We claim that momentum is conserved, yet most moving objects eventualjv.,qw.q,sxbee ;8 vply slow down .w 8s,e,vvb j; eqxqp.and stop. Explain.

When a person jumps from a tree to the ground, what qkti 5e/v4an)zh +v3 2g l:/taef wzj8happens to the momentum of the person upon striking the gzvvk5/haa:2+3lj/fe)8qtg e w4n itz round?

When you release an inflated but untied ballp:jjpwsj6.qq7 oc/y3jbn+e;q ;x 4daoon, why does it fly across the room? ;3qnp6jyqjj p;e7ca.x:db+ws 4/ qoj

It is said that in ancient times a rich man with (soy1jq3lj.7sf8p ,-b*vn r ft;l ovb a bag of gold coins froze to death while stranded on a frozen lake. Because the ice was frictionless, he could not push himself to shore. What could he have dnvo18ysbjj bo3;l-q t.(rv, 7*pffs lone to save himself had he not been so miserly?

How can a rocket change directio7era8+wu 9qan n when it is far out in space and is essentially in a vacuunu8ae79r+ waq m?

According to Eq. 7–5, the longer the impact time of an impulse, the smallyz09ggwion8 p+,q 9p;tr/n4zyfo wo4er 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 bags, which are intended to inflate during an automobile collision and reduce the possibility of fracture or deafpwn q rzz+i9;y04w4o98 /po ,tyg gnoth.

Cars used to be built as d wfib2+h/f,6hcaa)j;r2m.uw/ v djs rigid as possible to withstand collisions. Today, though, cars are designed to have “crumple zones” that collapse upon impact. What ihu2a ff.+i w h;ad/ )cmd2w,s/jv r6jbs the advantage of this new design?

Why can a batter hit a pitched baseball further than a bali,irrk yz -w 88txrrhamd(s/b.d h)/ ky e)v)6l tossed in the air by r)6e/w8hvk, krst ayi) mi/hdbx.(z8dyr) r-the batter?

Is it possible for an object ; auahf/.ujjfs/ ,x5 vto receive a larger impulse from a small force than s fvjuxf;a/, a.uh 5/jfrom a large force? Explain.

A light object and a heavy object have the same c(h ;ictznrxr:()a0znico . 8kinetic energy. Which has the greater momentum? Exp(o0 zh:nc;i rx(crtac )8.zi nlain.

Describe a collisionch*hcw;ghlbx/a 667j7s;r o d in which all kinetic energy is lost.

At a hydroelectric power plant, water is directed at high speed agap4i2(qfom3 k oinst 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 stmqo4 ko(f2pi3 op, or so that the water rebounds?

A squash ball hits a wall at a 45 hwnjb45qw- ;qhrxsu z/-; r/u$^{\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 plate (v8qu*7dfo7 hwfixed 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 the7d uo* 8fwvh7q 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 lufe5/ /z(qh(idbf h+yean backward when carrying a heavy load in your arms?

Why is the CM of a 1-m length of pipe at itsqh73 2hhvx.rn mid-point, whereas this is not true for your arm .n rh37vq2hxh or leg?

Show on a diagram how your CM shifts when you change from a lyino:qe-.yl/lv pi-)gb x-oi 8jng position to a sitting positiono-.n-byoijx:qp ) /8gi elv-l.

If only an external force can change the momentum of the center of mai+d f xa;)d7gx9 8okqd),o nupss of an object, how can the internal force o )gpu7d+okdq,8and)xo x ;f i9f an engine accelerate a car?

A rocket following a parabolic path through the air t67; /kj1s0gtrt ycwa suddenly explodes into many pieces. What can you say about 6/ 1t7rcg sttk;jya0 wthe motion of this system of pieces?

  What is the magnitude 63nlcp0n acc4*z ih7f of the momentum of a 28-g sparrow flying with a speed of $8.4 \; m/s$    $kg \; m/s$

  A constant friction force of exthn1n14 *epow9,h0m9; q p yvqsc6v 25 N acts on a 65-kg skier for 20 s. What is the skier’s changeyvhv1sp* emn htqn;x9wc1q 9e06 ,po4 in velocity?    m/s

  A 0.145-kg baseball pitched at 39 m/s is hit on a horiz8*huw;5)ffbrxqw q on 4 j-ff+l1mvo7ontal line drive straight back toward the 1wqx )fq;f5f rnom bwo4u v-8h7l+f j*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 6.40-kg packagj5llx0,l ad1 ze 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, and that of the boat is 45.0 kg. Ignore water resistance. j lzld,lx5a10 The magnitude of the velocity of the boat is    m/s

