We claim that momentum is conserved, yet mosi wo21 2ir.ly+nts )hbt moving objects eventually slow down andin.wti2 yols1b 2+r )h stop. Explain.

When a person jumps fr5:. fkwkm/dhn 61( :j6fqdkguk if so0om a tree to the ground, what happens to the momentum of the person upon strikiq:6sohdm k (:6 fffw.i5k dkg nj/1k0ung the ground?

When you release an inflated but untied balloon, why does itjy).orqui9:,kr1 xxy fly across the room.yq): ykxj91o,uxri r ?

It is said that in ancient times a rich manga-x zfe.* t cdjcgn++y04cy4 with a bag of gold coins froze to death while stranded on a frozen cz 4c.gcx*4ge taj+yf+-y 0n dlake. Because the ice was frictionless, he could not push himself to shore. What could he have done to save himself had he not been so miserly?

How can a rocket change direction when it is far out in space and is yu us.uu4jjim5 ;3le :essentially in u .5y;j 4:imjlu3eusu a vacuum?

According to Eq. 7–5, the longer the impact time of an impulse, the smaller th x4eij+cib5i8:q. vwm,f7 kure force can be for the same momentum change, and hence the smaller the deformation of the object on which thefj i:+,4v8iw5mq7cbx uri.ke 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. Tod d/;od-v1lr hxz(9fy/ vavv5may, though, cars are designed to have “crumple zones” that collapse upon impact. What is the advantage of thi-1 vvyafvd5; hvm 9or/x (d/lzs new design?

Why can a batter hit a pitched baseball further than a ball tossed in the air bhf;i2s ;e 7s/rygawhk )q,*fby the batter?sr;)w7,hiq*hk/ebsy2 fa ; gf

Is it possible for an object to rmqvkuo. jog .az )5t,*eceive a larger impulse from a small force than jam.zg)vk qo5ut.o *,from a large force? Explain.

A light object and a heavy object have the same kinetic energy. Which hasq6:sn b6+ zfng the grnsgbn:zf6q +6eater momentum? Explain.

Describe a collision in which all kinetic enegxsqz3b +dm:*rgy is lost.

At a hydroelectric po3gznr o :sweh8n;n 3;ev3wd 1zwer plant, water is directed at high speed against 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 stop, or so that the waswn new;e3d381;nzh3:o gzv rter rebounds?

A squash ball hits a wall at a 45jh o134+:ay vkzmag2v $^{\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 hu-v 9:tde n-q.)qjj oweight 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 co9wj- qonj-e:q.d v ut)nsider the ball and Earth as our system, during what parts of the process is momentum conserved? (c) Answer part (b) for a piece of putty that falls and sticks to the steel plate.

Why do you tend to lean backward when carrying a heavy load in you*;.bt b2 cx qt7p-hiqh/ded:ur arms?

Why is the CM of a 1-m lengxy1qw jyx;7 t6th of pipe at its mid-point, whereas this is not true for your;xyy1jw7q tx6 arm or leg?

Show on a diagram how your CM shifts when you change from +5uwk hpj5g d:fv9v +da lying position to a sitting pj5wvd 9h:+ upvgk+ d5fosition.

If only an external force can change c rv-uipjvjif 9q10l; v+qj/2the momentum of the center of mass of an object, how can the internal force of an engine accelerate a cf0ivl/ j+v- pjr19juvci q;2qar?

A rocket following a parabolic path through the air suddenly ns z5yhy)v+f +explodes into many pieces. What can you say about the motion h5z)sf+y +v nyof this system of pieces?

  What is the magnitude oozc 1 1j89,akvik2qqg f the momentum of a 28-g sparrow flying with a speed of 8.4 m/vk1q2ozi1gkc 9 , q8jas    $kg\;m/s$

  A constant friction force of 25 N acts on a 65wudcf3cq.s*p 0 u,( oj-kg skier for 20 s. What is the skier’s js.u3q*c w0 cfou d,(pchange in velocity?    m/s

  A 0.145-kg baseball pitched at 39 m/s is hit on a horizontal line drive straians,le(l0 mblox8m; hw1py*, 0tx*v bght back toward the pitcher at 52m/s If the contact time between bat and ball is( t0*a bmv8y n1hxoel p0w m*,lblx,;s $3\times10^{-3}$s calculate the average force between the ball and bat during contact.    N

  A child in a boat throws a 6.40-kg package out horizontally with a speed of 1 ny5 v0jldl;hv*yi )by0pq,k6 0 m/s Fig. below Calcun hyyiy,)6 0v;b dk0vjql*l5plate the velocity of the boat immediately after, assuming it was initially at rest. The mass of the child is 26.0 kg, and that of the boat is 45.0 kg. Ignore water resistance. The velocity of the boat is    m/s

