We claim that momentum is conserved, yet most moving objects eventualljk yhl 4lld1/(y slow down and sty1ljdl (h /4klop. Explain.

When a person jumps from a tree to the ground, what happens to the momentum oflaq/0tg ekb2 tp gf7+c2dx;3h3ogkp 4 the person upon striking tpttgog ; kgp27fb3d2 4hx3lea/qc k+0he ground?

When you release an inflated but untied balloon,qge i-vn9rvj p;li 36hzdxw;9sf6u25 why does it fly across the room 26rz;u vx i;9fd9-qg56swiel3npvj h?

It is said that in ancient times a rich man with a bag of gold coins froze to de dzw. h,/4k es.rxvuj+ath while stranded on a frozen lake. Because the ice was frictionless, he could not push himself to shore. What could he ha.e.x4kz u/v,sr jh+dwve done to save himself had he not been so miserly?

How can a rocket change direction when it is qxci(9orl9 r 9far out in space and is essentially in a vacul rx9 o99r(icqum?

According to Eq. 7–5, the longer the impact tgvq dq trtk; 4 ot6j+on(52og/ime 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 bags, which are intended to inflate during an automobile collision and reduce the possibility42oq6tt g+(o/qgrvkto ; 5jnd of fracture or death.

Cars used to be built as rigid as possible to withstand collisions. Today,5mr 0c3,jn hqdhxat,- though, cars are designed to have “crumple zones” that collapse upon impact. Whtd- n,5xqmr3,ca hj0hat is the advantage of this new design?

Why can a batter hit a pitched baseball further tbx,nu bt1u 20.v)6 acrna2ag9)chkpp han a ball tossed in the air by the )n pub2n91ta0c2a)v x cbapu .k 6rhg,batter?

Is it possible for an object to receive a larger impulse from a small force th apyj (iit0qdv57j j7+an from a large force? Explain.j77i(5aqt p0jyiv +dj

A light object and a heavy object have the same kineqcosv* kr; x71tic energy. Which has the gres*v cx1 r7ko;qater momentum? Explain.

Describe a collision in which all kinetic energy pf7q0j-*)jvv9ljm jd1g 4sh/8qou0 ojmml .eis lost.

At a hydroelectric power plant,q3q-dtk1 /m xq water is directed at high speed against turbine blades on an axle thaqt1- q/q mx3kdt 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 water rebounds?

A squash ball hits a w(z4*obj:(x7btbz r ogall at a 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 onh( t( psce6fu8g9htbux-z(toao2 w2 *to a hard steel plate (fixed to the Earth), from which it rebounds at very nearly its original speed. (a) Is the momentum of the ball conserved during any part of this process? (b) If we consider the ball and Earth as our system, during what parts of the process is momentum conserved? (c) Answer part (b) for a piece 2u(p ox hwgf2 euc tt*bt(o9h6az (-8sof putty that falls and sticks to the steel plate.

Why do you tend to lean backward when vq/my8j,ep it c6z; ca )0fxd(carrying a heavy load in your arms?

Why is the CM of a 1-m length of pipe at its mid-point, whereas this cv .wwfl. q)+ 5sp1bw/l;wb pdis not true for your abwvbwsw);1wp ldlf5 .cqp .+/rm or leg?

Show on a diagram how your CM shifts when you change from a lying pmqn:u ev)) z*+n,n/yn yzp/z qosition to a sitting pq:)y +z , mnvnyen/u*p)zqn/ zosition.

If only an external force984nrax8 ra5 tey9thvbku4:m can change the momentum of the center of mass of an object, how can the internal force of an en8ehv 8mrrk5atbx y449an9u t:gine accelerate a car?

A rocket following a parabolic path through the air suddenly explodesq4m zy.(..w wu hrhzzez8 k0z4 into many pieces. What can you say about the motion of this system4hk emwu.zzw04q.h r.y zz8(z of pieces?

