We claim that momentum is conserved, yet most moving objectkrmgp8s*r)feek wc19 g)n-x4 s eventually slow dowc9egn fk)w*4ek) r1 8pgm rs-xn and stop. Explain.

When a person jumps from a tree to the ground, what gnefq/f .lv2 ;m/du n6happens to the momentum of the person upon striking thn/ l;qf2eun/gf. 6m dve ground?

When you release an inflated but untied balloon,wxm j*:mbkva1pg0x9 k oe8 3j5 why does it fly across the room0wjo1gxek5 jk v9 xm*8ba:pm3?

It is said that in ancient times a rich man with a bag of gold coins froze -(pjh u+jlvn) .a( uxdto death while stranded on a frozen lake. Because the ice was frictioj(u.v)u+phj -ndl a(xnless, he could not push himself to shore. What could he have done to save himself had he not been so miserly?

How can a rocket chano: .5c yxp vk2dv,7ygige direction when it is far out in space and is essentially in a vgc vdkvp:,y. ox725yiacuum?

According to Eq. 7–5, the longer the impact time of an impulse, the smaller z 2+)fw3wjmp/kghj9 cthe 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 w3hmj2/ zpfw) kg9j+cinflate during an automobile collision and reduce the possibility of fracture or death.

Cars used to be built as rigid as possible to withs egv+7sn5 q;i y7g5)gewh wmky,2) sphtand collisions. Today, though, cars are dessigw,myeqy 7w5 7g 2e+hn)5k) pv ;gshigned to have “crumple zones” that collapse upon impact. What is the advantage of this new design?

Why can a batter hit a pitched basebaldf* ;adt w s0:oxc7gk-l further than a ball tossed in the air by th;acw gkxds-:0* f7tdo e batter?

Is it possible for an object to receive a larger impulse from a small force th1/plxps j h:16nbg1 pm3fp8 jqan from afq1xjnpp6s1 1g8hppm jbl/3 : large force? Explain.

A light object and a heavy object have the same kinguv( l7l*s +slosllf)8pm wl 7mw5)a0etic energy. Which has the greatllllpgvm(7o a ) 05us)+lm78sfswl *w er momentum? Explain.

Describe a collision in whic -p-jq w( *znn-g5xxvhh all kinetic energy is lost.

At a hydroelectric power plant, water is directez; (3gmza+zf 7gfz7o ud at high speed against turbine blades on an axle that turf+;azfu77mo g3 g( zzzns 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 1ypz(cw,s 8 u6wi)vr dwall at a 45 $^{\circ} $ angle as shown in Fig. 7–30. What is the direction (a) of the change in momentum of the ball, (b) of the force on the wall?

A Superball is dropped from a heightan;tqt vbxjb9bsr7;n3)d0(g v y ))ff h onto a hard steel plate (fixed to the Earth), from which it rebounds at very nearly its original speed. (a) Is the momentum of the ball conserved during any part of this process? (b) If we consider the ball and Earth as our system, during what parts of the process is momentum conserved? (c) Answer part (b) for a piece of puttyf9 7)0qn tg dax ( b;f3tnv;ry))sbbjv that falls and sticks to the steel plate.

Why do you tend to lean bacj5u gbmn2w l:9gg8q28 jp siz4kward when carrying a heavy load in your arms?

Why is the CM of a 1-m length of pipe at its mid-point, whereas t25;hbd1*6f g0m.ofvr cpeil this is not true for y o p1hf6*etr fm. cvig;50d2lbour arm or leg?

Show on a diagram how your 9 o.; mee(ze.xxoc:iaCM shifts when you change from a lying position to a sittin:9eoae(x.i e;mzc.x og position.

If only an external force can change the mya,ff)d1 h.syms :yec +t:/qfomentum of the center of mass of an object, how can the internal force of an engine accelerate a cartyhe/s s :c:, fyafmyf.+ 1d)q?

A rocket following a pxo (y+(o qla,farabolic path through the air suddenly explodes into many pieo(q, o +fya(lxces. What can you say about the motion of this system of pieces?