  Calculate the force exerted on a rocketn/yv* qaop1/o , given that the propelling gases are expelledo aq n//*y1vop 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 moving at yolg)o( xof8 -4mr 0geqcl1.jq(.a ij $4.1 \; m/s$ 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 frictionless track wit ptl1v h2pl;2 )zudsbs*2ok.th a constd tuhl*)klt v22oszpb1.2s; pant 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 2tcbmqd/7q6h2cf:qw h , r j/t$15 \; m/s$ 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 horizontally ad 4v(w1rfxe3srqvmsks,h av-1 yv 63b 2(.alht speeds of 100km/h If the air strikes a person at the rate of 40kg/s per square meter and is brousva4xq r -yv3(6lawrfvhke, (hd1s1.s m2v b3 ght 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 railro,l5 ta y*t1uvoad car coasts along with a constant speed of 8.6m/s on a level track. Snow begins to fall vertically and fills the car at a rate of 3.5kg/min Ignorin,uv5toy*1a tl g 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 aa(iw8zy ) ufux,+9 latn alpha particle in the direction of its velocity, and the remaining nucleus slows to 350m/s I auyfa)i +( utzw98,lxf 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 travelay4ty ifx:z je*t zb*0q943jsing 230m/s penetrates a 2.0-kg block of wood and emerges cleanly at 170m/s If the block is stationary on a frictionless surfacj yx t 4jz :tiab*sf04y9*3qeze when hit, how fast does it move after the bullet emerges?    m/s

  A 975-kg two-stage rocket is traveling a.4ioedr w.d8ek d06)vu mqb abb5s6;t t 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 traveling in outer spav nt r3(o)tz j3fhp8*2q8urpf ce with a velocity of 115m/* trqrj8n3zt p 8uo(fphfv)32s 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-o+nr-3q8p)dk mynqd of 45m/s The golf club was in contact with the dr-o8+ mk -pdqqn)3 ynball 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 .vgcr,u ) *rrj0c7na ynail at a velocity of 8.5m/s and comes to rest in a time interval of 8.0 ms. (a) What7n ,ra ur.jgcc )v0*ry 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 xssx2v f8 klw7qsnmx( c-m6qcl f3o1d::l9q3v=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 crashworthiness of new cjo+w)3: hdwet jf( 6cautomobile models. Cars are tested by smashing them into fixed, massive barriers at 50km/h (30 mp j3wfd(:+ h6cwo)ectjh). 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 bydvr0 :1fclo8 b(llep; a head-on tackl1vrbfelco; 0l 8:d p(le 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 yy og a;,v)mdc:f8)zkthe +x direction and is given by the graph of Fig. 7–33 as a function of time. Use graphical methods to estimateyadm)f8ky o)zvc g,:;
(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 lowerz9c 6len8a aq-gbb0nxwg; ;b3 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 (thaz;anbbn36cglbe 0 98q- xg;wat 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 directiol+y )i ,nue. yg 0sm-/lxk/)n t.cydlrn) with a speed of collides head-on with a 0y)0 ykglnysr. xt/, nm.)l /u-id cle+.220-kg ball at rest. If the collision is perfectly elastic, what will be the speed and direction of each ball after the collision?Let A represent the 0.440-kg ball, and B represent the 0.220-kg ball. $v'_A$    m/s  ----待选择----eastwest  $v'_B$    m/s  ----待选择----eastwest 

  A 0.450-kg ice puck, moving east with a speed of 3hcv+ 8pqz/x5l m/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 represe85 /pl hvxz+cqnt 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 us )zl y ld;bo(a1(;hvqndergo a perfectly elastic head-on collision. If one ball’s initial speed was 2m/s and the la1 ;sv ()bdz(qhy; olother’s was 3m/s in the opposite direction, what will be their speeds after the collision?(Let A represent the ball moving at 2.00 m/s, and call that direction the positive direction.Let B represent the ball moving at 3.00 m/s in the opposite direction. ) v'$_A$ =    m/s v'$_B$ =    m/s

