We claim that momentum is conserved, yet most moving objects eventually slow uj31 d;juiek(ovs5r ( down and stop. Explain3uvd5uo rj ((eksji; 1.

When a person jumps from a tree to the ground, what happe j+ti;zecp 3e. n*7om 8wapil8ns to the momentum of the ainwtj83+.p;7 om8 lpe ie zc*person upon striking the ground?

When you release an inflated but untied balli,l(x (hqjfo6 yj(u1foon, why does it fly across the room?l o qx1,f(jfihu ((j6y

It is said that in ancient times a rich man with a bag of gol v4t:zu+wukf2.;sw be d coins froze to death while stranded on a frozen lake. Because the ice was frictionless, he coulfw2u ;t uz.s4:kv+ewbd 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 f,s 1luv bu8o06nx6vzd ar out in space and is essentially in a v xonl6u 80,1ubzvvd6sacuum?

According to Eq. 7–5,uv) h1rqqai:d7 :1xrthp-v7 mmf1/iu the longer the impact time of an impulse, the smaller the 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 /t117iq1a:m dq-7 xf:p uh hvui)rv mrbags, 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 with4); 0wfizo 7vxv7djlqhz6/d sstand collisions. Today, though, cars are designed ; zhsw 4lq0xf/i z7od)jvv6d7to have “crumple zones” that collapse upon impact. What is the advantage of this new design?

Why can a batter hit a pitched baseball further than a ball tossed in the ; /m0 qjv-.ujw7-vvv unki p+cair by the batter?jw- vm0v j u;cqv+k ni-uv./p7

Is it possible for an object to r r: wihvc+2,bkeceive a larger impulse from a small force than from a, ibr:wc 2k+hv large force? Explain.

A light object and a heavy objectp +p 8.dx:cyng4*wxe56swf +/xa q8r ys1kuua have the same kinetic energy. Which has the grpxx s ydeas. pw 6+*aykrw1/4ngq8f 5cu:+8xueater momentum? Explain.

Describe a collision in which all kv:p-hwul ):i8op1x,1 va ad/ 5jkufnwinetic energy is lost.

At a hydroelectric power plant, wa9jawwrwqvep 3efe 7 (/*75jp*0zhsxbter 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 sto3 rq*we*50 vwa s7hpwe/9j7f(p ejbxz p, or so that the water rebounds?

A squash ball hits a wall at aeqrg:mzor: fm/gch:md0+h2 .(0i k md 45 $^{\circ} $ angle as shown in Fig. below. What is the direction (a) of the change in momentum of the ball, (b) of the force on the wall?

A Superball is dropped from a height h onto a hard steel plateh0 z7zrqqh:xzf1h6o 6 (fixed to the Earth), from which it rebounds at very nearly itsr 7h0qhz z:66o1h zqfx 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 of putty that falls and sticks to the steel plate.

Why do you tend to lean backward when carrying a heavy load in yous ) u.u0z/c,8tuha 9ggod+g44kpo g/ jlzta(vr arms?

Why is the CM of a 1-m lengt nv jhe+lbc*r:;r2s,sd7.ta ph of pipe at its mid-point, whereas this is not true for your bsc e2datrpvs7.*j:;h,l+ r narm or leg?

Show on a diagram how your CM shifts when yourtb:o 9 oi 3i+m)hws5l change from a lying position to a sitto lwo br 9:iihst5m)+3ing position.

If only an external force can change the momentum oxb/sp ;oie ;,nf the center of mass of an object, how can thn ep;,ox;/s ibe internal force of an engine accelerate a car?

A rocket following a paraht exz9vu-ottwmel63w j8*1 ; bolic path through the air suddenly explodes into many pieces. What38w-het9e;t xz ul*w1o6 tjm v can you say about the motion of this system of pieces?

  What is the magnitude of the momentum of a 28-g sparrow flying 9qg-i p* +ahrywed14 .cni: ul*vnq1y with a speed of $8.4 \; m/s$    $kg \; m/s$

  A constant friction force of 25 N acts on a 65-kg skier for 20 s. What isicu l v(0.3l cmvbm,(fk:rct1 the skier’s change in mk1vvr0c:,b f(tclm3.(c luivelocity?    m/s