  What is the magnitudog+qemvj p8oy 1 ((of.)lk2rkrbkj-4e of the momentum of a 28-g sparrow flying with a speed of 8+rlykgop. r( kf4kq8 jme b2oj (1v-)o.4 m/s    $kg\;m/s$

  A constant friction force ,qi; iqjsjh+( of 25 N acts on a 65-kg skier for 20 s. What is the skier’s changjh qq+;,i s(jie in velocity?    m/s

  A 0.145-kg baseball pitcp)x0yd:a;ieh eh +o-dw tsg8/ hed at 39 m/s is hit on a horizontal line drive straight back toward the pio/0eh: ;8yw) d-etxgh+ asdp itcher 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 witez- *4jceggu,k esssn /oq:14h 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 resistzg-e1ek u*/e4sq4 jo:gn,cs s ance. The velocity of the boat is    m/s

  Calculate the force exerted on a rocket, given that the p 9t51swj)*g4ifvn -)nae r fsaropelling gases are expelled at a rate of 1500kg/s with asw))ae4 1 sg-5vn9fjf antir* speed of $ 4\times10^{4 }$ (at the moment of takeoff).$a\times10^7$ N a =   

  A 95-kg halfback mov2r2y3t*+wnfti*4xzqvi-g8 oh k d ccnr.*vn 2ing at 4.1m/s on an apparent breakaway for a touchdown is tackled from behind. When he was tackled by an 85-kg cornerback running at 5.5m/s in the samer4*witk3r *ivx-8ofgcnyz d*tn.2 + q2v 2 nhc direction, what was their mutual speed immediately after the tackle?    m/s

  A 12,600-kg railroad car travels alone on alevel frictionle x*2 jn3mr6 ta;whgf/ess track with a constant speed of 18m/s A 5350-kg load,initially at rest, is dropped onto the ca 3a;xtg/rjh *nf6w em2r. What will be the car’s new speed?    m/s

  A 9300-kg boxcar traveling at 15m/s strikes a seconrxz(c,g5bh5+wq1-b jbd3 eztd boxcar at rest. The two stick together and move off with a speed of 6m/gh ,b 5zqdx3ct(-j5zb+b1 rwes What is the mass of the second car?    m/s

  During a Chicago storm, winds can whip horcbos0 g;;mr f3izontally at speeds of 100km/h If the air strikes a person at the rate of 40kg/s per;;omb c03sfgr square meter and is brought to rest, estimate the force of the wind on a person. Assume the person is 1.50 m high and 0.50 m wide. Compare to the typical maximum force of friction $\mu\approx1.0$ between the person and the ground, if the person has a mass of 70 kg.    N
$F_{on person}$  ----待选择----<> $F_{fr}$

  A 3800-kg open railrxm k(t)viab+i 0e 2ci0oad 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 Ignoring friction with the tracks, what is the speed of the car aftei vma02icxk ()eb 0+itr 90.0 min?$\approx$    m/s

  An atomic nucleus initially moving at 420m/s emits4pe+zn *pao: ce5wed1 an alpha particle in the direction of its velocity, and the remaining nucleus slows to 350m/s If the alpha pa p+*wep a15d4 no:eezcrticle 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 0gl. )et hwi-*j;caxb-kg block of wood and emerges cleanly at 170m/s If the block is stationary on a frictionless surface when hit, howg-c lj.i*bat)0e; x hw fast does it move after the bullet emerges?    m/s

  A 975-kg two-stage rocket is travelingcb or 5;f.,uoy 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 oexif5* c2l8o5*r hh4 b f4ftkauter space with a velocity of 115m/s To alter its course by5 *5ak e4htiff2 lh4*xbc f8ro 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 The golf cludse9v 1oplcngn; zi+ -ixo,*7b was z9 vl,g ci-+;nx7odp*si eon1in contact with the ball for $3.5\times10^{-3}$s Find (a) the impulse imparted to the golf ball,    kg*m/s
(b) the average force exerted on the ball by the golf club.    N