  What is the magnitude of the momentum of a 28-g sparrow flying w*fvn mjuzt/( ypma5 o7 xs6o-4ith a speed of $8.4 \; m/s$    $kg \; m/s$

  A constant friction force of 25 N acts onkc5goikd(z4 ,xmu, 0 y a 65-kg skier for 20 s. What is the skier’s com(g,y z,x 5i dk40kuchange in velocity?    m/s

  A 0.145-kg baseball pitched at 39 m/s is hit on a horizontal line drivr:4irwrw/d 4m e straight back toward the pitci m4rr4r/:wd wher 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 package out horizontally with a 9l n9kuhlr n/6speed of 10 m/s Fig. below Calculate the velocity of the boat immediately after, assuming it was initially at rest. The mass of t/lkn 6lu9rh n9he child is 26.0 kg, 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 that the propellitjt9rdpr m8 ff,8x)95o 5zqwwng gases are expellm9tzw wj895p )dfo8f 5q rx,tred 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 )+.7 zqid n6jtbk8v nh$4.1 \; m/s$ 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 travopoiwy+ wpv6h0j kuh4 b 6 n0a0).h:maels alone on alevel frictionless track with a constant speed of 18m/s A 5350-kg load,initially at rest, is dropped om0 a+u4w hoh k6 vij0)a yh.npb6:pwo0nto the car. What will be the car’s new speed?    m/s

  A 9300-kg boxcar traveling atug (v h5qqgi;. $15 \; m/s$ 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,+l . j1c0i3ckru;vng u winds can whip horizontally at speeds of 100km/h If the air strikes a person at the rate of 40kg/s per square meter and is brought to3 0cg;ilr+. kjun 1cuv 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 il 2kw yi.clgcq5-1 6v 9rzg(lcar coasts along with a constant speed of 8.6m/s on a level track. S21v-kg. ilg(5r9wcqllcz 6yinow 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 initiqo8(5 e ep,myoally moving at 420m/s emits an alpha particle in the direction of its velocity, and the remaining nucleus slows to 350m/s If the alpha particle has a mass of 4.0 u and the original nucleus ha8 (ooee,5mqy ps 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 of5q 4fz-pzrv l96zlrwc+3b gf ) wood and emerges cleanly at 170m/s If the block is stati g)f65rrb4- q +cvz3fz9lwzlponary on a frictionless surface when hit, how fast does it move after the bullet emerges?    m/s

  A 975-kg two-stage ro 1ckl vpiwtl/a5vp9,ko 195apcket is traveling at a speed of $5.80\times10^3\mathrm{~m/s}$ with respect to Earth when a pre-designed explosion separates the rocket into two sections of equal mass that then move at a speed of $2.20\times10^3\mathrm{~m/s}$ relative to each other along the original line of motion. Let “A” represent the upper stage (that moves away faster) and “B” represent the lower stage.
(a) What are the speed and direction of each section (relative to Earth) after the explosion? $v'_A$   m/s  ----待选择----away from the Earthtowards the Earth  $v'_B$   m/s  ----待选择----away from the Earthtowards the Earth 
(b) How much energy was supplied by the explosion? [Hint: What is the change in KE as a result of the explosion? $a\times10^8$ a =    J

  A rocket of total mass 3180 kg is traveling in outer space with a velociti: i6i 9m;thfoy of 115mioi hi96tm:f; /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 teet 2pyf*kgpo.3 at a speed of 45m/s The golf club was in contact with fg.tko * pyp23the 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 atob df)5rtxyb+3 mz1t6 a velocity of 8.5m/s and comes to rest in a time interval of 8.0 ms. (a) What is the impulse given to the nailty5d+1b morx6b3z t)f ?    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 aj/+: x gwx*zmunw 3u)o 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 ap+2dfij,b.t.q uwi2i ; uw g/new automobile models. Cars are tested by smashing them into fixed, massive barriers at 50km/h (p/ 2 i. qfui+,w;bug. jiwa2td30 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 andok;c.u35 szu n*r1nmoy)w c7 h is stopped in 0.75 s by a head-on tackle by a tackler running wsno;.c rom) z1unyuc 3kh75*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 hwk(mcmtx89) g6j) slon a tennis ball (mass 0.060 kg) points in the +x direction and is given by the graph of Fig. 7–33 as a function of time. Use grx96c) (lhjmtmg s8)kwaphical 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 withovf5bng/5f7oi7w3ia i4q: o vyut breaking the lower leg bone of either leg? Ignore air resistance and assume the CM of the person moves a distance of 0.60 m from the standing to the seated position (that is, in breaking the fall). Assume the breaking vooifw5:7/b54i 3n 7 yiqfavg strength (force per unit area) of bone is $170\times10^6\mathrm{~N/m^2}$ and its smallest cross-sectional area is $2.5\times10^{-4}m^2$ [Hint: Do not try this experimentally.]    m