  A 0.060-kg tennis ball, moving with a speed d*dhi, z/b gd qz0-4zmof 2.5m/s collides head-on with a 0.090-kg ball initially moving away from it at a speed of 1.15*zq z z,4mhdb di-d/0gm/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 0.2tgo ;v7.4zd fv8qza;t20 kg that is moving with a speed of 8.5m/s collides head-on and elastically with anothedv8oq 7;;fgvt 4za.tzr 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 amuseme 4m4wwguwii(**l b4hzn(ucnv+ obxf;9 tv * l7nt park ride collide elastically as one approaches the other directly from the rear (Fig. 7–34). Car A has a mass o n nvufti9gwm* ix;4b(w* + o*bvu4hwlc4z(l7f 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 makes an elastic head-on collision witha0nu7u e5i9ne a second ball initially at rest. The second ball moves off with half the original speed of tun0i 5e7e anu9he 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 fpwsgy7lo7 ws*k 8 xmy;*h3; mrrictionless incline as shown in Fig. 7–35, and elastically strikes another cube at the bottom that ispshw3 ;l8wgr*7kmx; y*myso 7 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 mal )3tpw -;gpcgss 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)n uyy99bld 0h experiment, projectile 1 results in a maximum height h of the pendulum equal to 2.6 cm. A second projec9yl hyunb9)0 dtile 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 travotqw-coo:w-gi9kv f6 mbv*00 eling 230m/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 the vertiow:w09q -bm- o ftv0gk6*vioccal and horizontal components of the pendulum’s displacement.vertical$\approx$    m horizontal =    m

(a) Derive a formula for the frac.px;p nh: wcu m),m0sm5a zcvp4* it5stion 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, in4,bgns e3es 4d *lpob9to 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 l*l e4sd ns4pgo9 3,bbeighter particle. ) KE'$_A$ =    J KE$_B$ =    J

  A 920-kg sports car collides into the rear end of a 2300-kg SUV so sva//yrr0 j7topped 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 impact0/ajyrv/ o7rs . What was that speed?(Let A represent the sports car, and B represent the SUV) $\approx$    m/s

  A ball is dropped from a height of 1.50 m andpy ml,,mkn fzme0agpfg5)+h( nfu 694 rebounds to a height of 1.20 m. Approximately n zgm0 h)ffe,pmapmf(k 5 6,4ylng9u+how many rebounds will the ball make before losing 90% of its energy?   

A measure of inelasticity in a head-on c oc5:bbg3 5t *zbl4 vjblnwf,3ollision of two objects is the coefficient3 5oj:gb5bclv3tbnz *l fb4,w 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 pcq8)+lm8gmu3nv c(mof 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 the ratio of distances each block tp8m)38gu lmvq+n cmc (ravels? ----待选择----1/91/101/81/6 

  A 15.0-kg object moving in the +x direction at 5.dv) mw)j88 cx ny2ok9 mbpr5-n5m/s collides head-on with a 10.0-kg object moving in thcnx8-)mndkr 8v b wo9p25)y jme -x direction at 4m/s Find the final velocity of each mass if:
(a) the objects stick together;   m/s
(b) the collision is elastic; v'$_A$ =    m/s v'$_B$ =    m/s
(c) the 15.0-kg object is at rest after the collision;   m/s ----待选择----not reasonable reasonable 
(d) the 10.0-kg object is at rest after the collision;   m/s ----待选择----not reasonable reasonable 
(e) the 15.0-kg object has a velocity of 4m/s in the -x direction after the collision. .   m/s ----待选择----not reasonable reasonable 
Are the results in (c), (d), and (e) “reasonable”? Explain
( Let A represent the 15.0-kg object, and let B represent the 10.0-kg object.)

  A radioactive nucleus at rest decays)o xvuc h)gpi6pkg p19 f:s-o9 into a second nucleus, an electron, and a neutrino. The electron and neutrino are emitted at 9ug-g)1f o:6xvppi9)k poshcright 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 mas)aki1(.rak 0:c .wzhd6hryde s $m_\mathrm{A}=0.400$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 m/oo.w bo,b-yd*u t og-ass, each having initial speed the two mod- obo-w,.*yuotg b o/ve off together with speed v/3 What was the angle between their initial directions?    $^{\circ} $

  Two billiard balls of equal mass move at reucs azssh83(4w lo;99p pr 2jight 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 balh a(jszp;e o8 ucsp2 r3ws499ll 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 collision with another apr1z -vkic+d9anm (.ntom at rest. After the impact, the neon atom tk-1.avi ( cmdr+9 nnpzravels 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 perfe ; o92ghegdtxk*f) jp9ctly elastic collision with another atom at rest. After the ieh)g g9tj92d;pk*foxmpact, 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 mas):mhfz)( hx c)zj e-rms of the three-mass system shown in Fig. 7–38. Specify relative to the left-hand 1.00-) fjchh()xez z-: )rmmkg mass.    m