  A 12-kg hammer strikes a nail at a velocity of 8.5m/s +.z0ryoe*tvja .8p +d3zppm band comes to rest in a time interval of 8.0 ms. (a) What is the im0d3 mtbej +az.r*op+y pv8zp.pulse 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* o(e :imqu-mh4fkx2 z and speed v=25m/s strikes a wall at a 45 $^{\circ} $ angle and rebounds with the same speed at 45 $^{\circ} $ (Fig. 7–32). What is the impulse (magnitude and direction) given to the ball?   kg*m/s to the  ----待选择----leftright 

  You are the design engineej:5im )9q9tljlunp/ qr in charge of the crashworthiness of new automobile models. Cars arupj tnl5q m/i9)ql 9:je 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;i3f2: lh bazp+tz*cj 4m/s to the east and is stopped in 0.75 s by a head-on tackle by a tackler runc +:lz pizt*a32jb h;fning 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 balz q. ilh4y1nlb m3lc3:l (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 graph3l .iblc1nml: h3y 4qzical 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 with, eg6j cn7fiw3out 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 ff67gwni,j 3ce all). Assume the breaking strength (force per unit area) of bone is $170\times10^6\mathrm{~N/m^2}$ and its smallest cross-sectional area is $2.5\times10^{-4}m^2$ [Hint: Do not try this experimentally.]    m

  A ball of mass 0.440 kg moving east (+x direction) with a spet.6lgmhs +dzt e)4 7died of collides head-on with a 0.220-kg ball a s d emlth764t.diz+g)t 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 3m/s hasc88gse :zyny 0 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 gen0zyy :8 8scobject 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 qp6if0b u 8jr6mass undergo a perfectly elastic head-on collision. If one ball’s initial speed was 2m/s and the other’s was 3m/s in the opposite direction,8pf uijb 6q06r 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 of 2.5m/s colli kgek uusa5 )fqv;i;u2 zm156xdes head-on with a 0.090-kg ball initially moving away from it at a speed of 1.15m/s Assuming a perfectly elastic collision, what are the spee21au; e g 6zkv fkmxqu)s5ui5;d 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 5;z(dhcwvsp; m)xb )pof 8.5m/s collides head-on and elastically with another ball initially at rest. Afterward the incoming softball bounces backward with a speed of 3.7m/s C;(psmb;p v)dxw c h)z5alculate
(a) the velocity of the target ball after the collision    m/s
(b) the mass of the target ball.    kg
(Let A represent the moving softball, and let B represent the ball initially at rest.)

  Two bumper cars in an amusement park ride collide elastically as one approc xb;ows0 0-nndgc,:jmahh43p01 o haaches the other directly from the rear (Fig. 7–34). Car A has a mass of 450 kg and car B 550 kg, ohw,; a acp njs-dxnm 0:h4h103ogc0bowing 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 anz .m,6+o 1-k;hrfoqh1 * i-axfinnkjp elastic head-on collision with a second ball initially at rest. The second ball moves off with half the origh1hnz*--nrfpk+o;qk6 i 1 m f.xoja,i inal 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)3f1uo7 ;skntf p ce* y-ytf(gezj(c+ as shown in Fig. 7–35, and elastically strikes another cube at the bottom that is only one-half its mass. If the incline is 30 cm high and the table is 90 cm off the floor, where does each cube land? [Hint: Both leave the incline se g;y +kf-nf*37 c(yojcfptte) 1zu(moving horizontally.]$\Delta x_{m}$$\approx$    m $\Delta x_{M}$$\approx$    m

ake the general case of 3(socdu+, zquqk 06e xan object of 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 resulz in2e* f prh05,9etrrts in a maximum height h of the pendulum equal to 2.6 *nf,zei t 02 rrrhp59ecm. 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 tvs kjt*2vf3) iq r73txj+ c.gwraveling 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 vertical and horizontal components of the pendulum’s dis* k3 v)+tscfijtq v73wj. x2grplacement.vertical$\approx$    m horizontal =    m