  A ball of mass 0.440 kg moving east (+x direction) with a speed of pe4l 5;bvwi;o xsvu4) collides head-on with a 0.220-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; vwsb);4olip 4x5vue 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, movinr-6 g5wyrx3 oig 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 collision, what will be the speed and direction of each object after the collision?Let A represent the 0.450-kg puck5yi r3-6 gowrx, 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 helwf ;p jw14ozp9g)x8aad-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 tz lxpj8wwag) 91p;f4ohe 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 of 2.5m/s collides head-orc i c-gjnc5qpw 1)lh)9k 5l7wn with a 0.090-kgnwc5j5 lw1lr-)pi9c q7gk)c h 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?(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 rx h0v;3bjhj* moving with a speed of 8.5m/s collides head-on and elastically with another ball initially at rest. Afterwardxr0 h*j j;hbv3 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 parqi:ym v0:*/a /t)m lb*lqfv xck 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 to differences in passenger masx m :qva):lqylt0c bfmv**//is. 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 colvqtfposoh7qgom* - sb- v)24 i74ec m8th/dh/lision with a second ball inits-*pe t/gv7 82b7h-ocm/ooq4) i vtqfd s4m hhially at rest. The 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 a frictionless incline as/hch yps/kx*o;w +52 w -fs /(an quep.hoqr,p shown in Fig. 7–35, and elastically strikes another cube at the bottom that is only one-half its mass. If the incline is 30 cm high and the table is 90 cm off the floor, where does each cube land? [Hs chq5,r/o/ps wpho+ wh y(u qa e-p*f/x.2k;nint: Both leave the incline moving horizontally.]$\Delta x_{m}$$\approx$    m $\Delta x_{M}$$\approx$    m

ake the general case of an object ofr)vbn.d ..oeewdr h (/ mass m$_A$ and velocity v$_A$ elastically striking a stationary object of mass head-on. (a) Show that the final velocities v'$_A$ and v'$_B$ are given by$v_{\mathrm{A}}^{\prime}=\left(\frac{m_{\mathrm{A}}-m_{\mathrm{B}}}{m_{\mathrm{A}}+m_{\mathrm{B}}}\right)\nu_{\mathrm{A}},v_{\mathrm{B}}^{\prime}=\left(\frac{2m_{\mathrm{A}}}{m_{\mathrm{A}}+m_{\mathrm{B}}}\right)\nu_{\mathrm{A}}.$(b) What happens in the extreme case when m$_A$ is much smaller than m$_B$ Cite a common example of this. (c) What happens in the extreme case when m$_A$ is much larger than m$_B$ Cite a common example of this. (d) What happens in the case when m$_A$=m$_B$ Cite a common example.

  In a ballistic pendulum experiment, projectile 1 results inwh11x mc(y )wl a maximum height h of the pendulum equal(l cxy)wm11 wh to 2.6 cm. A second projectile causes the the pendulum to swing twice as high, $h_2=5.2\mathrm{cm}$ The second projectile was how many times faster than the first? $v_1$ =    $v_2$ ([color=rgba(0, 0, 0, 0.85)]Round to three decimal places)

  A 28-g rifle bullet traveling 230m/xq98lcaj 2,vs; w4itg 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 vertical anq2wts,9xa4cj g ; vli8d horizontal components of the pendulum’s displacement.vertical$\approx$    m horizontal =    m

(a) Derive a formula for the fraction of kinetrk 1. acw8id8iic 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 bro *3p4mp8nusl lrqn6 (mu3 ba-eaks an object, 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 represel-*mpb 8s4oq6( n urm3ap3ulnnt the lighter particle. ) KE'$_A$ =    J KE$_B$ =    J

  A 920-kg sports car collides into the rear end oi5ju)g,hcqr*z * m s8lf a 2300-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 that speed?(Let A represen *s8jqic grmuz 5l,h)*t 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 a r8 :bm:1 1bxbp8fe 5aky:; qygm:y wsvheight of 1.20 m. Approximab b;yw1bev5:kyx8:pr 8g yfq 1m:asm :tely how many rebounds will the ball make before losing 90% of its energy?   