  A 0.145-kg baseball pitched at 39 m/s is mu,oz4mepqb7ndpkj *)e 198uhit on a horizontal line drive straight back toward the pitcherp*duez pn kujomm, e4q)9b178 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 throujt9ob1) qgp+ovc pj ,iz/c()wow5 9vws a 6.40-kg package out horizontally with a speed of 10 m/s Fig. below Calculate the velocity of the boat immediately after, assuming it was initially at rest. The mass of the child is 26.0 kg,z9j)co,uo+copj5iv)t 9v1 gbp (w/qw and that of the boat is 45.0 kg. Ignore water resistance. The magnitude of the velocity of the boat is    m/s

  Calculate the force exerted on a rocket, given thg,0ql5udxs: uat the propelling gases are expelxugqs ,: 0d5luled at a rate of $1500 \; kg/s$ with a speed of $ 4\times10^{4 } \; m/s$ (at the moment of takeoff). F =    $\times 10^7 \; N$

  A 95-kg halfback mov/ukr35xn vwia;k khmsfn33;.od 1us* ing at $4.1 \; m/s$ on an apparent breakaway for a touchdown is tackled from behind. When he was tackled by an 85-kg cornerback running at $5.5 \; m/s$ in the same direction, what was their mutual speed immediately after the tackle?    $m/s$

  A 12,600-kg railroad car travels alone on alevel frictbtm 5/a6mnzr /;6 j0n:ufsmpjionless track with a constant speed of 18m/s A 5350-kg load,bjmrm/ts6:5ufna jnp;/6 m0 zinitially at rest, is dropped onto the car. What will be the car’s new speed?    m/s

  A 9300-kg boxcar tra55/bc)ji :fjglc 0gruveling at $15 \; m/s$ strikes a second boxcar at rest. The two stick together and move off with a speed of $6 \; m/s$ What is the mass of the second car?    $m/s$

  During a Chicago storm, winds can whip hor,s sezjiy*zus 8dl4zas *+ 3uv.k:7+q tlg:ifizontally at speeds of 100km/h If the air strikes a person at the rate of 40kg/s per square meter anft : *l3 *j4zl:s.i vs+ig8 k,u7uszq eyzad+sd 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 with a constant sp dqfhw09al9 +3kgqm.91 qqlvaeed of 8.6m/s on a level track. Snow begins to fall vertically and filkq 3vlaa l9 991g.+0qf hdmqqwls 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 kzr tn*m;qi tm50-0hmmoving at 420m/s emits an alpha particle in the direction of its velocity, and thetn ; rm-0*t5zmk h0qim remaining 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 ano8aw*d+q 1q tlax/pbd+t u4fp35y b.ud emerges cleanly at 170m/s If the block is stationary on a frictionless surface when hit, how fast does it move after the bullet em.845+x/t 3yalbp* 1oafwdqq +dtuub p erges?    m/s

  A 975-kg two-stage rocket is traveling at a speed ofs ax 5z2il)mc* $5.80\times10^3\mathrm{~m/s}$ 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 traveling in outer space wim- xax1: 6j4oyb/3 :icpiwpes v5dm2 ith a velocity of 115mi2p 6c5dajwo3e m1i-ispbxmv:x / y:4/s 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 0.045 kg is hit off the tee at a speed of 45m/s Thei6o3 ,cdmk uginry:8 put23 o; golf club was in contact with ;d 8 uo,oyncp2 kuimrigt3:36 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 v,4p3 tt.:dccsr :m pjaelocity of 8.5m/s and comes to rest in a timt,ac4d 3pjcrs::m p.te interval of 8.0 ms. (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 wavd2hc4 3c9j bb/e wje/+po hiar:b5o+ll 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 a7v/8ls s mbx;of the crashworthiness of new automobile modelsxabm/ svs8l 7;. Cars are tested by smashing them into fixed, massive barriers at 50km/h (30 mph). A new model of mass 1500 kg takes 0.15 s from the time of impact until it is brought to rest. (a) Calculate the average force exerted on the car by the 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 0.75 s by a hj4.p; t2(5os)fd(ze ttwruvbert(jzfb.5tpvo(e4;sdu2 ) wt ad-on tackle by a tackler running due west. Calculate
(a) the original momentum of the fullback    kg*m/s
(b) the impulse exerted on the fullback    kg*m/s
(c) the impulse exerted on the tackler,    kg*m/s
(d) the average force exerted on the tackler.    N