  The distance between a carbon 1/3mm9cflv51w-ejcehpx 9k8eat0k;t u c n p5atom ($m_{\mathrm{C}}=12\mathrm{u}$) 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:g+z 9 o8egix rrzh36o 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 szzeohri:68r 9x+gog 3 eat 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 18 m, ot-fo fd9lq/7pzg h8 o0f 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 ferryboato-gltpo9h f0z 8/fqd7.$X_{CM}$ =    m $Y_{CM}$ =    m

  Three cubes, of sidesusny7q;, 4n 5d s4 frinxi09iy $l_0$,$2l_0$, 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 lj g- -lsu(8p4 htquwq4oad of identical cases of tomato paste (see Fig. 7–40), each of which is a cube of length l. Find the center of gravity in the horizontal plane, so that the crane operator h4qs(tu4 u8q- jl-pgw can pick up the load without tipping it.$X_{CM}$ =    l $Y_{CM}$ =    l

  A uniform circular plate of radius 2ft 8x7 qdw+a2rij ob(c+ne-5 f x/p)tkR has a circular hole of radius R cut 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? [Hi/bc)x8ixna f (rpq5 w7-t2k to +d+jfent: Try subtraction.]   R

  Assume that your proportions +m*n pdc*jm7zh )5pwchl)+ k oare the same as those in Table 7–1, and calculate the mass of one of your leg7jm*ho +n *l5phd wzpmc)k +)cs.    kg

  Determine the CM of an outstreto8goss+cr:er+spj; h ab m61: ched arm using Table 7–1.   % of the person's height along the line from the shoulder to the hand

  Use Table 7–1 to calculate the position of the CM of an arm bent at a3tt he0zlajh 5.q0 px;q9slr, right angle. Assume that the per jp3,9 q5;ls 0aeq.xtrht0lzhson is 155 cm tall. $X_{CM}$ =    cm $Y_{CM}$ =    cm

When a high jumper is in a position such that his arms and legs vd5x:7df b c 9e4l8opiare hanging vertically, and his trunk and head are horizontal, calculate how far belo 5o d97xdvc8:bi f4pelw the torso’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 are ict 1,:6vrh8do2s ye h$5.98\times10^{24}$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 st8,olg jpzqz 6u(9k ,zpand 10.0 m apart on frictionless ice.
(a) How far from the woman is their CM?    m from the woman
(b) If each holds one end of a rope, and the man pulls on the rope so that he moves 2.5 m, how far from the woman will he be now?    m
(c) How far will the man have moved when he collides with the woman? He has moved    m from his original position

  A mallet consists of a uniform cylindrical head of mass 2.00 kg an-) hv/t uzv4omd a diameter 0.0800 m mounted on a uniform cylindrical handle of mass 0.500 kg and length 0.240 m, as shown in Fig. 7–42. If this mallet is tossed, spinning, into the air, how far above the bottom of the handle is the point that will m)u4h -z/v tvofollow a parabolic trajectory?    cm

  A mallet consists of a uniform cylihormwn4v6, jgd/ 9zw+ndrical head of mass 2.00 kg and a diameter 0.0800 m mounted on a uniform cylindrical handle of mw9h+4 g /o v,6dwjrmznass 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 Example 7–14 (Fig. 7–29), .g rd/0j.puf7mz xx e*$m_{II}$=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 and0l oiw(ktlo67x :jqd/ its gondola, of mass M, are in the air and stationary with respect to the ground. A passenger, of mass m, then climbs out and slides down a rope with speed measured with respect to the balloon. With what speed and direction (relative to Earth) does the balloon then td :0xk(iqoj ol7w/l6 move? What happens if the passenger stops?

  An 0.145-kg baseball pitched horizontally at strikes a*0r wxxp7ws0/cvryu3yc.:gnr td 85c bat and is popped straight up to a height of*x:yvy5twcn80 csdr7wr uc px g3./0r 55.6 m. If the contact time is 1.4 ms, calculate the average force on the ball during the contact.    $^{\circ} $

  A rocket of mass m travelqvm4dmx -/c67/hyb jl ,8foof ing 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 5cr nw3fj(q dr q,*t/rcorner pocket shot shown in Fig. 7–43. Relative dimensions are also shown. Should the player be worried about this being a “scratcrd35jqtwq /nc ( f*rr,h shot,” in which the cue ball will also fall into a pocket? Give details.