A measure of inelasticity in a head-on coldplrt 5pl 6zr3j/ p0c(lision of two objects is the coefficient of resd rcp5 tjpr/3 pl(lz60titution, 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 twfmhk aj+ 8leyt7o5jv3)w,dh 6o pieces, one with three times the mass of the other. A depression is made in both faces of the cut, so that a firecracker can be placed in it with the block reassembled. The reassembled block is set on a rough-surfaced table, hjwmafk d)6vh8oj+3e 75yl,t 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 directioyjc;:pk;/ jau k4 wys*+dn tj7n at 5.5m/s collides head-on with a 10.0-kg object moving in the -x direction at 4m/s p*y/ ;nd7 ;ck:j wujj+a4tks yFind 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 e ;os g05 qvu4 :fxgbk8sw0cd*into a second nucleus, an electron, and a neutrino. The electcdgkv gbq; 4s0 8xws0:uo5 *feron and 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 mass o5soa;nu5e-v $m_\mathrm{A}=0.400$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 equalsmjq6gih),1 u mass, each hsgjh )muq,6i 1aving initial speed the two move off together with speed v/3 What was the angle between their initial directions?    $^{\circ} $

  Two billiard balls of equal mass move at riix** 741 lqd5zn,rhs8ny jonzght 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 i*s 8d1nj*4,yrh7 x5 lqzznon the x axis with speed 3.7m/s After the collision, assumed elastic, ball B is moving along the positive y axis (Fig. 7–37). What is the final direction of ball A and what are their two speeds? direction of ball A 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 iq zq(-2xgut: with another atom at rest. After the impact, the (u:t-qigz 2 xqneon 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) makes a pernj -bot3u7o(c fectly elastic collision with another atom at rest. After the imj-bnoc u o7(3tpact, 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 tbcf2(by :plr1* rv zr5hree-mass system shown in Fig. 7–38. Specify relative to the left-harfv (r 2:5zybcrpl*1bnd 1.00-kg mass.    m

  The distance between a carbon a)cbb y3 e,ylq;y,yqz2 tom ($m_{\mathrm{C}}=12\mathrm{u}$) 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 be:-zl* ug eh(mfs n*xm:hind 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, an-m:gxf *l*unzs e (mh:d three people sit in the back seat 3.90 m from the front? Assume that each person has a mass of 70.0 kg.    m

  A square uniform raft, 18 m by 18 m, of mass 686n5 8 gmvmiza +/h6fdu00 kg, is used as a ferryboat. If three cars, each of mass 1200 kg, o+8ihfa6mzngd5u/ m v6ccupy its NE, SE, and SW corners, determine the CM of the loaded ferryboat.$X_{CM}$ =    m $Y_{CM}$ =    m

  Three cubes, of sides .7tz;wpjn)4 szonq/x $l_0$,$2l_0$, 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 ident*-brq/1 odx ldical 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 can pick up the load witho1-rolxd /b dq*ut tipping it.$X_{CM}$ =    l $Y_{CM}$ =    l

  A uniform circular plate of radius 2R has a circular hole of radius R cua3 8 j;2z1xd r8nvewfqt out of it. The center of the smaller circle is a distance 0.80R from the center C of n r3x8djvq8ze 2;a 1wfthe larger circle, Fig. 7–41. What is the position of the center of mass of the plate? [Hint: Try subtraction.]   R

  Assume that your proportions are the same as those in Tabln-vgw/.izf;qizy76 t e 7–1, and calculate the mai./ vg z zny-7f6t;wqiss of one of your legs.    kg

  Determine the CM of an outstretched arm using Table 7gb cb5s xukui/+,ain m5.mf4/–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 a righ,v9;5hye -ntedj5z b ft angle. Assume that the person is 155 cm tall. nvyhf tb;, z95ee5d j-$X_{CM}$ =    cm $Y_{CM}$ =    cm

When a high jumper is in a position such that his 61wu y6uax pdp2-1 fuac0wt2 larms and legs are hanging vertically, and his trunk and head are horizontal, calculate how far a06 1uw x2fu awd1 -t6c2lyuppbelow 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 94 t1cetcnqh ivil*(-$5.98\times10^{24}$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 o e51k ka8h1flx,zq):rv)tktzn 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 and a dia)vtl,gnu3 d 0.*xiwg t- vpc9zmeter 0.0800 m mountec)id*uvx.03,z ltwgg9nt p v-d 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?    cm

  A mallet consists of a uniform cylindrical head of:eb.ex6kmi (* h/dgm q 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,m i(gh/kxqe.d eb6 m:* 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 Exam y.oiye 104c(f5 :zr 0qyqshg/au(gkcple 7–14 (Fig. 7–29), $m_{II}$=3$m_{I}$ Where then would $m_{II}$ land?    d(Round to two decimal places)
(b) What if $m_{I}$=3$m_{II}$    d

A helium balloon and its gondola, of mass M, are in the air and stationary witha sjvsv;z 5830ni b2gv respect to thnvv;0s2s5v z8ag 3bj ie ground. A passenger, of mass m, then climbs out and slides down a rope with speed measured with respect to the balloon. With what speed and direction (relative to Earth) does the balloon then move? What happens if the passenger stops?