  Suppose the force acting on a tennis ball (mass 0.060 kg) points in the +x di)ikqkspdm z e+o)s + cl+azih (q7m8+nqh2a67rection and is given by the graph of Fig. 7–33 as a functio2p+8nm+ssah) oz d6 c)l(7kiq + +qaekzi hqm7n 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 breakingze*:bky 2j/wc iog v9+ 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) ei/gz9wkyb*v+j : 2coof 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 h d .2pnp4ks.;oi4smpb ead-on with a 0.220-kg ball at rest. If the collision is perfectly elastic, what will be d.mi2 p4o;kppssbn .4the 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, m p)*f*. u4cwtd wxzi4toving east with a speed of 3m/s has a head-on collision with a 0.900-kg puck initially at rest. Assuming a perfectly elastic collis4 c*twtp 4fxw.idu* z)ion, 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 per dymc0zz5xer 02ri1p* fectly 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 1zc rx*y5d me20 pizr0at 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 spebw dt-7od65q fed of 2.5m/s collides head-on with a 0.090-kg ball initially moving away from it at a spee67odq5tb f-wdd 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 speed of 8.5m/s colliaohrqoi;(hgd7pqmsr m r0a8 2b0 n/0 4des head-on and elastically with another ball initially at rest. After r2os4oar q /ng0dr0p7( hh;imb0 8qamward the incoming softball bounces backward with a speed of 3.7m/s Calculate
(a) the velocity of the target ball after the collision    m/s
(b) the mass of the target ball.    kg
(Let A represent the moving softball, and let B represent the ball initially at rest.)

  Two bumper cars in an amusement park ride2/yoi7--j6pqrqxa, w je ag*p 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 to differences in passenger mass. If car A a7/-p,*qx6ioewg 2- jq paryajpproaches 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 collision with ie:r t3x coo:8a second ball initially at rest. The second ball moves off with half the original speed of t xtco r::3e8oihe first ball.
(a) What is the mass of the second ball?    kg
(b) What fraction of the original kinetic energy $(\Delta\mathrm{kE/KE})$ gets transferred to the second ball?   

  In a physics lab, a cube slides down a frictionless incline as shown in Fig. 7– y.txtnnkh 9sowq*96 735, and elastically strikes another cube at the bottom that is only one-half its mass. If the incline is n*s9h t owktq.x 79y6n30 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 myx)qv+i4 hz/;g4gt s+t3k hj hass 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 expdb ec56e4y2e ;/lpr7ur )svekeriment, projectile 1 results in a maximum height h of the pendulum equal to 2.6 cm. A second projectile causes the the pendulum tok vsd e 4 2;euecyrb/)75lrep6 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 j2cf dq 7mt0+yhanging on a 2.8-m-long string, which makes the pendulum swing upward in an arc. Determine the vertical and horizont fmty+ c2q70djal components of the pendulum’s displacement.vertical$\approx$    m horizontal =    m

(a) Derive a formula for the fraction of kinetic mr f6jeuuz/i0d y0ri6a/6 os;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, itn05sm/4 wt- mhmrogd(j53khnitially 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 them 0hg k-dj5rt(hn/stwm34 mo5 lighter particle. ) KE'$_A$ =    J KE$_B$ =    J

  A 920-kg sports car collides into the rear end of a 2300-kg SUV stopped qi r e19w(3gfyd;pl d0at a red light. The bumpers lock, the brakes are locked, and the two cars skid forward 2.8 m before stopping. The police officer, knowing that the coefficient of kinetic friction between tires and road is 0.80, calculates the speed of the sports car at impact. What was that speed?(Let A represent the sports car, and Bl qddy9e gi0fp(1;wr3 represent the SUV) $\approx$    m/s

  A ball is dropped from a height of 1.50 m and rebounds to3d n oae-eh)i(45mslr apr(d( a height of 1.20 m. Approximately how many rebounds will the ball make before l r 53(hmi r4-eae(sl(d )pndaoosing 90% of its energy?   

A measure of inelasticity in a head-on collisio.kh()pjrz8 -.vwi ka bn of two objects is the coefficiep..zvjirbkw(8k - a) hnt of 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 times the mass of the oth3 gb2x 6tuwpf9c hz8h6er. A depression ichtb 69uxp zhgwf 8236s made in both faces of the cut, so that a firecracker can be placed in it with the block reassembled. The reassembled block is set on a rough-surfaced table, and the fuse is lit. When the firecracker explodes, the two blocks separate and slide apart. What is the ratio of 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-opsh, o8 (t;-70ips 58 kapyexbp x2.u4p smbwsn with a 10.0-kg object moving in the -x direction at 4mm.,(4u 0px8pwp8kxytb ph2bsi 7se-p ;aos s5 /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 cce+j ;zk:kmbcev(-xm 4 7 *fbrest decays into a second nucleus, an electron, and a neutrino. The electron a;mcjcecb k* f7+v(x:4z mk eb-nd neutrino 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 mjh(fgw78fk 3lh)cj- aq7d ) vjcb2w:c ass $m_\mathrm{A}=0.400$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 ben a+s 8a.c- zpxx/uh8btween 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 uhn8-ax.zx/bs cpa8 + directions?    $^{\circ} $