  A 140-kg astronaut (including space suit) acqui mi ji80a/n 2r04xrluores a speed of 2.5m/s by pushing off with his legs from an 1800-kg spac0x2u4ra /j8lm 0 nioire 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 oecq;33 4xlakf.hjk94nyf eh 4ther 80 kg, are initially at rest in f3kx e4.jqhkhl4 4y9 ne fac;3outer space. They then push each other apart. How far apart are they when the lighter astronaut has moved 12 m?    m

  A ball of mass m makes a head-on elastic collision with a u ;o9 v8qq6efgsecond 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 sec gv8oq;u 6fqe9ond ball? $m_B$ =    $m_A$(Round to two decimal places)

  You have been hired as an expert witness in a court case involving u4prr08 t3;m r (bfnfhan automobile accident. The accident involved car A of mass 1900 kg wh0buf8 4p;ftm3rhnr( rich crashed into stationary car B of mass 1100 kg. The driver of car A applied his brakes 15 m before he crashed into car B. After the collision, car A slid 18 m while car B slid 30 m. The coefficient of kinetic friction between the locked wheels and the road was measured to be 0.60. Show that the driver of car A was exceeding the 55-mph (90km/h) speed limit before applying the brakes.    mi/h

A golf ball rolls off the top ofet.s,-w7f f)j ory8vu 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. I)osuet 8f.7- wjvr yf,f 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 rest directly +0yw m 8l9 f xb) p u:s,zr/7nl/uncdi9srji0kabove it. If the bullet has a mass of 29.0 g and a speed of 510m/s hop), 7njr+lisx9/nmyz b009u8fw scur d k/l:i w high will the block rise after the bullet becomes embedded in it?    m

  A 25-g bullet strikes and becomes embedded in a 1.35-kg block of woo :syf6wl2wn mt7ih f.1d 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 1y:fs7l2m t6iwhw.nfblock 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 rowboatj3l b;60bz+s9po poj 9xog5 sx of mass 80 kg. With the boat initially at rest, the two people, who have been sitting at opposite oljz o 9+p;s gx69 bos0x5bj3pends of the boat 3.2 m apart from each other, now exchange seats. How far and in what direction will the boat move? The boat will move    towards the initial position of the 75 kg person(Round to two decimal places)

  A meteor whose mass w05 k4heup*syaas about $ 1\times10^{ 8}$kg struck the Earth ($m_E$=$6 \times10^{ 24}$kg) with a speed of about 15km/s and came to rest in the Earth.
(a) What was the Earth’s recoil speed?    $ \times10^{-13 }$m/s
(b) What fraction of the meteor’s kinetic energy was transformed to kinetic energy of the Earth?    $ \times10^{ -17}$
(c) By how much did the Earth’s kinetic energy change as a result of this collision?    J

  An object at rest is suddenly broken apart into two fragment+aj :p rnc:k t6 w0qj/)dno,qhs by an explosion. One fragment a kaw+0/j th), nnpq::o 6qrcjdcquires twice the kinetic energy of the other. What is the ratio of their masses?   

  The force on a bullet is given by the formula F = 58 ormb397m5 3jcpncq3l0-( $1.8 \times10^{ 5}$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 .p.aaots)qp; m (ve r*k ss0*-vlg+uy$m_A$ = 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 radioactq/j+pr nk5zl2bx)p trun -f6-ively into an alpha particle and a smaller nucleus. What will be the speed of this recoiling nucleus if the speed of +tk-5plrnn/ 6 - pxrqbj2fu) zthe 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) qwj:/ ci93vzcis fired at an angle of 30 $^{\circ} $ to the horizon with a speed of 25m/s (Fig. 7–45). When it reaches the maximum height, it is hit from below by a 15-g pellet traveling vertically upward at a speed of 200m/s The pellet is embedded in the skeet.
(a) How much higher did the skeet go up?    m
(b) How much extra distance, $\Delta{x}$ does the skeet travel because of the collision? $\approx$   

  A block of mass m=2.2kg slides down a 30.0 d+.t16mol8zfp-kym 5de dbb/ $^{\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 uppb l3pff;ht-3ter limit on mass m if it is to rebound from M, slide up the incline, stop, slide down f h-;f3tlpb3tthe 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 the planet Saty+ rkspap)tqh;3 /e4r urn moving in the negative x direction at its orbital speed (with respect to the Sun) of 9.6km/s The mass +k yqh)st3rp4aep;r / 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