  Calculate the force exerted on a rockg q.k8,9 cawgzet, given that the propelling gases are expelled at a rate of 1500kg/s with g9kz.aqg c,8w a speed of $ 4\times10^{4 }$ (at the moment of takeoff).$a\times10^7$ N a =   

  A 95-kg halfback moving 8a)xq7ovj o+kat 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 immediateo 7)x8+vkqoa jly after the tackle?    m/s

  A 12,600-kg railroad car travels alone on alevel frictx*o ybue8a5-cionless track with a constant speed of 18m/s A 5350-kg loadby8eo*axuc- 5 ,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/s strik1jx 0:2 t7qtlme 0pl+ob z(kl8pqg h;pes a second boxcar at rest. The two stick together and move off with a speed of 60e 8q1(+bt7pmj;0kg2ozhl:lq p xplt m/s What is the mass of the second car?    m/s

  During a Chicago storm, wr yf,-t3jc(buxq h)4zinds can whip horizontally at speeds of 100km/h If the air strikes ah3b,4 c(j)t-qyxu rzf 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 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 caq2vms 8w8mx n-r coasts along with a constant speed of 8.6m/s on a level trackswn8q8m2x m -v. Snow begins to fall vertically and fills 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 initially moving at 420m/s emits an alphgo3z(+dcpx n6 a particle in the direction of its velocity, and the redx3n6zo +gp (cmaining nucleus slows to 350m/s If the alpha particle has a mass of 4.0 u and the original nucleus has a mass of 222 u, what speed does the alpha particle have when it is emitted?    m/s

  A 23-g bullet traveling 230m/s penetrates a 2.0-kg block of wood and emerg5 g , o 1 3;foptv..a;frxz1xhk6omawxes cleanly at 170m/s If the block is stationary on a fricxtf1;aa v ooz,ox6r 1gm;3kw .fhp. x5tionless surface when hit, how fast does it move after the bullet emerges?    m/s

  A 975-kg two-stage rocket is traved errc8 y7x,;8 gw xrkb)s5)svling 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 traqh0x m0khb etv9b; y/8veling in outer space with a velocity of 115m/s To alter itsv/h0mqb kt08;y9x h eb 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 ly in*w./z x0 oy*dq)hkg is hit off the tee at a speed of 45m/s The golf club was in contact with the*li0qz)dn. w yxo* /yh ball for $3.5\times10^{-3}$s Find (a) the impulse imparted to the golf ball,    kg*m/s
(b) the average force exerted on the ball by the golf club.    N

  A 12-kg hammer strikes a nail at a velocity of 8.5m/s and comes ,37qu ogwuxm y 8oahg l-32c0g;njvs f 0qm:*wto rest in a time interval of 8.0 ms. (a) What is the impul2 h7mw s0c-:glo*x 0w q 3v8qju3;mf nyagg,ouse given to the nail?    kg*m/s
(b) What is the average force acting on the nail?    N

  A tennis ball of masg,0 9mobou u gxkd0+9is m=0.06kg and 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 inlo1glf,kk.i7 lgq;d - 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 gl1dl7of ik-,. lkg;qthe 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 stopx ,2vt*ihqqq1ped in 0.75 s by a head-on txq1q*qi thv 2,ackle 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 0.060p3/ 2p0on9z/se;-pjq jf fiah kg) points in the +x direction and is given by the graph/;pjp i3 9hqsaj ef0n-/fp2zo of Fig. 7–33 as a function 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 a 75-kg person jump without breaking the lowedtf 3incy6 ++jr leg bone of either leg? Ignore air resistance and assume the CM of the person j+f3nc6dtiy +moves a distance of 0.60 m from the standing to the seated position (that is, in breaking the fall). Assume the breaking strength (force per unit area) of bone is $170\times10^6\mathrm{~N/m^2}$ and its smallest cross-sectional area is $2.5\times10^{-4}m^2$ [Hint: Do not try this experimentally.]    m

  A ball of mass 0.440 kg moving east (+x dirmbi-o 3 nga -c,tt2)ynection) with a speed of collides head-on with a 0.220-kg ball at rest. If the collision is perfectly elastic, what will be the speed and direction 2 -y 3m-og aic,tnbn)tof 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 w0vq-vc)tc ( :h zi*,xefsm6iiith a speed of 3m/s has a head-on collision with a 0.900-kg puck initially at restx*viv(m ef:z6t)c h- ,0is iqc. 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 perfectly elastic head-on 2cf8f 1::id b 7 6dnwxk.dhhhucollision. 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 represefhkh 2 d u:c71xfwib6d:8n .dhnt the ball moving at 2.00 m/s, and call that direction the positive direction.Let B represent the ball moving at 3.00 m/s in the opposite direction. ) v'$_A$ =    m/s v'$_B$ =    m/s

