 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 0.045 kg is hit off the tee at a s)sdwvh qx z)zn *+d8;bpeed of 45m/s The golf club was i8+n x;hqbd z)v*s)wdz n 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 i+g afcay50qjn1*3ya comes to rest in a time interval of 8.0 ms. (a) What is the impulse given to the nail31*5a iacagf+j0yyq n?    kg*m/s
(b) What is the average force acting on the nail?    N

  A tennis ball of mass m=0.06kg any st:trn-d+um t 1qi)4d speed v=25m/s strikes a wall at a 45 $^{\circ} $ angle and rebounds with the same speed at 45 $^{\circ} $ (Fig. 7–32). What is the impulse (magnitude and direction) given to the ball?   kg*m/s to the  ----待选择----leftright 

  You are the design engineer in charge of the crashworthines yd0pk 07rznl-v1*o gjs of new automobile models. Cars are tested by smashing them into fixed, massive barriers at 50km/h (30 mph). A new model ogv*n -l rop17yd 0kj0zf mass 1500 kg takes 0.15 s from the time of impact until it is brought to rest. (a) Calculate the average force exerted on the car by the barrier. $\approx$$a\times10^5$N a =   
(b) Calculate the average deceleration of the car.    m/$s^2$

  A 95-kg fullback is running at 4m/s to the east and is stopped in. a6glzqsc:f: 0.75 s by a head-on tackle byqczf 6ga.s ::l 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 kg) points w4oueufr(rgz ,q p i7knjly6906 8 ,gtin the +x direction and is given by the graph of Fig. 7–33 as a function of time. Use,ouq06( e j86piz9kl7g yu, fnw rtgr4 graphical methods to estimate
(a) the total impulse given the ball    N*s
(b) the velocity of the ball after being struck, assuming the ball is being served so it is nearly at rest initially.    m/s

  From what maximum height can a 75-kg person jump without breaking the lo 4p2p5j .p *-aeagwjnjwer leg bone of either leg? Ignore air resistance and assume the CM of the person moves a distance of 0.60 m from the standin e.-g2a j*j54ppjawpng 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 speed of collides hefckd *(nf( 7omu)3nz3 nzze1jad-on with a 0.220-kg ball at rest. If the collision is perfectly elastic, what will 3uz jezfcn()z*7mn( kdofn31 be the speed and direction of each ball after the collision?Let A represent the 0.440-kg ball, and B represent the 0.220-kg ball. $v'_A$    m/s  ----待选择----eastwest  $v'_B$    m/s  ----待选择----eastwest 

  A 0.450-kg ice puck, moving east with a spee ,f:zisb yrk2( uz/ 8mhlczb..d 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 repreyr8b l fs,. zb/z2(uhk. mc:zisent 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 coll *xvc7ycq(aezac 6+ r1hr7ff0 ision. 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 ba6y ch* f0a ex+r(vzar717qcc fll 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 collides head-on witudjfk;5 tg5p 5h a 0.090-kg ball initially moving away from it at a speed of 1.15m/s Assuming a perfectly elastic collision, what are the speed and direction of each ball after the colluk5dtp5j 5g f;ision?(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 s iza77v,g) c-nzhwl 1ipeed of 8.5m/s collides head-on and elastically with another ball initially at rest. Afterward the incoming softball bounces backward with a speed of 3.7m/s Calcul ziahng,l-czi7wv1)7ate
(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 approac58jat k3kfdh1)wqt 1h qd.chp.t8pp 3hes the other directly from the rear (Fig. 7–34). Car A has a mac dak3ppq..)15h1h8jqt 8dwftt h 3 pkss 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 md wa0sq3.l6twc-v k7qakes an elastic head-on collision with a second ball initially at rest. The second ball move qd.7t-0 3vqcswl6wkas 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 g9dmh+nnco. k y-9imrb/65nk incline as shown in Fig. 7–35, and elastically strikes another cube at the bottom that is only one-half its mass. If the incline is 30 cm hig5n.h k6knmb99/irdy+ noc m -gh and the table is 90 cm off the floor, where does each cube land? [Hint: Both leave the incline moving horizontally.]$\Delta x_{m}$$\approx$    m $\Delta x_{M}$$\approx$    m

ake the general case of an object of mass ml98y m (ab1j6arz3kz c$_A$ 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 experimeon. ow+ynfdl rp knqv-x5+r8ny(-1d ,t-ds:hnt, projectile 1 results in a maximum height h of the pendulum equal to 2.6 cm. A second projectile ndf,(:dq loh- nd.ty-nr k8-w5s x+r vn+1 ypocauses the the pendulum to swing twice as high, $h_2=5.2\mathrm{cm}$ The second projectile was how many times faster than the first? $v_1$ =    $v_2$ ([color=rgba(0, 0, 0, 0.85)]Round to three decimal places)

  A 28-g rifle bullet traveling 230m/s buries itself in a 3.6-kg pendulum hangin:js nb+zl:f6q g on a 2.8-m-long string, which makes the pendulum swing upward in an arc. D lqz6bnsj :f+:etermine the vertical and horizontal components of the pendulum’s displacement.vertical$\approx$    m horizontal =    m

(a) Derive a formula for7q d*9j -wtus- ctw)hm the fraction of 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 breaks an object, initially at rest, into two pat/ e:t dfa,ym.w .k:cieces, 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 dm :yft.:c,/.wkatearepresent 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 stopped hi8(f tvbba w fxpka8ld4s9 g2+iq.32at 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. Whfdag24vf l kti( 9xb3+2.q8wpbaish8at 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 anx(o 7v90 :hgnl lfj4lhd rebounds to a height of 1.20 m. Approximately how many rebounds will the ball make before losing 90% of its ene4 l7nfh:jxlovh 09 l(grgy?   