(a) Derive a formula for the fraction v. mx8i;qgrg- f 6c9eyof 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, initialig/9 mn+wg(crly at rest, into two pieces, one of which has 1.5 tic(w mn /rggi9+mes the mass of the other. If 7500 J were released in the explosion, how much kinetic energy did each piece acquire? (Let A represent the heavier particle, and B represent the lighter particle. ) KE'$_A$ =    J KE$_B$ =    J

  A 920-kg sports car collides into the rear end of a 2300-kg SUV stopped; v8f v-w d(pva+tw;m(c lfby. 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 s+-;(b fp;f 8mvaw wvyl.cd (tvpeed of the sports car at impact. 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 and rebounds to a height ze0. w y,3ytgzof 1.20 m. Approximately how many rebet0. ,wz3yg yzounds will the ball make before losing 90% of its energy?   

A measure of inelasticity in a head-on collision of two objects is the cqzl9 kz9s/e: bee0:k9p1gobv oefficient o: ek ek9qze91l s0pogb:b9v/zf 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 in95rb u plit6i*to two pieces, one with three times the mass of the other. A depression is made in both faces of the cut, so that a firecracker can be placed in it with the block reassembled. The reassembled block is set on a rough-surfaced table, and the fuse is lit. When the firecracker explodes, the t*6liur ipt5 9bwo 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.gkrdj3 7++djr:wy,st 5-bqu d 5m/s collides head-on with a 10.0-kg object moving in the -x direction at 4m/s Finddy d +w+q-d5rkt73:gubs,jjr 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 e)r *ij(z id)b.xu6xr rest decays into a second nucleus, an electron, and a neutrino. The electron and neutrino are emitted at right angles and havez*e( )6x)rbid. rjiux 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)x,94 j- qs yjf:-5t2 fsyggqyx4f vurs $m_\mathrm{A}=0.400$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 collisio c .6fa:4zhusyn between two objects of equal mass, each having initial speed the two moves4a6z. uf ch:y off together with speed v/3 What was the angle between their initial directions?    $^{\circ} $

  Two billiard balls of equal mass move -4 s (vfmtai65jw65azpsjdp ie0 r1 e3at right angles and meet at the origin of an xy coordinate system. Ball A is moving upward along the y axis at 51ej ap46 fw-p65i 0adej mz(sti3rvs 2m/s and ball B is moving to the right along the x axis with speed 3.7m/s After the collision, assumed elastic, ball B is moving along the positive y axis (Fig. 7–37). What is the final direction of ball A and what are their two speeds? direction of ball A 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 anot p*cqixm 0ao++her atom at rest. After the mqoa0*ipc+x +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) makes a perfek4grgh 7w (bt8r(nz2mctly elastic collision with another atom at rest. After the impact, the neon atkr24bw ((hr zg7g8nmtom travels away at a 55.6 $^{\circ} $ angle from its original direction and the unknown atom travels away at a -50 $^{\circ} $ angle. What is the mass (in u) of the unknown atom? [Hint: You can use the law of sines.](Let A represent the incoming neon atom, and B represent the target atom) $m_B$   u

  Find the center of mass of the three-mass system shown in Fig. 7tqocledg0c. sx70c n-ko9(* y–38. Specify relative to the left-hand 1.00-nx7cg0 yl.cos-e(*q09k c dotkg mass.    m

  The distance between a carbon atom .qb -mx4zpwr /y,ebld -352-ydm lfca($m_{\mathrm{C}}=12\mathrm{u}$) 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 bexj1zc-x4* .j hlzp1pz uz w d,,vm0-kqhind 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 lx1xjzz -*q1 h pcmd,zpukz4jw, -v.0front of the car, and three people sit in the back seat 3.90 m from the front? Assume that each person has a mass of 70.0 kg.    m