  A 0.060-kg tennis ball, moving with a speed of 2.5m/s collides head-on with a5vyglc.u9/y - cx ad;nru ,l70ax 0pqv 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 collision?(9yc,0yx5ludacp v un.;/ -la7x0g v rqLet A represent the 0.060-kg tennis ball, and let B represent the 0.090-kg ball.)v'$_A$ =    m/s v'$_B$ =    m/s

  A softball of mass 0.220 kg that is moving with a speed of 8.5m/;502l nvumw 7u))w:tayxj f n c2.babqs collides head-on and elastically with another 57: ynuj) nacb txul2bawfvm2w .)q 0;ball initially at rest. Afterward the incoming softball bounces backward with a speed of 3.7m/s Calculate
(a) the velocity of the target ball after the collision    m/s
(b) the mass of the target ball.    kg
(Let A represent the moving softball, and let B represent the ball initially at rest.)

  Two bumper cars in an amu ,tvxu9it l7:;)kym4qhhb 4nosement park ride collide elastically as one approaches the other directly from the rear (Fig. 7–34). Car A has a mass of 450 kg and car B 550 kg, owing hkxtm4n:y)4h q il;ou79tv b,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 bal1dyj7)kqld*v w c0h ;cn .q+qo ;q2qy/oq3nkbl makes an elastic head-on collision with a second ball initially at rest. noqw h+cvl7dcj;q. qy /*nyd2k3 ;qq0)oq1kbThe second ball moves off with half the original speed of the first ball.
(a) What is the mass of the second ball?    kg
(b) What fraction of the original kinetic energy $(\Delta\mathrm{kE/KE})$ gets transferred to the second ball?   

  In a physics lab, a cube slides down axuu njwn -*72a frictionless incline as shown in Fig. 7–35, and elastically strik u junx7awn*-2es another cube at the bottom that is only one-half its mass. If the incline is 30 cm high and the table is 90 cm off the floor, where does each cube land? [Hint: Both leave the incline moving horizontally.]$\Delta x_{m}$$\approx$    m $\Delta x_{M}$$\approx$    m

ake the general case of an object of mauw58 bxhbh +zkg4op)9 z o.5fdss 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, prye((j wcq a3k y,:u:oq:* aaxgojectile 1 results in a maximum height h of the pendulum equal to 2.6 cm. A second projwxka:yqguo::cy ( a 3eajq( *,ectile 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 23 -k,o-n3w 7fj+j azinc0m/s buries itself in a 3.6-kg pendulum hanging on a 2.8-m-long string, which makes the pendulum swing upward in an arc. Determine t-- ok7nwcajif +zn 3,jhe vertical and horizontal components of the pendulum’s displacement.vertical$\approx$    m horizontal =    m

(a) Derive a formula for the fraction of kinetic enerkrpk uc e)in-hs5 tjy 5973p0dgy 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 o,f7 0mgo b:w xfeghh8 /g2:btebject, initially at rest, into two pieces, 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, and B represent the lighter bgg:h2ef0 7teb:m ogwh8xf/ ,particle. ) KE'$_A$ =    J KE$_B$ =    J

  A 920-kg sports car collides into the rear end of a 2rasp+poo2 b.- g23svio+4b q t300-kg SUV stopped at a red light. The bumpers lock, the brakes are locked, and the two cars skid forward 2.8 m before stopping. The police officer, knowing that the coefficient of kinetic friction between tires and road is 0.80, calculates the speed of the sports car at impact. What was tht2pi+g rosqp2 o+ a3-bsbo4. vat 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 a9hno0z .sw)ftm xwt */2; spwu height of 1.20 m. Approximately how many rebounds will the ball 0.ww p zus*o sm9t;w /t)2nhfxmake before losing 90% of its energy?   