  Two billiard balls of equal mass move at right angles andeeq(+ b/w skv9 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 sew 9 b/+kv(qethe 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 perfecti,6 c5hh-iq agly elastic collision with another atom at rest. After t,a6ii cgqh -h5he impact, the neon atom travels away at a 55.6 $^{\circ} $ angle from its original direction and the unknown atom travels away at a -50 $^{\circ} $ angle. What is the mass (in u) of the unknown atom? [Hint: You can use the law of sines.](Let A represent the incoming neon atom, and B represent the target atom) $m_B$   u

  A neon atom (m=20u) nwx9x l,++pd)v pdvb 0makes a perfectly elastic collision with another atom at rest. After the impact, the neon a+d0wxd ,v +l)pbvp9n xtom 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 the6n7tz.(bb, m4sni bm8 vbvr; k three-mass system shown in Fig. 7–38. Specify relative to the left-hand 1.00-kg ibvb7 bk m.zrs,v 6(tm84bnn; mass.    m

  The distance between a cqiqm21odvz,9c9gwn /wk6c9u 6 j:mlv arbon atom ($m_{\mathrm{C}}=12\mathrm{u}$) and an oxygen atom ($m_{\mathrm{O}}=16\mathrm{u}$) in the CO molecule is $1.13\times10^{-10}$m How far from the carbon atom is the center of mass of the molecule?    $\times10^{-11}$m

  The CM of an empty 1050-kg car is 2.50 m behind /nav5epniq;zcg 2m :; 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 of 70.0 kn2n;5ci/ q z mep:a;vgg.    m

  A square uniform raft, 18 m by 18 m, of mass 6800 kg,a-p1 yqk+j6pins wp 5)u0 )vna is used as a ferryboat. If three cars, each of mass 1200 kg, occns5k1nyp6aj0p aiw) q -pv) u+upy its NE, SE, and SW corners, determine the CM of the loaded ferryboat.$X_{CM}$ =    m $Y_{CM}$ =    m

  Three cubes, of sides +hou ,w1kdoo.;pettvw 8cp :m),tp52/nrlr k $l_0$,$2l_0$, 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 caseolqrd .2rfovhc8t - 0.s of tomato paste (see Fig. 7–40), each of which is a cube of length l. Find the center of gravity in th2 0- hqt8dr.l r.coofve 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 circular hole of radius R cu ice4klnvk4-*al + lx3z x0xd(t out of it. The center of the smaller 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 s0xxl+ kll *c xadv k3e4-(i4znubtraction.]   R

  Assume that your proportions are the rh399 7 2 df6gjr2ekihrt(hl3js(s aisame as those in Table 7–1, and calculate the mass of one of yorde639(i7h3ah ir j gtk9hl22jrs(f sur legs.    kg

  Determine the CM of an outstretcbn/s g25na+vu5 b/(smaq vt8ohed 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 posixj8u/ 5eb bd58xk0kjbtion of the CM of an arm bent at a right angle. Assume that the person is k5b 80j5xxk ub /b8ejd155 cm tall. $X_{CM}$ =    cm $Y_{CM}$ =    cm

When a high jumper is in a position such that his arms and legs ar8 we3o)wbuw(y vc bz2:e hanging vertically, and his trunk and head are horizontal, calculate how far below the torse3 wb2wuyv cw(zb )8:oo’s median line the CM will be. Will this CM be outside the body? Use Table 7–1.

The masses of the Earth and Moon a525 / jbv ,frcgo/vhfhre $5.98\times10^{24}$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 friction ood3+k5 m1ztf3h m1utless 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 cylindrical head of mass 2.00 kg andq:i: u)/bn,i 1ptaa ddy2w c/:efd.4 rgbae1y 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 theip2bd:1a. ec,/r at )g /qb:du y4in:ydwa1fe handle is the point that will follow a parabolic trajectory?    cm

  A mallet consists of a uniform cylindri*0* wgzckbqe. ,z qpy,cal head of mass 2.00 kg and a diameter 0**p,0zbg .keqqz cw,y.0800 m mounted on a uniform cylindrical handle of mass 0.500 kg and length 0.240 m, as shown in Fig. 7–42. If this mallet is tossed, spinning, into the air, how far above the bottom of the handle is the point that will follow a parabolic trajectory?    d    d

  (a) Suppose that in Examp,7 crow0c))nkq ga0 +t fgiqe4le 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 inc/f,nkth,o d5i yt*v2 the air and stationary with respect to the ground. A passenger, of mass m, then climbs ou,hi*tfn5, t/do2ckv y t 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 stops?