  An 0.145-kg baseball pitched horizontally at strikes a bat and is e.3 vb1 f*3hal syw0rb(s n0jtpzu2 d+popped straight up to a height of 55.6 m. If the contact time is 1.4 ms, calculate the average force on the ball be01lawyv3br (z*u23spn t sd. f0+hjduring the contact.    $^{\circ} $

  A rocket of mass m travel.,k1dy 7hwndb( tkhh (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 corner pock*p de y f a7*9slak3ym/dr*k 5gxy73pjet shot shown in Fig. 7–43. Relative dimensions are also shown. Should the player be worried about this being a “scray9*j3yplegfm*37s 7 d/rk *p kx 5aaydtch shot,” in which the cue ball will also fall into a pocket? Give details.

  A 140-kg astronaut (including space suit) (.)u/,o3 ( hpdkygy+v69ljks hq-e.f n yhi rsacquires a speed of 2.5m/s by pushing off with his legs from an 1800- g hey()ypqo6 +fk9,ryhis/3jh-vnuk.d(s.lkg 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 a8,qx.x ok. lqwnd the other 80 kg, are initially at rest in outer space. They then push wxq oq klx..8,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 colliss/1i rie0o :.ahk*r ,s0yq 9y ulreyf0ion with a second ball (at rest) and rebkhf9 0srei0y:ro/es *0. 1luaryiqy , ounds in the opposite direction with 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 a9hds n 9(:q3xcn1z +ixy uh*lvs an expert 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 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 (9 dx*9vhl3 yh +q1cnx:ziu nsbrakes.    mi/h

A golf ball rolls off the top of a flight of concrete steps of total vert5omftq 6dsh37s8rpfxq+1k s +ical height 4.00 m. The ball hits four times on the way down, each time striking the horizontal part of a different step 1.0 m lower. If all collisions are perfectly elastic, what is the bounce height on the fourth 5 qopx86+7s sk+hmrft3fq1s dbounce when the ball reaches the bottom of the stairs?

  A bullet is fired vertically into a 1.40-kg block of wood at rest direcnp hbd oq) hhgbg*46:h :-ge;ctly above it. If the bullet has a mass of 29.0 g and a speec he4b-on p:6hqb:d)*;gghh gd of 510m/s how high will the block rise after the bullet becomes embedded in it?    m

  A 25-g bullet strikes and bec3ccf, ;orr4uz(x itq8omes embedded in a 1.35-kg block of wood placed on a horizontal surface just in front of the gun. If the coexfcq;(o crur8it3 z,4fficient of kinetic friction between the block and the surface is 0.25, and the impact drives the block a distance of 9.5 m before it comes to rest, what was the muzzle speed of the bullet?    m/s

  Two people, one of mass 75 kg and t3n)(iw, dv*: src sbkyhe other of 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 boat 3.2 m apart from each other, now exchange seats. How far and in what direction will the boat kr,:vn(* b3)dsw iycs move? The boat will move    towards the initial position of the 75 kg person(Round to two decimal places)

  A meteor whose mass was aboutn v78(gxjsb1h $ 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 apartv1k1nkr9eu,d/ d bw .j into two fragments by an explosion. One fragment acquires twice the kinetic ener1nw9ev,. /d krukd1 jbgy of the other. What is the ratio of their masses?   

  The force on a bullet is given by the formula F = 580-:3c r)tlor0 yl( $1.8 \times10^{ 5}$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 massesa4fp(y4j oekqt06 vl gjt/ 3v3 $m_A$ = 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 parti .il i .li**ubvumj9vp,sx 5f4cle and a smaller nucleus. What will be the speed of this recoiling nucleus if the speed o,sibm5*x.lp vvi.j4lf 9*uui f 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 an angle of 3wn q;9dx jtk(/0 $^{\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 sj73 +n0cfy0 w0aocs .0myhowk2ll j2a 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),gltpu6j vy 4vo )8by)3 what is the upper limit on mass m if it is to rebound from M, slide up the incline, stop, slide down the incline, and collide with M 6 u b3)g v4ovjtlpyy)8again?    kg (Let A represent mass m, and B represent mass M.)

  The gravitational slingshot effect. Figure 7–47 shows the planet Saturn moving 4(qzy jyo/5vfin the ne (fo/q4yv5zjygative x direction at its orbital speed (with respect to the Sun) 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