A measure of inelasticity in a head-on collision of two objects is the coe0 bfz: hko ic0ep7h+bm s51l5efficient o51i fem 0:p7l5 chbz0bh +kseof 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 into two pieces, one with three ti xpe7m)qdiq: g( rc;8vmes 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 reaqp:x qdme)vgrci8 ( 7;ssembled. The reassembled block is set on a rough-surfaced table, and the fuse is lit. When the firecracker explodes, the two blocks separate and slide apart. What is the ratio of distances each block travels? ----待选择----1/91/101/81/6 

  A 15.0-kg object moving in the +x direction at 5.5m/s collides head-on with au.qd vw5:iv :p ok/h-b1sw,m c 10.0-kg object moving in the -x direction at 4m/qvu- d:. : bh,/kvswpo1c5m wis 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 nucleus5tqfc3 hjrf/, at rest decays into a second nucleus, an electron, and a neutrino. The electron and neutrino are emitted at right angles and haqrcf/j,35 hftve 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 massl 72l2zlzhj jj+*j:mi $m_\mathrm{A}=0.400$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 equal mass, 1 64 iytmtg vc24z a4(q4cyuhwcx5:hkeach having initial speed the u4: q x4m4yc2 i 6at(hy1gt kvch4z5wctwo move off together with speed v/3 What was the angle between their initial directions?    $^{\circ} $

  Two billiard balls of eqlpe ims995bo; ual 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/sblei;5s99m p o After the collision, assumed elastic, ball B is moving along the positive y axis (Fig. 7–37). What is the final direction of ball A and what are their two speeds? direction of ball A is  ----待选择----x directionx direction v'$_A$ =    m/s v'$_B$ =    m/s

  A neon atom (m=20u) makes a perfectly elastic co*r wa,/rrh9sfllision with another atom at rest. After the impact, the neon atom travels away at h r/*asf9rrw, 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 ela1v u-dek- wba0stic collision with another atom at rest. After the impact,w 1vue a--k0bd 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-massf 5/nv.bdwtzc- 1z+akzc o- i; system shown in Fig. 7–38. Specify relative to the left-hand 1.00-kg m-5d.a;1twczo+vnz k b zfci-/ass.    m

  The distance between a carbon atom (wo)8uy u esp*v:qg7 z0$m_{\mathrm{C}}=12\mathrm{u}$) 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 p/jobecro.+ --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 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/prbc+oe .-o j of 70.0 kg.    m

  A square uniform raf114dvw p-epk qt, 18 m by 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, determine the CM of the loaded p4wq 1ke-p 1vdferryboat.$X_{CM}$ =    m $Y_{CM}$ =    m

  Three cubes, of sidesel,-fg(.r; 4 bdukgb r $l_0$,$2l_0$, 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 pasten1gn+ pdhjq15 tfr;7e (see Fig. 7–40), each of which is a cube of length l. Find the center of gravity in the d5rng+ jfe;pht11 7qn horizontal plane, so that the crane operator can pick up the load without tipping it.$X_{CM}$ =    l $Y_{CM}$ =    l

  A uniform circular plate of radius 2R has a circulsg9i6w7pu4 zmr 4j- pb.vk0 )ebv0ha kar hole of radius R cut out of it. The center of the smaller circle is a dishk v 0zbk)6b7pu4j4ei-m 09v wgrap.stance 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 qrae rozljd5 h)*85n72-f rer those in Table 7–1, and calculate the mass of one of your lfaor e*e)n 25rh r5q8-7drzljegs.    kg

  Determine the CM of an ol8rc vqmm xpr8wx )m-,13hk+q0*ufhr utstretched 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 atl71/h vc,izbrln .3qv a right angle. Assume that the peil/.lrq1,hbc3vz 7 nvrson is 155 cm tall. $X_{CM}$ =    cm $Y_{CM}$ =    cm

When a high jumper is in a position such that his apkw289;x v gurcvy,g: rms 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 Table 7r2vuwp,cx89ky;gg: v–1.

The masses of the Earth anbc:zvp1 zo 87ad Moon are $5.98\times10^{24}$kg and $7.35\times10^{22}$kg respectively, and their centers are separated by $3.84\times10^{8}$m (a) Where is the CM of this system located? (b) What can you say about the motion of the Earth–Moon system about the Sun, and of the Earth and Moon separately about the Sun?

  A 55-kg woman and an 80-kg man stand 10uc/6k.1 :lxtd6wb 7nam:cduf .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 cylindri;llnt4-j62 qk s st8ei z67t;nyme8lw cal head of mass 2.00 kg and a diameter 0.0800 m mounted on a uniform cylindrical 67w6l ; 4zqt lesn-tle2skjmt8 ;in8yhandle 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 will follow a parabolic trajectory?    cm

  A mallet consists of a uniformka:e4 ;u,7ev2:w- ennno hg bg cylindrical head of mass 2.00 kg and a diameter 0.0800 m mounted on a uniform cylindrical handle of mass 0.500 kg and length 0.240 m, as shown in Fig. 7–42. If this mallet is tossed, spinning, into g:vn:;4u,ek g2obne nhe-7 aw 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–l yuzb0;; hro;-tu0mu14 (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 stationary w 5a 7ex(*bbxkdw n ;y+jmxhy;9ith respect to the ground. A passenger, of mass m, then climbs out and y9kx(xdexb 5 j;7w*h am;n+ybslides down a rope with speed measured with respect to the balloon. With what speed and direction (relative to Earth) does the balloon then move? What happens if the passenger stops?