A measure of inelasticity in a head-oav*jonezp( w))z6n/ k n collision of two objects is the coefficient o)w vk (jn)na6p/z*zeof restitution, 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 iedl,h(0r7* owxz)8 mjt z m q;1l9cmywg6qd 5unto two pieces, one 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 150o)tg*(zm7l 6qx 98hey jdr,wdu lcwmq;mz the ratio of distances each block travels? ----待选择----1/91/101/81/6 

  A 15.0-kg object moving in the +x ccq wpr)0k 0)lbvho/( direction at 5.5m/s collides head-on with a 10.0-kg object moving in the -x direction at 4m/s Find ther q )lh/(0 bwvcpok)0c 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 nucleusf5m5bn imhk e)f42gu8 at rest decays into a second nucleus, an electron, and a neutrino. The electron and neutrino are emitted at right angi2kmbme) h5g 4u ff85nles 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 mwp(p :g m3wz1rass $m_\mathrm{A}=0.400$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 inelacca oqt 2v wmy(0i.zf,.qb *g1stic collision between two objects of equal mass, each having initial speed the two move off together with speed v/3 What was the angle between their initial directiof12aqto,v z..yc*b(w0 gi qc mns?    $^{\circ} $

  Two billiard balls of equ(gr9yruutaw /t* h 2c(al mass move at 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 speeds? direction of ball A hcr t2/( agur*(u9twy is  ----待选择----x directionx direction v'$_A$ =    m/s v'$_B$ =    m/s

  A neon atom (m=20u) makes tw,ms8xtcuv6 b7b gsp4l8 /w/a perfectly elastic collision with another atom at rest. After the impact, the neon atom tb cm v8wwt,g7/tsb6 /p84lu xsravels 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 perfectlygo.i ow2* lou.. kj3pp elastic collision with another atom at rest. After the impact, the neon atom travels away at a 5lgi3k 2p..j o* ou.opw5.6 $^{\circ} $ angle from its original direction and the unknown atom travels away at a -50 $^{\circ} $ angle. What is the mass (in u) of the unknown atom? [Hint: You can use the law of sines.](Let A represent the incoming neon atom, and B represent the target atom) $m_B$   u

  Find the center of mass of the three-mass system shown in Fig. 7–38. 5whjp- ,h(rmr Specify relative to the left-h,(- jpm hwr5rhand 1.00-kg mass.    m

  The distance between a carbon atomxkg7yn1, 59zh7cxpqe, fd 6p* awll.t ($m_{\mathrm{C}}=12\mathrm{u}$) 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.w:w bgsd fjl46o-b6pe+p +t1ra-hu8r How far from the6gr-s41wtd 6 j p8-raeubh+op b+w:fl front of the car will the CM be when two people sit in the front seat 2.80 m from the front of the car, and three people sit in the back seat 3.90 m from the front? Assume that each person has a mass of 70.0 kg.    m

  A square uniform raft, 18 m by fvtz.4w q(i j)18 m, of mass 6800 kg, is used as a ferryboat. If three cars, each of mass 1200 kg, occupy its NE, SE, and SW corners, )ftzvwiq.4 j(determine the CM of the loaded ferryboat.$X_{CM}$ =    m $Y_{CM}$ =    m

  Three cubes, of sides bs/3e:sku be ($l_0$,$2l_0$, 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 6c9* t , 1gdec9tpq.ppnkp-ygidentical 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 thap*-c, pkcy.1g ptegt 6 99dnpqt the crane operator can pick up the load without tipping it.$X_{CM}$ =    l $Y_{CM}$ =    l

  A uniform circular plate of radius 2R has a circular hole of radius R ctf7m ad( j.56ybx ctrs1;n b9*hg2s qmut out of it. The center of the smallertracx*;j 7mmbs 2 dgtq n9.s6b f5yh1( circle is a distance 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 samw7 bw,xdtv vb911 ;yn,e sc06e+grtioe as those in Table 7–1, and calculate the mass of onb;d,csrvb ,ei ye 1g1tn7o6 +w0w vtx9e of your legs.    kg

  Determine the CM of /czl+va(-gvhmv96 pmyd( 7iucn-k 1 aan 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 sq1j-h5,tpc * fsj/ju of the CM of an arm bent at a right angle. Assume that the person is 155 cm tall,s/qfj s j-5phc*t uj1. $X_{CM}$ =    cm $Y_{CM}$ =    cm

When a high jumper is in a position such that his arms and),saot6br*r v 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 to,6r av *)rsbTable 7–1.