  A square uniform raft, 18 m by 18 m, of mass 6801crze5;wvum wn9i 20l . pv.hc0 kg, is used as a ferryboat. If three cars, each of mass 1200 kg, occupy its NE, SE, and .zilp9w5;hcu1vw cr0 n2mv e .SW corners, determine the CM of the loaded ferryboat.$X_{CM}$ =    m $Y_{CM}$ =    m

  Three cubes, of sideuu8jr3urusn zgq) df-u.23 d(s $l_0$,$2l_0$, 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 5 xguco2t :0haidentical cases of tomato paste (see Fig. 7–40)htx5 u 2a0gco:, 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 without tipping it.$X_{CM}$ =    l $Y_{CM}$ =    l

  A uniform circular plate of radius 2R has a circular hole of radi r:yirwdkme;i1r 6:r;us 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? [Hint: Try subtraction.] y e6ri:i1m;:rrrkd;w   R

  Assume that your proports60 5t 9aofazub-i keu5k(5i rions are the same as those in Table 7–1, and calculate the mass of one of your legsuk(r5k5b -6a 0o5eizi9tsua f .    kg

  Determine the CM of an outstretched arm usin x6e hxsfv8yqk 6q.e97eg-xq2g 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 a right su8 q)r w6htpwuy7,7y angle. Assume that the person is 155 cm tph7yw7ys6 ,qu)t8rwuall. $X_{CM}$ =    cm $Y_{CM}$ =    cm

When a high jumper is in a position such that his arms and legs are hanging veqdl7abtfu9+m +en+59c+hxtirtically, and his trunk and he9eq7 tbid+f9ma5ltcuxn+++ had are horizontal, calculate how far below 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 d;dqfo6 pcy)/d yh( w3Moon are $5.98\times10^{24}$kg and $7.35\times10^{22}$kg respectively, and their centers are separated by $3.84\times10^{8}$m (a) Where is the CM of this system located? (b) What can you say about the motion of the Earth–Moon system about the Sun, and of the Earth and Moon separately about the Sun?

  A 55-kg woman and an 80-kg man stand 10.0 m apart onwiymu.p0 k v 8e2t55s1,ehtd g 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 hea bi:lcyn7ztc - 3w27fg7ix)xyd of mass 2.00 kg and a diameter 0.0800 m mounted ofcc7-ytl :)wib7xz3x ygn 7i2n 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 mass 2.00 kg ahvwwu .2z nt(2f6yuy 2nd a diameter 0.0800 m mounted on a uniform cylindrical handle of mass 0.2wy( 2n.w hf6uuvtz2 y500 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 Exa54em5rx0xzkpep 7 40d)dqsf kmple 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 6ly )pnj y)p6mair and stationary with respect to pm66l )ynpy j)the ground. A passenger, of mass m, then climbs out and slides down a rope with speed measured with respect to the balloon. With what speed and direction (relative to Earth) does the balloon then move? What happens if the passenger stops?

  An 0.145-kg baseball pitchl vy-q/+f;ywh5y 9xs ped horizontally at strikes a bat and is popped straight up to a height of 55.6 m. If the contact time is 1.4 ms, calculate the averageyw;yh p yx+9/q-vl5fs force on the ball during the contact.    $^{\circ} $

  A rocket of mass m traveling witbpoe ;ot19k0cvumxe 0 9 .mk(yh 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 pocket s8m/k(76jvi uaegwob1 hot shown in Fig. 7–43. Relative dimeaik uwm61g(b/ov78ej nsions are also shown. Should the player be worried about this being a “scratch shot,” in which the cue ball will also fall into a pocket? Give details.