  An 0.145-kg baseball pitched horu6xzvb 35noi 9 25llycdn(;u28fdrgjizontally at strikes a bat and is popped straight up to a height of 55.6 m. If the contact timvxng9b ;du c55z28ni l2 6fuyd(lo3rje is 1.4 ms, calculate the average force on the ball during the contact.    $^{\circ} $

  A rocket of mass m traveling wbot vv4 x9 skf+s*c.xj twl6 2tuy60,vith 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 corne1g4p pqv 8t,( aoe7 .1rocfqryr pocket shot shown in Fig. 7–43. Relative 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. p1r,8ey .c 17v4aor qoq(gftp

  A 140-kg astronaut (including space suit) acquir.6amrdzjc - x )arvzn)fm(95zes a speed of 2.5m/s by pushing off with acm 5j(z)amzfnr) v.dxz69r -his legs from an 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, are initia0yk4 + o6akpragl:2y-np ,k rilly at rest in outer space. They then push each other apart. How far apart are they when the okakrpl6gy42 0-n arp,+k :iy lighter astronaut has moved 12 m?    m

  A ball of mass m makes a head-on elieq)1q, p,dksastic collision with a second ball (at rest) and rebounds in the opposite direction witk 1d, qqsi,e)ph 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 involving an automobil,f wtg3/t-se z3 gs(sse 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 rs3(gwes/ftzs3 s ,tg-oad was measured to be 0.60. Show that the driver of car A was exceeding the 55-mph (90km/h) speed limit before applying the brakes.    mi/h

A golf ball rolls off the top of a flight of concrete steps of total vertical h hc)snv44+m 4zr(ln1v crria*eight 4.00 m. The ball hits four times on the way down, each time striking the horizontal pzl*4cr hircvvnr4 m4a 1n(+s)art 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 1.40-kg block of wood at restw9d. :z,3+z eqviaz xbbd*.+pyu6hbi directly above it. If the bbeihy+96wq.zvbz: 3d b,pud +za*i .x ullet has a mass of 29.0 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 and becomes sksuzs,f 84 m2embedded 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 tok 2f s84,mszsu 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 rowr ecl/ za6n5 sngbe6 23wgg7w5boat 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. Hogbe255gw7znl6c 3s6 a/n gw rew 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 3wzx5beqvc:7 was 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 71 hrcvj /k h952q9qgc:vgvhctwo fragments by an explosion. One fragment acquires twice the kinetic energy of the other.v:c 9v/ j hqg1chr97hg k52vcq What is the ratio of their masses?   

  The force on a bulle 4ow.5iaxz3bot is given by the 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 massesrszgnw2 *(tlo*e60w h-kj .zh $m_A$ = 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 rad u+n4rpbexo en4:4 7kwioactively into an alpha particle and a smal 4e:+o7e4 k4npwbrnxu ler nucleus. 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) is fird18r4yhgij mc h (5ik5+vyf s8ed 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 slid yu;q t:df6ic)ba1rgh:c )1+l(bmhxxes 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(u 4ew fszcb,- on mass m if it is to rebound from M, slide up the incline, stop, slide down the incline, and collide withsez4bc uf-w, ( M again?    kg (Let A represent mass m, and B represent mass M.)

  The gravitational slingshot effect. Figure 7–47 shows the pykaadduuc df u:-9+fnpu () 01vm*lf )8k xee/lanet Saturn moving in the negative x direction at its orbital speed (with respect to the Sun) of 9.udk: )e8u*f ue+ ml/1fx-k faaddc0p)9( uvny6km/s The mass of Saturn is $5.69 \times10^{ 26}$kg A spacecraft with mass 825 kg approaches Saturn. When far from Saturn, it moves in the direction at 10.4km/s The gravitational attraction of Saturn (a conservative force) acting on the spacecraft causes it to swing around the planet (orbit shown as dashed line) and head off in the opposite direction. Estimate the final speed of the spacecraft after it is far enough away to be considered free of Saturn’s gravitational pull.    km/s