The masses of the Earth and M+mpmk.c 4 nb8moon 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 frictionless.rnf j7sk,4wmdu-(j(vrr+x m 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 cyez(hz/jsy z3y 6 ylm 9kf(s+f)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 poielkj 9y s)3zmf(ysyh6z+f (z/nt that will follow a parabolic trajectory?    cm

  A mallet consists of a uniform cylindrical head ofjndl+ ,y9hspe4 sxh8/ 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 malletey 9/s+h d x8,4npjhsl 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 Examplee4dh fanhrpgwbjyn 281t28 *+ 7–14 (Fig. 7–29), $m_{II}$=3$m_{I}$ Where then would $m_{II}$ land?    d(Round to two decimal places)
(b) What if $m_{I}$=3$m_{II}$    d

A helium balloon and its gondola, of mass M, are in the air and stationaryxfg8 ar um 2)6mswqf-+6bil.a3yy mu5 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 happens if the passenger stopsfu5 6rmm6ag 2 q x.myi wusyb+fl)a8-3?

  An 0.145-kg baseball pitched horizontally at strikes a bat and is poppey*8e3xae ys(ad straight up to a height of 55.6 m. If the contact time is 1.4 ms, calculate the average force on the ball during the a xa83ysey*e (contact.    $^{\circ} $

  A rocket of mass m traeitj.) r+(qyy el4*xuveling 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 faced with the corner pocketvkd ok2fp-(q*g 5:pzv shot shown in Fig. 7–43. Relative dimensions are also shown. Should the player be worrig5vk:o( pzqfp 2*dk-ved 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 2.2f:m9 v1ymwi+jg df 4b5m/s by pushing off with his legs from adw9mmi ff1g b j4v:y2+n 1800-kg space capsule.
(a) What is the change in speed of the space capsule?    m/s
(b) If the push lasts 0.40 s, what is the average force exerted on the astronaut by the space capsule? As the reference frame, use the position of the space capsule before the push.    N

  Two astronauts, one of mass 60 kg and the other 80 kg, arew:drmso++p9v, xsp, g-ow(h*jm 1rv a21uw b g initially at rest in outer space. They then push each other apart. Hop*sjr29r1o +(,mvbuwmdgogas+:w xhw v1p ,-w far apart are they when the lighter astronaut has moved 12 m?    m

  A ball of mass m makes a head-on elastic c ox)3 /yiiwdkl1 qa)7i7j *tfpollision with a second ball (at rest) and rebounds in the opposite direction with a speed equal to one-fourth its original speed. What is the mass of the second balp 1x l77)a kijt)y w3dqioif/*l? $m_B$ =    $m_A$(Round to two decimal places)

  You have been hired as an expert witrz h(kxs)zeh 33a.g.c-n wd/wness in a court case involving an automobile accident. The accident involved car A of mass 1900 kg which crashed into stationa)3-z n/x e(wchrdakg3zshw. .ry 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 tx)ysda: bgl s6bvb*q6*3 jl(qhe top of a flight of concrete steps of total vertical height 4.00 m. The ball hits four times on the way down, each time striking the horizontal part of a different step 1.0 m lower. If all collisi3:l6q q6sbd sx*vyl*bga(b)jons are perfectly elastic, what is the bounce height on the fourth bounce when the ball reaches the bottom of the stairs?

  A bullet is fired vertically into a 1.40-k:aiv)5yx4c7 mpeihin4 b*rf c* /)qeeg block of 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 embef /iav4hyne*e4i e7ccbxr *5:)mpiq) dded in it?    m

  A 25-g bullet strikes and becomes embedded in a 1.35-kg block unyl12.z . gb2u0cvvp of wood placed on a horizontal 2z uby1g.pn20.l vvucsurface 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 the bullet?    m/s

  Two people, one of mass 75 kg and the other of mass 60 kg, sit in a rowboat9tad g ny-z5q5o. ox5t 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 ex5z5t5yaq o. nd9g- otxchange 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 aeibus) bc; :6qe8m 9ppbout $ 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 explosion.t y+ 0xgr,d. 1 ;zmdmrma8bddp14 ,pko One fragment acquires twice the kinetic energy of the other. What is the ratio of theid rpd xm4zm ;t,bmagd,y1+0.kp81ord r masses?   

  The force on a bullet is given by the formula q/5hk2m4t uthF = 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 masses1meidc : u)b99irg:es $m_A$ = 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 rest9 a8vxji/ta ia-cb136z1zw ul decays radioactively into an alpha particle and a smaller nucleus. What wiaz6x/ui i a8 wz1c3lv1jt-ba9 ll 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) is firenuv mh4c)j zx/m6xlm9o/ b3 8ad 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 sid mt7:r4k0bjiu.fe5 ouj h1l1 86lsnlides 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), what is the upper limit on mass m if it is to rebound:0adi 5 o( ewgpov:8rr from M, slide up the incline,i:e arrgov0:d8op5 ( w 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 thu -h9p1v gqx6ue planet Saturn moving in the negative x direction at its orbital speed (with respect to the Sun) of 9.6km/s The mass ouqu69- g vpx1hf 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