  A 140-kg astronaut (including space suit) acquires a speed of*2/9nz8fcb aytoj/u y 2.5m/s by pushing off with o*ybfnu9zaj 2 /c8/yt his legs from an 1800-kg space capsule.
(a) What is the change in speed of the space capsule?    m/s
(b) If the push lasts 0.40 s, what is the average force exerted on the astronaut by the space capsule? As the reference frame, use the position of the space capsule before the push.    N

  Two astronauts, one of mass 60 -s(*zplie0q1 r ely)5e+h btykg and the other 80 kg, are initially at rest in outer space. They tib5(0-y+t e ez ey)*hspl qlr1hen 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 second ball (at r7 q8 huihv(d-met,c1e est) and rebounds in the opposite direction withi1e t,hmhvqu7 8(dce- a speed equal to one-fourth its original speed. What is the mass of the second ball? $m_B$ =    $m_A$(Round to two decimal places)

  You have been hired as abu01v w:c q.bzp68 we(ot9-)dc nmfq tn 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 slivbwp( -cwqtf9dem):8.0 btuqozn6 c1 d 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 of a flight of concrete sto/m1vk79)gr ;hv qshveps 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 p)s kov;qrh19/vh mv7g erfectly elastic, what is the bounce height on the fourth bounce when the ball reaches the bottom of the stairs?

  A bullet is fired verticafjt.kb6 -.y ,isgau0 +fbzg+ylly into a 1.40-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 bullet becomes em.f6gysy. jiu kb+abft0z-g , +bedded in it?    m

  A 25-g bullet strikes and becomes embe )*oa )rq9 5jy,44apf ffil2xzsmwi-cdded in a 1.35-kg block of wood placed on a horizontal surface just in front of the gun. If the coefficient of kinetic friction between the block and the surface is 0.25, and the impact drives the block a distance of 9.5 m before it cofao-5 92p ,ri)cf4jifs xmza4 w)*qylmes to rest, what was the muzzle speed of the bullet?    m/s

  Two people, one of mass 75 kg and tu54x/o.e7ww o hong3y he 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 boate 5oon gxuhow w73y4/. 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 j ff:zthn((z fe6k*)qwas 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 sudden ccv p7 vcyk72)mw*nd(ly broken apart into two fragments by an explosion. One fragment acquires twice the kinetic energy of the other. What is the 7cw n*)v2yc 7v( kmpcdratio of their masses?   

  The force on a bullet is given bk( kse ig8io1;y the formula F = 580-( $1.8 \times10^{ 5}$t) over the time interval t=0 to t = $3.0 \times10^{-3 }$s In this formula, t is in seconds and F is in newtons.
(a) Plot a graph of F vs. t for t=0 to t=3.0ms
(b) Estimate, using graphical methods, the impulse given the bullet.    N*s
(c) If the bullet achieves a speed of 220m/s as a result of this impulse, given to it in the barrel of a gun, what must its mass be?    kg

  Two balls, of masses 9g6l w7bpuiw0$m_A$ = 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 intocjz*f/.g +o7b tv;6t 0/k nsngqkci 0s an alpha particle and a smaller nucleus. What will be the speed of this recoiling nucleus if the spengo/c6nsv0cz+ .i tqjbt 7f /g0;k*ksed 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 fim4l t)*w e7aeared 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 do b qp*4zh tn5f+a(nqy:wn a 30.0 $^{\circ} $ incline which is 3.60 m high. At the bottom, it strikes a block of mass M=7kg which is at rest on a horizontal surface, Fig. 7–46. (Assume a smooth transition at the bottom of the incline.) If the collision is elastic, and friction can be ignored, determine
(a) the speeds of the two blocks after the collision,v'$_A$ =    m/s v'$_B$ =    m/s
(b) how far back up the incline the smaller mass will go. $\approx$   (Round to the nearest integer) (Let A represent mass m, and B represent mass M.)

  In Problem 79 (Fig. 7–46), what is the upper limit on mass ;l0sy98 1tyzn ow q*d j1k)nlqm if it is to rebound from M, slide up the incline, stop, slid l8w)dyo nylqn901;1 tsz jqk*e down the incline, and collide with M again?    kg (Let A represent mass m, and B represent mass M.)

  The gravitational slingshot effect. Figure 7–47 shows the planet Saturn moving f0 z j2mc ),7hmyo5*/chhnrgw hw)l+din the negaw7ynzomg 2 5)c/,frj) mhhw hld*+c0htive 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