  An 0.145-kg baseball pitched horizontally at strikes a bat k dsfa 0aai342and is popped straight up to a height of 55.6 m. If thef34akad sai02 contact time is 1.4 ms, calculate the average force on the ball during the contact.    $^{\circ} $

  A rocket of mass m traveling wil*ckfzr: 9grnrm h6 m,o.2ij1th 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 witi9 coh/y vv tkto;ot+ o67f2n/h the corner pocket shot shown in Fig. 7–43. Relative dimensions are also shown. Should the player be worried aboutn//iv+ 2tok; ft7o9yv6c ooht 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+s dllt.g8 lbsssz9s9*1f zy5 a speed of 2.5m/s by pushing off with his legs f1l + lls dgfzby.ss8t *5ss99zrom 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 m igu+xti)7kb2: 5myu fass 60 kg and the other 80 kg, are initially at rest in outer space. They then push each other apart. How far au: ki+ b275xfg)u ytimpart 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 (a)-ay,,px gda w0- -dojfbp*pjt rest) and rebounds in the opposite direction with a speed equal to onej)yg,-fpa ajd*pb,w o p0x-d--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 vnt7b 3t1/jzr jm7w-hexpert witness in a court case involving an automobile accident. The accident involved car A of mass 1900 kg which crashed into stationary car B of mass 11007v7/1b3 r ntwhjz m-tj 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 owa*8hd ye j8k0tgxm3f l8 9rr+f 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 collisions are perfectly elastr3aw9 +8exj 8y0t kd fgmhr8l*ic, 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-zni absjb -lq( a2u n8c:c:; aag*i9nie +j6n+kg 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 bulletcab:ageb*9qnl i-asnzu ;(ia+6jn8 2cjni+ : becomes embedded in it?    m

  A 25-g bullet strikes and becomes embedded in a 1.35-kg block of wood p;t: 4bt7h.3iuc uvrbolaced on a horizontal surface just in front of the gun. If the coefficient of kinetic friction between the block and the surfacuh i4:;.v c b37trboute 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 ofvf2:3qk wbcufg2*irld d +h.+ mass 60 kg, 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 b 3:wdr kf+2dbfvc+hi* 2 guql.oat 3.2 m apart from each other, now exchange seats. How far and in what direction will the boat move? The boat will move    towards the initial position of the 75 kg person(Round to two decimal places)

  A meteor whose mass was a1nue 617p pgbvbout $ 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 a6e bf4up-qbjz2l/vuf7 ofm *0part into two fragments by an explosion. One fragment acquires twice the kinetic energy of the other. What ise6vo4 2jub f07/ u fpfmq-zb*l the ratio of their masses?   

  The force on a bullet is given by tu nz1 *rqr-wj1/gruj/he 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 +6g4 icroar: q$m_A$ = 40g and $m_B$ = 60g are suspended as shown in Fig. 7–44. The lighter ball is pulled away to a 60$^{\circ} $ angle with the vertical and released.
(a) What is the velocity of the lighter ball before impact?$\approx$    m/s
(b) What is the velocity of each ball after the elastic collision?v'$_A$ $\approx$    m/s v'$_B$ $\approx$    m/s(Round to two decimal places)
(c) What will be the maximum height of each ball after the elastic collision?    m

  An atomic nucleus at rest decays radioactively into an alpha part*e( (oqhgqq ;ficle and a smaller nucleus. What will be thee hq*(qoqgf (; 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 fired at ex9w wf a/ (ah8m-iu:fan 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 30 b98vygwyj-(z.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 rebouf2,r4a-r,kdduo)r9 y i +zvb qnd from M, a)r2rzd4q +ork 9iv,-f,duyb slide up the incline, stop, slide down the incline, and collide with M again?    kg (Let A represent mass m, and B represent mass M.)

  The gravitational slingshot effect. cqp7cqo/gd5w (ap )7 oFigure 7–47 shows the planet Saturn moving in the negative x direction at its orbital speed (with respect to the Su 7o75g( wqdp)cp/c aoqn) of 9.6km/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